Evaluating the effectiveness of the implemented models of ICT tools in teaching mathematics.

Vrdoljak, Anton ; Banjanin, Milorad ; Rakic, Kresimir 等

1. INTRODUCTION

Analyzing and evaluating the effectiveness of some implemented models of ICT tools in teaching mathematics, regarding the teaching of complex numbers and interactive geometry, are problems of this paper.

The last decade of the 20th and the beginning of 21st century has marked by the so-called digital revolution that has made major changes in the world. These changes comes as a consequence of technological progress, notably the progress of information and communications technology (ICT), which greatly affects the education and radically changing the existing process of teaching and learning in general. It is therefore understandable that one of the most current subjects in contemporary issues of teaching mathematics are teaching process and learning of mathematics supported by ICT, among them an important place belongs to the evaluation of the implementation models of ICT tools in the teaching process of mathematics.

Thinking about the differences between teaching process and learning of mathematics supported by ICT and traditional teaching process and learning of mathematics, suggests that teaching process and learning of mathematics supported by ICT has advantages or preferabilities over traditional teaching process and learning of mathematics.

The main reasons why we choose these subjects lies in our beliefs that by teaching process and learning of mathematics supported by ICT the student actually become a centre of the educational process, obtains information from various sources, progress in acquiring new knowledge pace that suits his abilities and knowledge and thoroughly understand the master content of the curriculum.

However, highlighting the advantages or disadvantages are not enough. Furthermore, no single paradigm is right for all situations--content domain, subject matter, target learners, type of assessments and the physical or virtual environment all play roles. Therefore, to ensure a greater or lesser effectiveness of some methods of teaching process or models of learning, it is necessary to conduct a research on the effectiveness of these methods of teaching process (models of learning), which is to be one of the goals of this paper. In our research we encountered some limitations that may have a significant impact on the obtained results. One of these limitations is the fact that the experiment was conducted with a group of students on a voluntary basis.

2. PROBLEM OVERVIEW

With the belief that learning theory should contribute to the delivery and practice of learning, DeVilliers advocates so-called the Hexa-C Metamodel (HCMm), what is an approach that integrates six interrelated concepts from contemporary learning theory: cognitive learning, constructivism, components, creativity, customization, and collaborative learning--into a framework that serves both as a design aid and as an evaluation approach for investigating existing resources from the perspective of learning theory (DeVilliers, 2007).

Three of C's: constructivism, cognitive learning, and components, are mainly theoretical components, while the others: collaborative learning, creativity, and customization, are practical methods used by educators to foster effective and affective learning. Figure 1 shows the hexagonal framework of the HCMm, representing its inter-related elements as merging segments around the hub of the technology as a means of delivery and emphasizing the importance of environment by embedding the whole within context.

According to DeVillier, when developing or investigating a particular environment or artefact, the educator, educational web developer, instructional designer, or evaluator should carefully consider the six elements, determining which are relevant to the content and context (DeVilliers, 2007). They should then consider to what extent, and in what ways, those elements could be optimally implemented. In other words, they should ensure that technology serves as a hub that delivers the message and does not distract or detract from the message.

The design, development, implementation and evaluation of e-learning can be enhanced by considering HCMm elements and applying those appropriate to the context. No single paradigm is appropriate--no 'one size fits all'--but its elements can be translated into principles, design guidelines, and evaluation criteria for different domains and subject matter.

[FIGURE 1 OMITTED]

According to Bates there are several quality factors in the educational content supported by technologies. In the context of higher education institutions, they are content, multimedia production, instructional design and implementation and support for students (Bates & Poole, 2003). These elements should not be restricted only to educational contents (materials) supported by technologies in higher education institutions. Their significance also, with minor modifications, may reflect the quality in the context of secondary education through the use of e-education.

3. IMPLEMENTATION MODELS OF ICT TOOLS IN TEACHING OF COMPLEX NUMBERS AND INTERACTIVE GEOMETRY

The text that follows will shortly describe some implemented models of ICT tools in teaching mathematics, and planning research and implementation of experiment. Within one year of educational-research project conducted at the Faculty of Civil Engineering, University of Mostar, we developed many modules or e-learning environments for teaching mathematics on level of secondary and high schools. These modules, written in Croatian, follow the ideas mentioned in problem overview, as well as other developed modules (Vrdoljak et al., 2006). In this paper we analyzed and evaluated the effectiveness of these two modules:

* Complex numbers, placed on following address: http://www. gfmo.ba/kompleksni_brojevi/

* Interactive geometry, placed on following address: http://www.gfmo.ba/giak/

First of them is already described in detail in one other scientific paper (Vrdoljak, 2009), and second too. These works point only some of the educational potentials and possibilities afforded with implemented models of ICT tools. Because our awareness regarding huge transformations of the workplace for teaching and learning of mathematics with an implemented models of ICT tools, for a main goal in our educational-research project we set an examination--has developed learning and teaching contents fully accomplish the profit of advantage of learning and teaching with an implemented models of ICT tools, and a determination--how to maximize motivational impact from ICT?

