master thesis 2011: 'alles maal

‘Alles maalt’ FMP by Eveline Brink 2011

Draft reportFinal Master Project M2.2‘Alles maalt’Help children with multiplications

StudentEveline Brink (S041262)[email protected]

Coachesdr.ing. Marco RozendaalDesigning Quality in Interaction

dr.ir. Tilde BekkerUser-Centred Engineering

Theme: Playful InteractionsDepartment of Industrial DesignEindhoven University of Technologythe Netherlands

August 2011

Abstract

This report documents and explains the process and results of my Final Mas-ter Project at the department of Indus-trial Design at the Eindhoven University of Technology. The goal of the project was to design a soluction to help chil-dren with their multiplication problems. Through research (literature, experts and observations) I noticed opportuni-ties to help children, aged eight to nine, who are behind with learning the multi-plication table.

To achieve my goal I had to create a good learning situation: motivate the child, guide the child (on the correct level) and give direct feedback. To pro-vide this I used TagTiles (this is a prod-uct from my client Serious Toys BV). This platform is able to identify objects and their position, and gives direct response by audio and light.

During three iterations I explored pos-

sible didactics, materials, theories, in-structions, and TagTiles together with experts (teachers and children).I have teach four children each week for four months. I also involved PARWO (expert on adaptive education) as my partner. They introduced new theories and gave feedback on my iterations. Eventually all findings were combined and the con-cept and the final design was evaluated by testing it in the field.

The final design is an application (the game ‘Alles maalt’) on TagTiles which asks the child to act out physical tasks, construct and solve the appropriate multiplication for each situation. The application makes sure the child gets a multiplication that fits with their pro-gress, by assessing the child during play.

The child gets direct feedback on their actions, to optimize the learning situa-tion. When the child struggles TagTiles

gives appropriate hints to make sure the child gets a feeling of success. In con-clusion the child improves their multi-plication skills by playing the game on TagTiles: it keeps the child motivated and takes little steps forward.

The final design should be tested and evaluated in the field, but unfortunately there was no time left to do so. The final design should be tested first to check my assumptions and the interaction. When the design is improved a longitudinal study is necessary to prove the game ‘Alles maalt’ is instructive.

By this project my identity as a de-signer has been changed. I started as a hard working and enthusiastic student, who wanted to complete a perfect pro-ject, but I ended much better. I achieved a good project which is not perfect, but I also realized that I need to change my attitude (my goals were too high).

I am triggered to help them with their development. Their development which prepares them for the real world and which determines how they will be in the future.

I have always had a special interest in math, working with numbers, finding solutions and understand the logic be-hind it. I like to teach math to others, to help them understand more about logic thinking.

As a child I needed extra tutoring in language due to my dyslexia. I know how it feels to be behind, compared to oth-ers. To get extra tutoring in something you don’t like, something you want to avoid, and fill in boring sheets again and again.

I am a user-centred designer; I don’t only work for but also with users. This is clearly visible when you look at my design approach. During each iteration I involved the users in their natural set-ting to get inspired, create empathy and test, discuss and evaluate ideas or sug-gestions.

My focus is always on how the user ex-periences my design, how rich the inter-action is and how to improve the inter-action and their experience. To achieve this, I start early with building proto-types, testing concepts and exploring possibilities. This inspires me to make the right choices.

I have a special interest in working with children. It is challenging to get into their world and help them communicat-ing what they experience. Find out what could be improved or is not succesful.

co-design sessions

user-test scenario

user-test textile with children

Preface

Preface

Report structureThis document reports my FMP start-

ing point, process, reasoning and end results. First it explains the background of my project; my goals and my litera-ture. Then I will discuss my proposal, in-cluding important decisions regarding to my intention of this project.

Next, I will describe my approach; get in touch with my target group and the creation of the prototypes. In the last chapter the final design will be de-scribed and eventually everything will be evaluated.

Hopefully everything is clear, when something is not clear or you have ques-tions please feel free to contact me: [email protected].

Enjoy reading,Eveline Brink

a delay I was not stuck with the project. But my delay was caused by CANS (also known as RSI).

During the fourth month of the pro-ject my body made clear I was working too hard and sitting too long behind the computer. Since then I have had physi-cal pains in neck, shoulders and back, mostly caused by stress.

This was a big learning moment, I learned to deal with it, how to prevent it and I changed my attitude. Because my body was damaged it will take me a while to recover completely.

By taking little steps forward and ad-justing my project goals. I managed to continue my project. Which resulted into a project which is not complete fin-ished yet, but due to the circumstances enough to complete my master pro-gram.

Project contextBefore I go into the concrete project

material, I first want to illustrate the context of my project. It took me one and a half years, instead of a half year to complete this project. The project was going well, and unlike others who have

ConclusionsAfter reflecting on my own devel-

opment and my interests I came to the conclusion that I want to help children with their math problems. This would be the start of my Final Master Project (FMP). The FMP is the main activity during the final (M2.2) semester of the Master program. It should reflect the skills and identity I have developed over the years and allows me to develop these even further.

Contents

Framing

1. Introduction 1.1 Orientation 121.2 Design opportunities 121.3 Approach 14

2. Theoretical foundations 2.1 Context 162.2 Learning 182.3 Didactics 202.4 Multiplication 222.5 Motivation 272.6 Business 32

3. Opportunity 3.1 Client 363.2 Partner 403.3 Design guidelines 41

Exploring

4. Iteration I 4.1 The field 464.2 Explore material 484.3 Field conclusions 50

5. Iteration II 5.1 Explore TagTiles 525.2 Analysis and conclusions 545.3 Focus group 565.4 Overall scenario 58

6. Iteration III 6.1 Set-up user-test 606.2 User-testing 626.3 Explore details 656.4 Conclusions 73

Final Design

7. Final design 7.1 Alles maalt 767.2 Design hardware 837.3 Design software 927.4 Validate 100

8. Evaluation 8.1 Reflection results 1028.2 Discussion 1048.3 Reflection process 1068.4 My identity 110

Acknowledgements 114References 116Appendices 123

framing1. Introduction2. Theoretical foundations3. Conclusions

What is the project about?What do I want to achieve?

Who are involved?

12FMP Eveline Brink Augustus 2011

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1. Introduction

1.1 OrientationTo complete my FMP in the given time

it is very important to define the scope my project as much as possible. First I explored opportunities which fit with my FMP goal to help children with their math.

I found out that there is a growing concern and a public debate about the quality of math of the primary educa-tion in the Netherlands [appendix A]. In-vestigations showed [KNAW 2009] that the children’s mathematical proficiency needs improvement. Worldwide the Netherlands scores high, but eac year it get’s worse. It is expected that this will cost the government six billion euro each year [Steeg 2011]. To improve the quality of math you have to start with improving the basic knowledge. There-fore children from four to ten need to work on basic math, to realize complex

math later on. When having issues with the basic math this means big issues later on.

Experts [appendix B] indicate that mul-tiplication is a stumbling block, and is of high importance to realize complex math problems later on. A lot of children are behind or never realize the memo-rization of the multiplication (more de-tails in 2.4).

People are trying to improve the qual-ity of math, but the lack of time, money and knowledge in the field does not do any good. New technologies give oppor-tunities to improve didactics: give teach-ers extra support, information about the child (progress) and motivate the child. But old didactics are used on the new technologies, this could be done better, which is a missed opportunity.

After orientating this field I could con-clude that helping children with their multiplication problems is a good start for my project: use the opportunity of new technologies and new knowledge about didactics.

1.2 Design opportunitiesIn February 2010 I presented my pro-

ject proposal [appendix C]: design a product that helps children with autom-atization of the multiplication table. To realize this I want to use new didactics on new technologies. It should give the child prolonged experience of success and the child becomes more confident (figure 1).

Current solutions are old-fashioned and not optimal for the available tech-nology. A new solution could be new didactics by using new technology pos-sibilities.

After reflecting on my own development and my interests, I came to the conclusion that I want to help children which have trou-ble with learning math. This is the start of my FMP and should be transformed into a more detailed problem statement/design opportunity.


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Experts indicated they miss something like this; there is a clear market for a tool. People try to create such a tool, but often lack knowledge of technology (possibilities) or lack expertise in didac-tics. I could be the one who links those two.

I concluded that there is a clear prob-lem: too many children have not autom-atized the multiplication facts at the end of class five, although it is essential as foundation for arithmetic operations.

figure 1: visual from project proposal; help children who have trouble with learning the multiplication facts (who experience the circle of failure) by pro-viding an interactive, tangible tool that gives direct feedback. The end result should be a happy child with knowledge about the multiplication (who experi-ence the circle of success).


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To realize this it is very important to investigate the complete area: context (the children, school, teacher, etc.), learning, didactics, multiplications, mo-tivation, used materials, and the new technologies.

1.3 ApproachThe design vision that I want to imple-

ment requires a couple iterations with involvement of each iteration close ex-pert (children, teachers and research-ers).

I started with a theoretical and field study to analyze the current situation. Then, get insights about didactics and other context related issues. Finally cre-ate empathy with the child and teacher to understand the situation.

I wanted to keep involving people from the field during the complete de-

sign process. By this, I make sure that not only the product ‘works’, but also fits with the users latent needs. This wil let the user experience scenarios to im-prove the concept and protocol. This will help to make choices towards the right direction. Combine this with scientific research to validate my decisions.

Not only keep involving the users but also other experts. Ask for their feed-back on my decisions, because I am aware of the fact that it is not realistic to become an expert like them in such a short period of time. They have years of experience in this field and have differ-ent backgrounds.

It is also very important to keep an eye on the progress of the project dur-ing the first few weeks. Because I know I am motivated to make sure each de-tail is thoroughly investigated. This will result in slowing down the process and

eventually end with a half project. Make sure I make decisions on time and keep focusing on the big picture and relevant details.

Eventually I want to realize a scenario demonstrated with a (partly) working prototype which illustrates how the product should look like and work. This scenario should be validated by scien-tific research, experts and user-testing. The scenario will not be worked out into details, but will be a start to create such a product for real.


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ConclusionsI could conclude that my prob-

lem statement is: to help children with their multiplication problems by designing a tool with the use of new technologies. Motivate the children by creating a rich and meaningful experiences. I will real-ize this by close user involvement during the complete process, ex-ploring concepts in the field and validating my choices by the use of research, experts and the field. But first I will summarize my theoretical findings.

pictures of previous projects represent-ing my approach in a project (row on the left: MoZo; user-testing with children, row on the right: SleepSupportSystem, user-test by letting the user experience different scenarios, materials, etc.)


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2. Theoretical framework

2.1 ContextWhen talking about learning the multi-

plication table, we are talking about chil-dren aged seven to nine (in the Nether-lands group four and five). The goal is to have memorized all multiplication facts at the end of group five. But a lot of chil-dren (aged eight to nine) are behind and need extra help; this help is currently not optimal.

For this project information about learning, didactics and mul-tiplication are necessary. But it also required information about motivation, because there is no learning when there is no moti-vation. I will start with summarizing findings about the context and end with the business aspects.

Characteristic for this age (middle-childhood), it that children attend school and learn large amounts of information. Their overall development includes their physical, cognitive, social and emotional growth. They begin to manage their own behaviour and start to find their place in the world, they develop self-esteem.

Children begin to note their internal qualities and realize that they are good at some things, and not good at others. More details will be discussed in chapter 4.1.

The context of use will be at school, probably in the classroom. In the Neth-erlands 1,5 million children go to pri-

Watterson 1987, page 57


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mary schools [CBS 20-12-2010], and sit in their classroom with an average of 24 children. But because of cuts of the gov-ernment they will grow to 26 [Besturen-raad 2011], which means higher working load for the teachers and less attention for each child, probably resulting in low-er quality.

In the room itself each child has his/her own table and against the wall extra materials are stored. Teachers use their chalkboard or smartboard (Dutch: digi-bord) in front of the class to give instruc-tions. Often in the back of the classroom there is a computer corner, probably my project would be used in that corner.

Based on this, I will design for chil-dren from the age eight to nine. More information about how they learn (2.2), didactics (2.3), multiplication (2.4), and how to motivate (2.5) them, you can read in the following sub-chapters.

pictures of classrooms at primary schools (top: Beppino Sarto group seven,left: Bi-jenkorf group 5)

pictures of computer corners in classrooms (left: Bijenkorf group 5, right: Beppino Sarto RK group seven)


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Learning can be acquiring (recording), processing (constructing), practicing (gain knowledge), or a combination of those [Boekaerts 1995].

Next; when are we learning? Humans learn continuously, each experience is a learning activity. Some are only stored in the short memory, but in this context we are focusing on the long-term memory.

What do we learn? Benjamin Bloom [1956] has suggested three domains of learning: cognitive, psychomotor and af-fective. When learning math at school we mostly focus on the cognitive do-main (involves knowledge and the de-velopment of intellectual skills).

How do we learn? Anderson il-lustrated the process of learn-ing [figure 2] as a pyramid [Forehand 2010].

Not everyone is learning in the same way; there are different learning types. Visual learn type (read and consider), auditory learn type (listen), motorial learn type (learn by doing), and com-municative learn type (discuss and ex-change). Also keep in mind that each child is unique. It is not realistic to make the perfect tool for each child. By mak-

2.2 LearningLearning is very complex. Like Brandt-

Williams [1997, page 9] says: “As human beings, learners are inherently complex. They bring divergent sets of values, ex-periences, abilities, and motivations to the learning process.”

Many theories try to explain “learning”, some of them are: Behaviourism (condi-tioning) [Pavlov 1927, Atkinson 1983], Cognitive theory [Newell 1972], Mental functions [Vygotsky 1978], Metacogni-tive [Brown 1980], and Constructivism [Paris 1989]. I will not go into the details of those theories, instead I will describe some conclusions which are relevant for my project.

First what is learning? Learning may occur consciously (informal) or without conscious awareness (formal). The edu-cational system should use a combina-tion of them.

figure 2: pyramid from Anderson based on the taxonomy pyramid from Bloom. The learning process starts at the bot-tom with the lower order thinking skills. [source: http://en.wikipedia.org]


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ing it flexible and adaptive, I want to help as many children as possible.

How to improve our learning? Learn-ing can be easier with motivation (read more in 2.5). Improve learning by mak-ing it fun, children learn as a result of play. Several theorists say that play is the first form of learning. When children play they experiment with the world, learn the rules, and learn to interact. Vy-gotsky [1933] agrees that play is central for children’s development (they make meaning of their environment through play).

Learning can also be improved by using more senses during the learning process. There is a theory [Treichler 1967] saying that by just listening, people remember 20% of what they learned, by just see-ing 30%, by seeing and hearing 50%, by combining seeing, hearing, and talking about it 70%. Eventually by seeing, hear-ing, talking and acting out 90% of what

they learned is remembered. But critics say those numbers are fraudulent and shouldn’t be taken too literally [Thal-heimer 2006]. But I think I can use the theory as an inspiration for my project because it gives an idea how important multiple senses stimulation is for learn-ing (stimulate this by rich interaction).

To improve the learning of children, teachers should:1. Determine a clear goal, motivate to reach ad guide towards that goal.2. Give the child confidence that it is able to reach that goal (have positive expectations, keep their interest and in-trinsic motivation).3. Scaffold the child by making sure it is working on the right level (make sure the child likes the challenge, by avoiding too much threats and keeping control).4. Assess the child to know its progress toward the goal (so the previous point could be realized).

When learning, the child needs the do-main specific knowledge, skills, and cognitive strategies. But also equally important are metacognitive knowledge (insights about your own learning) [Boe-kaerts 1995]. For the age six to nine, children have a lack of this cognitive knowledge [Flavel 1971], so young chil-dren need extra guidance, in order to be successful in learning.

In conclusion, I could say that when I am designing I should reckon with several aspects: support the cognitive learning for long-term memory by motivating the child and stimulating multiple senses. Communicate a clear goal, and give the child confidence about achieving this goal, by assessing the child and work on the right level. Therefore I will design a flexible and adaptive tool which helps the children to learn the multiplication table. But because each child is unique, the effectiveness of the tool will be user dependent.

“We learned how to talk and walk, not by being taught how to talk, or taught how to walk, but by interacting with the world... whereas at about the age of six, we were told to stop learning that way and that all learning from then on would happen through teaching.”

[Negroponte 2006]


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“self-confidence is a result of good performance, not the

cause”

2.3 DidacticsTo make an instructive tool, under-

standing didactics is necessary. Not only read (scientific) papers and talk to ex-perts, but also get feedback from them on the current situation and explore how didactics are realized in the field (chapter 4.1).

Education materials and teachers should support the learning process (chapter 2.2). Teaching should change the behaviour of the child [Boekaerts 1995]. First demonstrate new skills and motivate the child. Next create the per-fect surrounding to acquire. Finally give enough time and space to consolidate (maintaining behavior).

Without motivation there is no learn-ing. When a child wants to learn some-thing, it is willing to put energy in it. Make sure the child understands the urge of learning those facts (more in chapter 2.5).

The problem is that schools are mainly focussed on the end results (perfor-mance oriented) and not on the effort and process. This results in avoiding and problems with criticism. Whereas learn oriented results in willingness to learn, don’t see learning as a threat but as a challenge [Nicholls 1987 and Ames 1988].

When having trouble with a calcula-tion, a child needs support. Never give the answer immediately, but guide the child towards the answer. The way to-wards the goal is more important than the actual goal. So make sure the child understands the answer and is able to get the answer by itself next time. This instead of asking the child to remember the correct answer.

Children that have issues with a topic have continuously negative experiences: this results in avoiding the subject. This means even more issues (negative spi-

ral). The trick is to let them experience positive results (correct answer finded on their own) by instructing the right level of calculation. This will give them more confidence.

Success is partly a self-fulfilling proph-ecy. The results of low expectations are more harmful comparing to high ex-pectations. High expectations results in higher results (Pygmalion-effect) [Jun-gbluth 1996]. Teachers believe they al-ways need to give students with special needs a helping hand. But this results that these students don’t get the op-portunity to learn to think and reflect on their own [Luit 2009]. When a child knows it has a disability (dyslexia or dys-calculia), the result will be that the child will act like it. This results in lower per-formances. Therefor it is very important to have high (realistic) expectations.

