Instructional Design for a unit of instruction

by

Nickesha Senior

308003276

A Paper Presented in Partial Fulfillment

Of the Requirements of

EDID 6505 Systems Approach to Designing Instructional Materials

Trimester II, 2015-2016

Email:

Student ID:

nickesha.seniorwhynn@open.uwi.edu

308003276

University:

University of the West Indies Open Campus

eTutor& Course Coordinator :

Dr. LeRoy Hill

Table of Contents

Needs Assessment ………………………………………………………………………4

Goals …………………………………………………………………………….4

Objectives ……………………………………………………………………….4

Target Audience ………………………………………………………………...4

Purpose of the Needs Assessment……………………………………………….5

Optimals ………………………………………………………………...5

Actuals ………………………………………………………………….5

Causes …………………………………………………………………..6

Feelings ………………………………………………………………....7

Solutions ………………………………………………………………..8

Hypothesis ……………………………………………………………………...8

Source of Information ………………………………………………………….9

Methods ………………………………………………………………………..9

Technique 1 ……………………………………………………………9

Technique 2 ……………………………………………………………9

Use of Information to Design Workshop………………………………………9

Task Analysis ………………………………………………………………………….9

Performance Objectives ……………………………………………………………….10

Assessments …………………………………………………………………………...11

Learner/Contextual Analysis ………………………………………………………….11

Instructional Strategies ………………………………………………………………..12

Reflection ……………………………………………………………………………..12

References …………………………………………………………………………….15

Appendix A – Technique 1:Participant Observation………………………………….16

Appendix A1 – Personal Interview Instrument ……………………………………….18

Appendix B – Technique 2: Personal Interview……………………………………….19

Appendix B1 – Personal Interview Instrument …….………………………………….22

Appendix C1 – Task Selection Worksheet………….…………………………………23

Appendix C2 – Procedural Analysis ………………..…………………………………27

Appendix C3 – Flowchart…………………………..………………………………….31

Appendix C4 – Prerequisite Analysis………………..………………………………...32

Appendix D – Rubric ………………………………..………………………………...33

Appendix E – Assessment Items ………………………………………………………36

Appendix F – Learner/Contextual Analysis………….………………………………...39

Appendix G – PowerPoint Lesson……………………………………………………..42

Appendix H – Advanced Organizer……………………………………………………45

Appendix H1 – Comparative Organizer………………………………………..45

Appendix H2 – Graphic Organizer……………………………………………..46

Appendix I – Analogies ………………………………………………………………..47

Appendix I1 – Analogy 1……………………………..………………………..47

Appendix I2 – Analogy 2………………………………………………………48

Needs Assessment

Goals

The purpose of this assessment is to evaluate the need for skills training for a group of teachers and to create a unit of instruction to provide the necessary training in the areas of need. The various curriculums, the present skills of each teacher as well as the available resources for training will be assessed to satisfy the requirements of the intended programme.

Objectives

At the end of this assessment the instructional designer should be able to identify:

· any lack of skill the teachers at the Excellence Centre have in meeting the demands of the K-12 syllabus, GCSE syllabus and the CSEC syllabus

· any challenges faced by the teachers at the Excellence Centre as a result of those lack of skills

· if the desired learning outcomes are being achieved by the students for each curriculum

The assessment will also help in ascertaining which skills teachers already possess that need sharpening.

Target Audience

The Institute is very small and thus employs only three teachers full-time and one teacher part-time. The part-time teacher is responsible for teaching English Language while the full-time teachers focus on mathematics and science. There is also an intern who deals with the accounts and billing as well as a part-time sales manager. The assessment will be done for the three full-time teachers; two (2) undergraduate teachers and one (1) graduate teacher at the Excellence Centre Institute who are preparing students to meet the requirements of the K-12 Algebra I and II specifications, GCSE O and A level examinations as well as the CSEC examinations.

Purpose of the needs assessment

Optimals

· need to be flexible and open to new strategies and methods

· quick on their feet to meet the needs of the student

· knowledge of the K-12 syllabus, GCSE O and A level syllabus and the CSEC syllabus

· assess and evaluate the syllabus to know what to pass on to the students

· the effective use of a graphing calculator

· using various methods to solve questions in matrices, trigonometry, logarithms, exponents, functions and relations

· be sensitive to quick changes in topic based on the limited time frame

Actuals

· none of the teachers are fluent in using a graphing calculator

· 67% of the teachers are experts in the CXC syllabus to include CSEC and CAPE as opposed to the K-12 syllabus, GCSE O and A-Level syllabi

· there are areas in the Geometry and Algebra II K-12 syllabus that are new concepts to be taught by the teacher, therefore it requires further preparation

· teachers have to teach all three syllabi, with different topics relating to each syllabi within the same class session

· topics require teachers to apply varying techniques in different syllabi with 50% of the teachers finding it difficult to transition

· teachers have to teach to facilitate multiple intelligences

· teachers have most of their experience in teaching only one syllabus in regular school

· many of the children have learning disabilities such as ADHD, Dyslexia and Dyscalculia which require lesson traditional ‘chalk and talk’ techniques

Causes

As adopted from Rossett (1995):

