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A Study Of The Use Of Mathematics Laboratory For Teaching Mathematics By Developing A Strategy And Testing Its Effectiveness

Guide:      Dr.S.S.Chaugule, Reader & Head Special Project Research Centre, YCMOU, Nasik, Maharashtra

Research student: Donnipad Manjunath

INTRODUCTION:

Mathematics, according to National Education Policy 1986, should be visualized as the vehicle to train a child to think, reason, analyze and articulate logically. Apart from being a specific subject, it should be treated as a concomitant to any subject involving analysis and reasoning. With the introduction of computers in schools, educational computing and emergence of learning through understanding of cause-effect relationships and the interplay of variables, the teaching of Mathematics will be suitably redesigned to bring it in line with modern technological devices so that learning takes place effectively.

Learning often takes place best when students have opportunities to express ideas and get feedback from their peers. But for feedback to be most helpful to learners, it must consist of more than the provision of correct answers. Feedback ought to be analytical, to be suggestive, and to come at a time when students are interested in it. And then there must be time for students to reflect on the feedback they receive, to make adjustments and to try again- a requirement of mathematics education that was neglected, due to rigorous practice of traditional methods of teaching. It was also observed that; students who frequently try to solve exercises related to new mathematics topics by finding the inter-connections and who discuss practical problems related to everyday life tend to score good in mathematics examinations. Teachers, who use of active learning strategies like students working on mathematics projects, connecting mathematical knowledge to everyday life when solving mathematics problems and actively participating in peer-group interaction have always significantly contributed to good performance in mathematics.

The traditional didactic methods of teaching are no longer adequate to meet the demands of mathematics education in line with National Education Policy 1986. In the light of National Education Policy 1986, to develop the skills reiterated in the policy and to provide practical experience of mathematical concepts, assumptions, assertions and rules, an appropriate method of instruction or a strategy for teaching mathematics  and a suitable platform to use such strategy is the need of hour. "Any idea or a concept presented in a simple & appropriate form and the way that is suitable to learner's ability and aptitude provides the best of understanding of it (Bruner 1966)".

Every student has a unique way of thinking, learning and making sense of what he/she listens or observes. Their active imagination constantly builds new connections and assimilates new information. If the teacher is active speaker and persistently using traditional methods, the learning takes backseat and in the process some faulty ideas can also form and lead to several learning gaps. These learning gaps need to be identified, questioned and corrected before they result into misconceptions. These misconceptions lead to low self- efficacy among students resulting low performance in the subject of mathematics.  Learner learns faster, when he is influenced by his peer group and developing a sense of positive interdependence, besides reducing the role of teacher to facilitator. However, reducing the role of a teacher to facilitator and creating an atmosphere of positive interdependence among students, a change in methods of teaching is inevitable requirement. In a normal course of teaching mathematics in a classroom, creating such atmosphere as mentioned above is not possible.

So, a strategy for teaching mathematics in a different but suitable atmosphere that would transform the position of the teacher to facilitator of learning from an authoritarian and active speaker's role was the need of the hour. Hence this experimental study was taken up.

OBJECTIVES:

1. To find out various methods being used in teaching Mathematics in regular classes 

2. To find out teachers views about Mathematics Laboratory

3. To develop a strategy to be used in a Mathematics Laboratory set - up.

4. To test the effectiveness of the strategy developed for teaching in Mathematics Laboratory set-up

5. To suggest recommendations for the development of Mathematics Laboratory and training of Mathematics teachers

HYPOTHESIS

There was no difference between teaching Mathematics through Traditional Methods of teaching to that of teaching through a strategy developed for teaching mathematics in Mathematics Laboratory atmosphere.

ASSUMPTION

Teachers were not using Mathematics Laboratory as a platform for teaching Mathematics

LIMITATIONS OF STUDY

The study was limited to only Kendriya Vidyalayas' functioning in & around Nasik district and schools governed by State Government and affiliated to Central Board of Secondary Education as well. The students' sample of study was limited to class 10th students of Kendriya Vidyalaya, AFS Ojhar Nasik District, while teachers' sample was limited to schools functioning in and around Ojhar, Nasik District. The investigation did not develop any standardized tests or psychological tests for the purpose of study, but prepared a questionnaire and got validated by experts from Department of Education, Yashwantrao Chavan Mahrashtra Open University.