Working on the right level is crucial. The level of a calculation is depending

[Thomaes 2007]



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on the process of the child. Take little steps forward and when having trouble take a step back. This asks for an adap-tive system which assesses the child and translates this into a certain calculation on a certain level that should be asked to the child.

To know which action is correct a child should get feedback on their actions. When getting the feedback later, there is a change the child saved a wrong answer in their head. So direct feedback on ac-tions is crucial when learning.

But when giving feedback don’t focus on lack of skills, but instead on giving

hints how to improve their action; so don’t give product orientated comments (“You have two mistakes”). Go for pro-cess orientated comments, with ac-ceptance and compassion (“wat heb jij ontzettend goed je best gedaan!”) [Ee-rkens 2011].

As I said in chapter 2.2; “each experi-ence is a learning activity”. High impact experiences characterize themselves by high stimulation of multiple sensors but also by meaningful context. So learning does not only depends on the medium, but also how active and meaningful the learning experience is. Recent research shows also that moving your body im-

proves the learning results [Houwen 2011].

So in conclusion I understand the di-dactics and know how to optimize this: Give the child more confidence, assess the child, work on the right level, sup-port the learning process (guide), give direct feedback, motivate the child, have high (realistic) expectation, make the ex-perience active and meaningful. Beside this, also focus on the effort and pro-cess, not on the end results. In the next subchapter I will continue my didactic research but on a more specific level: multiplying.



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2.4 MultiplicationTo narrow the project I chose to fo-

cus only on learning the multiplication table. Experts and teachers pointed out that this is a big issue in the math

didactics. This knowledge is part of the basic knowledge of math. It is crucial to automatize this to be successfull in more complex math problems.

When learning the multiplication, you

figure 2: The iceberg metaphor from Frans Moerlands, illustrating how important the investment in activities and insights are to reach a formal level of mathematics (the top of the iceberg) source: Boswinkel 2003, theory Moerlands 2009.

start with concrete material to under-stand the meaning of multiplying (re-peatedly sum up). If done correctly, the concrete examples used are meaningful material from a child’s perception. This is really important, because every indi-vidual is inclined to reason on the basis of meaningful information (more than on the basis of formal and fixed rules of reasoning) [Girotti 2004, p.122].

Children start with the easy calcula-tions (2x 5x 10x). In between children add 1x and 0x. At this stage the child creates insights which are of high im-portance when going to the next level. Make sure this is sufficient before enter-ing the next level. These insights are the foundation of knowing the multiplica-tion table, this is often misunderstood in the field (the attention of most teach-ers is focusing on the formal level) [Luit 2009]. To illustrate this Frans Moerlands used the iceberg metaphor [figure 2].



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The concrete material can be repre-sented in different ways (all three of them are important, no one should be left out).

Line model:Have material put behind each other

in a line [figure 3], to make it more easy reorder in length of ten. The advantage: to counting easy, the disadvantage: no

clear overview with big amounts and very attractive to keep counting.

Surface/square model:Have material ordered like a rectangle,

count amount of “blocks” [figure 4]. Ad-vantage: still able to count (easy to take a step back), clear representation, often used in real life. Disadvantage: still able to count (not going forward).

Box modeHave objects which can be filled with

material and put in each object the same amount [figure 5]. Advantage: able to hide what’s inside the box: little step towards formal notation, not able to count anymore. Useful to act out the neighbor strategy. Disadvantage: it does not provide a clear structured overview.

Figure 3: an ex-ample of a line model [Dawson 2003]

Figure 4: an example of a surface model [Brodie 2005]

Figure 5: an example of a box model [Greaves 2008]


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By little steps the level of difficulty is ascending,: first introduce 3x,4x, 6x and 9x and eventually learn 7x and 8x [figure 6]. But meanwhile the materials used should change from concrete material towards formal notation [figure 7, next page].

How this process will look like and what the learning speed will bei, is dif-ferent for each child. So again an adap-tive tool who assess the child is needed. But make sure to make small steps for-ward (towards formal notation), when having trouble take a step back. It is very important to make sure the child keeps understanding the insights.

Eventually, when the child understands the calculation on the formal level, the next level is the automatizing. At this stage the child is able to find the answer for a calculation by knowing which strat-egy to use and is able to give the correct

figure 6: visual showing all possible multiplication answers up to 10 x 10. The col-ours show how difficult children find them when learning. It is remarkable that when knowing just the easy multiplications, you already know 70 % of the complete multi-plication table to ten. And just 10 % of the calculations are very hard to learn.



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answer in approximately 10 seconds; no material and context are needed. The final goal is to memorize the calcula-tion, which means that the child knows the answer, no calculation is needed. To make sure to keep on this stage, repeat-ing is needed.

The problem in the field is that schools and teachers are rushing towards the end goal: memorizing. A lot of children just repeat the calculation aloud with-out knowing the meaning (called ‘drill and preactice’ [Kroesbergen 2003]. They miss the foundation. So later on, when they forget one fact, they are not able to find the answer.

Children who are behind with the mul-tiplication table and keep practicing on the formal level will not only have ‘float-ing capacity’ [Luit 2009], but this results also in a lot of failure (confidence is shrinking, multiplication gets stupid, get

figure 7: learning traject for multiplication table inspired on Frans Moerlands theory. You start learning the multiplication at the easy level (like 2x4) with the use of con-crete (physical) material to understand the meaning of the calculation. Slowly the calculation becomes harder but also the context changes towards a more formal notation. How this process looks like depends on the child, each child is learning on their own way and speed.


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more behind). Experts told me that the problem is that the teachers and math book publishers miss the didactic knowl-edge, time and materials to do so.

To find the correct answer for each multiplication, different kinds of strate-gies could be used. The most important and used one is the neighbor strategy: add or minus one multiplicand [figure 8]. There are a lot of strategies, but the children who have trouble with multipli-cation are advised not to use too many different strategies. They get confused, so keep it simple [Luit 1999]. The best way is to let the children ‘discover’ a strategy by themselves, by this they will understand the background of a strategy and when to use it in practise.

When observing the child during mul-tiplication you can analyze not only the level of the child but also what kind of

figure 8: example neighbor strategy and example mistakes children make during this strategy.

7 x 6 = ?

neighbor from 6 is 5:

7 x 6 = 7 x 5 + 77 x 5 = 3535 + 7 = 42so 7 x 6 = 42

often made mistake:7 x 6 = 7 x 5 - 7 = 28or 35 + 7 = 40 - 2 = 38

mistakes the child makes. A lot of chil-dren create their own strategy which is often incorrect or cumbersome. It is of high importance to correct the child. By keeping an eye on what kind of mistakes the child makes. Some common mis-takes are known [figure 8].

In conclusion when learning the table of multiplications it is very important to start concrete with easy multiplications, and slowly go towards more formal cal-culations and more difficult ones. Make little steps forward, when having trouble go back. Guide the child by hints (using strategies or counting). For my project I chose to focus on the multiplication table to ten, to scope my project even further.



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2.5 MotivationWhen learning, motivation is a key

component (concluded in chapter 2.3). To answer the question how to motivate a child, it is important to know what motivation is and how to stimulate this. When children are not motivated, they are not prepared to invest time and en-ergy to acquire new skills.

Motivation means that an individual comes in a certain state, when one or more motives (influenced by circum-stances) are updated [Boekaerts 1995]. You have performance, intrinsic and ex-trinsic motivation.

Performance motivation triggers to pursue success and avoid failure. This

relates to choices and perseverance from an individual. And those are based on their expectations, which are partly created by previous experiences.

A task can be intrinsically motivating; just doing it is its own reward (e.g. be-cause it is fun). Or a task can be extrin-sically motivated; if I do it I will get re-



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theory into a pyramid [figure 9]. This is used to understand people’s their mo-tives for action. I can use this for my pro-ject. A child at a Dutch school has met the physiological needs and I hope the child lives in a safe environment and is healthy. The child should have family and friends to get a feeling of belong-ing and acceptance. Then comes the most important layer for this project: es-

warded (e.g. with money, the absence of punishment). Extrinsic motivation arises when the reward is not connected to the task/activity but external.

It is a fact that people have a natural need to feel efficient and competent, called competence motivation [White 1959]. The feeling of progress causes positive emotions. Another influence comes from the fact whether the action is obligated or freely chosen [DeCharms 1968].

In conclusion there should be motives to learn the multiplication table, create the right circumstances and make sure children have good expectations. In the second part are some relevant theories from Malone, Maslow, Csíkszentmihályi, Vygotski, Keller and Fontijn which in-spire my project.

Malone [1981] presents a theoreti-cal framework for intrinsic motivation in the context of designing computer games for instruction. Malone argues that intrinsic motivation is created by three qualities: challenge, fantasy, and curiosity. Challenge depends upon ac-tivities that involve uncertain outcomes due to variable levels, hidden informa-tion or randomness. Fantasy should depend upon skills required for the instruction. Curiosity can be aroused when learners believe their knowledge structures are incomplete or inconsist-ent. According to Malone, intrinsic mo-tivating activities provide learners (with a broad range of challenge, concrete feedback, and clear-cut criteria) good performances.

Maslow [1943] presented a theory of human motivation, focusing on humans’ natural curiosity. He translate his

figure 9: Maslow’s hierarchy of needs, translated into a pyramid wit the more basic needs at the bottom [source: http://en.wikipedia.org]



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provided to the child should change over time. So the child should not only work on the right level, but the support should be on the right level as well. This asks for an adaptive system.

teem. The child desires to be accepted and valued by others. It should engage themselves to gain recognition and get the feeling of self-valued. When learning the multiplication, the child is intrinsi-cally motivated to master the multipli-cation table to get status, recognition and self-confidence, independence and freedom.

Csíkszentmihályi [1990] created a theory about optimal experience. He says that people are most happy when they are in the state of Flow. In this state they are concentrated and noth-ing else seems to matter (optimal state of intrinsic motivation). To achieve this state balance must be found between the challenge of the task and the skills of the performer (if it is too easy or too difficult, flow connect occur) [figure 10]. This proves that when a child is learning the multiplications, it should work on the right level.

Vygotski [1978] created a theory which was probably the inspiration for Csík-szentmihályi: the Zone of proximal de-velopment (ZPD) [figure 11]. This term is used to illustrate the range of tasks that a child can complete independently. And the task completed with the help of others. It captures the child’s cogni-tive skills. This shows that the support

figure 11: visual of Vygotskis Zone of proximal development theory [source:

http://en.wikipedia.org]

figure 10: visual of Csikszentmi-halyis Flow theory [source: http://

en.wikipedia.org]


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The next source, discovery, comes from gaining knowledge which is stimulated by curiosity. And the last source, bond-ing, is linked with recognition, being part of a group (like the third layer of Mas-low’s pyramid).

There is one last thing which influences a child motivation; feedback. Don’t re-act enthusiastic after each achievement [Kohn 2001]. As mentioned in chap-ter 2.3 the feedback should be process oriented comments and not product oriented comments. But Kohn also sug-gests three options:

Based on the same facts Lazeron (2010) concludes that cribbing (“spieken”) is a very important part of a learning pro-cess, so it should be used more often.

Keller (1983) presents an instruction-al design model for motivation that is based upon a number of other theo-ries. His model suggests a design strat-egy that includes four components of motivation: arousing interest, creating relevance, developing an expectation of success, and producing satisfaction through intrinsic/extrinsic rewards.

Like mentioned before we know that intrinsic ‘rewards’ works, but there is a discussion about the consequences of extrinsic rewards. Kohn [1993] argu-ments that every reward is killing in-trinsic motivation. This is demonstrated with an experiment with twenty chil-dren on the Oprah Winfrey show [Coens 2000]. The children were asked to evalu-ate new puzzles, ten children were re-

warded (dollars), the other ten didn’t get a reward. After the evaluation the children were left alone with the puz-zles, all ten children who had not been rewarded went back playing with the puzzles, only one child who had been re-warded was doing the same. So the re-ward has killed the intrinsic motivation to play with the puzzles.

Another theory is from Fontijn [2007]; Functional Fun. He describes how fun can be used to maximize the learning potential of smart toys using tangible interfaces. To achieve this at least one of the three core sources should be re-alized: accomplishment, discovery and bonding (if you have all you have a more powerful motivation). Getting a sense of accomplishment is influenced by goals (clear cut criteria) which can be met and influenced by the progress towards those goals. A balance between chal-lenge and control is important (flow).

“Motivation is that which gets a behavior started and

keeps it going. ” Svinicki 2000



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1. say nothing2. say what you saw (let the child know

you noticed, the child will be proud on what (s)he did, example: “Boy, you made a lot of calculations today!”)

3. talk less, ask more (“Which calcula-tion was the hardest to solve?” this will feed his/her interest in multipli-cation)

When giving feedback it is important to reckon with the effects of doing so. Make sure the feedback is helping the child to feel a sense of control over his/her life, help the child to become excited about what he/she is doing in its own right. And don’t give feedback which re-sults in letting the child constantly look to us for approval or turning the activity into something (s)he just wants to get through in order to receive a pat on the head.

So a lot of important elements related to motivation are mentioned in this chap-ter. In conclusion I should reckon with:

- balance between difficulty and ability (create a challenge)

- accomplishment (satisfaction, clear cut criteria, overview achievements)

- discovery (curiosity, arousing interest, exploring)

- bonding (recognition, self-valued, expect success, cooperation, competi-tion)

- control (autonomy, independent)- appealing (fantasy, create relevance,

meaningful)- don’t give extrinsic rewards- give direct correct and concrete feed-

back

In general; when learning the multiplica-tions it is about repeating the same over and over. Variation is key to prevent it becomes boring.


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2.6 Business For this project it is also important to

look from a business perspective. I ex-plored and evaluated the market of di-dactic materials with regard to multipli-cation and interactive learning materials [figure 13]. This varies between books, board games, simple plastic or wood objects, and computer programs. Most of them are used at school and are used

individually. When assessing [example; figure 12] I can conclude that those ma-terials focus a lot on the formal notation, in general they lack in giving insights and are not adaptive.

All the materials use old didactics, al-though new technologies offer much more possibilities. Most materials don’t give insights but keep repeating boring

formal notation calculations. They don’t fit into the requirements to be a good instructive tool. They should assess the child and should provide calculations that are on the right level of difficulty. This is a big opportunity for my project. The market misses a good assessment tool, which reflects on the level of the child and adapts its scenario on this. And it should not cost the teacher extra effort nor time.

figure 12: didactic materials assessed, horizontal axes describes a couple of crite-ria for my design and the vertical axes shows seven product which I assess and the

last question mark is how my project schould be



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figure 13: didactic materials used to learn the multiplications


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You would expect that such an as-sessment tool is already developed for use on a computer. But as far as I know there is no such program on the market yet. Right now companies started with developing such a program. This is a bit late, but I am glad they realize this. But games on the computer are not a perfect tool to learn the multiplication table. The interaction is not optimal, physical material in the real world is an added value when a child needs to understand a multiplication [O’Mally 2004, page 3].

To realize physical materials and the ad-vantages of new technologies, I can use tangible interaction.

With tangible interfaces people can in-teract with digital information through the physical environment. This provide a lot of benefits to the educational world [O’Malley 2004]. There are several new products on the market realizing this,

like the Sifteo [figure 14], the I-Blocks [figure 15] and the SmartUs [figure 16]. But they miss thoughtful didactics. Therefore my focus is to create a ‘new’ market (Design-driven innovations) [Verganti 2009].

figure 15: SmartUs concept; traditional play elements combined with technolo-

gies, learn and play in one [JSW 2007]

figure 16: I-Blocks; intelligent blocks that children use to learn spelling.

[www.Heutink.nl]

figure 14: Sifteo; “The alternative game system for truly hands-on play”

[www.sifteo.com]



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Motivate the child by giving them confidence by letting them experi-ence positive results (feeling of ac-complishment), by challenging the child, give a feeling of control and by letting them discover.

Make it more instructive by giv-ing direct feedback to the child and having and active and meaningful learning experience by stimulating multiple senses (tangible interac-tion).

Use new technologies to realize this, support the teacher by sav-ing her time and effort. And finally keep in mind each child is unique.

ConclusionsI will design an extra tool for chil-

dren (aged eight to nine) who are behind with learning the multipli-cation table. Support their learning by having an adaptive system who assess and guide the child on the right level. Not only on the difficul-ty level but also on concrete-formal representation (which support the learning process).

Make sure the child understands the insights of each multiplication, so eventually the child automatized all calculations of the multiplication table up to ten.

According to teachers and experts, the focus of this project should be chil-dren who are behind with learning the multiplication. The result of my project should be an extra tool in the classroom that helps children to get back on track with their math skills. The tool should be independent from a publisher, so every school which is interested can buy this tool. Eventually the tool will not be the only tool that is used for learning multi-plications, but it should be used next to other tools.

On the next page you can read a sum-mary of this chapter; the theoretical framework. In the next chapter I will use these to set up requirements.


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3. Opportunity

3.1 ClientTo realize my project in the given time,

I chose to involve a client in my project. Two companies were interested and eventually I chose Serious Toys from Den Bosch to become my client. Be-cause I could use their platform, TagTiles and their expertise to realize my project quicker.

Serious Toys is a spin out of Royal Philips Electronics (since 2008). One PhD student (Janneke Verhaegh) from our faculty of Industrial Design TU/e was involved in the pre-development of TagTiles.

Serious Toys focuses on merging fun and personal development. They make learning aids that adapt to the abilities and needs of each individual child. It al-lows children to reach their full potential in a pleasant way, without pressure. This vision fits perfectly with my project vi-sion so far.

By combining all the knowledge and the whishes from client (Se-rious Toys) and partner (PARWO), I created my design guidelines for this project.

“Their first product is TagTiles (TikTegel in Dutch). This is a game computer in a form of a tablet, without keyboard, mouse and play area. Children play with the board by placing play pieces on them. It is very easy to use, because the pieces you use to control the computer, form an integral part of the game that is played. This makes the task easy to un-derstand and a lot of fun.”

“It is a flexible and intrinsically moti-vating learning aid with which the child works independently. While the child completes game tasks, TagTiles assesses the capabilities of the child. The board adapts interactively to those capabili-ties by tuning the difficulty level of the game tasks and providing help where needed.” [quoted from the site: www.SeriousToys.com].

figure 17: TagTiles the innovative learning aid from Serious Toys (den Bosch)


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[1] Play area: underneath this surface RFID (Radio frequency identification) technology makes it possible to iden-tify and locate each tagged object which is put on this surface.

