what is the future of the integration of ict in teaching mathematics

8/3/2019 What is the Future of the Integration of Ict In Teaching Mathematics

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Karolina Dobi Barii1, Ivanka eri

2, Ljerka Juki

3

12Faculty of Teacher Education, University of Osijek, Cara Hadrijana bb, 31000 Osijek,

CROATIA3Department of Mathematics, University of Osijek, Trg Lj. Gaja 6, 31000 Osijek, CROATIA

1

[email protected],2

[email protected],3

[email protected]

WHAT IS THE FUTURE OF THE INTEGRATION OF ICT INTEACHING MATHEMATICS

Abstract. In recent years the need for introducing information and communication

technology into the teaching process has posed one of the unavoidable changes in the

educational system. Present generation of students are so proficient in usage of the

information and communication technologies in their daily lives, that this change in the

educational system can not be viewed as an investment in a better future, but as a necessity in

order to keep pace with technology and students. Considering the integration of ICT inteaching mathematics, it is clear that the replacement of board and chalk with digital

presentation material does not cover all the aspects that technology and mathematics can

improve when working hand in hand.

One of the important prerequisites for quality integration of ICT in teaching mathematics is

the teachers personality, i.e. his knowledge, willingness and desire to improve his lessons

bringing mathematics closer to the present generations of pupils.

The aim of this paper was to investigate the readiness of the future mathematics teachers at

the elementary and high school levels to integrate ICT into their teaching of mathematics.

Factors influencing described readiness that are considered in this paper are teachers

university education and initiative with regard to personal digital competence andinfrastructure.

We conducted the survey research on the samples of individuals from the population of

students enrolled in final years of a five-year Master of Arts in Teaching Primary Education

programme at the Faculty of Teacher Education in Osijek, Croatia (n = 196), and Master of

Arts in Teaching Mathematics and Computer Science programme at the Department of

Mathematics in Osijek, Croatia (n = 36). The obtained results indicate that identified aspects

have impact on considered readiness and that teachers university education causes the

differences in the attitudes towards his digital competencies necessary for quality integration

of ICT in mathematics lessons.

Key words: teaching mathematics, ICT integration, teachers university education, teachers

initiative, digital competences.


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Introduction

Information and Communication Technology (abbreviation: ICT) has changed our daily

activities in many ways. Since these changes are evident amongst younger members of our

society, they are evident on primary and secondary schools students. Considering that ICT

plays an increasingly important role in society, especially if we take into account social,

economic and cultural role of computers and the Internet, it is clear that the time has come forthe actual entry of ICT in the field of education. The combination of ICT and the Internet

certainly opens many opportunities for creativity and innovation, but also for approaching the

teaching material to current generation of students.

Since some authors even in year 1980 predicted that till year 2000 the main methods of

teaching will include the application of computers at all levels and in all areas (Bork, 1980),

we can conclude that even 30 years ago the application of ICT in teaching was the subject of

study and research.

Visualisation of teaching materials facilitates understanding in mathematics and the use of

ICT tools facilitates appointed visualisation process. Therefore this paper deals with the

introduction of ICT in the teaching mathematics.

The future of the ICT integration into the teaching mathematics definitely depends on future

generations of mathematics teachers who are: (i) teaching primary education students who

will teach mathematics in the lower grades of primary education, (ii) teaching mathematics

students who will teach mathematics in the upper grades of primary education and in all

grades of secondary education. For that reason this survey research is conducted on the

sample of individuals from these two populations of students.

We assumed that university education is causing the difference in attitudes towards self-

initiatives focused on digital competences and infrastructure. Accordingly, in this study the

direction of that influence is investigated. Furthermore, we investigated how a university

education, and described self-initiatives affect the willingness of teachers to use ICT in

teaching mathematics.