VARIABLES OF THE STUDY

INDEPENDENT VARIABLE

Use of Strategy evolved to teach mathematics in a Mathematics Laboratory

DEPENDENT VARIABLE:

Performance of students and improvement in their result

SAMPLE OF THE STUDY

For this experimental study purpose, two different samples were chosen namely students' sample and teachers' sample. The students' sample of the study consisted of a total of 80 students of class X standard of Kendriya Vidyalaya, Ojhar and while teachers' sample consisted of 100 teachers of mathematics working in schools in & around Ojhar Nasik District

The sample of 80 students was divided into two groups' viz., controlled and experimental group. The two groups were matched on the basis of their marks obtained in class IX on the basis of Continuous & comprehensive evaluation, a criteria being used in all Kendriya Vidyalayas' for assessing the performance students at the end of an academic year.

The sample of 100 teachers from Primary to senior secondary level was chosen. However, 80% of teachers chosen were secondary teachers who handled class 10th Mathematics.

  TOOLS

 Tools like questionnaire, Visits, Observations and Interviews were used in the study. Various Mathematics Laboratories located different parts of country were visited and observations were recorded, besides visiting online Laboratory at Lower Columbia College, Washington State University, USA. Mathematics Laboratory at NCERT, New Delhi, Ramanujam Institute of Mathematics Learning Chennai, Mathematics Laboratory in Mysore based schools functioning at Bangalore and Mathematics Laboratory at Homi Bhabha Science Education Centre, Mumbai and Department of Mathematics, IIT, Powai, Mumbai were visited and Interviews were conducted on various strategies and techniques being employed to carry out the activities in Mathematics Laboratory.  Based on recorded observations and Interviews from Head, DESM, NCERT, Laboratory curators at Chennai and Bangalore questionnaire consisting of 18 questions was prepared to administer among 100 teachers selected as teachers' sample study.

RESEARCH DESIGN

The research design of the study was "Two Groups Posttest Experimental Design". Two groups namely, Control group and Experimental group were taken with each of them having a total of 40 students. The Research Methodology was Quasi Experimental Research Methodology.

STRATEGY EVOLVED FOR TEACHING MATHEMTAICS IN A MATHEMATICS LABORATORY

A strategy consisting of three different methods namely; Expository method, Cooperative Learning Method and Problem Solving method coupled with Modelling was evolved. These three methods were administered as one unit but in three stages while teaching mathematics in a Mathematics Laboratory. Each stage was defined with specific input and anticipated output. The role of teacher was active during first stage as teacher teaches mathematics using Expository method and during later two stages where Cooperative Learning at 2nd stage and problem solving coupled with modelling at 3rd stage the role of teacher is a facilitator of learning. At 3rd stage teacher's role is not only a facilitator of learning but also ensures a learning outcome viz., social relevance of knowledge being assimilated by students.

PROCEDURE OF THE RESEARCH

• ¬ Mathematics Laboratories functioning at NCERT, New Delhi and few other Laboratories located in different part of the country were visited to record the observations on the use of Mathematics Laboratory in day-to-day teaching leaning process. Interviews of Heads and Laboratory curators were carried out.
• ¬ Laboratories functioning abroad visited online and observations were made. Interviews were also carried out with a Lab Head-cum-Teaching assistant of college of Lower Columbia, USA.
• ¬ Suggestions and guidance seeking mail correspondence was done with a senior Lecturer, Department of Mathematics Education, Education, School of Education, University of East Anglia Norwich. These suggestions and guidance were sought before preparing the questionnaire and formulating the strategy for teaching mathematics.
• ¬ On the basis of observations and interviews, a questionnaire consisting of 18 questions was prepared and was validated by two experts, Department of Education, Yashwantrao Chavan Maharashtra Open University, Nasik
• ¬ Questionnaire was administered among those 100 teachers selected to gather their views and opinion on use of Mathematics Laboratory, various Teaching Methods and use of software in teaching mathematics.
• ¬ On the basis of responses; a statistical analysis and interpretations were drawn and then, a strategy consisting of three methods; viz., Expository method, Cooperative Learning Method and Problem Solving method coupled with Modelling was developed.
• ¬ The strategy evolved was used for 10 weeks on the Experimental group to teach mathematics in a Mathematics Laboratory atmosphere. The control group was taught the same mathematics content using normal classroom teaching.
• ¬ The methods of teaching mathematics to control group were Traditional methods. The lesson plans (excluding the method of teaching and Mathematics Laboratory), worksheets and modules were the same to both control and Experimental groups.
• ¬ At the end of 10 weeks; a Posttest was administered to both groups to evaluate and assess the performance of students. Meanwhile the data gathered through Questionnaire administered on teachers of mathematics and posttest administered on students was analyzed and Hypothesis was tested using statistical test of significance.
• ¬ Hypothesis was rejected on the basis of statistical inference drawn and concluded that; the strategy evolved to teach mathematics in a mathematics laboratory was effective than the traditional methods of teaching.