[2] Tagged objects: these objects will be recognized by the surface because these wooden blocks have an unique tag underneath or inside them.

[3] Log in: each child can have their own unique card, to log in they place the card here and now TagTiles knows who is playing the game.

[4] Audio output[5] USB connector[6] SD-card[7] power supply

1

32

74 5 6

figure 18: side view of TagTiles figure 19: top view of TagTiles


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It a platform that recognizes each ob-ject (with an unique tag) and its location by using new localization technologies. This makes it possible to interact with TagTiles by simply manipulating physical objects on the surface. Already over one hundred games are created for TagTiles to help children from different ages with learning space insights, reading, math, safety, etc. Each game (example figure 20) exists out of software (which is pro-grammed in the dedicated language ES-Pranto), physical objects and a foil. This foil lays on the play area of TagTiles. It is a visual printed on a transparent plastic that blocks or transfers the light from TagTiles LED array underneath the play area.

TagTiles offers me the opportunity to focus my project and to quickly test a potential concept. The tangible interac-tion is an added value to my project.

figure 20: Example of one game for on TagTiles: “Keer op Keer”; ref. 012101. Game to learn the multiplications. Age 6-8, players: 1-4 and price: €129,00. De-veloped by ThiemeMeulenhoff. On the left: the complete game existing out of the foils, instructions and packaging.


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Serious Toys is involved in this project as a client, but also as an expert. My contact person Willem Fontijn was able to give me feedback during my process and helped me with finding knowledge on the field of motivating the child. They helped me not only by sharing knowl-edge, but I also borrowed TagTiles to do some tests with (chapter 5).

The interaction of TagTiles fits with my intention of using tangible interactions. With TagTiles children can explore and manipulate physical objects. By tagging

the objects, each object will be recog-nized by the console. This provides me freedom when designing, objects can be

whatever I want them to be. But there are some limitations, the objects will not be recognized when they lay on top of each other and they will only be rec-ognized when laying on the play area. This is something to reckon with while designing.

In conclusion, Serious Toys B.V. will be my client for my project. I will design an application for on their product: TagTiles (in Dutch: “de TikTegel”). They pro-vide me knowledge and materials (like TagTiles). To align this, we agreed I do an internship at Serious Toys.

figure 21: logo from Serious Toys B.V.


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3.2 PartnerAnother company was interested in my

project and asked to be involved dur-ing my entire project. Which is good for my project, because they have a lot of knowledge and an innovative vision which fits to my project. Together with Serious Toys we agreed to include them as an official partner.

My partner are the companies from the project PARWO (‘PAssend Reken- Wiskunde Onderwijs’, translated: Ade-quate Mathematics) which is an organi-sation created by collaboration between educative design agency Edumat and SSOT in 2005.

SSOT (Stichting Speciaal Onderwijs Til-burg) exists out of schools for special education. Edumat is an educational design agency initiative by and based on the theory of Frans Moerlands.

Frans Moerlands previously worked at the Freudenthal Institute in the Neth-erlands. He created an underlying phi-losophy how and what children should learn during mathematical education. I referred to his knowledge and vision in chapter 2.4 (iceberg). He points out that new didactics are needed for the new technologies. The new technologies create new possibilities, but publish-ers don’t use those possibilities but just copy-paste the old didactics on the new devices. This is a missed opportunity.

More information can be found on their sites: parwo.yurls.net, www.edu-mat.nl and www.ssot.nu.

PARWO helped me during my project by giving feedback on my project. But more important, by sharing their exper-tise of didactics and learning materials aiming on supporting lessons for (spe-cial) elementary education.

figure 22: logo from PARWO


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3.3 Design guidelinesAfter an inventory of the world around

math issues, I saw an opportunity to de-sign a tool to help children with multi-plication problems. I collected all men-tioned aspects of the previous chapters [figure 23].

I translate this mapping into a clear structured visual which represents all the important aspects regarding my project [figure 24, next page]. To make my project more concrete and realistic to realize in the giving time, I need to scope my project further. So I chose to

figure 23: impression of a mapping of all mentioned aspects of the previ-ous chapters. The aspects are linked to each other when they influence each other. By this I get an overview of what is important for my project and where I should focus on.


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focus on just a couple aspects: adaptive, insight and direct feedback.

This results into a project which does not include multiple players (social). Al-though this would be an added value, to realize this would cost me too much time. Because when having multiplayers assessing each child will be very com-plex. It would be nice to add this social aspect again when the project is real-ized.

figure 24: visual representing all key components of the project (all men-tioned in the previous chapters). In the middle of the wheel you see the two main aspects of my project: the child and the tool (TagTiles). Around the cent-er all important aspects are illustrated. In the outer circle the aspects are speci-fied.


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1. Design a tool (physical aid device) to help children (aged eight to nine) with their multiplication (until table of 10) problems (unable to autom-atize the multiplications after reasonable amount of instructions and practice).

2. The tool should be an application for TagTiles from Serious Toys (client).

3. Design a system that adapts on the child’s level of multiplication skills. Let them experience success, this way they become more confident about themselves.

4. Design a system that adapts on the child’s level of formulation. Make sure the child creates a strong foundation of multiplication insights.

5. Make a tool which is instructive, by motivating the child (make it fun) and give direct feedback.

6. Focus on individual use only (easier to design for and able to keep track on one child’s progress).

7. Create a tool which helps the teacher to observe the children’s progress and which doesn’t cost extra time and effort.

The circle on the left inspired me to create the design guidelines for this pro-ject (on the right). This will be my start-ing point of my first iteration, described in the next chapter.

In the following chapters I will describe the design process and the results of each iteration.

exploring4. Iteration 15. Iteration 26. Iteration 3

How to combine all the findings into a validated design?

How will the scenario look like?


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“the best way to learn about them is to spend time with them”

4. Iteration 1

4.1 The fieldMy way of designing is to involve the

user in each iteration in my design pro-cess. The user is an expert of their own experience and it is very relevant to know what kind of experience to de-sign. This gives insights in understand-ing how users translate their surround-ings and interactions into an experience. This kind of information should not be learned from a book, but discovered in the field: understand the context which I am designing for and look for opportu-nities. I realised this by visiting schools, observing and interacting with the chil-dren.

My design process exists of four iterations, in each iteration I do/perceive, ideate/integrate, validate, analyse and update my vision. During my first iteration I explored the field and materi-als which already exist and linked it with my theoretical frame-work. This gave me inspiration for my project.

I observed the children in their natural habitat, look at the world through their eyes. When attending a math class I was shocked about the huge gap between literature (chapter 2) and practice. I saw enough points of improvement, but for the time being I stayed focussed on my project.

Notable is the willingness of children to learn new things, they want to learn. They are curious, like to understand things and are proud on what they have learned. But they miss direct feedback and are often confused (when the teach-

er is going to fast or they miss relevant knowledge for that topic). Children help each other, but often that is not enough. It is difficult for just one teacher to see it all and to help all the 25/30 children at the same time.

To learn more about those children I taught four children each weak individu-ally at school and one at home. By this I was able to test an idea (based on litera-ture, expert or my own opinion). I made a prototype [figure 25 on page 50] and put it to the test.

I did not only focus on the end goal:

how to learn the multiplication, but also other aspects like: motivation, materi-als, interactions, learning (how quick), concrete/formal material, boring/frus-tration, skills, instructions/feedback, uniqueness, etc. I will discuss the out-comes in the next subchapters.[Markopoulos 2008]


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I tried to analyze the level of the child on multiplications. By asking the child to put each multiplication in one of the three cups: easy, normal or difficult. This informs me which multiplications are known by the child and which multipli-cation need extra attention. A nice side effect of this ‘game’ was to see how the children notice their own progress.

They grow up with the thought that they are bad with multiplications. But when seeing the cup easy completely filled, they realized that they already knew a lot of multiplications. In fact 70% of the multiplications is already covered when they know the 0x, 1x, 2x, 5x and 10x. When knowing also 3x and 4x they know already 87%. Their feeling of fail-ure is caused by just a little amount of really difficult calculations. It is impor-tant to let the child know how many multiplication they already know.


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“hey look! I com-pleted the table of six by myself!”

4. Iteration 1

4.2 Explore materialWhen teaching the children multipli-

cation I evaluated a lot of existing basic materials which are used for ages. I will discuss the four most important materi-als: boring sheets, wooden puzzle, gold-en blocks and an old computer.

Standard sheets

Plain white paper with calcula-tions seems to be also motivating when the child has success. This material is used all the time at school, and should not be ignored. It is very clear material without any distraction. But it is important that this material is used at the right moment with the right calcula-tions, to make sure the child expe-rience success. Make sure to let the child notice their progress.

Wooden puzzle

Wooden pieces with all the mul-tiplication on them (on front the calculation, on back the answer). They are triggered to complete the whole puzzle, it motivates to see how many calculations they already know and structure their progress. It is an open-ended game, create their own rules/goals. Variations: row by row (neighbor strategy) or random. I could use some interest-ing aspects from this: let the child create and show progress.

[a child during teaching, play-ing with the wooden puzzle]


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This is just a selection. The first repre-senting the traditional way, second the old fashion way, third a ‘modern’ tangi-ble way and the last an old interactive way (no tangibles).

I also observed the child playing mul-tiplication games on the computer [Am-braSoft 2000]. They were motivated and their direct feedback was good. But the interaction was poor. I still missed the in-sights and it wasn’t instructive for a child who only choose to practice the table 1x and 2x, because he already knew them and wanted to score some points.

All these findings inspired me for my project and I summarized them in the next subchapter.

Math-table blocks

Simple small wooden blocks, in-dividual or clustered together. This creates the possibility to quickly create surfaces which represents multiplications. This visualizes the meaning of a multiplication and easily shows the neighbor strategy. When adding the context gold or money it gets an interesting dimen-sion for them. The children like to order them and create surfaces which help with their multiplication insights.

Old Computer

When I was young I really liked to learn from this ‘computer’. With little lights on the side and sound it was exiting to link answer with question on the sheet. I made my own games [appendix D] and no-ticed it is very motivating to play with this. The game is very struc-tured, a bit adaptable and most important direct feedback. But it misses creating deeper under-standing why something is wrong. Trial and error was often used to find the answer.


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“It would be interesting to have new di-dactics with new technology and not old

didactics on the new technology”

4. Iteration 1

4.3 Field conclusionsFrom the first iteration I learned how

the world of multiplication looks like in practice. I was shocked about the gap between the research world and the classroom. The quality of math educa-tion could be easily improved by bring-ing research findings into practice. The cause of this gap is discussed and a lot of people blame the PABO (educating teachers), the math book publishers and the fact that teaching math at a primary schools has become a less im-portant topic [KNAW 2009]. Instead that it should be one of the most important

topics. Like recently published [Steeg 2011] this will costs the Dutch govern-ment 6 billion euro each year.

But back to my findings. I concluded that this is even a bigger opportunity then I was hoping for. Everyone is con-vinced of how it could be better by using the new technologies, but no one is able to realize this (lack of technology or di-dactic knowledge).

Now I am up to date about the situa-tion and I noticed some big opportuni-ties and know with what kind of pitfalls I have to reckon with while I am in de-signing.

figure 25: pic-tures of low fi-delity prototypes which I used dur-ing teaching the children.

[Frans Moerlands]


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Conclusions from field[1] Almost everything could be fun when it is new and not played too often. So

the games should change and have different kinds of layers to keep it fun for prolonged use.

[2] The children like to enrich their experience by using their imagination, add a context like gold or money.

[3] The children like to be active with their hands, it becomes more fun and tangible material makes the calculation also more alive. This will help them with creating deeper understanding of the meaning from the multiplication.

[4] The children are eager to learn, understand new stuff and proud when they achieved something.

[5] I noticed a lot of confusion during class and playing games. When creating a game make sure it has a clear structure and gives the child the opportunity to ask for extra explanation.

[6] Also show their progress, this also motivates them too see how many mul-tiplications are learned.


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5. Iteration 2

5.1 Explore TagTilesAs mentioned in chapter 3.1, I will use

the platform, TagTiles, to realize my concept. To do so I introduced TagTiles to the children by letting them explore the general games and some under con-struction multiplication games.

Their first reactions were very positive. They were really excited, privileged to be the first child at school who plays with such a high-tech board. They are very concentrated when playing the games.

During the second iteration I explored TagTiles in the field and combined this with my previous findings. This resulted into an overall scenario.

The interaction becomes clear by try-ing out, they take a block and notice the reaction on the play area. But it takes a long time before they really understand the interaction. The advantage of this interaction is how it triggers social play. They often shared the interaction and created their own extra rules.

It took a while before they understood the games. They needed extra instruc-tions to understand the meaning of the game and the interaction.

The children often complained about TagTiles, that it was wrong. The child was convinced of her answer and was disap-pointed when TagTiles didn’t seems to react. It is important that in these kinds of situations TagTiles gives feedback, for example: “rethink your answer”.

Like all games, to keep the child en-gaged with the game make sure it does not get boring. Variation in tasks, con-text, feedback and adding advanced levels should be considered. This can be achieved by adding small features such as time pressure.

Overall the children were very enthusi-astic, liked to play with TagTiles for quite some time. After a while the interaction was clear and fun. It is really important to make the instructions as clear as pos-sible and give feedback often enough to make sure the child understands what is happening.

“I want this game, I am going to use all my savings to buy this!”

[a child during teaching, when using TagTiles for the first time]


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pictures of children playing with TagTiles; standard games, but also multiplication games which were at that point still under construction. Now these games are on the market (see an example in chapter 3.1, figure 20 on page 38).


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And last of all publishers will put the game on the market. This means that the game is not independent. By this a lot of schools will not choose this game because of their chosen publisher.

But using TagTiles for my project influ-ences my process positively. It gives me the opportunity to create a working (ad-vanced) prototype to start testing with the children. It also helps to focus my project further which means the project will be more concrete. But it also means a lot of project choices are already made, because of the (limited) possibili-ties of TagTiles.

Observing the children gave me inspi-ration to sketch some possible interac-tion object for on TagTiles regarding learning the multiplication [figure 26].

5.2 Analysis and conclusionsBy observing the children and testing

scenarios on TagTiles I became inspired how to use TagTiles for my project. Here are some conclusions why and how I could use TagTiles.

From a business perspective it is wise to design a game on an already existing platform. This makes the game itself less expensive and schools who already in-vested in TagTiles are extra triggered to buy this game.

When looking at the technical aspects it is also smart to use TagTiles. The inter-action from TagTiles is ideal when creat-ing a tangible concept. The electronics works, new technologies are optimized to work more precise (which is a must when designing for such an interaction).

The design features of TagTiles are also useful for my project. The object has the right size, fits on the child’s table, easy to transport and still enough space for exploration. Sound and light feedback are perfect, because this fits with the tangible input and children with weak reading skills have no issues.

The most important aspect is the fact that TagTiles gives direct feedback on tangible activities and can record the ac-tions of the children.

But of course there are also negative points about the use of TagTiles for my project. First of all, you can only play the game when you have bought an ex-pensive platform. Second are the limita-tions of interaction. Stacking object on TagTiles is difficult to recognize. Because the RFID recognition is on a 2D-area.

5. Iteration 2


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figure 26: sketches of possible interaction object for the project to use on TagTiles, representing multiplications


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5x95. Iteration 2

5.3 Focus groupDuring this iteration I did not only

look at what children think of TagTiles, but also what the opinion of teachers is about TagTiles and about my project plans. To find this out I organised a focus group with teachers.

To achieve this I cooperated with a PABO student; Ester Lathouwers. She was doing her graduation project about games during math lessons. We agreed to work together for a while, she helped me contacting teachers (at her school Beppino Sarto, Eindhoven) and I helped her by sharing my literature research.

On the 14th of April in 2010 we gath-ered four teachers who teach group five to seven. We introduced ourselves, TagTiles, TagTiles games and my project. They discussed, gave their opinion and even brainstormed about possible solu-tions.

This resulted in a clear view of every-one’s opinion and a lot of practical tips how to realize details. They were very critical and it was nice to see the influ-ence of difference ages of the teachers. Young teachers were more open minded for new technologies and old teachers hesitated more (as described by Mi-rande 2006). This teacher didn’t saw the added value of TagTiles in comparing with the computer.

They agree that learning the multi-plication table can be improved a lot. Children who have issues with the mul-tiplication tables don’t get the correct material, they ask the child to just repeat the formal notation calculations. After a while teachers give up and give the child the multiplication table card (figure 27).

In general they were very enthusiastic about TagTiles, but didn’t like the price. They could think of a lot of extra appli-

cations, like: parsing sentences, learning fractures, percentages, decimal system, section table, but also for history, geog-raphy, coordinations and music lessons.

The teachers suggested to improve TagTiles by making the scenario quicker, light brighter, skip big introductions, have a clear voice (don’t use childish voice for this age), add limit on how often asking help, add game elements

figure 27: an example of a multiplica-tion table card, includes all calculations


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(such as: next level, game over), and make sure TagTiles doesn’t make sounds which become annoying after a while. They agreed that it is very important to communicate clearly to teachers what the learning goal of the game is.

They advice me to make sure I chose an interesting contexts for the age eight-nine: diamonds, money, bling-bling, fan-cy cars or famous persons.

I also presented my project at the PABO (Pedagogische academie voor het basisonderwijs, translated: Educational Academy for primary schools) during an information day at the Fontys. A miniconference on May 27th 2010 called: “Verfrissend perspectief voor onderwi-jsontwikkeling” (translated: refreshing perspective for educational develop-ment). The goal of this conference was to exchange practical examples of edu-cational development on the field of cul-

ture, ICT and/or science and technique. I presented together with Esther Lathou-wers. Important people attended this presentation (including head of PABO and teachers of the PABO).

They were interested in TagTiles, but also in my project. They agreed with my conclusions and were very positive about my plans. The gave me advice on how to continue my project and agreed that this is a promising project.

Conclusions focus groupThey were enthusiastic about TagTiles and agreed with my con-clusions. There only problem are the costs. But near the costs they can image using my application to help their children with learning the multiplication.

The teachers agreed with the fact that learning tools for multiplica-tions can be improved. The current situation is sad. Too many children are behind and are depending on their multiplication table card.

The teachers gave a lot of practi-cal information and advised me to choose an interesting context.


