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Mathematics Laboratory – an Alternate Method of Instruction

MATHEMATICS LABORATORY – An Alternate Teaching method

Donnipad Manjunath

Research Student

YCMOU, Nashik.

Guide: Dr. Chaugule S.S

Head Special Research Center, YCMOU.

Introduction

Mathematics education has traditionally emphasized the worst face of mathematics. Students are taught many mathematical facts, but they are rarely taught what the “mathematics process” is and how to employ it. As a result, engineers and scientists today often do not know how to use mathematics, and the population as a whole has failed to understand the relevance of mathematics. The mathematics process is both a creative and explorative process and is the most important face of mathematics. It is the fountainhead from which mathematical knowledge flows and a central component of the infrastructure that makes today’s technological and informational world possible.

Every student of mathematics needs to learn the mathematics process. The best way to learn the process is to practice it. However, high school and university students are given little chance to experience the full process of creating and exploring mathematics. Instead, they are taught merely about the byproducts of the process/facts using perfunctory procedures and calculations separated from the process, which made them.

Mathematics is an indispensable part of education. Its practical utility is not understood by many. This has happened because of sheer ignorance of educators and learners of mathematics. This ignorance has led to skepticism or phobia of mathematics. Mathematics is not born skeptical but made skeptical due to heterogeneous factors. The National Education Policy 1986 (NEP 1986) has brought many thoughts in the education system. These thoughts are the milestones to bring development into the system. The policy makers had studied the heterogeneous factors that have over the years made mathematics skeptical thoroughly and recommended a few suggestions towards improvising mathematics education in the country. Further, National Curriculum Framework 2005 (NCF 2005) also called for Mathematization of the child’s mind.

Mathematics, according to NEP 1986, should be visualized as the vehicle to train a child to think, reason, analyze, and articulate logically. Apart from being a specific subject, mathematics 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, teaching of Mathematics will be suitably redesigned to bring it in line with modern technological devices. According to NEP 1986, the following are basic tenets of mathematics teaching at school level.

i. The teaching and learning of Mathematics should enable the child to consolidate the mathematical knowledge and skills acquired at Primary stage.

ii. Assimilated knowledge of mathematics should enable the child to solve the real-life problems by developing abilities to analyze, to articulate, to reason and to see inter-relationship involved, to think and reason.

iii. To develop the ability to articulate logically.

iv. To develop necessary & sufficient skills to work with modern technological devices such as calculators, computers etc.

v. To develop appreciation for mathematics as a problem – solving tool in various fields, for its beautiful structures and patterns etc.

So, to make the Teaching learning compatible to the above tenets, an alternate method of instruction or teaching method has to be evolved so that, teaching process of Mathematics at school level becomes effective and meaningful.

Role of Mathematics in Education

Education is the manifestation of the perfection already in man. Knowledge is inherent in man, no knowledge comes from outside and is all inside stuff that gets discovered or unveiled with the help of Education. But the process of unveiling must be done by the teacher. So, teacher is expected to possess a greater precision, ingenuity and resourcefulness in order to unveil the hidden and innate talents of the students. However, education is not the amount of information that is put into brain and runs riot there, undigested all through the life. It must be life-building, character making and assimilation of ideas with real life implications. It should strengthen the mind and expand one’s intellect thereby enabling one to stands on one’s own feet. Furthermore, any subject learnt should make one to express his ideas freely and make the right use of the same in real life and so is Mathematics education.

Mathematics education is the study of the practices and methods of teaching mathematics. The goals of mathematics education are (i) to develop a sense of enjoyment rather than fear it; (ii) to learn mathematics as a process of deriving new knowledge to be applied in real life situations but not as mere formulae and perfunctory procedures; (iii) learner must see mathematics as something to talk about, to communicate, to discuss among themselves, to work together on; and (iv) use the abstractions to perceive relationships, to see structure, to reason out things, to argue and articulate the truth or falsity of statements. Mathematics knowledge imparted should cultivate the values such as development of concentration, Economical living, the Power of expression, self-reliance, Attitude of discovery and above all the quality of hard work and all these qualities are essential for a human being to survive in the world. So there is a definite place for mathematics in education. However, for such all-round development, teaching of mathematics at school level should be very effective. For such effective and meaningful teaching of Mathematics, it has to seriously deal with constructive invention, motivating intuition, application and aesthetics within the frame work of “deductive form of Mathematics. The question is how to make such effective and meaningful teaching of mathematics, when present status of teaching of mathematics at school level is at doldrums due to varied factors.

