Mathematics and computer-aided learning.

Abstract

This study examines two groups (one group as a control) of secondary school students and studies the effects of using the computer as a tool for teaching and learning on their performances. A mathematical teaching and learning tool, TRANSLAB is developed and evaluated with the students. One group of student follows the same content in a classroom-led instructional setting while the other group used the TRANSLAB tool for learning the same content. At the end of the experiment, both groups are tested using a common test paper and student feedbacks are obtained via survey forms. We conclude that there is no significant difference in the performance of the students subjected to both approaches. However, the pilot students who used the computer-aided tool displayed more confidence in translation concepts and more positive attitudes towards mathematics.

Introduction

With the traditional way of teaching Mathematics especially the Transformation topics, we have noticed that many students had difficulties in understanding the whole concept itself. The transformation topics deal with subtopics like rotation, reflection, translation, enlargement, sheer and stretch. Transformation, for instance essentially deals with finding the geometrical position of an object when it is displaced, or its new size when it is enlarged by a multiplying factor. Moreover, an assessment given to the Form V students of the Manilall Doctor State Secondary School in Mauritius showed that the majority of students were unable to achieve the passing mark, out of 30 students only five passed. In line with the Government vision of Mauritius becoming a cyber-island and the School Information Technology Project (SITP), which is about equipping the 600 primary and secondary schools of Mauritius with networked computer labs and computers running educational software, this study aims to investigate how technology can be used to effectively help students in understanding concepts better and in a more innovative way. This study is therefore designed to investigate whether computer-aided learning will help students learn and perform better than when they are taught in traditional classroom settings. We also aim to see students' responses and motivation towards using computers as a tool to help them in enhancing their learning experience. In this context, a mathematical teaching and learning tool, TRANSLAB is developed and evaluated with the students. One group of student follows the content in a classroom-led instructional setting while the other group used the TRANSLAB tool for learning the same content. At the end of the experiment, both groups are tested using a common test paper and student feedback is obtained via survey forms.

Computer Aided Learning (CAL): Application to Mathematics

Computer-aided learning (CAL), which is becoming widely available as an instructional medium, seeks to individualize the teaching and learning process so that learning is more effective (Askar et al., 1992). The aim is to provide the learners with an environment that is tailored to their learning needs and goals (Clancey & Soloway, 1990). Current reforms in mathematics education have proposed infusing the mathematics curriculum with technology and creating technology-intensive instructional environments. The Principles and Standards for School Mathematics Discussion Draft (1989) from the National Council of Teachers of Mathematics (NCTM) of the United States outlines six guiding principles for school mathematics instructional programs. According to NCTM's Technology Principle:

   Mathematics Instructional programs should use technology to help all
   students understand mathematics and should prepare them to use
   mathematics in an increasingly technological world.

Mathematics curricular programs should promote students who are seen as low performing students as well as high performing students. It is good to note that the use of the term "performing" denotes a dynamic view of the students as active learners. One of the advantages of computer-aided learning is that it is well suited to offer help in the area of remedial teaching because of its flexibility, i.e. course modules incorporating varying levels of expertise, and drill and practice exercises (McDonough et al. 1994b). In our context, the development of such a package may help as remedial education especially for those encountering problems in understanding the transformation concepts. Furthermore CAL allows the students to work at their own pace. Different students may have difficulty with different concepts. Fast learners can go ahead (McDonough et al., 1994a). The students are allowed to spend more time on areas with which they have difficulty. Students may concentrate on specific areas without holding up the rest of the group.

TRANSLAB: A Description of the System

TRANSLAB has been developed using the MATHLAB package, which is a specialized mathematics software tool. The system consists of a student module also known as a student model and a tutoring module. The student module allows the system to store relevant knowledge about the student and to use this stored knowledge to adapt the instructional content of the system to the student's needs. The student model in TRANSLAB is a simple overlay model and uses simple performance measuring to evolve itself. On the other hand, the tutoring module contains teaching strategies and essential instructions to guide the learning path of the student. The principal purpose of this module is to reduce the knowledge differences between the expert and the student to a minimum or to none. It controls the presentation, ordering and selection of material most appropriate for the student. Moreover it is able to answer questions from the student and it determines which type of help should be given to students. A student can use TRANSLAB in two modes: the tutoring mode and the test mode. The tutoring mode allows the student to follow the instructions for the subject and is subject to simple questions after each section completed. Finally, in the test mode, the student may take a test on a single chapter or a test for the whole subject.