FINDINGS

• ¬ Teachers who were trained through behaviourist model were not aware of methods like cooperative Learning; guided-Expository and problem-solving method integrated with modelling. So, these methods were less preferred to teach mathematics as compared to traditional didactic methods like Lecture; Lecture-Demonstration methods
• ¬ Mathematics laboratory is not an integral part of curriculum framework in Maharashtra.
• ¬ Mathematics laboratory cultivated research attitude among students, when it was integrated with strategy evolved
• ¬ Mathematics Laboratory and its utility were given less importance during teaching degree pursuit. Majority of in-service teachers lack the knowledge of the modus-operandi using mathematics laboratory for teaching mathematics at school level.
• ¬ Majority of teachers were not given in-service training in using computers and software to teach mathematics.
• ¬ Use of computer and mathematical software to teach and provide conceptual knowledge of mathematics in a Mathematics Laboratory yielded positive reinforcement among students.
• ¬ Use of computers and allied software was not in the curriculum of teaching degree pursuit. Hence teachers of mathematics were not aware of using computer and allied software to teach mathematics.
• ¬ Strategy evolved to teach mathematics helped in effective content management.
• ¬ Computer and mathematical software used in Mathematics Laboratory has provided hands-on experience of mathematical knowledge taught
• ¬ The strategy evolved has also helped students to know the social relevance of knowledge learnt.
• ¬ 3rd stage of the strategy helped teacher to create learning problems and situations that will actively involve students and stimulate interest in how mathematics is applied in real life situations.
• ¬ There is significant difference between the mean scores of Experimental Group and Control group. The t-test revealed that the t-value statistically arrived was 5.59 for the degree of freedom 78. When t-value was compared with 0.05 level and 0.01 levels of significance for the same degree of freedom, the t-value arrived was significantly greater than both levels of significance. So, the strategy evolved for teaching mathematics in a mathematics laboratory was effective than didactic traditional methods.

RECOMMENDATIONS

• ¬ The teachers of mathematics shall the newly developed methods or strategies to teach mathematics instead of following age-old methods of teaching.
• ¬ The teachers shall use the strategy evolved for teaching mathematics in mathematics laboratory to enrich their teaching experiences.
• ¬ Mathematics laboratory should be made an integral part of curriculum of mathematics
• ¬ Mathematics Teaching could be carried out in a Mathematics Laboratory by integrating mathematics laboratory into regular curriculum.
• ¬ A specific curriculum in the form of credits shall be prescribed as regular syllabi for Mathematics Laboratory and could be made it mandatory to students to complete.
• ¬ Process of Evaluation and Assessment shall be based on minimum number of credits completion. Completion of this minimum number of mandatory credits by each student at each class could be made mandatory. Promotion to next class could be linked with this mandatory completion.
• ¬ Process of Evaluation and Assessment techniques shall be changed to a different format such as making rubrics for positive interdependence, group investigation skills etc., so that; academic performance of students could be improved along with social skills and peer interaction.
• ¬ Teaching through computers shall be introduced in the Basic teaching degree pursuit. All the pre-service teachers shall get ample exposure in using embedded atmosphere to teach mathematics.
• ¬ All In-service teachers shall be given training in Information & Communication Technologies, so that; the teaching experiences could be enriched. Pre-service teacher-students be given an exposure to Mathematics Laboratory and its usage in teaching mathematics. Techniques or strategies to integrate it ICT shall be taught during their teacher education programme.
• ¬ Addition human resources with mathematics background could be given for mathematics laboratory so as to enable the students to use the laboratory not only during their allotted periods, but also during leisure periods
• ¬ In every school Mathematics Laboratory shall be established and teaching of mathematics shall be carried out through mathematics laboratory.