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5.4 Overall scenarioEventually I summarized all conclu-

sions so far into an overall scenario [fig-ure 28]. This scenario orders the main activities which are important to realize an instructive game when using TagTiles. To achieve this I focussed on the main issues:

- keep the child motivated- assess the level of the child- adapt level of calculation to child- guide the child- give direct feedback- communicate progress to teacher

Reasoning why each stage should be motivating for the child is included in this visual. Details about the scenario are left out because I want to investigate them further in the next iteration.

This scenario makes sure the child un-

derstands the foundation of multiplica-tion (start with concrete material) and

that the child finds the right answers by her/himself (get a better feeling about themselves). This is crucial when learn-ing and remembering the multiplication table for the rest of their lives.

This scenario makes sure the child will be motivated to continue to play this game (feeling of control, discovery, ac-complishment and challenge) and also by variation of the context. It is an adap-tive system which assess the child dur-ing play, this is an ideal situation for learning.

And finally this scenario makes sure the teacher doesn’t need to invest extra time, but will be up to date about the child’s progress.

In the next iteration the scenario should be validated and investigate the details of the scenario (context, mate-rial, feedback, etc.).

Notes overall scenarioStart: TagTiles and a child with mul-tiplication issues. A. Get multiplication (audio and visual) and ask the child to con-struct this calculation.B. Support the child with giving the right answer.C. When answer is correct, give feedback.D. Use data (time, errors, support, actions) to reflect on level of the child. Translate this into their over-all progress (and communicate this with the teacher).

Eventually back to A, another calcu-lation at a certain level (depending on progress). When having trouble at B, even after enough support, take a step back (go directly to-wards D).


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A.

B. C.

D.

figure 28: overall scenario, combined previous find-ings into a scenario, details will be added later on


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6. Iteration 3

6.1 Setup user-testDuring this iteration I created a cou-

ple of scenarios and tested them in the field. In subchapter 6.2 I will describe and evaluate each scenario, but first I will explain the context of the user-test.

I tested the different scenarios with the different materials by the use of a Wizard of Oz prototype [figure 29]. This means that I created my own fake TagTiles (a plastic mould with under-neath a laptop) which looks like it was working (when acting, it gave the cor-rect responds with light). But by the use of an external keyboard, I was control-ling the fake TagTiles in real time.

Using this Wizard of Oz prototype has several advantages. It makes the pro-totype very flexible without any bugs. I was able to anticipate on the situation. Details and possible exceptions didn’t have to be worked out before the test,

After creating an overall scenario, details must be investigated and tested in the field. Make choices about how the final con-cept should look like and link back with previous findings.

but could be filled in during testing. Such a prototype is much quicker and easier to program. And finally I didn’t have to borrow an expensive TagTiles for a long period of time.

Of course this prototype influences how the children experienced the game. This doesn’t show how the child will act exactly when it will play the same game with a real TagTiles. But this prototype will give me a clue and inspires me how it could look like.

With this prototype I tested initially the overall scenario from chapter 5.4. I looked how motivated the children were, how clear everything was and what is the best way to instruct the child.

So during tutoring I placed the pro-totype in front of the child. I asked to construct a certain calculation with the materials (see chapter 6.3) on the

yellow surface. Then I asked them to lay down the first number; size of one item. For example with the pizzas; how many mushrooms, lay down nine. This number should be laid down on a little blue surface, which I created with my keyboard. When correct I made this sur-face green, when incorrect I made it red and asked to look again. The same for the next number (times set is repeated) and for the answer. Then the play area is cleaned and start over with another calculation.

I also looked at input possibilities, not only what kind of material to use to con-struct the calculation, but how to input the formal calculation notation and the answer. Another important aspect is to look how to guide the child, not only through the process, but also how to help the child when it is stuck: What kind of hints are possible, in which order and when to give such a hint.


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figure 29: Wizard of Oz prototype usedduring user-testing. Left: picture of the prototype setup.

Top: program I wrote in Processing 1.2.1 to make sure I could control the play area by using my keyboard. And in the mid-dle: visual how the software should look like on the play area.

material

child

me

laptop

plasticempty

prototype

keyboard: input


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6.2 User-testingThe Wizard of Oz prototype was used

to test the overall scenario and four de-tailed scenarios. I will illustrate those three detailed scenarios in this subchap-ter by describing and evaluating each one of them.

The outcome of these user-tests will be used in chapter 6.3, where I will discuss each detail.

Snakes

Simple wooden blocks connected to each other by the use of an elas-tic. The child can construct a surface by ordering the snakes. Then ask the right calculation and answer.

This represents the surface model (subchapter 2.3), within an interest-ing context for the child. By acting physical they get a better feeling about what an calculation means. The snakes make it also easier to act out a strategy.

They were very enthusiastic about the snakes, they liked to order, reor-der and build things with the snake. Some children added a complete sto-ry to the snakes.

It is a clear representation, with the option to act out a strategy. When using the snakes, make sure they cre-ate the snakes out of loose blocks, otherwise you will need to many snakes.


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They loved the context and liked to build big piles with the empty CD boxes. It wasn’t a problem at all that just one box contains a pizza. They used their imagination to think all the boxes were filled.

It is a good representation of the boxes model, sometimes it was diffi-cult to count a huge pile of empty CD boxes because they are a bit transpar-ent.

Pizza boxes

Used empty CD boxes to represent pizza boxes. Create one foam pizza to stimulate their imagination. The pizza has four tomatoes, nine mushrooms and existed out of six slices. This is used to represent the box model. You have on each pizza nine mushrooms and a pile of eight pizzas, how much mushrooms are there in total?


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Cubes

After practicing the scenario with the snakes and boxes I translated this concrete material in a more formal representation. Instead of a pizza box with six tomatoes, a sim-ple cube was representing this.

The child was still motivated be-cause of the intrinsic motivation to achieve a higher level in multiplica-tion and noticing their progress.

Flowers

Almost similar with the pizza box-es, instead of a pizza the empty CD boxes were filled with little colour-ful fake flowers. Girls like this con-text very much.

In one box were six pink, seven purple and nine red flowers. This resulted into multiplications. This representation was a little less rep-resenting the reality, because why would someone put flowers in a flat box?


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6.3 Explore detailsWhen testing different scenarios in the

previous subchapter I used simple ma-terials. This made me realize that those children don’t need fancy designed ma-terials to get motivated. In this context it is more important to have a design which is practical, cheap and most important of all: clear.

When looking at the sce-nario, there are four things which need to be designed [figure 30]: material that represents all possible multiplications (to ten), input material (the numbers and asking for help), foil (surface on TagTiles) and the output (sound and light on TagTiles).

Each thing mentioned above will be explored more into detail. Together they will be the final design which will be pre-sented in chapter seven.

figure 30: four things which need to be designed; material that represents all pos-sible multiplications (orange), input material (purple), foil (green) and the output (red).


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Represent multiplication materialThis material should represent all pos-

sible multiplications to ten. To make the game as instructive as possible, it is im-portant to have material which repre-sents the line-model, surface-model and the box-model. But also material which represents in a more formal way is nec-essary (like the cubes on page 64).

The representation of the line and surface model can be combined by us-ing something like the snakes [figure

it is not (yet) possible for TagTiles to recognize objects on each other. So it should be ‘boxes’ who are laid down on TagTiles, next to each other [figure 33].

It should also not have a clear surface by itself. Because children can get con-fused when a box looks too much like the surface model.

31], by laying the snakes behind each other (line-model) or next to each other (square-model).

To realize this as cheap as possible and to make sure children do not spend too much of their time constructing the snakes, there should be different sizes [figure 32].

The representation of the box model is much more complicated. The pizzas where a big success, but unfortunately

figure 33: a TagTiles with boxes on the play area. On the left a concrete representation and on the right a more formal representation.

figure 31: snakes used to represent the multiplication 3 × 3 by using the line- and the square-model.

figure 32: preconstructed snakes, one of five blocks, one of two blocks and three of one blocks. You can not take these apart.


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The solutions are little bags from cloth which can be filled with things [figure 34]. To motivate the children an interest-ing context will be connected: money/gold. So the box model will be repre-sented by little bags which can be filled with gold pieces.

The bags should be semi-transparent, which makes it possible to show the contents (how many pieces of gold) by putting the light on underneath the bags when laying on TagTiles [figure 35]. By this a small transformation from con-crete towards a more formal represen-tation is possible.

To realize a representation of the com-plete multiplication table to ten with the bags, you need ten bags and just ten pieces to put in the bag (just one bag will be filled). Again children’s im-agination will be used, to pretend all the bags are filled with the same amount. As shown in the pizza concept they don’t have trouble with this.

Input materialTo make sure children understand each

multiplication and know the correct an-swer it is very important to check the multiplication including the answer. To achieve this children need to ‘build’ the calculation on TagTiles in the correct no-tation: infix notation (most common no-tation). Each multiplication exists out of five components [figure 36].

figure 34: illustration of little bags, that can be filled with things, to represent the box-model.

figure 36: infix notation1. first factor: multiplicand (size of the set)2. multiplication sign (‘×’)3. second factor: multiplier(times set is repeated)4. equal sign (‘=’)5. product (answer of the calculation).

figure 35: illustrating how the light of TagTiles can assist with the box-model representation. On the left a bag with no light on the play area. Inside the bag are three pieces, but you can’t see them. This helps to go to a formal notation. But when the child has trouble TagTiles can put the light on (illustrated on the right). Now you can see the content (take a step back to a more concrete representation.

2 × 4 = 81.

2.

3.

4.

5.


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es of each number should be available (three units and one dozen). The zero don’t need a dozen, but need five units 10 × 10 = .. (some children could answer 1000). Also the ones are an exception, three units, three dozens and one hun-dred.

So five zeros, seven ones and four piec-es of each number between two to nine. This means (5+7+4×8) 44 pieces with numbers on them (32 units, eleven doz-ens and one hundred).

This big amount of pieces also influ-ence the design of one piece. It should be easily stored (otherwise it will cost too much space) and as cheap as pos-sible.

During the user-tests it was a bit cha-otic, all the numbers standing around TagTiles. It took often a while before

6. Iteration 3

It is of high importance to let the child construct the calculation themselves. This way, learning the correct notation is stimulated and practiced. The best way would be to let the child write the mul-tiplication down (on paper/touch play area). But in this context it is hard to re-alize this, because that kind of recogni-tion hardware is too expensive.

Another used solution is pushing the corresponding number (keyboard). When looking at the interaction this is a bad way of learning the notation, be-cause children are forced to type direct in the right order. For example 45, chil-dren are used to write first the five and then the four, when typing they type, without knowing, 54.

So no writing and no typing, which re-sults in tangible interaction, construct-ing the calculation by connecting com-

ponents. This fits perfectly with TagTiles and is still didactically responsible.

During the user-test I used paper cards which I borrowed from PARWO. Those cards are cheap, simple and very clear. By folding them they stand up. I used the ten units and nine dozens. It is very instructive to have separate units and dozens cards (to learn the difference).

When talking only about the multi-plicand, multiplier and product (the numbers) it is not enough to have just one five, when you need to lay down: 5×5=25. You would think three would be enough, but this will result in a lot of question marks when a child wants to lays down 5×5=55, even though this is a wrong calculation the child should be able to put this down. If so the Tagtile is aware of the child’s mistake.

To give the child some space, four piec-


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the child found the correct number. This could be a problem because TagTiles thinks the child is thinking too long about a calculation. So it is very impor-tant the child can quickly lay down the correct number as soon as the child knows it.

In conclusion the 44 number pieces should be clear, cheap, easy to find, easy to grasp, easy to place, easy to put back and easy to store, without taking too much space. In addition there should be a clear multiplication sign and equal sign.

Some sketching [figure 37] resulted into four concepts: simple loose pieces laying, loose pieces standing, dice and stations which each include the nine numbers. It would be nice to try them out in the field.

figure 37: sketches how the input mate-rial can look like. The child will use this to construct the (in)correct calculation on TagTiles.

possible positions of numbers including the position of the tag


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FoilEach game used on TagTiles consists

of input material, output and a foil that lays on the play area of TagTiles. This foil creates a context, which supports the scenario and makes the game more at-tractive. This foil is a visual printed on a transparent plastic that blocks or trans-fers the light of TagTiles play area.

For my game the foil should help to structure the interaction. It should be clear for the child were to lay down the multiplication representation and the calculation in formal notation. So there are just two surface which need to be designed.

When thinking logically it is more prac-tical to put the calculation in front of the representation. Because the child lays down the representation first and this could block the view on the calculation. It is practical to make the representation

front a field of three by twelve squares are left for the calculation [figure 38].

Often the field used for the represen-tation for a multiplication will be much smaller. The calculation can be put a bit higher. This should be possible, so TagTiles should be loose about the exact location of the calculation as long as it is standing in the right order.

Or maybe the foil is not a flat surface but a construction, where the child can scroll between the numbers as shown in figure 39.

area ten by ten squares (to realize the surface model). The play area has twelve by twelve squares. So this means that just a row of two squares are left for the calculation.

This makes it a bit cramped, so the field will exclude the calculation ten multiply ten for the surface model. So on the

figure 38: sketch of how the foil could look like. Two areas: back, lay down the multiplication representation material (ten by nine squares) and the front, lay down the calculation by using the num-bers (twelve by 2,5 squares).

figure 39: sketches how the foil could look like, when not using the loose number pieces, but stations connected to the foil.


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Output To prevent confusing and frustration

the output should be tested over and over, to make sure children understand the scenario and what is expected from them. The output exists out of light and sound.

The light can be designed in each col-our in squares from 20 x 20 mm on the play area. By making the material which is put on the play area a bit transparent, the objects can change colour.

The light should indicate were to lay down the representation. Like men-tioned at the previous page the repre-sentation surface is ten by nine squares big. TagTiles can show surface represen-tations by using the light. This could be used for example when a child has trou-ble laying down a surface model.

But the light can also assist with the box-model representation as shown in figure 35 on page 67. By lightning the bag from beneath, it shows how many gold pieces are inside the bag (to take a step back to concrete).

The light can also support the child when constructing the calculation. By indicating if the correct number is put on the correct place [figure 40].

The sound output should be further investigated. It will exists out of a voice telling instructions, giving help, giving feedback and sounds indicating correct actions. It is very important to give clear instructions and have variations in feed-back. As mentioned in 2.3 the feedback should not be focussed on the lack of skills but on giving hints how to improve. Don’t give product oriented comments, but process oriented comments (“you have done your best!”).

figure 40: illustrating how the light can contribute to get direct feedback on the constructed calculation. When asking to lay down a certain number, indicate this by flashing a couple of squares blue. When the correct number is positioned on the right place, give it a yellow colour. But when it is incorrect make it blue (not flashing. Make sure children don not use trail and error, if child is just guessing, stop with indicating by colour, but give hints. When the complete multiplication is correct, they all change in green.


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figure 41: scenario so far


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6.4 ConclusionsDuring iteration three I made a lot of

progress by testing and investigating the details of the overall scenario. Overall the children understood the scenario, but some extra time is needed to be sure the details work.

So far the scenario [figure 41] will be act out by using first the snakes (surface-model) and gradually the bags are used. Each time a multiplication is constructed with the material and then the correct calculation should be constructed on TagTiles. The level of difficulty and how concrete the material will be, depends on the progress of the child. To realize this, a well thought through algorithm should be designed and validated, to re-alize an adaptive system.

To keep the game interesting it is im-portant to have variations in multipli-

cations, contexts, feedback and show progress of the child. To achieve this an extra foil could be used with all the multiplications on it. When laying it on TagTiles, TagTiles will indicate, by using light, which calculations are making pro-gress or already known by the child.

It should also look nice, not too fancy. I noticed this has no extra value later on. It would be nice to give the school the possibility to expand the game by add-ing extra versions of the game.

The details which are explained in this chapter should be connected to each other. An overall context would make the game more interesting and coher-ent. The final design will be illustrated in the next chapter.

final design7. Final Design8. Evaluation

What is the final result from my FMP?What are the reactions on my FMP?

How does this FMP changed mewho I am as a designer?


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7. Final Design

7.1 Alles maaltThe final design is an application on

the TagTile, the game named: ‘Alles maalt’. To explain clearly how this game will work and look like, I will first dem-onstrate the scenario. In the following subchapters I will go more into detail; how the hardware looks like (chapter 7.2), how the software should work (chapter 7.3) and why this design should work (chapter 7.4). Before I illustrate what the final scenario looks like, I will first refresh your memory in what kind of context this design should be used.

Context‘Alles maalt’ should be used by chil-

dren in group five, age eight-nine, who have trouble with learning the multpli-cation table. At the end of a daily math lesson children are free to choose a math related activity. Then the child can

By combining all findings and solutions, from previous itera-tions, a final design can be presented. Not only how it should be, but also why it should work. First I will demonstrate the overall game, later I explain the details of the hard- and software.

chose (or recommended by the teacher) to play the game ‘Alles maalt’.

In the back of the classroom, in the computer corner, TagTiles is stored. The child gets TagTiles, including the Alle maalt attributes, and lays it down on his/her table. Plugs the power in and puts on the headphone. Then (s)he will play the game for approximately ten minutes. When finished another child can play the same game, another game or the child stores the TagTile. It would be nice to play this game a couple of times each week.

Whenever the teacher needs an up-date, the teacher can connect the TagTile with the computer. By using the ‘Alles maalt’ program (included with the game), the teacher can check the pro-gress of each child. It gives an overview, but also (when necessary) detailed ad-

vice how to help a child with a certain representation or calculation. By us-ing internet the data can be uploaded. An expert can look at it (when teacher wants) or researchers can use the data.

ScenarioBut what happens when the child turns

on the TagTile? To start the game ‘Alles maalt’, the child should first lay down the foil of that game on TagTiles. By a tag in the foil TagTiles knows to start the game ‘Alles maalt’. Then it will start with the introduction, followed by the actual game and closed by a reflection [figure 42].

1. The introductionWhen TagTiles knows the child wants

to play Allles maalt, it shows a fancy il-lustration and plays a recognizable tune. By this the child gets feedback from TagTiles that the foil is placed correct.


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figure 42: flow chart how the scenario of the game ‘Alles maalt’ looks like. Start at the top left with the introduc-tion, after the actual the game ends on the bottom right with a reflection on the progress of the child.