Adaptability and Adaptivity in TRANSLAB The concept of 'adaptation' is an important issue in research for learning systems (Nikov and Pohl, 1999). TRANSLAB is an interactive tool whose prototype student model considers both the adaptive and adaptable techniques (Patel & Kinshuk, 1997). Initially when students branch into the testing phase, two options are offered. This is an adaptable method where he has to choose either the graphical or a non-graphical method of testing. After the proper selection of the desired method, two options are presented. The first option is an adaptable method, which provides the user full access to choose the level and types of questions desired. The second option is an adaptive method where the learner has no control on the types and level of questions to be asked. In fact, the system provides questions from a lower to higher level. If the student fails to satisfy a certain criteria, he may even be downgraded to a lower level.

Scaffolding techniques in TRANSLAB Scaffolding is an instructional technique whereby the teacher models the desired learning strategy or task, then gradually shifts responsibility to the students. Clay and Cazden (1992) point out two scaffolding strategies in teaching reading: working with new knowledge and accepting partially correct responses. TRANSLAB aims at making students understand the subject with initially a lot of support like tutoring help. In fact, it offers specific help to the student when he or she is stuck with a particular problem. As the student's understanding of the subject increases, the support by the tool decreases and thus allowing the user to take his own decision.

The Problem

It has been observed through assessment exercises, that there is a lack of motivation and interest in Mathematics Learning from students in our Secondary Schools. In this paper, we shall address the following research questions:

1. Does a computer-based mathematical tool help secondary school students to enhance their knowledge in numerical subjects like Mathematics and thus increase their performance?

2. Does technology-intensive instruction help in reshaping and improving students' attitudes towards mathematics education?

3. The significance of the effects of computer-aided instruction on a group that used CAL modules for learning compared with a control group that received traditional classroom-based instruction.

We choose two groups of students of the same class (Form IV) and classify them randomly to form part of each group. The first group also known as the control (n = 31) follows traditional classroom based instruction on the topic. The experimental group (n = 30) follows the instruction using the computer-aided learning tool. A test paper is given to the students to test whether there is significant difference in their performance and a summative evaluation of the TRANSLAB tool is carried out using a questionnaire that has been given to the students who used the tool. The two hypotheses we set out in this research study are the following:

HO (1): There will be no statistically significant difference between the experimental group test scores and the control group test scores in math.

HO (2): There will be no statistically significant difference when comparing students' perceptions of their own motivation toward math class when comparing technology based and traditional teaching methods.

The control group was taught using the same traditional classroom-based instructional method. The teacher explained to students how to do a particular kind of problem, given time to practice, and then assigned homework. For the experimental group, a different approach was adopted to the teaching of the Translation topic. Students were asked to go through the lessons and practice the examples of TRANSLAB for four weeks on a 1 hour/week duration. They were also given ample time to go through the self-assessment problems in TRANSLAB. They were allowed to go over the material again if they felt the need for it. The same content was taught to the control group in the classroom for four weeks on a one-hour tutoring per week. In the first half-hour the teacher explains the concepts and carries out sample questions while the next half-hour is left for classroom practice.

Results

Graph of error plot of test scores for both the control and experiment We plotted a graph of error of test scores and found that we had a larger variation of the marks scored by the control group than did those of the experimental one. However, the mean score of the experimental group was higher than that of the control. This might show us that may be the technology has an impact on the performance.

