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.
2Improving 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
3Teacher’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
4Methodology
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
5Descriptive 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
6difference 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
7Descriptive 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 < ).
8Both 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
9considered 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.
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