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Meanwhile the game is loading and asks the child to place their name tag on the top left of the play area.

When the tag is placed correctly, the tag is recognized, TagTiles welcomes the child by saying: “Welcom Susan, let’s play Alles maalt!”. When no name tag is placed, to TagTiles will start the trial scenario, to give an impression how this game should work. But for now we as-sume that Susan is logged in. Then there are two options: 1. Susan is playing it for the first time or 2. Susan has played it before.

In the first case TagTiles will give a short, clear, interactive introduction. To make sure Susan understands where to lay down the numbers and the represen-tation material. This will be realized by showing light and asking to put the ma-terial on this place. When done correct, the first task can start.

When Susan has played the game be-fore, TagTiles refresh Susans memory. By repeating what she did last time (“Do you remember last time? ...”). This is realized by a short, clear, interactive summary of what kind of material Susan used on what kind of level. When done correct, the first task can start.

2. Actual gameThis is the main part of the game.

Starts after a short introduction and fin-ishes when the reflection is started. In this middle part a simple scenario is ex-ecuted: construct a representation of a given calculation and then lay down the correct corresponding calculation. Then construct a new representation and lay down the new calculation, and so on.

In the beginning of the task TagTiles asks (for example) to lay down two snakes, of each four blocks, in a certain place (indicated by flashing blue light).

When done correctly, the light turns yel-low (direct feedback). When having trou-ble, the task is repeated and explained in more detail (“Get the snake cubes out of the box, connect them by...”).

7. Final design

figure 43: overview of play area, with in-dication where to lay down everything, 1: the multiplicand, 2: the multiplication sign, 3: the multiplier, 4: the equal sign and 5: the area for the answer.

1.

2.

3.

4.

5.


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When the material lays in place, TagTiles asks to construct the corre-sponding multiplication. In the begin-ning this is done piece by piece. Start with asking to lay down the multiplicand (size of one snake), by saying: “How many blocks does one snake have?”. At the same time the place where to lay down the multiplicand [figure 43] is flashing blue.

When laying down the correct number (4) the light turns into yellow, when it is wrong the reaction depends on the pro-gress of the child. The light will stay blue, but quits with flashing. TagTiles asks if the child is certain about this answer. More hints will be given (depending on the progress) and eventually TagTiles starts to count aloud (supporting by the light) and eventaully asks “How many blocks did we count?“. Then asks the child to take that number and place it on the play area.

When the correct multiplicand is laying on the correct position TagTiles will ask: “How many snakes are laying on me?”. Now the blue light will flash at the mul-tiplier place, when correct number (2) is placed the light turns yellow. But when the wrong answer is placed the same story as for the multiplicand counts.

At this stage the child has placed the multiplicand (4) and the multiplier (2) on the correct place. When it is the first task, the child has to place the multi-plication sign and the equal sign on the correct place. This is stimulated by ask-ing to create the corresponding multi-plication. When the child has trouble, explain in detail where to lay down each sign, indicated by light.

Then the correct calculation is laying in place. It is time to place the correct an-swer behind it. Again blue light will flash and when the correct asnwer (8) lays, it

will turn yellow. But when the wrong an-swer is placed, or it takes too long, hints will help the child finding the answer.

The child can asks for the hints sooner by using the question mark. The amounts of hints, and what kind of hints, depends on the progress of the child. But TagTiles will never give the correct answer! The child has to find it by themself. When the correct answer lays in place, all the light change from yellow to green. This indicates the calculation is finished. Now TagTiles will ask the child to write this calculation on a clean piece of pa-per. And then all the numbers and the snakes should be stored, to start with the next task.

Those tasks will be done in sequence. So get instructions, lay down represen-tation material and construct the cor-rect calculation. Different materials will be used (snakes, bags, cubes or maybe


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also dices). This depends on the pro-gress of the child, more details in chap-ter 7.2 and 7.3.

After five minutes of executing those tasks, TagTiles asks if the child wants to continue. When Susan wants to quit, she places the question mark up side down in the middle of the play area. When she wants to continue she does not do anything, or when she is in a hurry, she places the question mark on a certain place. After a total of ten minutes play time, TagTiles asks again, if she wants to quit and after 15 minutes the TagTile ends the game by itself. What happens next will be explained on the next page.

When executing the tasks, TagTiles is using a complex algorithm. This algo-rithm assesses the child’s multiplication skills and makes sure the child gets the correct calculation (on the right level of difficulty and material). To realize that I

created three levels of difficulty and four levels of material. They both will be ex-plained in chapter 7.3.

3. ReflectionWhen the child indicates (s)he wants

to quit the game (or has played for 15 minutes), it is time to wrap up. Before shutting down the game, it is time for re-flection. A special (smaller) sheet should be laid down on top of the other foil [fig-ure 44]. On this foil all multiplication are printed.

When the child lays it on the the cor-rect place, the lights will indicate which calculation were played today (guided by a voice). After concluding that the child has done a lot, TagTiles will show all the calculations the child knows (so include previous results). The colour of the light indicates how well Susan knows each calculation (orange means well and birght yellow means very well). A voice

7. Final design

figure 44: top: the second foil, a smaller sheet with all multiplications. Bottom: when laying the foil on the play area TagTiles shows the progress of the child by using lights.


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tells that Susan knows already a lot of calculations.

The visual gives the child a clear over-view and gets more confident, feels proud. Even though she did not make any progress today, she can be proud, because she solved a lot of calculations today. Eventually TagTiles thanks the child for playing and asks if she wants to play again soon.

The introduction, the actual game and the reflection together, form the com-plete game. This process is explained global on the last pages. But the ‘Alles maalt’ game is much more. I will explain some aspects further: guidance (feed-back and hints), variation and expan-sions.

GuidanceTo make sure the game is instructive,

it should be adaptive, tangible, giving

direct feedback and motivating. But the correct guidance is also very important. First of all the instructions should be clear (easy to follow), appropriate and no too boring (concise). But guidance is much more then instructing, it should give feedback and hints to.

It is very important to get direct feed-back on each action. The feedback can be just a sound, voice, light or a com-bination of them. The sound and voice feedback become quickly monotonous, so light feedback is prefered. Voice feed-back should be more rare, for example when the correct calculation is solved really quick (for that child). Sounds can be used to indicate that another task is completed.

Hints are also communicated by sound, voice, light or a combination of them. This is a complex process, because the type of hint depends on the progress

of the child. In the beginning hints are given more quickly, but later on TagTiles should be more reserved with giving hints. Hints will automatically start when a child did not act for a long time. But by laying down the question mark on the play area, the child can ask for a hint sooner. When the child is advanced, ask-ing for hints is limited. For example for every five minutes the child can just use three question marks. By this the child will be more cautious and is stimulated to think more by themselves.

When a child asks for a hint TagTiles can give different hints. The first hint is small, some kind of reminder. The next one (when the first was not enough)is more into detail and the last one is counting together. The amount of hints used for each calculation will be saved and used for assessing the progress of the child (more details in chapter 7.3).


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VariationTo keep the child motivated, the game

should not get boring after a while. This is provided by offering the child a chal-lenge. But when learning the multiplica-tion table, it means the child needs to repeat each calculation again and again. To make this a bit more pleasent, vari-ation at different stages should be of-fered.

Variation can be created by adding and changing an exiting context to the mate-rial (for example, the two snakes get a baby, now you have three). But you can also variate with the calculations (do not repeat the stupid 8x8 calculation, but vary with easy calculations in between). You can also variate by adding new rules. For example; only lay down the answer, add time pressure or draw surface (with two blocks) instead of laying down the snakes.

The best way to create variations is to give some control to the child. Let them choose which calculation they want to lay down. Or decide which calculation to do next by throwing two dice. Those last variations do not match with the whole algorithm of making the calculation on the right level. But when a child made a lot of progression, this control does not damage the algorithm.

All those variations can be added to the game. But be careful with selecting the moments of those variations and make sure the child does not get confused. Be-cause it is very important that the child understands the overall structure.

ExpansionsThe ‘Alles maalt’ game described in this

chapter is the basic game to start with. It would be a smart bussiness value to make sure expansions are available

on the market after a school buys this game. By this more variation is offered, and children who played the game for a while get some refreshment.

Expansions for the game could be ex-tra material; new kinds of surface or box material, new kind of foil or maybe different numbers. But also adding ad-vanced levels (have smaller numbers), were you work with calculations up to 20. But also the guidance can be ex-panded, or even updated by using in-ternet. Download new feedback lines or sounds can refresh the whole game.

Now I described the game scenario, in the next chapters I will describe the hardware into detail.

7. Final design


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7.2 Design hardwareThe game ‘Alles maalt’ should be in-

structive and attractive, by the realisa-tion of two major aspects. The first is the adeptiveness (explained in chapter 7.3), and the second major aspect is the Tangible interaction.

By the tangible interaction the game is instructive, because it motivates the child, creates deeper understanding and gives direct feedback. It is motivating because children like to be active (build-ing and ordering objects), by this they have a sense of control.

The tangible objects create deeper understanding of multiplying. The child build examples of multiplication repre-sentations, those are meaningful con-structions. So it provides insights about what multiplication is and it stimulates the children to find strategies by them-selves. But it also helps the child with re-

membering their new insights, by stimu-lating multiple senses (seeing, hearing, touching and doing).

But the game will be instructive mostly because of its direct feedback. Not only feedback about the actions of the child are notices by TagTiles. But also feed-back on the constructed calculation, is the answer right? By knowing this immediatly, it prevents that the child stores the wrong answer as being prob-ably right.

The game ‘Alles maalt’ contains the fol-lowing hardware components; TagTiles, the foil, the input numbers, and multi-plication representation material. I will describe them in the following sections.

TagTilesTo realize this tangible instructive

game, the existing product, TagTiles is used (chapter 3.1). When looking at

the hardware, it is a platform (320x298 mm) with a play area (240x240 mm) [ap-pendix E]. The play area is the interac-tive field (the input), each tagged object placed on the play area will be recog-nized. The output is 144 LEDs of the play area (12 by 12) and sound (speakers or headset). How they will act is explained in chapter 7.3. But first I will describe the foil, the numbers and the tagged ob-jects used on TagTiles when playing the game.

FoilTo start the game, the child places the

foil (with one tag) of the game ‘Alles maalt’ on TagTiles. This foil is a visual printed on a transparant plastic (blocks or transfers the light of the play area). On the foil there are two areas: on top the field to lay down the multiplication representation material and at the bot-tom the field to lay down the numbers. On the edge the title is printed.


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When looking at the use of colour, it is important to make sure it does not look childlish. It should be cool and modern, so I choose refreshing and hard colours. The corresponding colours are figure 45); black, light and dark gray (metal-lic look), light and dark blue (colour of TagTiles). These colours are clear, and stands for alert, exact, progression, and intellectual [Kobayashi 1998].

I will add contrast by using the colours of the LEDS and the gold and bling mate-rial. By having a relative dark design the LEDs will be easier to see. I try to avoid the colour red, although it is a power-ful colour, the association with failure, wrong is too big. I will come back to the colours when describing the complete setup.

There are two options for the design. Just a plain design (no distraction, figure 45) or a design which support a story

7. Final design

figure 46: design of foil (laying on TagTiles) which support a story; inves-tigate the cave together with a spider (question mark) and explore snakes and gold to finally find the treasure.

figure 45: design of foil (laying on TagTiles) plain design, bottom: the cho-sen colours for the foil design.


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(extra motivation, figure 46). I am not sure which one is better, it would be nice to test both in the field. But unfor-tuneatly I do not have time over, so this should be researched later on.

The top area of the foil (for the rep-resentation material) is transparant, 90 LEDS (10 by 9) will be active in this field (200 x 180 mm) to support the construc-tion of the representation.

The bottom area is used to lay down the calculation. To minimize the costs and the space for storing the numbers I chose to use flat numbers. But to make them easier to read from the child’s per-spective, I use the foil to lay them in an angle [figure 47]. This also prevents an-other problem; when child is asked to clean the calculation it is stimulated to put the numbers back one by one, in-stead of sweeping them of TagTiles.

Two bars are attached to the foil to re-alize the angle of the numbers. By mak-ing those bars transparant (perspex) light, colours indicating the correctness of the numbers, will be easier to recog-nize.

figure 47: side view of the design of the foil. Two bars attached to the foil make sure the numbers which are put on TagTiles are easily to read and easy to grasp.


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Input numbersTo lay down the correct calculation on

the foil (on the board) tagged objects with numbers on it are needed. The yshould be easy to store (so be flat), easy to grasp (add grip), easy to place (on the bars) and easy to put back (in a box). This box makes it possible to find the numbers easier.

Eventually I created a flat design [fig-ure 48]. Also transparant (perspex, opal acrylic, cost per game ± four euro) so it is easy to tell if the number is correct or not. The sign (equal and multiplication) are the same, but a bit smaller to make sure they stay on their place (they do not need to be placed over and over, they can lay down during the whole game).

All the 44 numbers and the two signs are stored in a box. That box lays in front of TagTiles. I leave out the option of hav-ing tens and ones, but maybe in an ex-

7. Final design

figure 48: design of one number object (technical drawing, scale 1:1, unit mm)


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pansion version this could be realised. Because it has an added value (alot of those children still have trouble with the correct position of the numbers).

The 44 pieces of numbers need 44 tags. This could be an expensive joke. There is a cheap solution [figure 49]. It works, which means children can input the numbers they like. But the interaction is bad. When creating the right number it takes a lot of time and children of this age find it very confusing. Eventually the constructed calculation will look a bit odd. Not very attractive, but much cheaper. I will keep this solution in mind when the costs become too high.

figure 49: back up option for inserting the numbers much cheaper, but this interaction

is really bad.


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Representation materialBy now I have described the foil and

the numbers. Next I will discuss the hardware used on TagTiles as represen-tation material. As described in chapter 6.3 there will be three different materi-als; the snakes, the bags and the cubes.

SnakesTo represent the line- and surface-

model I use the snakes. The child can build a snake by connecting cubes with Velcro. There are one hundred cubes, each cube (17 x 15 x 20 mm) is made out of transparant perspex (per game ± sev-en euro). The cubes are sanded (get rid of the sharp corners), by this the snakes become the colour of the light under-neath them.

To cut the costs and to minimalize the constructing time, there will be cubes connected to each other [figure 50].

7. Final design

figure 50: top: drawings of the snakes from different views. Right: pictures of the snakes laying on TagTiles. Bottom: snakes in predefined sizes (five, two and three times one).


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Each bag and golden objects should be tagged. The golden pieces should be recognized by TagTiles. For that reason the pieces have to lay flat in the bag (not on top of each other). To stimulate this the pieces should have a shape like this [figure 52]. The pieces itself do not need much detail. The imaginition of a child will be enough to get the children excit-ed. The gold pieces (15x 15 mm) can be made out of wood and painted yellow.

BagsTo represent the box-model I use the

bags. One of the ten bags can be filled with golden pieces. The rest of the bags could be fake to save some time and costs. The bags (70 x 90 mm) shoud look like the left sketch in figure 51, but to minimize the costs, the right will do. The material could be off-white cotton (a bit transparant). By laying the bag on the play area, the LEDs make the contents visible. Make sure the golden pieces block the light. There should be ten golden pieces to realize all multipli-cation representations.

figure 51: inspiration how a bag should look like (source: creacarmen.webklik.nl), right: sketch of a simple model of a bag to realize the bags.

figure 52: the golden pieces which are used to fill the bags.


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CubesTo create a representation which is

more formal, but still a bit concrete, cubes can be used. Ten cubes will be needed for the basic version of ‘Alles maalt’. The cube can be very simple, it would be nice to make it also transpar-ant. But make sure there is a clear differ-ent between these cubes and the cubes from the snakes.

Each cube should be tagged and has a surface of 20 x 20 mm [figure 53]. The hight should be less then 20 mm, be-cause it should be clear what the top side is. When it is made of perspex 15 mm would be clever (standard size).

Now I described all representation material. But to make sure the materi-als are easy to access and to store, more hardware is needed. I will explain this when describing the final setup.

the question mark. When opening the box the numbers should be put in front of TagTiles [figure 54].

I chose for an interesting context, which fits with the game, a treasury. How this box is realized depends on a lot of fac-tors which I did not investigated yet. It would be nice to make it out of wood.

When the story is added to the sce-nario (foil in figure 45), the question mark will be replaced by a sweet spider, called: “Spinnie”. Spinnie and the child together will investigate a cave, find snakes, bags with gold and try to solve the whole treasure map (the second foil).

All hardware of the game ‘Alles maalt’ is explained. To get more information you can look at the technical drawings [appendix F]

Setup during playWhen playing the game all materials

should be easy to find. When storing the game, it should be as compact as possible. The solution is a box, contain-ing the numbers and signs, the snakes, the bags, all gold pieces, the cubes and

7. Final design

figure 53: the cubes, each cube repre-sention a certain amount.


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figure 54: get an imprssion how the setup during play and the box could look like. On top the scenario how the the numbers are installed. On the left the materials which are used to represent a multiplication on the TagTiles’ play area and on the right a sketch how the material will look next to TagTiles.


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7.3 Design softwareTo make everything work properly,

software is needed. Each object is tagged with a RFID tag, by using new lo-calization technologies, TagTiles is able to recognize the identity and location of each tag (object). This is the input of TagTiles. But to generate the correct output, sound and light, software is cre-ated for processing. This software is pro-grammed in the language ESPranto SDK, on a computer with linux and put on a SD-card. The SD-card is put in TagTiles and TagTiles use this software to act.

So the software contains the complete scenario, each detail of the scenario is programmed. The software for the game ‘Alles maalt’ should execute the scenar-io described in chapter 7.1. The software describe how the audio (voice instruc-tions and sounds) and light (144 LEDS) will act.

But the software is also the brain be-hind the program. It should reason which scenario to follow (influenced by the actions of the child). So an algorithm is needed, by this an adaptive system can be realized. This is very important, because adaptiveness is one of the two major aspects of the game ‘Alles maalt’. By making the game adaptive, it will be more instructive and attractive (prevent that the child gets bored).

Link input-outputBefore explaining the complex algo-

rithm, I will first describe how the out-put is realized.

At the beginning of a task, a voice gives an instruction to the child. Then TagTiles waits for the responds (lay an object on the play area) of the child. Depending on the responds (correct or incorrect) TagTiles gives different outputs.