· Lack of skill/knowledge

· The teachers are required to teach varying syllabi within a limited space of time, at times they are not fully prepared for the lesson

· There is lack of training in the use of many technological items such as a graphing calculator

· A lack of training in teaching topics in geometry and Algebra II in the K-12 syllabi

· Flawed environment

· At the centre where most of the teaching takes place there is a small space with two teachers teaching at the same time which can be distracting to the students and the teachers

· The is need for teaching aids and tools such as computers

· The teacher-student ratio is very high for the purpose of the institution. (Most students are expecting to get individual attention)

· Improper Incentives

· Teachers are warned if mistakes are made in delivery or if tasks are not done

· Very little time is given to get tasks done

· Gratitude expressed verbally is the only incentive

· Unmotivated Employees

· The teachers are self motivated, they complete tasks according to their job description

· Teachers at times are not confident in their delivery as they are not confident in the area being taught

· The teachers are trained however they need to do professional developments to improve their knowledge base and skills

Feelings

· The teachers feel overworked and underpaid

· Teachers are of the opinion that they need to get more time to familiarize themselves with the syllabi

· The hours of work are too much for the teachers to get time to focus on developing their skills

· The teachers are of the opinion that one day off (Sunday) is not sufficient for them to be fully prepared for all lessons. Preparation time takes away from family time.

· Considering that students are entitled to individual attention the teachers feel overwhelmed when one teacher is faced with five students within the same session expecting individual attention.

Solutions

· Training of staff on using instructional tools such as the graphing calculator

· Get more instructional materials such as computers, graphing calculator as well as a better arrangement of the facility

· Training and discussions to allow staff to become familiar with each syllabi

· Considering the student-teacher ratio more specialists need to be hired

· The working hours need to be revised given more time for teachers to prepare for their lessons

· Teachers should be offered other incentives for getting tasks done on time, well and they go above and beyond the call of duty.

· Monthly professional development days will be instituted to enhance the teachers understanding and presentation of various topics in the different syllabi

Hypotheses

Based on observation it is seen that:

· There is a lack of training in various situations and with specifically the American based syllabus

· There is a need for the familiarity of the syllabi especially the American syllabus

· There is a need for specialists in that area

· More teachers need to be employed to meet the varied needs of the students

Source of information

The information needed will be gathered from the teachers themselves as they are the ones directly affected by the situation. They would have first-hand knowledge as to all the processes that take place and what areas need improvement. They are aware of the areas of each syllabus that are most difficult for them to handle and why.

Methods

Technique 1: Participant observation (See Appendix A for details on participant observation)

Example of Observation Instrument(See Appendix A1 for the example of the instrument)

Technique 2: Personal interview (See Appendix B for details on personal interview)

Example of Personal Interview Instrument(See Appendix B1 for the example of the instrument)

Use of Information to design workshop

The information gathered will help in identifying the challenges of the company and thus give an idea as to what issues need to be addressed by the workshop. It will also aid in giving ideas as to possible ways of addressing the issues and the best way of structuring the workshop. It will help in identifying the skills of the workers that can be utilized in the workshops.

Task Analysis

According to Jonassen, Tessmer and Hannum (1998)“task analysis is used extensively in designing different forms of instruction, including performance support, direct instruction, and open-ended learning environments”(pg. 6). This unit seeks to design a face-to-face instructionalworkshop for the target audience. After the needs assessment a task selection was done which determined that the top three tasks that needed to be addressed were teaching aspects of trigonometry in the Algebra II syllabus, presenting the topic directed numbers to students with varying learning styles and using a graphing calculator. The latter was selected for this unit of instruction. (See Appendix C1 for the Task Selection Worksheet)

The two methods of analysis used for this unit were the Procedural Analysis and the Prerequisite Analysis. The procedural analysis outlines the procedures for completing the unit, (See Appendix C2 and C3 forthe Procedural Analysis and Flowchart). The Prerequisite Analysis however gives the sequence of how to acquire the skills offered in the unit, (See Appendix C4 for the Prerequisite Analysis).

Performance Objectives

Terminal/General Objective:

· After engaging in a two day training workshop the participants will demonstrate the use of the graphing calculator to do operations and calculations in the K-12 syllabus without assistance and with at least 90% accuracy.

Enabling/Specific Objectives:

By the end of this unit of instruction participants will:

· identify the keys on the graphing calculator used for graphing, solving matrices and trigonometric questions 90% accurately without assistance(Recall, comprehension)

· independently perform various calculations in matrices, trigonometry and functions using the graphing calculator with 90% accuracy(Psychomotor)

· solve given questions using the graphing calculator with 90% accuracy without assistance(Cognitive, Analysis, interpretation)

· validate answers produced by the graphing calculator without assistance with 100% accuracy(Cognitive, Evaluation, Problem solving)

· attempt plotting graphs on the graphing calculator with minimal assistance(Affective)

· help other participants by demonstrating the use of the graphing calculator to add, subtract and multiply matrices with 100% accuracy(Affective)

Assessments

In seeking to assess the learning of the participants the varying learning styles and abilities were considered. However the aim was to go beyond the norm to allow participants to be engaged in the lesson. Thus participants will construct their responses while the assessments and rubric will assess directly what the participants are engaged in within the lesson. (See Appendix D and Appendix E for the Rubric and Assessment items for this unit of instruction)

The Rubric will be used throughout the lesson at the beginning, during and after the lesson to check the participant’s progress and changes on understanding. Assessment item number 1 will be assessed directly after the students have been exposed to the keys on the calculator to see if they have understood the process and the keys necessary. All the other assessment items will be used at the end of the lesson.