The term competence involves the knowledge, skills and attitudes required for performing a

job. Special types of competences are digital competences that comprise safe and critical use

of ICT in work, leisure and communication (Mareti, 2010). Core digital competences

include using the multimedia technology to locate, access, storage, produce, present and

exchange of information and also to communicate and participate in the Internet network

(Ala-Mutka, 2008). As a final conclusion about digital competences, we can say that digital

competences include reliable and critical use of ICT for employment, learning, self-

development and participation in society (Mareti, 2010).

Study framework

Way that young teachers can contribute their knowledge about different forms of ICT use, the

Swedish associate professor at Linkping University, Sven Andersson, explored. The survey

was conducted in Swedish elementary schools, and as a final conclusion regarding to the

application of ICT in their work, teachers have found that new technologies improve their

attitude toward finding the knowledge to develop their own competences, finding teaching

materials and methodological ideas and the relationship between student and colleagues.


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Improving their digital competences gave them the idea and inspiration for the development

of teaching methods, their own knowledge of computers or, a starting point for the upcoming

ICT activities in schools (Andresson, 2006).

A study conducted by Sang, Valcke, van Braak and Tondeur shows the influence of gender,

constructivism beliefs, self-efficacy in teaching, self- efficacy in the use of computers and

attitude about computers. The study was conducted on 727 students of a Chinese university.The results showed that the potential integration of ICT is in correlation with all these

variables, except gender (Sang, 2010).

The paper by Drent and Mellissen discusses the influences that stimulate or limit the

innovative use of ICT by teachers in the Netherlands. Some of the factors that were studied

are: pedagogical approach, ICT competences and personal entrepreneurs. The results showed

that all these factors have an impact on innovation in the use of ICT. The authors conclude

that the ICT competences are requirement for the use of ICT in teaching, but that the

innovative use of ICT is affected by other factors (Drent, 2008).

In the area of Flanders (Belgium), unlike Great Britain and Canada, ICT competences are not

included in the national curriculum, just the guidelines for schools to focus innovative

educational processes in the process of integration of ICT into teaching are given. This studyexplores how, the school in general and teachers personally, conduct the new expectations

arising from these guidelines. Specifically, it examines the ICT competences that teachers

currently adopted (for actual use in teaching), and which competences they intend to adopt in

the future (prefer using them). Research has shown that the majority of teachers is familiar

with the concept of ICT, but still 2.6% of respondents has never use a computer, either in

class or preparing for teaching. Of the total number of hours per week spent at the computer,

most of them is related to professional help, then leisure and finally at teaching. The main

result of research shows that teachers in the primary education tend to increase and expand

their ICT competences (Tondeur, 2007).

Model, sample, data

The inception of this survey research is marked with the discussion about aspects of some

issues influencing teachers readiness to integrate ICT in teaching mathematics. It resulted in

establishing model of situation (Figure 1) and designing survey for collecting data about the

populations of interest.

Figure 1 Conceptual model


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Teachers self-initiatives taken with purpose of quality integration of ICT in teaching

mathematics were analyzed with respect to personal digital competence and infrastructure of

teacher himself. Digital competences were deliberated in terms of acquiring, holding,

developing and updating, and categorized as core and special. Holding core digital

competences were analyzed through possessing knowledge in following: fundamental

components of computer, basic Internet terms, using electronic mail, creating digital textual

and presentational materials, creating spreadsheets, drawing and image processing, creatingand publishing web-sites, and using Internet as additional source of information necessary for

creating teaching materials. Further, holding special digital competences were analyzed

through possessing knowledge and skills in using some specialized ICT tools appropriate for

integrating in mathematics lessons, such as IT board and educational mathematics software.

Specific attention was assigned to the existence of awareness about necessity of constant

developing and updating of digital competences. Teachers personal ICT equipment is

modelled by model variable digital infrastructure.

Method for data collecting employed in this research is an online survey. Data are obtained

from the samples of individuals from the population of students enrolled in final years of a

five-year Master of Arts in Teaching Primary Education programme at the Faculty of Teacher

Education in Osijek, Croatia (n = 196), and Master of Arts in Teaching Mathematics andComputer Science programme at the Department of Mathematics in Osijek, Croatia (n = 36).