For example, the child gets the instruc-tion to lay down two snakes of four blocks on the play area. After giving this instruction the child should build two snakes of four and lay them down on TagTiles. When doing so, TagTiles local-izes eight tags (with the identity snake) on the play area (positioned next to ea-chother, creating a rectangle from two by four). TagTiles compares these posi-tions and identities with the positions and identities of what is programmed. When they match TagTiles instruct the corresponding LEDs to become yellow. By this the child gets feedback, that the snakes are in the correct place.

But when the child does not lay down what should be layed down, the reaction of TagTiles should be different. The re-action depends on what is going wrong. When the child does not act at all, the instructions will be repeated, with the

7. Final design


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added instruction: “When you don’t un-derstand this instruction, please place the question mark on the play area”. When the child lays down the wrong objects, TagTiles says: “Those are no snakes, you have got the bags, please take them of me and get the snake cubes”. When the child is laying down the wrong amount, TagTiles will ask to recount one length of one snake. And so on and so forth.

Almost the same happends when TagTiles gives the instructions to lay down the calculation (and show blue flashing light on the location). When the correct object is placed on the correct location (TagTiles compares input with programmed rules), TagTiles instructs six LEDs (underneath the number) to be-come yellow. The child knows now (s)he placed the correct number on the cor-rect place.

When the wrong number is placed, the LEDs should not become yellow, but stays blue and quits flashing. TagTiles starts the sound sample: “Are you sure about this number?”. When the number is removed, the blue light starts flashing again.

Depending on the progress of the child (explained in the comming sections), TagTiles does not give immediatly feed-back on each number which is layed down (to prevent trail and error). When the child should understand the calcula-tion and the answer, TagTiles waits with giving feedback. When the child is sure about the complete calculation the child places an object on the play area. Then TagTiles shows the child if the calcula-tion is correct.

The question mark is also an input, TagTiles should act when this object is

placed on the play area. The reaction de-pends on the situation. When the ques-tion mark is placed after an instruction to lay down representation material, the instruction will be repeated and ex-plained into detailed. When the question mark is placed when the child should lay down a number TagTiles will give a hint. What kind of hint depends on the situa-tion, this is explained on page 98.

AlgorithmBut for the game ‘Alles maalt’ more

software should be designed, as men-tioned before; the algorithm. This al-gorithm makes sure TagTiles assesses the child during play, to realize an in-structive game. By assessing the child TagTiles makes sure the child is working on the right level (keep in the flow), and prevent the child from getting frustrated or bored.


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It is very imporant that those complex aspects are not visible for the child. The child should think it is playing a simple and clear game, which is coincidental in-structing the right level of calculation at the right moment. By this the child is not distracted by complex goals and rules.

But how to realize such an algorithm? To achieve this clear goals should be formulated. What kind of aspects influ-ence this algorithm. Then a structure should be created, showing all the as-pects and connections between those aspects. And eventually the rules should be formulated and translated into the ESPranto SDK language. Then programm the software (combine all rules into one file) and put it on a SD-card. Meanwhile test everything with a TagTiles, to make sure those parts are working. Finally the ‘Alles maalt’ game will be realized. But of course it is not realistic to build a work-ing prototype in the given time for this

project. For now I will explain the goals and how the structure of the algorithm will look like.

Algorithm goalsThe child’s multiplication skills need to

be assessed on two dimension: which calculation is solved right and on which level (concrete - formal) is this calcula-tion solved. This needs to be assessed because the order of multiplications matter. Before instructing a difficult cal-culation, an easy calculation should be solved first. And before solving a calcula-tion on the formal level, the calculation should be solved on the concrete level. This is to make sure the insights are there, the child understands the mean-ing of the calculation. Therefor the cor-rect calculation should be instructed on the right time.

A calculation is solved right, when the notation is correct and the answer is

correct. But when used too many hints the calculation will be repeated later on, on the same level. And when the child’s skills are more advanced, the correct no-tation will not be enough. The time re-quired to solve the calculation should be not more then a couple seconds (so the time will be measure to).

But there are more goals, not only the calculation should be traced and in-structed on the right time, but the feed-back (hints and responds on mistakes) is also linked with the progress of the child on the concrete - formal level.

Those goals should be realized by the use of the algorithm. To achieve a prac-tical and ordered algorithm a structure should be created.

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Algorithm structure calculationsFirst I will structure the two dimen-

sions (which calculation and which level) separately. When learning the multipli-cation table up to ten, you need to know eventually 121 calculations (that is in-cluding the table of 0). In chapter 2.4 I showed a visual [figure 6] which divided all the mutliplications into three differ-ent difficulty levels. 70% of those mul-tiplication are easy to learn, 20% is not easy and not hard and the last 10% is hard to learn.

This distinction will be used for the structure [figure 55]. Every multiplica-tion has changed into a code (35 is the code foe 3x5) and all the multiplication are ordered. This order is most likely the order how a child learns the multiplica-tion order. No child will learn it in this particular order (precisly), because each child is unique. But it gives a clue how a progress could look like.

figure 55: All the multiplications ordered. TagTiles use this structure to decide which calculation is next. This will happen in the following order:1. instruct green calculation random (from the top)2. instruct green calculation random (from the bottom)3. instruct orange calculation random (from the top) 4. instruct orange calculation random (from the bottom)5. instruct red calculation random (from the top)6. instruct red calculation random (from the bottom)


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Figure 55 describes a order, which is re-alized when the child answers them all right the first time. But when the child has trouble with a calculation, this order stops and the next calculation will be one step back [figure 56]. After the child had trouble with two calculations, the child will return to one. To make sure the child passess all the 121 calculations, the child returns to one, also when eight calulcation has been solved well in one sequence.

Which calculation is used from a sec-tion is choosed randomly. Calculations will not be repeated for a while when they are answered right. But when the child had problem with a certain calcu-lation (let’s say, 48), this calculation will be repeated after getting in the forth section for the second time (so at least three different calculations will be in be-tween).

The above described model makes sure the child gets a variation of calcu-lations, gets calculations which are not exrtemely difficult for them and repeat-ed the difficulty calculation after a while.

Algorithm structure levelsThere is also another dimension: each

calculation can be solved on different levels. Those levels are inspired on the iceberg from Frans Moerlands [figure 2]. The child should start with mathemati-cal world orientation, but this should be realized by looking around in their world, collecting examples of multiplica-tions. Realizing this by using TagTiles is possible (lay down pictures on TagTiles with tags), the game ‘Alles maalt’ starts with one level above: model material, all the way to the top: formal notation.

Each calculation should be solved at three levels: concrete model level, semi-concrete model level, formal level. For

each level different materials will be used. The snakes and bags are used at the concrete model level. The cubes are used at the semi-concrete level and throwing dices can be used on the for-mal level (but can also be done without).

When the child has reached the for-mal level it starts with automatizing the calculation (solve multiplication in 1o seconds). When this is achieved, there is an extra level to achieve: memorizing (knows answer immediately, described in chapter 2.4).

In order to achieve the memorizing level, it is very important to have a good foundation (iceberg). To realize this, the child should construct each multipli-cation on almost each level (concrete model, semi-concrete and memorize).

Those levels should be structured and linked to each other. To realize this each

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figure 56: rules that determines which order of all multiplications is used in the algo-rithm. Start at level one and eventually all the multiplication should pass by.


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level gets a character and rules. A = memorizing (correct < 5 sec.)B = automatizing (correct < 12 sec.)C = semi-concrete model (correct, use

cubes for representation)D = concrete model (correct, use snakes

or bags for representation)

The upgrading and downgrading be-tween those levels depends on the ac-tions of the child. Obviously the multipli-cation gets a level higher when the child did everything correct and will return to previous level when the child couldn’t find the right answer.

But it is much more complicated then that. Because the up- and downgrading is also influenced by other aspects. Like the amount of hints used, how well did it go last time, how quick is this multi-plication progressing and how long did it take to solve the multiplication. How

7. Final design

figure 57: structure for each mutliplica-tion, each multiplication starts at level D and eventually should achieve level A.


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they influence the progress is illustrated in figure 57.

As you can see, the child does not have to answer the multiplication four times, in order to reach level A for that multi-plication. When the child gives the cor-rect answer very quick in level C (within 12 seconds) the multiplication get a su-per upgrade, goes from C to A. By this the algorithm prevents that the child gets bored.

And I added an extra level below level D. This level is used when the child has a lot of trouble with solving this multi-plication in level D. In level E the mean-ing of multiplication is demonstrated (repeatedly add) by using concrete ma-terial. Very slowly the child is guided how to solve the multiplication (count together).

AlgorithmIn order to create a working algorithm,

the above explained structures should be combined. This is visualized in appen-dix G. It is important to control the over-all process, to make sure the child is not confused. One way of realizing this, is by making sure the child is not hopping be-tween different levels each time it starts a new multiplication. Because when the child needs to use for each time differ-ent materials, it becomes too complex. So the algorithm should try to work on the same level for a couple of multiplica-tions, before changing to the next level.

In conclusion the algorithm must en-sure that each multiplication has passed and that every multiplication goes from D to A. The process towards memoriz-ing all the multiplications, can be differ-ent for each child. Not only the speed, but also how they achieved their goal

can be different for each kid. As long as the end result stays the same, the game is succesful. The end result could be to memorize all the multiplications, but for some children it is enough to automatize them or only solved them with the help of concrete models. The most important goal is to let the child experience some successes in solving multiplications.


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7.4 ValidatingThe whole scenario and its details are

explained in the previous subchapters. This concept should be validated to find out if it works. To achieve this, a user-test should be realized. This is achieved by creating a full working prototype and let the children use it for a while. In or-der to realize scienitfic proof of concept, a longitudinal study is needed. Because learning the multiplication table is a long process (talking about a one or two years).

Three groups of children should be an-alyzed. The first group should learn the multiplication table how it is teached at the old fashion schools (use of books and non technical tangible tools). The second group of children should learn the multiplication table on a more mod-ern school (that uses also the books and tangible tools, but also the new tech-

nologies such as computers and digi-boards). And the last group schould be children who learn the multiplication table the same way, but with the ‘Alles maalt’ games as an extra tool.

After a while, data should be collected. Not only about how many multiplica-tions are known by the child, but also the attitude towards learning the mul-tiplication table. The children will be asked if they like to learn the multiplica-tion table and also their opinion about their own multiplication skills. Do they think they are bad in multiplications, or do they think they are making a lot of progress?

It would be nice to realize such a user-test in the project, but due to time is-sues, this is not realistic. Especially be-cause a longitudinal study is necessary.

Another way to validate the design is by asking feedback from experts. Their experiences from the field would be usefull to find out if it would work in practice. Experts in combination with a small user-test with just a few children could give an idea if the game could re-ally work.

But my priorities for my graduation were the report and presentation, due to illness there was no time left to test the final design in the field. Therefore I can validate the final design only by re-flecting on the design with the use of previous tests.

Why would this game be instructive? First of all by having an adaptive system.The child gets the appropriate multipli-cations to ensure the child becomes not bored or frustrated and to make sure the crucial foundation is present.

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The second major aspect is the tangi-ble interaction. By manipulating physical objects, multiple senses are stimulated and the child gets a deeper understand-ing of what a multiplication means. The tangible interaction also gives direct feedback, this is very important to pre-vent learning the wrong facts.

Both mentioned aspects make sure that the game is instructive, but also makes sure the child keeps motivated.

The following questions need to be an-swered. Why would this game be a suc-cess? What is the added value in com-paring to other products on the market? What would be the selling features? First of all it is design-driven innovation, untill now there is no such product on the market. The product is for a new market, a niche market. Mostly because a lot of companies are incompetent to

realize such a product (do not have the didactic and the technology knowledge).

Experts indicated that there is a niche market for products with the following features: an adaptive instructive tool by using tangible interaction with direct feedback. There are instructive tools with direct feedback, but those comput-er programs miss the advantages of tan-gible objects. There are instructive tools with tangible objects, such as wooden puzzles, but they often lack in giving di-rect feedback. And recently companies are developing adaptive tools with di-rect feedback, but those programs are realized on the computer, so they miss the advantages of tangible objects. So this new gamecombines all the good as-pects from old materials and new com-puter programs.


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8. Evaluation

8.1 Reflect on resultsAt the end of chapter three, seven de-

sign guidelines were formulated. Those guidelines were inspired on my theor-itical framework and my project inten-sions. I compare these guidelines with the end results, did I achieve them?

In the red boxes on the right you can read why each design guideline is achieved. But does this mean that the ‘Alles maalt’ game is perfect? Not com-pletely (as every design is), while design-ing I had to make choices which made the game less instructive then hoped for. The most important point of improve-ment whould be to add the bottom layer of Frans Moerlands Iceberg into the de-sign (chapter 2.4, figure 2). I could not achieve this, because it would make the game too big, and too complex.

Another point of improvement would be the possibility to put material upon

Eventually I reflect on the complete project, not only the results and proces, but also reflect on the influences it has on me as a designer.

1. Design a tool (physical aid device) to help children (aged eight to nine) with their multiplication (until table of 10) problems (unable to autom-atize the multiplications after reasonable amount of instructions and practice). As far as I have tested, children (aged eight to nine) are helped with learining the multiplication table when playing the game ‘Alles maalt’ (an physical aid device). Because it is used as an extra tool in the classroom, it is possible that only children with multiplcation problems play the game.

2. The tool should be an application for TagTiles from Serious Toys (client). The ‘Alles maalt’ game is designed to be played on TagTiles, by this the game ‘Alles maalt’ will be less expensive, becauset it uses existing tech-nology.

3. Design a system that adapts on the child’s level of multiplication skills. Let them experience successes, so they become more confident about themselves. By using the algorithm the game ‘Alles maalt’ is adaptive. Therefore children experieces successes. By reflecting on the child’s pro-gress (with second foil) the child gets an overview of their progress. If all goes well, the child will become more confident about itselve.

4. Design a system that adapts on the child’s level of formulation. Make sure the child creates a strong foundation of multiplication insights. By starting each multiplication on a concrete model level, the child gets more insights about the multiplication foundations. By taking little steps forward (only when the multiplication was right) the game makes sure that the foundation is present, before going to the next level.


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eachother. But because of the limita-tions from TagTiles, it was not possible to realize the recognition of the materi-als.

One last point of improvement would be to simplify the algorithm. Right now the algorithm is quite complex, when

writing the software this could results into a lot of bugs (errors). This will cost a lot of time. It would be wise to start with a simple algorithm which later on could be expanded to make ‘Alles maalt’ more advanced. I’m sure that during fu-ture testing, a lot of improvements can be made.

5. Make a tool which is instructive, by motivating the child (make it fun) and give direct feedback. ‘Alles maalt’ is instructive because it is adap-tive and has tangible interaction with direct feedback. The child will be intrinsicly motivated by letting the child control, discover, feel accomplis-ment and have a good balance between challenge and skills (by making it adaptive). But also making it attractive because it is tangible.

6. Focus on individual use only (easier to design for and able to keep track on one child’s progress). The game ‘Alles maalt’ is designed for single use only, in the beginning the child logs in, by this TagTiles knows who is play-ing and can record all her/his actions.

7. Create a tool which helps the teacher to observe the children’s progress and which doesn’t cost extra time and effort. By connecting TagTiles with the computer the teacher can read out the statistics of each child. This should be done without any effort. When the child is playing the game ‘Alles maalt’ teachers intervention is not needed.

When looking at the results more gen-eral I could say that this project is quite successful. The final design has a clear added value in comparing with existing products on the market. During the 25 user interventions it became clear that the children were very enthousiastic about my ideas. Experts from the field always responded very positive on my concept. Teachers agreed with my con-clusions and like my concept solutions.

My project results such as this report and prototype are of lower quality then I was hopling for. But due to my illness I should be happy with this result.


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8.2 DiscussionThe question now is: what’s next? As

mentioned before there is a clear mar-ket for this concept, experts indicate that something like this is really needed in the classroom. So it would be regret-table to finish project and put it away.

It would be nice to continue this pro-ject, to make it ready for the market. To realize this a couple of things need to be done.

First of all, the materials used on TagTiles should be optimalized. The

design of the materials should be opti-mised, to make sure that TagTiles is reck-onizing everything.

As mentioned before a longitudinal study should be realized. This is needed to test how the game ‘Alles maalt’ will

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be used by children. Therefore many questions can be answered: Is this tool more instructive in comparing with other products? How can the design be improved? How can the interaction be optimized? How can the algorithm be realized? Is a story relevant or not? The user group should be of sufficient size, because each child is unique. It is not realistic to expect that the game ‘Alles maalt’ will be the best tool for every child with multiplication problems. But it would be nice realise a tool which will help as many children as possible.

The game ‘Alles maalt’ could also be an inspiration concept, which makes designers of didactic materials aware of this market. Aware of the possibilities of the new technologies (tangible interac-tion) and aware of the importance of an adaptive system. The game can also be an inspiration to create similar games,

but then with different goals. Such as learning division sums, learning percent-ages or for younger children learning other basic math aspects.

Designing a game for division sums or multipling has a lot of simularities. It is easy to change the game ‘Alles maalt’ into ga game for learning division sums. The same material could be used, but the question will be asked in the opposit direction: you have 5 bags, with a total amount of 45 pieces gold, those pieces are equally divided, how many pieces are in each bag?

In conclusion I could say that this pro-ject is a big inspiration for the field and has great potential when developed fur-ther. There is a clear market for this con-cept, but that does not mean it will be easy to have success on this market. A well thought out marketing plan is need-

ed. During this project, the business as-pect was outside the scope. I mainly fo-cussed on the users and the interaction.

So hopefully this concept will be con-tinued, and it will help a lot of children who are in need of such a tool. Because I noticed how important this game can be for the development of a child.


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8.3 Reflect on process When looking back at the process of

this project, you can see how I have changed over time. In total I have worked on this project for two years; a half year of preparation, eventually just six months of hard work and one year delay (because of CANS). When I started the project I was very enthusiastic. May-be too enthusiastic; I worked very hard, wanted to explore every aspect into de-tail and was only satisfied with perfec-tion. This resulted in a strong foundation of my project (a lot of literature, many users involved and experts contacted). Choices were only made when I was sure about the answer, and preferable validated by two other sources.