Learner/Contextual Analysis

This section comes before instruction and the main purposes are to motivate and prepare participants to learn cognitively, (Tessmer& Richey, 1997). (See Appendix F for the Learner/Contextual analysis for this unit of instruction).

Instructional Strategies

The First Principles of instruction from David Merrill were very significant in the completion of this section of the unit. It sought to bring about the activation of the participants prior knowledge, allowing them to demonstrate what is being learned, also to apply what is learned and integrate it into their everyday lives. Various methods were used in this section to include a PowerPoint lesson (See Appendix G), Advanced Organizers (See Appendix H) and Analogies (See Appendix I). The PowerPoint presentation gives the details of the lesson and shows how each instructional strategy will be incorporated in the lesson. These strategies such as organizers and analogies help in tying the pieces of the lesson together as well as enhancing the presentation.

Reflection

The target audience of this unit of instruction comprised of three trained, degreed teachers of the Excellence Centre. These teachers have a mandate of preparing students to meet the requirements of the K-12 Algebra I and II specifications, GCSE O and A level examinations as well as the CSEC examinations. These teachers are ‘old school’ and thus are not proficient in using a graphing calculator to meet the demands of especially the K-12 Algebra I and II specifications. For this reason,the aim was to engage these teachers in hands-on learning where they would get a firsthand experience in constructing their general understanding. The lesson included games, advanced organizers and analogies. It incorporated various analyses such as task analyses and learner/contextual analysis.

At the beginning participants were allowed to express themselves thus helping to activate their prior knowledge. They were engaged in a ‘lucky dip’ whilst a comparative organizer was used to link their prior knowledge to what is to be learnt. Then some analogies were made to give them an understanding of what matrices really are and how they can apply to real life. From there they watched a video as well as viewed demonstrations from the instructor.A graphic organizer was used to help in summarizing the concepts learnt on the importance of the order of matrices in adding, subtracting and multiplying. They were then assessed on the use of the calculator. They were allowed to demonstrate their understanding of the topic by instructing their peers. After which a general assessment was done.

For the most part it was an effective lesson. Participants were able to effectively use the calculator at the end of the workshop. The objectives were attainable and the participants were fully engaged. One of the areas I would have improved is to have more technological tools readily available. Using the groups to provide feedback was a welcomed idea however I believe with more time we would have made it even more meaningful. Through the help of my peer group I now have a better understanding of the elements of a needs assessment and the significance of items such as the optimals, actuals, causes, feelings and solutions. These are areas that were used in guiding the designer in choosing the task that is of utmost importance in being addressed. I gained an appreciation in being systematic in designing units. It allows for clarity not only for the designer but the members of the team who might refer to the document.

The introduction to task analysis was clear, interesting and turned out to be fun. I have always been writing objectives a certain way, but now I see the significance of sections such as the criteria. It adds clarity to the objective and makes it easier when writing a rubric and developing assessment items.The learner/contextual analysis were relatively straight forward however the instructional strategies took a lot more investigation. All these are things that I would have done in teacher training however under different contexts and sometimes in less detail. Overall this course was relevant, interesting and worth the experience.

References

Glynn, S. (1995). Conceptual Bridges: Using Analogies to Explain Scientific Concepts. Science Teacher, 62(9), 24-27.

Jonassen, D. H., Tessmer, M., &Hannum, W. H. (1998). Task analysis methods for instructional design.Routledge.

Merrill, M. D. (2002). First principles of instruction. Educational technology research and development, 50(3), 43-59.

Morrison, G. R., Ross, S. M., Kemp, J. E., &Kalman, H. (2010). Designing effective instruction.John Wiley & Sons.

Rossett, A. (1995). Needs Assessment.In Anglin, G. J. (Ed). Instructional technology: Past, present, and future, p.183-196. Englewood, CO: Libraries Unlimited, Inc.

Tessmer, M., & Richey, R. C. (1997).The role of context in learning and instructional design. Educational technology research and development, 45(2), 85-115.

Appendix

Appendix A: Technique 1: Participant observation

Statement of Purpose: Observations will be done to see how comfortable the teachers are with each syllabus and the areas that might need improvements or the use of different methods for clarity. The nature of the available resources will also be assessed to see if the instructional materials present are sufficient and meets the needs of the students. The overall operation of the institute will also be assessed to see if the student-teacher ratio is feasible.

Information Sought:See optimals, actual, causes, feelings and solutions

Anonymity/ Confidentiality:This is not likely in this situation as all participants are known.

Procedure:It will be clearly communicated that the assessment is not a way of critiquing the business but to aid in improving its processes. The observer will try not to make it obvious especially to the students that an observation is taking place. Observations will be done over a period of time of each syllabus.

