# WHAT IS THE FUTURE OF THE INTEGRATION OF ICT IN TEACHING MATHEMATICS

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Karolina Dobi Bariši 1, Ivanka eri2, Ljerka Juki 3 12 Faculty of Teacher Education, University of Osijek, Cara Hadrijana bb, 31000 Osijek, CROATIA 3 Department of Mathematics, University of Osijek, Trg Lj. Gaja 6, 31000 Osijek, CROATIA 1 kdobi@ufos.hr, 2idjeri@ufos.hr, 3ljukic@mathos.hr WHAT IS THE FUTURE OF THE INTEGRATION OF ICT IN TEACHING 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 in teaching 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 teacher’s 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 teacher’s university education and initiative with regard to personal digital competence and infrastructure. 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 teacher’s 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, teacher’s university education, teacher’s initiative, digital competences.

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 for the 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 (Mar eti , 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 (Mar eti , 2010). Study framework Way that young teachers can contribute their knowledge about different forms of ICT use, the Swedish associate professor at Linköping 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. 2

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 study explores 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 3

Teacher’s 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, creating and 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. Teacher’s 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 and Computer 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 (%) STUDY Teaching primary education 196 84,48 PROGRAMME 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 completely agree”. In table below (Table 2) statistical distribution of variables of interest, that model aspects of teacher’s self-initiatives with respect to personal digital competences and infrastructure, is described. Descriptive statistics of Relative frequencies of evaluation sample Considered feature Standard 1 2 3 4 5 Mean 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 4

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 utilizing z-statistics. Outcomes This study investigates in what manner teacher’s 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, Table 4) 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 Confidence interval (95%) sample for mean estimation Considered feature Standard Lower Upper Mean deviation bound 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 5

Descriptive statistics of Confidence interval (95%) sample for mean estimation Considered feature Standard Lower Upper Mean deviation bound 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 4,816154 Table 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. Bo x & Wh i ske r Plo t: POSEBNO 5 ,5 5 ,5 5 ,0 5 ,0 4 ,5 4 ,5 4 ,0 4 ,0 3 ,5 3 ,5 SPECIAL CORE 3 ,0 3 ,0 2 ,5 2 ,5 2 ,0 2 ,0 1 ,5 1 ,5 1 ,0 1 ,0 M ed ia n 0 ,5 0 ,5 25 %-7 5 % 0 1 0 1 M in -M a x UFOS UFOS B o x & Wh iske r P lo t: A K T UA L IZA CIJA B o x & Wh iske r P lo t: INFRA S T RUK T URA 5,5 5 ,5 5,0 5 ,0 4,5 4 ,5 4,0 4 ,0 INFRASTRUCTURE 3,5 3 ,5 UPDATING 3,0 3 ,0 2,5 2 ,5 2,0 2 ,0 1,5 1 ,5 1,0 1 ,0 M ed i an 0,5 0 ,5 25 %-75 % 0 1 0 1 M in -M a x UFOS UFOS Figure 2 Categorized box plot for aspects of self-initiatives Furthermore, 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 6

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 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). Descriptive statistics of Confidence interval (95%) sample for mean estimation Considered feature Standard Lower Upper Mean deviation bound 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 3,825179 Having knowledge in using Internet as additional source of information 4,816327 0,482450 4,748363 4,884290 necessary for creating teaching materials Necessity of having knowledge and skills in utilizing IT board 3,790816 1,053501 3,642408 3,939225 Necessity of having skills in applying some educational mathematics 4,112245 0,904492 3,984828 4,239662 software 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 2,498579 Personal 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 2,087335 Updating of digital competence of mathematics teachers is necessary for 3,811224 0,877103 3,687666 3,934783 proper application of ICT tools in teaching. In order to update own ICT skills and to integrate ICT tools in appropriate way in teaching, the mathematics teachers should regularly 3,678571 1,054295 3,530051 3,827092 read the relevant IT publications. In order to update own ICT skills and to integrate ICT tools in appropriate way in teaching, the mathematics teachers should regularly 3,750000 1,019678 3,606356 3,893644 monitor the relevant web portals. In order to update own ICT skills and to integrate ICT tools in appropriate way in teaching, the mathematics teachers should attend 4,112245 0,975417 3,974836 4,249654 computer science seminary. In order to update own ICT skills and to integrate ICT tools in appropriate way in teaching, the mathematics teachers should self- 4,112245 1,001360 3,971182 4,253308 initiative and independently study ICT tools. The prerequisite for quality preparing of mathematics lessons is owning a 4,469388 0,879441 4,345499 4,593276 personal computer (at home). The prerequisite for quality preparing of mathematics lessons is having 4,454082 0,878772 4,330288 4,577876 Internet access (at home). Table 6 Descriptive statistics and confidence intervals for estimating mean for the sample of teaching primary education students 7