A positive aspect of this project was that I was having fun during the whole project. The subject was very interesting and I was inspired to work on the pro-

ject the entire time. I was never stuck, I always knew what to do next and even after two years of multiplications, I still love them. Therefor I could say that the subject I choose two years ago was well chosen and that this is very important.

I loved the challenge to work with the children, this age group was new for me. While creating empathy I was inspired to help them with their ‘development’. It was a challenge to get honest feedback on my ideas. Because when a child is younger they do not feel they need to be nice to the person who designed it, they are completely honest. At the age eight to nine they start to think about what people want to hear, they think they are being polite when they say something that a person would like to hear, instead of telling the truth. Therefor I needed to look at non-verbal signs of the children; are they easily distracted, are they excit-

ed, would they like to play it again next time? Concluded, I could say that I like to work with them, creating empathy was not very hard, I started to think as a child very quick.

When looking at the reason of my CANS, it was clear that i have spended to many hours behind my computer. At that moment I thought I did not have a choice, to achieve as much as possible in the given time I spend every free minute behind my computer. Weekends and long days were filled with project activi-ties, to prevent pressure on the end of my project. I sticked to a good planning, but when the report deadline suddenly shifted to two months earlier, I thought the only solution would be to start typ-ing the report all day long. Together with my perfectionism and the time pressure, this resulted in the ideal situation to get CANS.

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just one month was not enough. It took me a year of exercises, reflection and resting to understand how to deal with it and to know what would be the best way to finish my project. A lot of people supported me, and together we agreed that finishing my project by reporting and presenting what I did so far was the best thing to do.

By slowly ending this project (working on my computer each day just for two hours) I realized how hard it is to let my old habit go. I know I need to change my attitude towards perfection, but to achieve that in reality is much harder. I was used to achieve everything what I wanted, and now I have to be satisfied with less. This obviously feels less sat-isfied, but I know it is the best way to eventually get the most out of it.

By taking a break, I took a step back, I became aware of the disadvantage of my approach. I was expecting too much from myself and this resulted into a lot of (non-relevant) work and too much information (which makes decision mak-ing sometimes harder). I realized that I do not have to be one hundred percent sure about every design decision. Of course it is important to make the right decisions, to prevent bigger issues later on. But making wrong decisions and ad-mit them later, is not a waste of time. Every experience is a learning moment. And eventually it will save time by mak-ing decisions quicker.

It also made me realize that involving four users each week from the begin-ning of the project was a good start, but also very tiresome (I recorded more than one hundred hours of video). I should be more effective when involving

8. Evaluation

My body warned me that I had gone too far. It was time to stand still and reflect on my actions. So I took a step back, evaluated the situation and con-cluded that I had a choice, and that I made the wrong choice. I am just a hu-man, with limitations. I realized that per-fection does not exist, or everything is already perfect. Because when you want to achieve something to be perfect, you will never be finished. You will never be satisfied with the result, because it can always be done better somehow.

I realized that my attitude towards work needs to be changed and learn how to relax my body. I contacted experts and they helped me realize that even when I think I am relaxed, my whole body is still very tense. My muscles had been over used for a long period of time, which results in muscles who are shorter. To lenghten my muscles again, resting for


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When looking at the iterations they were a good foundation for the final design. But I miss some exploration of more extreme ideas, the ideas which I used were not extremely out of the box. This was not realized during this pro-ject, because after my break I had just one priority: finish my master. By this I only focussed on reporting and present-ing. I chose to work out the most obvi-ous ideas, to make sure I had an idea to present. When typing the report I devel-oped the concept further, so that is why it looks like I reported a well thought fi-nal design. But personally I miss a broad exploration of innovative solutions. I do not say this project has failed, but my personal goals are not completely achieved, which is caused by my high ex-pectations of myself.

I only missed one thing in this project; investigate the actual interaction. I like to optimize the interaction by letting the user experience the interaction for a couple of times. But due to my CANS there was no time left to investigate this further. The interaction which I designed in this project is not put to the test and I expect that it can be improved a lot.

In general, I conclude that my design process was a big learning moment. It started how I was used to design and ended completely different then I was used to design. But still it is a good pro-ject with all the necessary aspects (user, technology, design and a bit of business), but some aspects were carried out into detail and others were less elaborated. Even though I still feel pain in my body, I think I improved myself.

the users. Only involve the users when empathy is needed (after two weeks I already achieved that) or when I have a clear goal for the involvement (such as testing a theory, an idea, or asking feed-back). User involvement in the begin-ning of a project is still very important, but try to prevent user-tests which are not relevant, but still time and energy consuming.

During my project I was very organized, after each activity ((such as meetings, reading books, teaching children, and after analysing products) I wrote down a summary. This is a good habit, but I should keep an eye on how detailed this is, because again I was too much of a perfectionist. After starting such a summary I could not resist to make sure nothing was missing. I should continue making those summaries, but make sure it becomes a useful summary (therefor: do not make it too long).


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vated student, I like what I am doing and I do everything very thorough (per-fectionism). My strong points are: work closely with the users, create empathy, be enthusiastic (have intrinsic motiva-tion), quickly create prototypes, use visualization skills, use experts, relies strongly on intuition, envisage where to go, see various connections and able to establish priorities and approach. Some of those qualities create my pitfall, working too hard and focus too much on each detail. The challenge for this pro-ject was to find out how many research is relevant, execute the activities in less details. My corresponding allergy would be that I would make choices without a good validation.

Due to my CANS experience I reflected more on my attitude during this project in comparing with previous projects. Being very thorough in everything I did

took its toll, and I was forced to be less precise and to take a step back. It is very hard to be satisfied with less, but by un-derstanding that less is also enough to reach the same, it became (after a while) easier to let the perfectionism go. I do not worry about each detail anymore, and when I notice I do, I tell myself to quiet worrying and drop it.

But my identity is more than just my attitude, it is also how I do things and how I achieve things. I spread my wings and went into the field, came out of my comfort zone to see and feel the state of art. I do not only think about the most obvious places, but also try to look to the reality from different perspectives. For example in this project I did not only contacted schools and teachers, but also other stakeholders (researchers (with different expertise), special educa-tion schools, companies who develop

8. Evaluation

8.4 My identityIn the preface I explained who I was as

a designer at the beginning of my pro-ject. During this project a lot happened, I got more experience with designing, but also learned more about who I am and who I want to be. My vision on de-signing decided my approach for this project, I focussed a lot on the user: ob-served and involved them and let them experience my concepts by quickly build prototypes. I made sure every choice was validated by involving experts, lit-erature and by doing user-tests.

But how did this project change my identity? To answer this question I will first demonstrate how other people de-scribe me when giving feedback to me. They see me as a professional (espe-cially in organizing and planning), hard working, and creative student with quite a passion for design. I am a very moti-


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8. Evaluation

In order to communicate what I want by using drawings and prototypes, I de-veloped knowledge about how people experience different designs. I devel-oped my design skills to know how to create certain designs for different pur-poses. Not only to make it attractive, but also to make it clear, keep it simple and still interesting. Design the correct inter-face, to create the interaction which is needed to achieve a certain goal. How this is experienced should be tested with different people, because they are experts of their own experiences, values and wishes. Testing a designed interac-tion is another design challenge, I want to help the users with giving feedback on what to experience. I have executed different ways to achieve this, co-de-signing, cultural probes and acting out a scenario. During my final master project I tried something new to achieve this; involve the children each week. This was

very tiresome, but this gave me the op-portunity to validate little concepts and a couple of theories. Next time I would use the user involvement less frequent and more effective.

Now I discussed my user, technology and design skills, but during this project I also involved business aspects. By in-volving the client I learned a lot about the company itself and how to look at the market of didactic materials. Sev-eral experts explained their view on this market, this helped me to realize the influence of the business aspects on my design. Eventually I chose to take those business aspects into account while de-signing. But I did not investigate them further, because I chose to focus more on the user. Personally i took those busi-ness aspect more serious than before, next time I will collect the business as-pects earlier in the design process (not

didactic materials, organisations which advice schools and even mothers who have children with math issues). I do not only observe the field, but also use their expertise to get feedback on my design decisions.

In order to use my experts as efficient as possible, I use my design skills for op-timal communication. Make drawings, prototypes or even let them experience my concept (this stage is not achieved in this project for experts others then the children). To (quickly) make prototypes, knowledge about the state of the art of technology is necessary. Over the years I learned to use different technologies (from basic electronics, to program-ming, to wireless communication with XBees), which helps me to have an over-view which technology is appropriate for which situation.

ConclusionsMy identity is to design together

with the users (by using my tech-nological and design skills), but I changed my vision on how to put this into practice. More does not mean better, sometimes less is more. My work could be still of very good quality, even though I do not try to achieve a perfect de-sign. I should not involve the user too often and i should not focus too much on the small details. Fur-thermore, i should make decisions earlier, even though a decision is not validated a couple of times and i should trust more on my instincts.

too early, because this can influence my creativity).

My ambition is to help children with their development, I like to work with them and help them with communicat-ing what they experience. I like to try out different interaction methodes and look at the reactions of the children. I feel happy when I help people, and even more happy when I design for children. They are more pure, are not damaged by the society yet; they still use their im-agination, are more creative and just do what they feel like doing.

In the last two years a lot of people helped me with realizing this project, namely the children I involved, several experts, my coaches, but also family and friends who helped me out. Many thanks to the following people:

Willem Fontijn for his time and sup-portive coaching and for giving me the opportunity to work at his company Se-rious Toys.

Frans Moerlands and Dirk van der Straaten for their time and for sharing their (innovative) expertise with me. They gave me useful and critical feed-back on my concepts.

My coaches Marco Rozendaal, Tilde Bekker and Oscar Tomico Plasencia for their support and guidance during my project. They advised me and made sure that I was reckoning with all the impor-tant aspects of designing.

Acknowledgement

Jan Rouvroye for his feedback on my report and advice how to finish my pro-ject. And other experts from the TU/e for their help and sharing their time and expertise: Rene Ahn, Saskia Bakker, Chet Bangaru, Harm van Essen, Jelle van Dijk, Esther Gielen, Bart Hengeveld, René de Torbal and Diana Vinke.

All the experts and researchers of the field of didactics who responded to my mail and shared their experiences and opinion with me; Marije Bakker (CPS), Marjoke Bakker (PhD Freudental In-stituut), Ria Brandt (CPS), Joop Daemen (teacher Fontys Tilburg), Anne Mieke Dekkers (Balans zuid-oost Brabant), Han-neke Graaf (remedial teacher at Joost Meulers Talent ontwikkeling BV), Wim Joosten (Stempelfabriek & Jegro), Hans van Luit (Professor dyscalculia, Utrecht university), Janneke Romeijnders (teach-er PABO Fontys Eindhoven), Raymond de Ruijter (Jumbo), Ber Suilen (Rolec),

Belinda Terlouw (Freudenthal Instituut), Janneke Verhaegh (Philips research) and Jeroen de Weerd (Biggle Toys BV).

The schools and teachers for their time: JenaPlan Basisschool De Bijenkorf (director: Lenny Voets and the teachers: Annelies, Daisy and Trees), basisschool Tweelingen (director: Rian Vums), Bep-pino Sarto school and SBO de Petra-school (director Kim de Vos).

The four children from the Bijenkorf who I teached for a couple of months and their parents for giving permission to record all my lessons.

The students from the PABO, Fontys Eindhoven: José Van Bergenhenegou-wen and Ester Lathouwers. It was nice to work together and to help each other with our graduation projects. I want to thank Ester also for arranging the focus group at her school and the presenta-

tion at the Fontys.My colleagues at Serious Toys in den

Bosch for having fun, feeling welcome and their helping hand: Bert Bogaerts, Frank van Gils, Tjeerd IJtsma, Joost Meijles, Patrick Schevers, Sander Smit, Wijnand van Tol and Wies van Wierin-gen and.

My family and friends for supporting me, giving me feedback on my report and helping with building my proto-type: Bart Brink, Michiel Brink, Monique Brink, Dirk Gooren, Zanne de Visser and Thomas de Wolf. Especially I want to thank my partner Dirk van Ginneke for his time and help throughout the whole project and of course my parents for their support.

Finally I want to thank you (the read-er) for your patience while reading my report, because I know that my writing skills are not one of my stronger points.

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Steeg, van der, M., Vermeer, N. and Lanser, D. (2011). Niveauonderwijs daalt, Vooral beste leerlingen blijven achter. Centraal Planbureau, Den Haag, NL.

Thalheimer, W. (2006). People remember 10%, 20%...Oh Really? 01-05-2006 http://www.willatworklearning.com/2006/05/people_remember.html, retrieved July 2011.

Treichler, D. G. (1967). Are you missing the boat in training aids? Film and Audio-Visual Communication.

References

Van Luit, J.E.H., Nelissen, J.M.C. and Peltenburg, M.C. (2009). Learning Mathematics by interaction in young students with spe-cial educational needs. Chapter 9 in Early education, Mottely, J.B. and Randall, A.R. Nova Science Publishers. Inc.

Verganti, R. (2009). Design Driven Innovation: Changing the Rules of Competition by Radically Innovating What Things Mean. Harvard Business School Publishing Corporation, Cambridge, USA.

Vygotski, L. S. (1967). Play and its role in the Mental development of the Child. Volume 5, Number 3, Journal of Russian and East European Psychology, New York, USA.

Vygotsky, L. (1933). Play and its role in the Mental Development of the Child. Translated by Catherine Mulholland in Voprosy psikhologii, 1966, No. 6; Online Version: Psychology and Marxism Internet Archive (marxists.org) 2002, Moscow, Russia.

Vygotsky, L.S. , Cole, M., John-Steiner, V., Scribner, S. and Souberman, E. (1978). Mind in Society, the development of higher psychological processes. Harvard University Press, Cambridge, Massachusetts, London, UK.

Vygotsky, L.S. , Cole, M., John-Steiner, V., Scribner, S. And Souberman, E.(1978). Mind in Society, the developmentof higer psy-chological processes. Harvard University Press, Cambridge, Massachusetts, London, UK.

Watterson, B. (1987). Calvin and Hobbes. Andrews McMeel Publishing, Kansas City, Missouri, USA.

White, R.W. (1959). Motivation reconsidered: The concept of competence. Psychological Review, Vol 66(5), Sep 1959, 297-333, USA.

appendices

A media math NLB list of expertsC FMP proposalD games madeE technical drawing TagTilesF technical drawing materialsG algorithm

appendix A: public debate in the media about quality of math (NL)

appendix B: list of experts used for this project

Directors from the following schools:- Jenaplan Basischool de Bijenkorf (Lenny Voets)- Basischool Tweelingen (director: Rian Vums)- SBO de Petraschool (director Kim de Vos)

And the teachers from the JenaplanBasischool de Bijenkorf:Annalies, Daisy and Trees.

Appendix B: Experts

Name

Function Company Relevant expertise Meeting

Rene Ahn dr. Ir. Universitair Docent

TU/e, DI Design and Architecure of Intelligent Systems

08‐04‐2011

Marjoke Bakker Ph. D. student Freudental Instituut effects of mathematics computer game

03‐11‐2009

José Van Bergenhenegouwen

student PABO fontys Eindhoven Automatize multiplications 13‐01‐2010

Joop Deamen Teacher trainer (physics and mathematics)

Fontys Lerarenopleiding Tilburg

Teaching mathematics 12‐11‐2009

Willem Fontijn Founder and Managing Director

Serious Toys BV Motivation and the TagTiles Weekly meetings

Hanneke Graaf remedial teacher Joost Meulers Talent ontwikkeling BV

Teaching children with math problems

04‐01‐2010

Bart Hengeveld Ph.D. student (then) TU/e, DQI (then) Interactive toys and playful learning

12‐11‐2009

Frans Moerlands Leading member Edumat (PARWO project) developing innovative math education for primary schools

Several meetings

Wim Joosten Managing director Jegro B.V. (then) Educational materials and serious games

Several (unofficial)

Ester Lathouwers student PABO fontys Eindhoven Game interventions during math lessons

Several meetings

Hans van Luit Professor dyscalculia Utrecht University Dyscalculia and math difficulties 03‐11‐2009Janneke Romeijnders

Teacher trainer PABO Fontys Eindhoven teaching 13‐01‐2010

Marco Rozendaal Dr. ing. TU/e, DQI (then) Engagement Several meetings

Dirk van der Straaten

MSc. SSOT (PARWO project) Teaching and innovative math theories

Several meetings

Belinda Terlouw Teacher trainer Freudenthal Instituut teaching 03‐11‐2009Janneke Verhaegh Ph. D. student Philips Research, Connected

Consumer Solutions doing research with the TagTiles January

2010

appendix C: project proposal

FMP proposal “Alles maalt”Eveline Brink (s041262)Oscar Tomico PlasenciaDiscovery and LearningDecember the 17th 2009

2

FMP proposal “Alles maalt”Eveline Brink (s041262)Oscar Tomico PlasenciaDiscovery and Learning

December the 17th 20093


Vision

I am a user-centred designer; to create successful prod-ucts I do not only work for but also with the user. My slogan is: “design is creating new experiences”. I want to give a product more value through rich (tangible) in-teractions, fit it to the user and the context and make it meaningful to the user. To achieve this I involve the user many times and make sure the design is a balance between function, form and interaction.

To achieve a well balanced design I have a hands-on approach:- quickly create working prototypes (and test them)- explore and experiment (myself and (with) the users)- keep reflecting on decisions (involve extern experts)

I am visually oriented; I prefer to communicate by visu-als instead of words. For me an experience is highly influenced by vision. In my design I focus a lot on the visual appearances, make sure they feel ‘right’ and make sure it is clear, focussed, pleasant and functional. To achieve this experimenting and feedback are very important, but also understanding people’s perception and know the ‘rules’.

I am interested in working with young users. It is a true challenge to get useful feedback from them, under-stand their perception of the environment and com-municate on the same level with them (I previously researched longitudinal use of an open-ended game MoZo (picture 1). I like to design for them, help them with their development in a playful way (prevent prob-lems in their future) and I like their ‘world’ (I have no problem to enter their world). To communicate with them it is useful to use visuals.

Picture 1: longitudinal test of the open-ended game: MoZo, object which make sound when they move.


4

Design opportunity

I also like math, work with numbers, structure things, solve problems and also help others understand math and physics. During teaching I always used the theory active learning. I experienced the efficiency of this the-ory by myself during my language problems because of my Dyslectic.