Development Cost/ Ease:There is no development cost as the observations will be done within the workplace and will be easy to develop. Research will be done as to the timetables in terms of when each syllabus is being presented and the best times to observe each individual.

Administration cost/ Ease:It is a very small institute therefore it will not take a lot of time to do the observations however to make it less biased more than three lessons of each syllabus will be observed. This will not incur any cost.

Scoring/ Analysis Cost/ Ease:The observations will take about one month to be completed.

Probable Response Rate; Risks:The response will be immediate upon observation. After the month is finished then the final result of each observation will be compiled into a final document. The possible risks could be observer bias and many assumptions made based on what occurs during observation. Also considering that the participants will not be aware that an observation is taking place the observer will not be making notes, therefore details might not be completely reliable at times.

Buy In/ Persuasion Potential:This is not very necessary in this situation as the participants are open to improving their skills and the processes of the institute.

Diversity of Opinions Sought:Not applicable in this situation.

Product/Results:A report will be generated at the end of the observation period.

Problem/Situation Complexity:The ratio of teachers to students is a concern, therefore observation might overlap. Varying syllabi are done on the same days at the same time by the same teachers.

Objectivity of Data:This is going to vary based on the workload that the teacher under observation might have during the time of observation.Availability of instructional material will also affect how much a teacher might be able to achieve in a given lesson.

Advantages:This method will allow the observer to get firsthand knowledge of the processes that take place in the institute as well as the skills and challenges the teachers face. This method is non-threatening to the normal processes of the business and will not affect teachers’ performance.

Disadvantages:The teacher to student ratio might affect how much can be observed in one lesson as well as it might limit the amount that a teacher can get covered. A lot of the observation will be based on the observer’s opinion and therefore it might not be very reliable.

Appendix A1: Observation Instrument

Curriculum :

Date:

Observer:

Instructor:

Instructions: Evaluate the overall performance of a teacher in the delivery of each curriculum by rating each of the behaviours below. Use these results to determine the needs for skills training, curriculum development and/or increase in instructional material.

Rating Scale:

C – Consistency and competency in an area under observation. As well as the necessary resources are available. Very Good performance.

I – improvement needed in the stated areas or instructional materials needed. Poor performance.

G – Generally well done there is room for improvement. Average performance.

Work Behaviours/ Skills/ Curriculum Knowledge

Demonstrates confidence in presenting the topic being taught

C

I

G

Teacher is adequately prepared for the lesson

C

I

G

Teacher has all the instructional material needed for demonstrations

C

I

G

The teacher refers to books, handouts, YouTube, general internet

C

I

G

The teacher has knowledge of the curriculum being used, is able to do various transitions from one subtopic to another

C

I

G

Requested the assistance of other teachers

C

I

G

Appendix B:Technique 2: Personal interview

Statement of Purpose:Questions will be asked to ascertain what lack of skills, challenges and the needed instructional material for the Excellence Centre. These interviews will provide information on the feelings of the teachers and for them to provide personal solutions based on their concerns. This method will allow them to be more open to conversation and thus share their ideas on solving any problems identified.

Information sought:See optimals, actuals, causes, feelings and solutions

Group size: This will comprise of one interviewer and one interviewee.

Procedure:The interviewer in preparation for the interview will refer to the purpose of the needs assessment and prepare questions that are directly related to the information needed. The teachers will be the ones who will be interviewed.It will be clearly communicated that the interview is not a way of critiquing the business but to ascertain their opinion on the processes of the institute. The interviewer will try to ask questions that will not undermine or be too suggestive to the interviewee. These questions will be asked based on the actuals and optimals.

Anonymity/ Confidentiality:This is not likely in this situation as all participants are known and will be aware of the interview beforehand.

Development Cost/ Ease:There is no interview cost as the interviews will be done during the lunch break for three days. The interview instrument will be easy to develop. Research will be done to find out the days that are most appropriate for each teacher. Since the interviewer is familiar with the setting it should make both parties feel more at ease.

Administration cost/ Ease:It is a very small institute therefore it will not take a lot of time to do the interviews. This will not incur any cost.

Scoring/ Analysis Cost/ Ease:The interviews will be completed within one week.

Probable Response Rate; Risks:The response will be immediate upon the interviewee answering the questions. After all the interviews are finished the final result will be compiled into a final document. The possible risks could be some participants might be afraid to state certain challenges within the institute as they might be fearful of the director hearing their opinions. This will be eliminated however as any challenges or concerns given will be recorded anonymously. As well as room has to be made for any diversions from the questions or topic at hand.

Buy In/ Persuasion Potential:A polite and courteous personality will help in making the interviewer more persuasive and thus make the interviewee more open to discussion. The director will also be interviewed therefore he will be able to make decisions based on any challenges or lack of skills noted.

Diversity of Opinions Sought:Opinions will be sought from the three persons directly involved in the institute. Each person has his or her own challenges and concerns and will be able to give their ideas of how to minimize those challenges.