232 responses were recorded from November 2010 till January 2011 from the sample of

individuals from the populations of interest. Sample structure is depicted in table below

(Table 1).

Feature Category Frequency Relative frequency (%)

Teaching primary education 196 84,48STUDYPROGRAMME Teaching mathematics 36 15,52

Table 1 Sample structure

Responds collected from the sample of individuals are discrete quantitative data that were

recorded on meaningful integer numerical scale from 1 to 5. They label a grade given to

certain statement, where 1 stands for I totally disagree and 5 stands for I completelyagree.

In table below (Table 2) statistical distribution of variables of interest, that model aspects of

teachers self-initiatives with respect to personal digital competences and infrastructure, is

described.

Relative frequencies of evaluationDescriptive statistics of

sampleConsidered feature

1 2 3 4 5 MeanStandard

deviation

Core digital competences 0,006705 0,021073 0,068966 0,144636 0,758621 4,627395 0,760839

Special digital competences 0,281609 0,100575 0,21408 0,217672 0,186063 2,926006 1,478185

Constant updating of digital competences 0,018103 0,064655 0,244828 0,326724 0,34569 3,917241 1,003039

ICT infrastructure 0,006466 0,036638 0,090517 0,19181 0,674569 4,491379 0,854369

Table 2 Statistical distribution of variables of interest


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Methodology

After obtaining data about variables of interest from the sample of individuals, we performed

statistical analysis directed to estimation of population mean and proportion as well as to

testing of hypothesis formulated on the basis of research hypotheses and with purpose of

making inferences about considered populations.

We estimated population mean and proportion based on a single sample from the population

of interest using large sample confidence intervals. Confidence level applied for the purpose

of this paper is 95%.

Tests of hypothesis are carried out by implementing the following steps (McClave et al.,

2001): (1) introduction of null hypothesis representing status quo, (2) introduction of

alternative hypothesis, (3) selection of appropriate test statistic, (4) determining the rejecting

region referring to the values of the test statistic considering level of significance , (5)

collecting data from the sample, (6) computing test statistic, (7) making decision whether to

reject null hypothesis, (8) making inference about population. Level of significance (-value)

of the tests conducted for the purpose of this paper is 0,05. In order to make inferences about

difference between two population means and proportions we performed large-sample tests of

hypothesis utilizingz-statistics.

Outcomes

This study investigates in what manner teachers university education influences the

assessment of self-initiatives directed to acquiring, holding, developing and updating own

digital competences and infrastructure.

From the data obtained from the sample of students we computed sample numerical

descriptive measures and estimated population mean utilizing 95% confidence interval for

previously mentioned aspects of self-initiatives. Results are depicted in table (Table 3, Table4) and they indicate that teaching mathematics students evaluated all considered aspects of

self-initiatives with greater grades than teaching primary education students.

Descriptive statistics of

sample

Confidence interval (95%)

for mean estimationConsidered feature

MeanStandard

deviation

Lower

bound

Upper

bound

Core digital competences 4,619615 0,770176 4,583649 4,655580

Special digital competences 2,876701 1,468281 2,792696 2,960705

Constant updating of digital competences 3,892857 1,002423 3,830019 3,955695

ICT infrastructure 4,461735 0,878015 4,374547 4,548922

Table 3 Descriptive statistics and confidence intervals for estimating mean for the sample of

teaching primary education students


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sample



MeanStandard

deviation

Lower

bound

Upper

bound

Core digital competences 4,669753 0,707465 4,592430 4,747076

Special digital competences 3,194444 1,506317 2,992427 3,396462

Constant updating of digital competences 4,050000 0,998742 3,903103 4,196897

ICT infrastructure 4,652778 0,695250 4,489402 4,816154Table 4 Descriptive statistics and confidence intervals for estimating mean for the sample of

teaching mathematics students

Quantitative data obtained from the samples of students are described by graphical method

utilizing numerical measures pth percentile and range (Figure 2) with respect to identified

categories of students.