Active learning means for me that you learn faster when you have a more rich experience, the related ex-perience stimulates multiple senses actively and has a high impact on you. People learn by making mistakes (learn how not to do it) and by having positive experi-ences (learn one way of doing it right). Besides under-standing the experience, it is relevant to remember the previous experience (learning moment), and by making this experience more rich it is easier to remember.

In the Netherlands there is a growing concern and a public debate [Volkskrant 2009] about the quality of Math of the primary education. The KNAW researched [KNAW 2009] the conditions and concluded that the children’s mathematical proficiency needs improve-ment.

In the coming semester I will start my Final Master Project (FMP) with the goal (figure 1) to help children with their math problems through active learning. This is also inspired by my own experiences when I was a child (remedial teaching for languages was a night-mare).

Help with automatizing multiplication table at school (age of 8-9 years).Help the child with developing, by realizing visually interactive productsthrough close user-involvements. Help learning by ‘active learning’and make sure the child goes from circle of failure to circle of success.

Figure 1: visual where myproject is located

myproject




Project

I propose to design a product that helps children with automatizing the multiplication table. Automatization means that children understand a multiplication sum and know how to solve the sum correctly, but don’t know the answer directly (that could be the next lev-el called memorization) [Van Luit]. Automatizing is a problem in the Dutch education and the reason why children don’t keep up. Most teachers underestimate the importance of automatizing and the math methods mention the importance but don’t provide the time and material for it [Deamen].

I chose a clear defined context on purpose: automatiz-ing of the multiplication table. The multiplication is the foundation to understand and solve the math which follows [Deamen]. I will not create a new method, but my tool should be used as something extra next to the used method, so it should be method independent [Van Luit].

The design will be a tool that support the child like a scaffold, which will enhance the calculation powers. This results in giving the child prolonged experience of ‘success’ and become more confident [Van Dijk].

In short the tool should be:- Instructive (active learning, measure progress)- Physical (tangible, visual and provide structure)- Interactive (direct feedback, embodied and fun)- Motivate (playful, interactive, diverse activities)- Independent (no intervention of teacher needed)My design challenge is to motivate the child and make it instructive. I want to make use of their will to explore and their curiosity.

The tool should help the child from going out of the circle of failure into the circle of success and eventually become quicker, makes fewer mistakes and eventually be able to calculate all by him-/herself. The tool should know the level and reasoning of the child, by making the tinkering process visible/tangible, and use this to steer the child, provide the right level (of abstractness and difficulty sum) and give feedback.

For now I choose the school context, it should be clear for the child that he/she is learning multiplication ta-bles at that moment. My goal is to create a new way of playful learning which may be used in other education areas or will be used as inspiration to create more in-teractive learning devices.


6

Current maths tools are physical or computer pro-grammes. The physical tools, like robes, cards, dices etc., are successful because the child has an overview, can create structures and is stimulated to be active. The disadvantages are that the child misses guidance (teacher is needed) and feedback about the correct-ness of his/her actions.

On the other hand they use computer programmes, like little internet games [rekenweb.nl]. The computer is a motivator, gives direct feedback and one compu-ter offers a lot of different tools. The disadvantages are that the child misses the overview (positioning) and the interaction is nothing more than clicking or typing.

My conclusion is that my tool should be physical, but also interactive (this is linked with active learning). Re-lated projects are the Tagtiles (picture 2), Max (picture 3) and i-Blocks (picture 4).

Picture 2: Tagtiles, a tangible electronic board game for educational purposes from Royal Philips Electronics.

Picture 3: Max, learncards with self-control

Picture 4: i-Blocks, innovative educational tool which makes language tangible and practice fun.




Key aspects to consider

Learning:Acting is important for learning: “Learning and acting are interestingly indistinct, learning being a continuous, life-long process resulting from acting in situations.” [Brown 1989]. Explorations (making mistakes) are a must; discovery by yourself is the best way to learn [Terlauw, Deamen and Van Luit 1999]. The problem is that education says: “mistakes are the worst thing you can ever make” [Robinson 2006].

Learning is context dependent [Brown 1989, Van Luit 1999] and supported by mental images [..]. So it should be instructive to let the child act in the right context and help to use mental images to recollect the knowl-edge.

You can give structured instructions (explain how to solve tasks and let them practice) or guided instruc-tions (work together, children demonstrate and there are a lot of discussions) [Kroesbergen 2002]. To let the child discover it by himself/herself guided instructions are preferred, “you should not provide solutions but lead the discussion about suggested strategies.”[Van Luit 1999]

“We didn’t learn to talk and walk, not by being taught how to talk, or taught how to walk, but by interaction with the world... whereas at about the age of six, we were told to stop learning that way and that all learn-ing from then on would happen through teaching.” [Negroponte 2007]


8

Teaching mathsWhen teaching maths you start simple and slow (con-crete) and step-by-step introduce strategies, start au-tomizing (practice) and become quick (abstract), illus-trated in figure 2. To walk through this process you use little iterations interaction, construction and reflection [Van Luit 2009].

To automatize successfully you should practice and re-peat maths (on the right level) each day for 5/10 min-utes [Deamen and Van Luit]. This means that the tool should be flexible, have space to experiment (try and check procedures) and give insights (aha-erlebnissen) [Moerlands 1994].

Direct feedback is very important [Deamen], when the answer is correct: compliment the child, but when the child is wrong: let the child know the sum was too dif-ficult, so let the child feel it is not his/her fault. In case the sum is wrong, make sure the child notices this visu-

Figure 2: when learning maths you start easy and concreteand through iterations go to difficult and absract

learning traject for multiplication table




ally. Go back to concrete material to let the child do it right and eventually go back to the abstract level. When possible administrate and analyze the mistakes and progress, this is also useful for the teacher [Dea-men].

Most important are the emotions of the child, the child should be motivated and get more confidence [Dea-men]. For children with low achieved maths skills this would be the first problem to encounter. At the mo-ment the child has trouble with maths the child experi-ence a circle of failure (figure 3). By having no success, the child get less motivated to work with maths and get more behind, which cause more bad performances.

Important is to stop the circle of failure and change it in a circle of success (figure 3) [Desoete 2008]. Very im-portant is to have patience, build certainties and have time to careful get more self-confidence [Moerlands 1994].

circle of succes

more self-convidencemore pleasure in doing

betterperformance

more practice, concentratemore on the subject matter

positive expectationsbefief in own capacity

circle of failure

negative expectationsabout future performance

fear of failure,avoid subject

less practice, less focuson the subject matter

badperformance

goal

Figure 3: circle of failure

and circle of succes


10

Motivate childTo motivate the children I could think about the cat-egories from Malone [1987] which are: challenge, cu-riosity, control, fantasy, cooperation, competition and recognition. I could focus on one or more of them to get and keep the child’s attention. Important is to offer challenge and give feeling of control [Hengeveld] and keep them balanced [Verhaegh 2007].

An important motivator would be the interaction, like Verhaegh [2007] mentioned after evaluating the Tagtiles (picture 2, page 6): “they [children] liked the game because it is different from the ones that they are familiar with, as it differs from screen based computer games and it is more interactive than traditional board games.”

To motivate the child it is very important that the child itself becomes a central part of the activity, “rather

than just watching something evolve like in computer games.” [Price 2003]. The tool should be driven by the learner [Negroponte 2007]. It helps when physical ar-tefacts and physical actions (natural and intuitive [Mar-shall 2007]) are combined. To achieve these physical actions embodiment is also interesting to consider.

Another motivator would be playful learning, make it fun to use. According to Price [2003]: “playful learning should entail, is one where interaction with informa-tional artefacts involves fun and where the boundaries between play and learning are blurred.” Fun is impor-tant in learning: “Fun and enjoyment are well known to be effective in children’s development [Clements, 1995], both supporting and deepening learning [Res-nick, 1999] as well as facilitating engagement and mo-tivation.” [Price 2003].

Children will be more empowered through play. Play helps the brain to develop the contextual memory [Brown 2008] which is important for my context.

When developing a ‘playful learning’ device, I should encompass [Price 2003]: (i) fun, (ii) exploration through interaction (discovery), (iii) engagement (increasing at-tention to the activity, concentration and promotes ‘useful’ learning [Stoney 1999]), (iv) reflection, (v) im-agination, creativity and thinking (different levels of ab-straction) and collaboration.

“Learning maths is a matter of doing it a lot of times, so it helps when it is fun.”

“make it fun to motivate the child”.[Van Luit]

[Bakker]




InteractionThe values of tangible electronics for learning has been discussed [Marshall 2007 and O’Mally 2004] and de-scribed as: “they can be used for shared play and learn-ing, they are assumed to be more motivating than tra-ditional learning materials and it is claimed that they support explorative behaviour... they may be very use-ful in helping children to solve complex abstract prob-lems” [Verhaegh 2009] like in my context.

To accomplish a rich interaction (new) technologies will be used, this technologies should be distinguish or in-visible, so that “the technology itself is not the primary focus for exploration, but rather the interaction with the tangible and their effects” [Price 2003]. Through a couple of explorations and validations the right ap-pearance, actions (sensors and actuators) and tangibil-ity should be created.


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process

I want to realize this project by going through a cou-ple iterations (3 to 5), each iteration containing user involvement, building ‘prototypes’ and reflection (use feedback from experts), for more details look at my planning (appendix C).

The first iteration will be exploring boundaries and cre-ating empathy by just start building and experiencing how children experience their math. In the second it-eration I want to use the results from the first to gener-ate a co-design session [Sanders 2003] or a cooperative inquiry [Guha 2005], generate different concept direc-tions and reflect on this. In the third session I will use the outcome of the user-sessions to explore the direc-tions and use the concepts as input for little user-tests with children. Use the outcomes for inspiration to de-fine design directions and eventually (maybe by more iterations) create a final tool which is evaluated, fine tuned and validated on the end.

To validate my decisions and results I ask feedback from experts (the children (math and without math prob-lems), parents, teachers, researchers and stakeholders) and I will test everything with the help of (low-fidelity) working prototypes and close user involvement. To conclude if the child(ren) are making more progress with the multiplication table I will compare their ‘CITO-toets’ results from January with July with their class-mates.

To realize the feedback from all the different experts I will use a blog on the internet. This blog makes it pos-sible for everyone to follow my progress and also helps me with recording my own process and creating my re-port.




Feasibility and risks

1. Client; I try to get a client involved in my project.

2. Collect users; it is crucial I find children to work with.

3. Collaborative or individual; to learn math [Price 2003, Stanton 2002 a,b] and do user-tests [Sturm] col-laborative use is very important, but individual exercise are also important [Van Luit 1999] and design for an individual would be less complex.

4. Each child is unique; the process of learning math is very personal [Brown 1989, Van Luit]. I should reckon with the personal differences of the children.

5. How much freedom will the tool provide; it is posi-tive to have rich action possibilities (more space for exploration, open-endedness [Bekker 2008]), but it is also scary and confusing to have too much freedom [Rozendaal].

+ =


14

References

Bekker, M. M., Sturm, J., Wesselink, R., Groenendaal, B. and Eggen, B. (2008). Interactive Play Objects and the Effects of Open-Ended Play on Social Interaction and Fun. Proceedings of ACE’08.

Brown, J.S., Collins, A. and Duguid, P. (1989). Situated Cognition and the Culture of Learning. Educational Re-searcher, Vol. 18, No. 1. (Jan. - Feb., 1989), pp. 32-42.Brown, S. (2008). Stuart Brown says play is more than fun. www.TED.com.

Clements, D. (1995). Playing with computers, playing with ideas. Educational Psychology Review 7 (2), 203–207.

Desoete, A. and Braams, T. (2008). Rondom het kind, Kinderen met dyscalculie. Boom Amsterdam.

Guha, M.L., Druin, A., Chipman, G., Fails, J.A., Simms, S., and Farber, A. (2005). Working with Young Children as Technology Design Partners. In Communications of the ACM, Vol. 48, No. 1, pp. 39-42.

KNAW (2009). Reken onderwijs op de basisschool, analyse en sleutels tot verbetering, advies. Koninklijke Nederlandse Akademie van Wetenschappen, Amster-dam.

Kroesbergen, E. H. and Van Luit, J.E.H. (2002). Teaching multiplication to low maths performers: Guided versus structured instruction. Instructional Science, 30, 361-378.

Malone, T. W. and Lepper, M. R. (1987). Making learn-ing fun. Aptitude, learning, and instruction: Vol. 3. Cog-nitive and affective process analysis, Hillsdale, NJ: Erl-baum, 223--253.

Marshall, P. (2007). Do tangible interfaces enhance learning? Chapter 4 - learning through physical interac-tion TEI’07, 15-17 Feb 2007, Baton Rouge, LA, USA.Moerlands, F. (1994). Leercurve, leertijd en vaardig-heid. www.Edumat.nl.

Negroponte, N. (2007). Nicholas Negroponte on One Laptop per Child. www.TED.com.

O’Malley, C. and Stanton-Fraser, D. (2004). Literature review in learning with tangible technologies. Nesta FutureLab Series, report 12.

Price, S., Rogersa, Y., Scaifea, M., Stantonb, D.and Neale, H.(2003). Using ‘tangibles’ to promote novel forms of playful learning. Elsevier Science B.V.Interacting with Computers 15 (2003) 169–185.




Reijn, G. (2009). Rekenen op pabo al jarenlang beneden peil. de Volkskrant, 4 November 2009.

Resnick, M., Bruckman, A. and Martin, F. (1999). Con-structional Design: Creating New Construction Kits for Kids. Morgan Kauffman, USA, The Design of Children’s Technology.

Robinson, K. (2006). Ken Robinson says schools kill cre-ativity. www.TED.com.

Sanders, B.-N. and Stappers, P.J. (2008). Co-creation and the new landscapes of design. In CoDesign,Taylor & Francis, March 2008.

Stanton, D., Bayon, B., Abnett, C., Cobb, S. and O’Malley, C. (2002b). The effect of tangible interfaces on chil-dren’s collaborative behaviour. Proceedings of Human Factors in Computing Systems (CHI 2002), ACM Press.

Stanton, D., Neale, H. and Bayon, V. (2002a). Inter-faces to support children’s co-present collaboration: multiple mice and tangible technologies. Computer Support for Collaborative Learning (CSCL), ACM Press, Boulder,Colorado, USA, January 7th–11th.

Van Luit, J.E.H. and Naglieri, J.A. (1999). Effectiveness of the MASTER program for teaching special children multiplication and division. Journal of Learning Disabili-ties, 32, 98-107.

Van Luit, J.E.H., Nelissem, J.M.C. and Peltenburg, M.C. (2009). Learning Mathematics by interaction in young students with special educational needs. Nova Science Publishers. Inc.

Verhaegh, J. and Fontijn, W.J.F (2009). Integral skill de-velopment with the TagTiles console. SeriousToys.nl.

Verhaegh, J., Hoonhout, H.C.M. and Fontijn, W.J.F (2007). Effective use of fun with a tangible interaction console. In Proc. of the 4th International Symposium on Pervasive Gaming Applications PerGames 2007, Shaker-Verlag, Aachen, 177-178.


16

Appendices

A. List of Experts:People I contacted for my project, with their function, company, relevant expertise and date of meeting.

B. Planning:My proposed planning according to the reflective trans-formative design process. On the left the weeks and in the next comlumn what kind of activities. The under-lined activities are deliverables. The dots represent the activities and show when and where they take place in the reflective transformatice design process.

Resources pictures

Picture 1:research project: MoZo, photographer: Eveline Brink

Picture 2:a. Concept Tagtiles. Source: www.serioustoys.comb. Tagtiles. Source: Verhaegh 2009

Picture 3:Max. Source: www.k2-verlag.de

Picture 4:i-Blocks. www.jegro.com/i-blocks

Figure 3:Circle of failure and succes. Source: Desoete 2008

The rest of the pictures and figures:Illustrator: Eveline BrinkPhotographer: Eveline Brink.




List of experts

planning

iteraction 1

1. create empathy, experience their math moodboard2. experience and

tools3. improve vision of project, list of demands

1. create co-design sessions: plan and materials2. co-design sessions: 3. analyse results co- design sessions4. improve vision of project, list of demands

draw conclusions2. create 3 concepts3. create prototypes4. test/feedback on 3 scenarios5. analyze feedback, draw conclusions6. improve vision, list of demands

2. explore decisions3. validate decisions test/expert feedback4. draw

experts feedback on drawings6. prepare prototype7. update vision and

prototype

user-test3. perceive user-test, collect data4. analyse data with experts

how to improve tool

7. create report

1. generate last improvements

3. collect feedback: user-test / experts

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iteraction 2

iteraction 3

iteraction 4

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green light

project week

1.February

project week

2.February

project week

3.February

project week

4.March

project week

5.March

project week

6.March

project week

7.April

project week

8.April

project week

9.April

project week

10.May

project week

11.May

project week

12.May

project week

13.June

project week

14.June

INTRIM

blog up to date?

blog up to date?

blog up to date?

Doing

PerceivingValidating IdeatingIntegrating analysis vision

Doing

PerceivingValidating IdeatingIntegrating

analysis vision

planning

iteraction 1







prototype


how to improve tool

7. create report



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green light

project week

1.February

project week

2.February

project week

3.February

project week

4.March

project week

5.March

project week

6.March

project week

7.April

project week

8.April

project week

9.April

project week

10.May

project week

11.May

project week

12.May

project week

13.June

project week

14.June

INTRIM

blog up to date?

blog up to date?

blog up to date?

Doing


Doing


analysis vision

planning

iteraction 1







prototype


how to improve tool

7. create report



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iteraction 4

iteraction 5

green light

project week

1.February

project week

2.February

project week

3.February

project week

4.March

project week

5.March

project week

6.March

project week

7.April

project week

8.April

project week

9.April

project week

10.May

project week

11.May

project week

12.May

project week

13.June

project week

14.June

INTRIM

blog up to date?

blog up to date?

blog up to date?

Doing


Doing


analysis vision

appendix D: new games created for the old computer from Jumbo

appendix E: technical drawing of TagTiles

appendix G: algorithm

master thesis 2011: 'alles maal

Documents

final design

child motivated

design approach

final master project

child struggles tagtiles

alles maalt help children

good project

perfect project