Problem/Situation Complexity:Questions will be stated in a way to prevent misunderstanding and to allow the interviewees to share their views. Since it is a face to face setting there will be very little room for misunderstanding as any such occurrence can be dealt with immediately.

Product/Results:At the end of each interview we will do a recap of the main points. Also at that point the interviewee will be directly asked if there is any other thing that he or she would like to share or clarify. The use of the information will be shared so they are clear about the anonymity of their responses and that further action will be taken to address the issues or challenges.

Objectivity of Data:The data will be very objective as there will be no prejudice and all party will be treated with respect and fairly.

Advantages:This method allows the interviewer to get firsthand knowledge as to the processes of the institute and the feelings of the workers. Solutions can also be deduced from these interviews.

Disadvantages:Interviews might take longer than anticipated. The interviews can take various turns not in keeping with the plan outlined.

Appendix B1: Personal Interview Instrument

Date: ______________________

Interviewer: ________________________

Position of Interviewee: ____________________

General information/ Challenges/Suggestions

1. How long have you been working at the Excellence Centre?

2. How did you hear about the institute?

3. What are your roles in the institute?

4. What qualifications do you have to perform those roles?

5. What aspects of your job do you find easy to perform? What makes those aspects easy?

6. What aspects of your job do you find difficult to perform? What makes those aspects difficult?

7. How would you propose to make those difficult tasks easier?

8. What aspect of each curriculum do you find to be challenging? Why?

9. How do you suggest these challenges be minimized?

10. What instructional material do you think will aid in making the day to day processes easier?

Running head: INSTRUCTIONAL DESIGN 1

INSTRUCTIONAL DESIGN3

Appendix C1: Task Selection Worksheet

Criteria for Task Selection Worksheet

Criticality

40 pts

Universality

10 pts

Frequency

10 pts

Standardization

10 pts

Difficulty

30 pts

Total

100 pts

Notes

Priority

TASKS

#1

#2

#3

#4

#5

#6

#7

#8

Present the topic directed numbers to students with varying learning styles

30

10

10

10

25

85

This is an important topic especially in algebra I and II. Majority of the topics involve the use of directed numbers hence the points awarded.

2

Use a graphing calculator

35

6

5

7

30

83

This is an essential skill to the K-12 syllabus however the processes that these perform can be done effectively without its use hence the low frequency rating.

3

Demonstrate a knowledge of the K-12 system

35

7

7

7

25

81

The K-12 syllabus is not the most commonly used at the institution however it is the most comprehensive. Therefore it is rated heavily across the board.

4

Explain and demonstrate concepts in the topic loci

20

3

5

5

20

53

This is a topic that is of importance in the GCSE syllabus. We do not have a large amount of students doing this programme hence the low rating. However it is an important to the syllabus.

6

Teach all aspects of trigonometry in the Algebra II syllabus

40

10

5

8

30

93

This is a very important topic in all syllabi at the institute hence the high critical rating. Algebra II encompasses a wider area of the topic than the other programmes.

1

Use varying methods to solve questions in matrices

10

5

5

5

25

50

This is a topic in the CSEC and K-12 syllabi however not having a good grasp of it does not affect the other aspects of the syllabus.

7

Effectively graph and transform functions including logarithmic and exponential functions

30

7

4

7

30

78

This is a topic that is essential to the GCSE and K-12 syllabus.

5

Appendix C2: Procedural Analysis

Procedural Analysis

Subject: Using a graphing calculator

Unit of Instruction/Task: Teaching a tutor to use a graphing calculator to deliver lessons to students doing Algebra II – Matrices.

LEVEL I

1. Turn on the calculator

2. Select the mode from the menu

3. Enter each matrix one at a time

4. Choose the operation needed

5. Use matrices on the graphing to solve simultaneous equations using the Inverse Method or the Guass-Jordan Elimination Method

LEVEL II

1. Turn on the calculator

1.1 Identify the type of calculator

1.2 Check that it is functioning properly

2. Select the mode from the menu

2.1 Identify the mode key

3. Enter each matrix one at a time

3.1 Click the matrix button

3.2 Enter the dimensions of the matrix

4. Choose the operation needed

4.1 add and subtract matrices

4.2 multiply matrices

5. Use matrices on the graphing to solve simultaneous equations using the Inverse Method or the Guass-Jordan Elimination Method

5.1 Solve simultaneous equations using the Inverse Method

5.2 Solve simultaneous equations using the Guass-Jordan Elimination Method

LEVEL III

1. Turn on the calculator

1.1 Identify the type of calculator

1.1.1 Examine the calculator

1.2 Check that it is functioning properly

1.2.1 Perform basic operations using the calculator

1.2.2 Reset the calculator

2. Select the mode from the menu

2.1 Identify the mode key

2.1.1 locate the mode key

2.1.2 select the mode that best suits the operation

2.1.3 switch between the classic mode and math print mode

3. Enter each matrix one at a time

3.1 Click the matrix button

3.1.1 identify the matrix button

3.1.2 select 2nd function and click the x-1 button

3.2 Enter the dimensions of the matrix

3.2.1 clear any existing matrix dimensions

3.2.2 select the matrix letter

3.2.3 click the edit button

3.2.4 state the dimensions of any matrix

3.2.5 identify the dimensions of the matrices in the question

3.2.6 enter the dimensions

3.2.7 return to the home screen

4. Choose the operation needed

4.1 add and subtract matrices

4.1.1 explain when two matrices can be added or subtracted

4.1.2 go to matrix to get the names of the matrices entered

4.1.3 insert the necessary symbol

4.1.4 read the correct answer matrix from the screen

4.2 multiply matrices

4.2.1 explain what criteria has to be met for two matrices to be multiplied

4.2.2 go to matrix to get the names of the matrices entered

4.2.3 insert the necessary symbol

4.2.4 read the correct answer matrix from the screen

5. Use matrices on the graphing to solve simultaneous equations using the Inverse Method or the Guass-Jordan Elimination Method