0 1

UFOS

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

4,5

5,0

5,5

CORE

:

Median

25%-75%

Min-Max0 1

UFOS

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

4,5

5,0

5,5

SPECIAL

:

0 1

UFOS

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

4,5

5,0

5,5

UPDATING

:

Median

25%-75%

Min-Max0 1

UFOS

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

4,5

5,0

5,5

INFRASTRUCTURE

Figure 2Categorized box plot for aspects of self-initiativesFurthermore, we conducted large-sample one-tailed test for comparing two population means,

and thus compared respondents judgements of analyzed self-initiatives directed to digital

competences and infrastructure with respect to faculty education. The alternative hypothesis

represents the existence of a difference between the means of judgements of analyzed self-

initiatives in favor of teaching mathematics students. This hypothesis is designed on the basis

of previous discussion. From results depicted in table (Table 5) at = 0,05 we conclude: (i)

the samples do not provide sufficient evidence for us to conclude that there is a statistically

significant difference between considered means, (ii) there is a statistically significant


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difference in means of judgements of last three aspects of analyzed self-initiatives in favor of

teaching mathematics students.

Considered feature p-value = 0,05 z z = 1,644854 H0

Core digital competences 0,12383 p > 1,15604 z < z not reject

Special digital competences 0,00211 p < 2,86061 z > z reject

Constant updating of digital competences 0,026241 p < 1,939156 z > z reject

ICT infrastructure 0,020156 p < 2,050542 z > z reject

Table 5 Results obtained from the one-tailed test for comparing two population means of

judgements of analyzed self-initiatives with respect to faculty education

In addition we analyzed closely each of previously introduced aspects of self-initiatives by

computing sample numerical descriptive measures and estimating population mean utilizing

95% confidence interval (Table 6, Table 7).


sample



MeanStandard

deviation

Lower

bound

Upper

bound

Having knowledge in fundamental components of computer 4,571429 0,771279 4,462777 4,680080

Having knowledge in basic Internet terms 4,760204

0,504999

4,689064

4,831344

Having knowledge in using electronic mail 4,877551 0,372526 4,825073 4,930029

Having knowledge in creating digital textual document 4,903061 0,359188 4,852462 4,953661

Having knowledge in creating digital presentational materials 4,877551 0,411758 4,819546 4,935556

Having knowledge in creating spreadsheets 4,397959 0,919752 4,268392 4,527526

Having knowledge in drawing and image processing 4,448980 0,854820 4,328560 4,569400

Having knowledge in creating and publishing web-sites 3,658163 1,185591 3,491147 3,825179Having knowledge in using Internet as additional source of information

necessary for creating teaching materials4,816327 0,482450 4,748363 4,884290

Necessity of having knowledge and skills in utilizing IT board 3,790816 1,053501 3,642408 3,939225Necessity of having skills in applying some educational mathematicssoftware

4,112245 0,904492 3,984828 4,239662

Personal ability of working in Geometer's Sketchpad-u 3,448980 1,087198 3,295824 3,602135

Personal ability of working in GeoGebra 2,316327 1,293748 2,134074 2,498579Personal ability of working in Wolfram Mathematica 1,301020 0,720540 1,199517 1,402524

Personal ability of working with IT board 1,923469 1,163223 1,759604 2,087335Updating of digital competence of mathematics teachers is necessary forproper application of ICT tools in teaching.

3,811224 0,877103 3,687666 3,934783

In order to update own ICT skills and to integrate ICT tools in

appropriate way in teaching, the mathematics teachers should regularly

read the relevant IT publications.

3,678571 1,054295 3,530051 3,827092

In order to update own ICT skills and to integrate ICT tools inappropriate way in teaching, the mathematics teachers should regularlymonitor the relevant web portals.

3,750000 1,019678 3,606356 3,893644

In order to update own ICT skills and to integrate ICT tools inappropriate way in teaching, the mathematics teachers should attend

computer science seminary.