One-way Analysis of Variance (ANOVA) From the ANOVA testing, the mean of the experimental group is ~ 22.60, is slightly higher than that of the control group, which is ~ 22.16. Furthermore, the experimental group has a minimum standard error of 0.518 compared to 0.685. Assuming homogeneity of variances, the ANOVA test was performed. From the analysis, we noted that the F-statistic is 0.259 with p-value equal to 0.613. Hence we concluded that the F-statistic value is large inside the region of acceptance and therefore we could not reject HO, which states that there is no significance difference between the two groups. Thus the analysis of variance showed that there is no significant effect of the technology in the performance of the experimental group when compared to the control group.

Chi-square Tests For processing of the survey results, we used chi-square tests to draw out the conclusions. The first question, "Do you prefer to learn math from the classroom or using computers?" had twenty students respond that they would prefer computers. This produced a chi-square of 9.314. With two degrees of freedom and an alpha level of .05, the critical value of chi-square is 5.99. Therefore, we can reject the null hypothesis HO and safely assume that students prefer to learn using computers. However, the question, "Would you like to see all subjects taught using computers?" had fifteen students respond 'yes'. This produced a chi-square of 5.00. With two degrees of freedom and an alpha level of .05, the critical value of chi-square is 5.99. Therefore, we may postulate that students would not prefer to learn all subjects by using a computer-aided learning tool. The question, "Is mathematics more fun to learn in the classroom or with the computer?" had twenty-five students respond that they have more fun using computers. This produced a chi-square of 15.27. With two degrees of freedom and an alpha level of .05, we can reject the null hypothesis Ho (2) and we can assume that students believed that they have more fun using computers.

Discussion

From our results it is clear that there was no significant difference between the achievement of learners in the control group and the experimental group for the test. The same effect has been observed in other studies. For instance, Petsangsri (2002) found no effect on student performance when students used a web-based learning system with embedded scaffolding strategies. Furthermore, from a number of other studies (Kinshuk, 1996), the use of adaptive systems did not have significant effects on students' performance. We therefore propose to shift the discussion towards improving the overall learning process with respect to students' motivation, perceived learning and satisfaction rather than just focusing on performance.

Students in the experimental group were more highly motivated in mathematics class during the treatment than when mathematics was taught using a traditional classroom approach. The different statistical tests show that students felt that they learned more with, bad more fun with, and preferred doing mathematics using the computer. This shows that computers are generally well accepted by students in the school. The multimedia capabilities of the computer help to meet the learning preferences of learners. As a result they become more motivated to learn the subjects offered. This factor also aligns well with the idea of the School IT Project mentioned in the beginning of the paper where ICT (Information and Communication Technologies) is being integrated through the school curriculum. This result also supports the findings of former studies (Sinko & Lehtinen, 1999; Ketamo & Multisilta, 2003), where computer-aided learning has mostly helped low and average skilled pupils. Low and average achievers normally perform better when taught through their learning styles (Dunn, R, 1989). Computer-aided learning with multimedia can prove very helpful to meet a variety of learning preferences to improve learning and students' satisfaction.

Conclusion

It has been clearly shown by this study that computer-aided learning does not necessarily help in improving student performances in aptitude tests. However, we found that students are highly motivated to learn mathematics using this instructional technique and they feel better than receiving instruction from the classroom. Firstly, this may imply that it is time to ponder on other methods to assess student learning based on new instructional techniques that are implemented. Furthermore, computer-aided learning with multimedia also helps to meet individual learning preferences since information can be presented in a variety of formats (oral, visual, kinesthetic) to the students. Finally, there is a cultural paradigm shift in our society where the Government is promoting the integration of information and communication technologies in different sectors of the Mauritian economy especially in the education sector. This is also a key factor in the motivation caused in the students to learn with computers.

References

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Mohammad Isaack Santally, University of Mauritius

Romeenah Boojawon, Manilall Doctor State Secondary School

Alain Senteni, University of Mauritius

Santally has been working as Instructional Designer in the Virtual Centre for Innovative Learning Technologies for 2 years. Boojawon is a Mathematics Teacher. Senteni is a Professor in Computer Science and is currently the Director of the Virtual Centre for Innovative Learning Technologies.