5.1 Solve simultaneous equations using the Inverse Method

5.1.1 define simultaneous equations

5.1.2 rearrange the equations to line up the coefficients

5.1.3 write simultaneous equations as equivalent matrices

5.1.4 find the inverse of a matrix on the calculator

5.1.5 multiply the inverse by the answers to the equations

5.1.6 read the answer from the screen correctly

5.2 Solve simultaneous equations using the Guass-Jordan Elimination Method

5.2.1 line up the coefficients

5.2.2 define augmented matrix

5.2.3 check the RREF function from the home screen

5.2.4 go to the matrix button

5.2.5 move right to MATH, choose B: RREF

5.2.6 choose the name of the matrix and hit enter

5.2.7 read the last column which gives the answer

Appendix C3: Flowchart

Appendix C4: Prerequisite Analysis

Appendix D: Rubric

Terminal/General Objective:

· After engaging in a two day training workshop the participants will demonstrate the use of the graphing calculator to do operations and calculations in the K-12 syllabus without assistance and with at least 90% accuracy.

Using a graphing calculator - Assessment Rubric (4 marks each)

Item

Exceeds Expectations

4

Meets Expectations

3

Some Expectations met

2

Limited Expectations

1

Below Expectations

0

1. state the steps in adding, subtracting and multiplying two matrices with 100% accuracy without assistance

The participant is able to state each step correctly, in the correct sequence. The explanation is understandable and easily followed.

The participant is able to state most of the steps correctly, with few errors in the sequence. The explanation is mostly understandable and can be followed.

The participant is able to state some of the steps correctly, with some errors in the sequence. The explanation is not clearly followed.

The participant is only able to state one or two steps correctly, with more than three errors in the sequence. The explanation is difficult to understand and cannot be followed easily.

The participant is not able to state any of the steps correctly, with no attempt at giving a sequence. No explanation given.

2. Demonstrate plottinggraphs using a graphing calculator correctly without assistance.

The participant is able to produce the correct graphs of the functions from the equations in all the questions given.

The participant is able to plot three out of four typesof graphs correctly.

The participant is able to plot two out of four types of graphs correctly.

The participant is only able to plot one type of graph for example linear.

The participant is unable to plot any graph on the graphing calculator.

3. Solve systems of equations using the inverse and Guass-Jordan Method with the use of graphing calculator without assistance.

The participant is able to use both methods effectively and correctly.

The participant is able to solve some questions with both methods with less than two errors.

The participant is able to solve only a few questions with both methods with three or four errors.

The participant is able to solve questions using only one method.

The participant is not able to solve questions using any of the methods.

4. Read answers produced by the graphing calculator correctly without assistance.

The participant is able to find all the necessary information on polynomials from the calculator such as intercepts, domain and range. They are able to correctly read answers from the Gauss-Jordan elimination method.

The participant is able to find four out of five of the necessary information on polynomials. They make one or two errors. They are able to read the answers from the Guass-Jordan elimination method with one error.

The participant is able to find three out of five of the necessary information on polynomials. The participant is able to read the answers from the Guass-Jordan elimination method with about three errors.

The participant is able to find only one or two of the items from the graph of polynomials and is able to read less than two of the answers from the Guass-Jordan elimination method.

The participant is not able to read any information from the graphs on the calculator or the answers from the Guass-Jordan Elimination method.

Appendix E: Assessment Items

Assessment Items – Scenario Items

Objective 1: To identify the keys on the graphing calculator used for graphing, solving matrices and trigonometric questions accurately without assistance

1. You need to solve a question using the Guass-Jordan Elimination method. With the use of the graphing calculator investigate which of the following steps will help you in finding the RREF button in this method?

a. Go to Math, select the MATRX from the matrix menu, go right to select ALPHA B to select rref

b. Go to MATRX to access the matrix menu go right to access the math menu then ALPHA B to select rref

c. Go to Mode, select MATRX to select the matrix menu, go right select ALPHA B to select rref

d. Go to ALPHA select B to select rref

Objective 2: To perform various calculations in matrices, trigonometry and functions using the graphing calculator without errors independently

2. Your class is planning to make some wooden picture frames for father’s day. The frame will be cut out of a piece of wood; however the area of the frame should be 30cm2. The inner part of the frame is 6 cm wide and 10cm long. What would be the width x of the actual wood frame? Use a graphing calculator to find your answer rounded off to two decimal places.

a. x = -1.08

b. x = 0.85

c. x = 0.34

d. x= -1.34

Objective 6: To demonstrate the use of the graphing calculator to add, subtract and multiply matrices with 100% accuracy

3. The totals of two brands of items from two companies are shown in the matrices below. Using a graphing calculator show the total overall production for both brands.

a.

b.

c.

d.