4,112245 0,975417 3,974836 4,249654


appropriate way in teaching, the mathematics teachers should self-initiative and independently study ICT tools.

4,112245

1,001360

3,971182

4,253308

The prerequisite for quality preparing of mathematics lessons is owning apersonal computer (at home).

4,469388 0,879441 4,345499 4,593276

The prerequisite for quality preparing of mathematics lessons is having

Internet access (at home).4,454082 0,878772 4,330288 4,577876


teaching primary education students


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sample



MeanStandard

deviation

Lower

bound

Upper

bound

Having knowledge in fundamental components of computer 4,583333 4,349266 4,817401 0,691789

Having knowledge in basic Internet terms 4,805556 4,647486 4,963625 0,467177

Having knowledge in using electronic mail 4,972222 4,915830 5,028614 0,166667

Having knowledge in creating digital textual document 4,972222 4,915830 5,028614 0,166667Having knowledge in creating digital presentational materials 4,972222 4,915830 5,028614 0,166667

Having knowledge in creating spreadsheets 4,888889 4,781047 4,996731 0,318728

Having knowledge in drawing and image processing 4,722222 4,548541 4,895903 0,513315

Having knowledge in creating and publishing web-sites 4,611111 4,392914 4,829308 0,644882Having knowledge in using Internet as additional source of informationnecessary for creating teaching materials

4,944444 4,831661 5,057228 0,333333

Necessity of having knowledge and skills in utilizing IT board 4,138889 3,845558 4,432220 0,866941Necessity of having skills in applying some educational mathematics

softwares4,666667 4,485810 4,847523 0,534522

Personal ability of working in Geometer's Sketchpad-u 4,083333 3,849266 4,317401 0,691789

Personal ability of working in GeoGebra 3,361111 2,861523 3,860699 1,476536

Personal ability of working in Wolfram Mathematica 3,166667 2,783012 3,550321 1,133893

Personal ability of working with IT board 1,750000 1,412859 2,087141 0,996422Updating of digital competence of mathematics teachers is necessary for

proper application of ICT tools in teaching.

3,972222 3,736607 4,207837 0,696362


appropriate way in teaching, the mathematics teachers should regularlyread the relevant IT publications.

3,777778 3,406153 4,149402 1,098339

In order to update own ICT skills and to integrate ICT tools inappropriate way in teaching, the mathematics teachers should regularly

monitor the relevant web portals.

3,861111 3,463615 4,258607 1,174802


appropriate way in teaching, the mathematics teachers should attendcomputer science seminary.

4,083333 3,727317 4,439349 1,052209

In order to update own ICT skills and to integrate ICT tools inappropriate way in teaching, the mathematics teachers should self-

initiative and independently study ICT tools.

4,555556 4,306992 4,804119 0,734631

The prerequisite for quality preparing of mathematics lessons is owning a

personal computer (at home).4,666667 4,424022 4,909311 0,717137

The prerequisite for quality preparing of mathematics lessons is having

Internet access (at home).4,638889 4,407948 4,869830 0,682549


teaching mathematics students

In addition for each of the previously introduced aspects of self-initiatives we performed

large-sample test for comparing two population means of judgements of analyzed self-

initiatives. The alternative hypothesis represents the existence of a difference between the

means in favor of teaching mathematics students. At = 0,05 we revealed:

The samples do not provide sufficient evidence for us to conclude that there is astatistically significant difference between means of grades for necessity of having

knowledge in fundamental components of computer and basic Internet terms (p=0,46289;p=0,29858). The necessity of acquiring and/or holding all other considered core digital

competences is evaluated statistically significant higher by teaching mathematics students

than by teaching primary education students (p < ).

The necessity of acquiring and/or holding all by this paper covered special digitalcompetences is evaluated statistically significant higher by teaching mathematics students

than by teaching primary education students (p < ).