For the sample on which we have carried out research and realized the experiment, we chose a group from a total of 105 students (the first year of undergraduate civil engineering study in an academic 2008/2009 year at the Faculty of Civil Engineering, University of Mostar). Students were assigned codes, and were divided into experimental (52 students) and control group (53 students), by a random selection.

The experimental group had one week of teaching and learning on a set of complex numbers and geometry based on the module of complex numbers and interactive geometry (implemented models of ICT-tools). The control group did not have access to these modules, and has learned and been taught (traditionally) from a previously received text material (literature).

Upon completion of both weeks students of the experimental group together with students of the control group wrote so-called flash-test regarding the content of complex numbers and geometry. The test was evaluated with points from 0 to 43, to see if there is any difference in knowledge, or the speed of answering, consistency and safety in response between the experimental and control groups, or to see are the teaching and learning based on the implemented models of ICT tools (the modules of complex numbers and interactive geometry) more efficient than traditional teaching and learning in the process of teaching mathematics.

4. RESULTS

Analysis of the results begins with the determination of whether there is a statistically significant difference between control (in Table 1. control group is marked as G2) and experimental groups (in Table 1. experimental group is marked as G1) in the results regarding the flash-test. In this regard, the first step is to set null hypothesis for the results from the flash-test H: There are no statistically significant differences between experimental and control groups in the results of flash-test.

As seen in table 1, value t = 5.65 is greater than 1.96, and value p = 0.000 is less than 0.05, so the hypothesis H0 is rejected (not accepted) and concludes that there is a statistically significant difference between the experimental and control groups in the results of flash-test. Therefore, according to the results of t-test, we can conclude that any differences between the experimental and control groups could not arise as a result of errors, or it could be coincidental.

5. CONCLUSION

These general findings are in accordance with results of some other referred authors (Christmann & Badgett, 2000). It is obviously that this result we can thanks mainly to the integration and implementation of observed models of ICT tools in teaching mathematics. Technology brings to pupils and their teachers the opportunity to individualize learning--to generate illustrative examples, as well as dynamic and rich presentation of a given subject, to follow interesting topics to the desire depth, to choose their own problems and appropriate tools for solving them. For our further research we will develop an interactive educational web-portal with different mathematical contents. Comparing with other countries in our neighbourhood, Bosnia and Herzegovina has to move over a long way to reach them.

6. REFERENCES

Bates, A. W. & Poole, G. (2003). Effective teaching with technologies in higher education: Foundation for success, Jossey-Bass, ISBN 0-7879-6034-9, San Francisco

Christmann, E. P. & Badgett, J. L. (2000). The comparative effectiveness of CAI on collegiate academic performance. Journal of Computing in Higher Education, Vol. 11, No. 2, (March, 2000) 91-103, ISSN 1042-1726

DeVilliers, M. R. (2007). The Six C's Frameworks for e-Learning, In: Advanced principles of effective e-learning, Buzzeto-More, N. A., (Ed.), 1-25, Informing Science Press, ISBN-10 1-932886-02-8, Santa Rosa

Vrdoljak, A.; Aoyama, K.; Yahara, H. & Isoda, M. (2006). Development of Mathematics Learning Contents with ICT Focused on Complex Number Contents of "Interactive Lessons", Proceedings of the 30th annual meeting of JSSE, Vrdoljak, A. (Ed.), 265-266, ISSN 0913-4476, Tsukuba, August 2006, Japanese Society for Science Education JSSE, Tsukuba

Vrdoljak, A. (2009). Implementation models of ICT in teaching of complex numbers, Proceedings of the 3rd Nordic EWM Summer School for PhD Students in Mathematics, Vrdoljak, A. (Ed.), 251-256, ISBN 978-952-12-2278-8, Turku, June 2009, Turku Centre for Computer Science, Turku

Tab. 1. Results of the t-test, arithmetic mean and standard
deviation for the flash-test

G1 Std. Std.
vs. Mean Mean Dev. Dev. F-ratio
G2 G1 G2 t-value P G1 G2 Var. p Var.

 19.798 9.830 5.650 0.000 9.882 8.126 1.479 0.163