Objective 3: To solve given questions using the graphing calculator with 90% accuracy without assistance.

4. You have decided to take a school trip. You inquire about the prices for teachers and students. You are told that 3 teachers and 20 students cost $150 while 12 teachers and 50 students cost $450. Using the inverse method on your graphing calculator find the cost for a teacher's ticket and a student’s ticket.

a. Teacher’s ticket = $10 , student’s ticket = $ 5

b. Teacher’s ticket = $5 , student’s ticket = $ 3

c. Teacher’s ticket = $11.67 , student’s ticket = $ 3.50

d. Teacher’s ticket = $16.67 , student’s ticket = $ 5

INSTRUCTIONAL DESIGN 36

Appendix F: Learner/Contextual Analysis Worksheet

-2 Greatly impedes

-1 Slightly impedes

+1 Slightly facilitates

+2 Greatly facilitates

The effects are in bold.

Orienting Context

Learner Factors

· All trained teachers with at least a first degree-2 -1 +1 +2

· A mixture of males and females between the ages of 30 – 45 -2 -1 +1 +2

· All teachers having over 10 years of experience in teaching-2 -1 +1 +2

· Each person has at least intermediate computer skills-2 -1 +1 +2

Immediate Environment Factors

· There are two locations of the business-2 -1 +1 +2

· Lack of resource materialssuch as projectors, calculators, books -2 -1 +1 +2

· There is a need for more teachers to lessen the teacher-student ratio-2 -1 +1 +2

· Environment facilitates one-on-one and small group tutoring -2 -1 +1 +2

Organizational Factors

· All persons are employees of the Excellence Centre -2 -1 +1 +2

· All have prior experience in teaching in a regular school system-2 -1 +1 +2

· The teachers are familiar with the operations of the business-2 -1 +1 +2

· Flexibility of work hours-2 -1 +1 +2

· Above average salary when compared to other similar organizations-2 -1 +1 +2

· Private sector organization-2 -1 +1 +2

Instructional Context

Learner Factors

· All trained teachers have training and experience -2 -1 +1 +2

· Increase skills of using graphing calculators-2 -1 +1 +2

· There is some familiarity with the content or prerequisites of it -2 -1 +1 +2

Immediate Environment Factors

· The area to conduct the workshop is well lit and ventilated -2 -1 +1 +2

· There is no particular equipment set up for projectors-2 -1 +1 +2

· All equipment will have to be sought external to the business-2 -1 +1 +2

· Graphing calculators will have to be sourced-2 -1 +1 +2

Organizational Factors

· The workshop is going to be a bit costly because of the lack of resources-2 -1 +1 +2

Transfer Context

Learner Factors

· Participants will be able to better explain the processes to their students-2 -1 +1 +2

· There information from the workshop will be applied in the administration of lessons on a regular basis -2 -1 +1 +2

· Teachers confidence level will be increased in many concepts-2 -1 +1 +2

Immediate Environment Factors

· The resource materials from the workshop can now be used in the institute -2 -1 +1 +2

· There will be an increase in the accessibility of resources -2 -1 +1 +2

Organizational Factors

· The workshop will help in improving the reputation of the institute in offering these areas-2 -1 +1 +2

· This will be another area that can be advertised as being offered by the institution-2 -1 +1 +2

· There will be more clients accepted who are studying under the K-12 system. -2 -1 +1 +2

· Revenue will be increased-2 -1 +1 +2

Appendix G: PowerPoint Lesson

Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Appendix H: Advanced Organizers

Advanced Organizers

Appendix H1: Comparative Organizer

New Material

Organizer Topic

Type of Organizer

Matrix addition, subtraction and multiplication using a graphing calculator

Differences and similarities in adding, subtracting and multiplying matrices.

Comparative

(Discuss the importance of the order in manipulating matrices that is, adding, subtracting and multiplying. What are the implications of not abiding by these rules?The columns in the first must match the rows in the secondAddition Multiplication Subtraction The order of the matrix mattersThe order of each matrix must be the sameManipulating Matrices ) (Manipulating Matrices )Appendix H2: Graphic Organizer

Appendix I: Analogies

Analogies

Appendix I1: Analogy 1

An analogy can be drawn between a scoring table of a sports tournament and a matrix.

Description of a matrix

Scoring tablecompared withFormat of a Matrix

(Analog) (Target)

Tablerectangular array

Rows and columnsrows and columns

Cells elements

Team

Win

Lose

Draw

Barcelona

5

4

3

Real Madrid

3

4

5

Table Matrix

Pictorial representation

Differences

· Tables most often have lines separating each row and column. The elements of a matrix are not bounded by lines.

· Tables are enclosed in a box however matrices are surrounded by square brackets or parentheses.

· In tables the rows and the columns might not always be of the same length nor does the number of rows on one side have to match the rows on the other. However these are features of the matrix.