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Both categories of students equally recognized the necessity for constant updating of

digital competences by reading ICT publication and attending ICT educations (p > ).

Teaching mathematics students evaluated statistically significant higher the necessity ofself-initiative and individual studying of ICT tools with purpose of updating ICT skills

and quality integration of current ICT tools in teaching mathematics (p=0,000885).

The samples do not provide sufficient evidence for us to conclude that there is a

statistically significant difference between means of grades for necessity of owning a

personal computer and having Internet access (p=0,072; p=0,07746) in order to prepare

mathematics lessons.

Afterwards, respondents evaluated if their self-initiatives, that they are taking in order to

update their knowledge, skills and digital infrastructure, made them ready to utilize ICT in

teaching mathematics. Using large-sample 95% confidence interval we estimated population

mean for described readiness. In that manner we obtained intervals [3,776023; 4,335088] and

[3,501265; 3,784449] for teaching mathematics and teaching primary education students,

respectively. Besides we conducted large-sample test for comparing two population means of

previously mentioned evaluation. The alternative hypothesis represents the existence of a

difference between the means of that evaluation in favor of teaching mathematics students.

This hypothesis is designed considering previous analysis. Gained result (p=0,003934) at =

0,05 reveals that there is a statistically significant difference in means of evaluation of

analyzed readiness influenced by taken self-initiatives in favor of teaching mathematics

students.

Ultimately, by utilizing large-sample 95% confidence interval for a population proportion we

estimated the proportions of students who are ready to integrate ICT in teaching mathematics,

i.e. those students whose grade for identified readiness is at least 4. Thus we gained intervals

[0,54397; 0,84492] and [0,48656; 0,62568] for teaching mathematics and for teaching

primary education students, respectively. Utilizing the same method we estimated the

proportions of students who are not ready to integrate ICT in teaching mathematics, i.e. those

students whose grade for identified readiness is at most 2. Thus we gained interval [0,07229;

0,162404] for teaching primary education students, while in the sample of teaching

mathematics students there is no such student. Furthermore we conducted large-sample test of

hypothesis for comparing two population proportions of the students who are and are not

ready to integrate ICT in teaching mathematics. The alternative hypothesis represents the

existence of a difference between mentioned proportions in favor of teaching mathematics

students and teaching primary education students, respectively. This hypothesis is designed

considering previous analysis. Gained results (p=0,054888486; p=0) at = 0,05 reveal the

following: (i) samples provide insufficient evidence to detect the difference between the

proportions of the students who are ready to integrate ICT in teaching mathematics, (ii)

proportion of the students who are not ready to integrate ICT in teaching mathematics is

statistically significant greater in the population of teaching primary education students thanin the population of teaching mathematics students.

Conclusion

The results obtained in this study indicate that faculty education causes differences in attitudes

towards self- initiative focused on digital competences and infrastructure. We have shown that

higher levels of computer education causes more positive attitudes about the application of


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considered self-initiative, as we expected. The teaching program of primary education study

covers less computer science areas and covers them at a lower level than a program of

mathematics teacher study, it is expected that teaching mathematics students will better

evaluate the self-initiative focused on digital competences and infrastructure, which was

shown in this research.

However, we must emphasize that the teaching primary education students and teachingmathematics students recognized the need of constant actualization of digital competences by

following the appropriate computer science publications and participation in education. This

finding gives us the right to claim that the teaching primary education students are directed

towards in terms of IT training, because the awareness of the necessity of the update

knowledge and skills is extremely important in working with ICT tools.

We will endeavour to follow the difference in this work considered phenomena between these

two populations of interest. Considering the fact that ICT increasing its part in the teaching

process, students themselves should understand that their digital competences are bond that

binds them to the creative and innovative application of ICT in teaching. This research is the

starting point of a larger study which is planned to cover different populations of future and

current teachers of mathematics at the elementary and high school level.

References

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school: tutor, tool, tutee (New York, Teachers College Press).

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what is the future of the integration of ict in teaching mathematics

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