Descriptive statistics of Confidence interval (95%) sample for mean estimation Considered feature Standard Lower Upper Mean deviation bound 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 0,166667 Having 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 0,644882 Having knowledge in using Internet as additional source of information 4,944444 4,831661 5,057228 0,333333 necessary for creating teaching materials Necessity of having knowledge and skills in utilizing IT board 4,138889 3,845558 4,432220 0,866941 Necessity of having skills in applying some educational mathematics 4,666667 4,485810 4,847523 0,534522 softwares 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 0,996422 Updating of digital competence of mathematics teachers is necessary for 3,972222 3,736607 4,207837 0,696362 proper application of ICT tools in teaching. In order to update own ICT skills and to integrate ICT tools in appropriate way in teaching, the mathematics teachers should regularly 3,777778 3,406153 4,149402 1,098339 read the relevant IT publications. In order to update own ICT skills and to integrate ICT tools in appropriate way in teaching, the mathematics teachers should regularly 3,861111 3,463615 4,258607 1,174802 monitor the relevant web portals. In order to update own ICT skills and to integrate ICT tools in appropriate way in teaching, the mathematics teachers should attend 4,083333 3,727317 4,439349 1,052209 computer science seminary. In order to update own ICT skills and to integrate ICT tools in appropriate way in teaching, the mathematics teachers should self- 4,555556 4,306992 4,804119 0,734631 initiative and independently study ICT tools. The prerequisite for quality preparing of mathematics lessons is owning a 4,666667 4,424022 4,909311 0,717137 personal computer (at home). The prerequisite for quality preparing of mathematics lessons is having 4,638889 4,407948 4,869830 0,682549 Internet access (at home). Table 7 Descriptive statistics and confidence intervals for estimating mean for the sample of 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 a statistically 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 digital competences is evaluated statistically significant higher by teaching mathematics students than by teaching primary education students (p < ). 8

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 of self-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 than in 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 9

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 teaching mathematics 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 [1] Ala-Mutka, K., Punieand, Y., Redecker, C., (2008). Digital Competence for Lifelong Learning, European Commission, Joint Research Centre, Institute for Prospective Technological Studies [2]Andersson S. (2006). Newly qualified teachers’ learning related to their use of information and communication technology: a Swedish perspective. British Journal of Educational Technology, 37(5), 665-682 [3] Bork, A. (1980) Learning through graphics, in: R. Taylor (Ed.) The computer in the school: tutor, tool, tutee (New York, Teachers College Press). [4] Drent M., Mellissen M. (2008). Which factors obstruct or stimulate teacher educators to use ICT innovatively?. Computers and Education, 51, 187-199 [5] Marceti A., Krstanovi I., Uzelac Z., (2010). Klju ne kompetencije za cjeloživotno u enje – digitalne kompetencije. CARNetova korisni ka konferencija – CUC [6] McClave, J. T., Benson, P. G., Sinncich, T. (2001), Statistics for business and economics, Prentice Hall [7] Sang G., Valcke M., van Braak J., Tondeur J. (2010). Student teachers’ thinking processes and ICT integration: Predictors of prospective teaching behaviours with educational technology. Computers and Education, 54, 103-112 [8] Tondeur J., Valcke M., van Braak J. (2007). Curricula and the use of ICT in education: Two worlds apart?. British Journal of Educational Technology, 38(6), 962–976 10

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