Appendix I2: Analogy 2

An analogy can be drawn between a sky scraper building and a matrix.

(Columns/height) (Rows/ Width)

Sky scraper compared withMatrix

(Analog) (Target)

Differences

· In a sky scraper the windows are of the same size and type however with a matrix each element does not have to be the same size or type of number.

· A sky scraper can start out with equal amount of windows at the bottom but can reduce as it goes to the top. With a matrix it maintains a rectangular shape so the numbers of elements in the rows and columns throughout are consistent.

÷

÷

÷

ø

ö

ç

ç

ç

è

æ

363

441

4

315

199

3

198

436

2

689

158

1

Q

Q

Q

Q

BrandY

BrandX

ComA

÷

÷

÷

ø

ö

ç

ç

ç

è

æ

189

553

4

563

411

3

363

639

2

111

153

1

Q

Q

Q

Q

BrandY

BrandX

ComB

÷

÷

ø

ö

ç

ç

è

æ

1565

1234

BrandY

BrandX

÷

÷

ø

ö

ç

ç

è

æ

1226

1756

BrandY

BrandX

÷

÷

ø

ö

ç

ç

è

æ

2791

2990

BrandY

BrandX

÷

÷

ø

ö

ç

ç

è

æ

2982

2799

BrandY

BrandX

To independently demonstrate the use of the graphing calculator to add, subtract and multiply matrices with 100% accuracy.

To independently demonstrate the use of the graphing calculator to add, subtract and multiply matrices with 100% accuracy.

Enabling Objective

Questions on matrices will be written on strips of paper and placed in a basket. Each participant will pick a strip from the basket, read the question to all the other participants and answer the question. If they are unable to answer then any other participant can answer. The questions will include questions on:

Identifying the order of matrices

Identifying elements in matrices

rules when adding , subtracting and multiplying matrices

manually.

How to add, subtract and multiply on the calculator

A comparative organizer will be incorporated

to assess as well as assist in participant’s understanding of the concepts.

Questions on matrices will be written on strips of paper and placed in a basket. Each participant will pick a strip from the basket, read the question to all the other participants and answer the question. If they are unable to answer then any other participant can answer. The questions will include questions on:

Identifying the order of matrices

Identifying elements in matrices

rules when adding , subtracting and multiplying matrices manually.

How to add, subtract and multiply on the calculator

A comparative organizer will be incorporated to assess as well as assist in participant’s understanding of the concepts.

Activating prior knowledgeLucky Dip

The teacher will use two analogies to explain the

concepts of matrices .

The participants will watch a video on entering

matrices into the calculator and the basic operations

on matrices using the calculator. Video link: https://www.youtube.com/watch?v=7e1uywDtOnc

The teacher will then demonstrate entering the

matrices and doing each operation to the participants while they follow on their graphing calculator.

The teacher will use two analogies to explain the concepts of matrices .

The participants will watch a video on entering matrices into the calculator and the basic operations on matrices using the calculator. Video link: https://www.youtube.com/watch?v=7e1uywDtOnc

The teacher will then demonstrate entering the matrices and doing each operation to the participants while they follow on their graphing calculator.

Demonstration

Matrices will be written on strips of paper with different orders and a specified operation to complete. The answers to these questions will be lined out on a table. Each person will do the calculation using a calculator given only 10 seconds. They will then have to select their answer from the table and show it to everyone who will clap if the answer is correct.

A graphics organizer will be used in assisting in

clarifying steps that are critical in adding, subtracting or multiplying matrices.

Matrices will be written on strips of paper with different orders and a specified operation to complete. The answers to these questions will be lined out on a table. Each person will do the calculation using a calculator given only 10 seconds. They will then have to select their answer from the table and show it to everyone who will clap if the answer is correct.

A graphics organizer will be used in assisting in clarifying steps that are critical in adding, subtracting or multiplying matrices.

ApplicationActivity 1

Participants will be placed in groups of 3, they will be given 50 questions on the basic operations on matrices to complete in 2 minutes using the graphing calculator. The team with the most questions completed with the correct answer wins.

The participants will use the concepts brought about

by the comparative organizer to assist them in completing this task.

Participants will be placed in groups of 3, they will be given 50 questions on the basic operations on matrices to complete in 2 minutes using the graphing calculator. The team with the most questions completed with the correct answer wins.

The participants will use the concepts brought about by the comparative organizer to assist them in completing this task.

Activity 2

All the participants are teachers and therefore they will be required to write a lesson plan which will be used to teach a group of k-12 students on how to use their calculator in adding, subtracting and multiplying matrices.

All the participants are teachers and therefore they will be required to write a lesson plan which will be used to teach a group of k-12 students on how to use their calculator in adding, subtracting and multiplying matrices.

Integration

÷

÷

ø

ö

ç

ç

è

æ

5

4

3

3

4

5

÷

÷

÷

÷

÷

÷

ø

ö

ç

ç

ç

ç

ç

ç

è

æ

-

1

1

4

1

8

1

3

9

3

5

1

7

9

7

1

1

6

3

9

3

3

1

5

8

1