EDUCATIONAL IMPLICATIONS

This study has an influence on the initiation of using mathematics laboratory in teaching of mathematics at secondary level. As the need for good strategy for teaching mathematics so as to improve the result and performance of students in board examinations, the study has thrown a light on the use of appropriate strategy that is the integration of three methods of teaching namely Expository, Cooperative and Problem Solving method coupled with Modelling in a laboratory atmosphere. As per this study, use of strategy evolved for teaching mathematics in a Mathematics Laboratory as described there are States like Mahrashtra where Mathematics laboratory is not an integral part of curriculum framework. So this study signifies that, mathematics laboratory could be made an integral part of curriculum framework and create mandatory use of lab for teaching mathematics. The ultimate result of the study revealed that; strategy was more effective instructional paradigm for teaching mathematics as compared to traditional methods of teaching. Furthermore, mathematics laboratory appeared to be a befitting platform for creating positive interdependence as compared to classroom.

CONCLUSION

The study established that; traditional didactic methods of teaching do not facilitate learning by understanding nor provide opportunities to students to relate their knowledge with real life, besides making low performers in the subject of mathematics. It was further established that, use of strategy evolved integrating three different methods for teaching mathematics in a Lab atmosphere yielded improved performance of students. So, the study found a positive and significant correlation between the academic achievement of secondary school students and the use of different methods of teaching in a Laboratory atmosphere. Hence, teachers teaching mathematics shall use Mathematics Laboratory as a platform and by using the strategy or any method other than didactic methods to make a significant impact in the knowledge construction so as to improve the performance of secondary school students.  

REFERENCES:

• Alyas Qadeer Tahir, (2005), "A Comparative Study of the Effect of use of Information and Communication Technology in Varied Teaching Approaches on Achievement and Retention of Students of Mathematics, Gomal University, Pakistan.

• Anderson, H (1989). The mathematics Teaching Around the World, Mathematics Teacher, 5 (I), 13 - 17

• Bhalwankar, A.G. (1985); A Study of Effects of Expository and Guided Discovery Methods of Teaching Mathematics on the Achievement of Students of Different Levels of Intelligence; Pune University, Pune

• Bharadwaj (1987); Standardization of Comprehensive Diagnostic Test and preparation of Remedial Material in Mathematics for Middle Standard students of Haryana; Kurukshetra University.

• Bernard Cohen, Sidney M. Edelstein Lecture, Baylor School, Kenneth Tobin, Research on Science Laboratory Activities: In Pursuit of Better Questions and Answers to Improve Learning, School Science and Mathematics, 90 (5), May/June 1990, p. 414.

• Buch M.B., Fourth Educational Survey (1983-1988), Volume - I, published by NCERT, Ministry of Human Resources Development, Government of India, New Delhi

• Buch M.B., Fourth Educational Survey (1988-1992), published by NCERT, Ministry of Human Resources Development, Government of India, New Delhi
• Dave, R.H., & Saxena, R.C. (1965), Curriculum & Teaching of Mathematics in the Higher Secondary Schools, NCERT, New Delhi
• David, W. Johnson (1994): Learning Together; Westport press, Connectuit, London Dutta, A., (1986),
• Bruner, J. (1966). Toward a Theory of Instruction. Cambridge, MA: Harvard University Press.
• Iqbal Muhammad (2004); Effect of Cooperative Learning on Academic Achievement of secondary school Students in Mathematics; University of Arid Agriculture, Rawalpindi
• Jain, S.L.; Burad. G.L. (1988) for Rajasthan Secondary Education Mathematics; Kasat, B.S. (1991) for Palghat Tehsil Chel, M.M.; (1990) for West Bengal Secondary Education Mathematics; Fifth Educational Survey (p.371 - p.375)
• Prof. Ramanujam, R. Dr. Ravi Subramanian & Group (2006) Position Paper - National Focus Group on Teaching of Mathematics - National Curriculum Framework (2005), NCERT publications, New Delhi
• Methods of Communication, A book for M. Ed students of YCMOU Nasik
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About the Author

Working as a teacher in Christian missionery schools functioning in India. Teaching standard K - 12 Mathematics. Doing research work in Mathematics Eduacation.