Present Status of Mathematics teaching and learning:

The present status of teaching and learning of Mathematics is far from being satisfactory and is not due to limitations on any one single component at work. In understanding the present status of Mathematics teaching and learning, we need to introspect, the areas such as Faculty problems, Text books, Syllabus, lack of interactive methods of teaching.

(i) It is a widespread defect in any educational format that, teaching profession is least preferred for well qualified and befitting individuals. Usually qualified entities take up this job as a last resort to win the bread and butter. Apart from this, in some schools, besides teaching, teachers are given other responsibilities and as a result the teacher shows less interest towards his fundamental duty. Owing to the undue pressure of completing the administrative work assigned sometimes teachers miss the classes leading to complacency and sometimes overlook their duty. In some cases teaching is carried out as a mere formality and other works takes priority.

(ii) There is too much of dogmatism in the gist provided in text books. Practical utility of the concepts learnt by children is totally missing. Students learn the concept by rote memory and reproduce the same either as homework or in tests. However a slight change is seen after NCF – 2005. NCF – 2005 has revamped the curriculum to make a few additions such as Mathematical modelling, which directly deals with the implications of mathematical knowledge in real life situations.

(iii) The methods of teaching adopted are teacher-centered. Teachers follow age old methods such as lecture method (chalk & Talk) in a classroom. As a result, the power of thinking, understanding and retention are not developed amongst students. Owing to which, the students show less interest towards mathematics learning. It is a known fact that, quality in teaching is directly proportional to students’ performance. However the methods of teaching being followed by teachers have left no scope for an effective communication between them and students and it goes to negative significance when a large chunk of 45 to 50 students are being handled by a mathematics teacher in the present day classroom. Furthermore, teaching of any subject in an interesting way is subject to an appropriate pedagogy. Undoubtedly, the traditional methods being used all along have served the society. However, these methods at large have failed to develop the skills such as (i) Skill in formulating, modeling, and solving problems from diverse and changing areas; (ii) Interest in, knowledge of, and flexibility across applications; (iii) Knowledge of and experience with computation, (iv) Communication skills, spoken and written and (v) Adeptness at working with colleagues (teamwork). It is therefore, an alternate method of Instruction (teaching) which acts like a concomitant between teacher and learner to have effective and meaningful communication so that learning of mathematics is realistic in terms of achieving the aims and objectives laid down by National Curriculum Framework 2005, besides becoming a pleasant activity.

Importance of Mathematics Laboratory

Teaching of mathematics should deal with the process and not just confine to transferring the knowledge from the mind of the teachers to notebooks of students through the tip of a pen and for such a phenomenal change in teaching of mathematics, a right ambience is required and it is definitely the Mathematics Laboratory. It is because, Mathematics Laboratory can act like a concomitant between teacher and students and provides an opportunity to understand and discover the beauty, importance and relevance of mathematics as a discipline. It can be expected to enhance the pupil’s understanding of the subject as taught at the school and can also provide a glimpse of what is beyond.

The Mathematics Laboratory is a unique concept in the field of mathematics education that was introduced in the year 1994. It has come a long way in enriching mathematics at primary, secondary and senior secondary level. In developed countries, the Mathematics Laboratory is an integral part of regular curriculum. However, in India, teachers, researchers, experts and scholars of mathematics education have been giving thought to the present system of teaching of mathematics and to change it to Learner Centered, but the efforts have proved to be futile as they are tending towards Teacher Centered. Mathematics Laboratory has now become an inevitable component to be absorbed as one of the mainstream methods of teaching of mathematics, which might make the learning of mathematics Learner Centered. In spite of the fact the Mathematics Laboratories are established in some of the schools, still the method of teaching in Mathematics Laboratory is at large Teacher Centered. The following reasons can be attributed as factors influencing the teaching of mathematics, a teacher centered method.

1. Manual manipulatives being used to explain mathematical concepts.

2. A classroom of mathematics in India at large is a mixture of heterogeneous potentials and psychologies, apart from being large in size, which is much more than what is stipulated by the National Education Commissions.

3. Virtual manipulative such as Computers, embedded environments are not integral part of Mathematics Laboratory.

4. Lack of expertise and exposure on the part of teacher of mathematics to use virtual manipulatives or embedded environments in an effective way to make teaching lively.

5. Lack of previous knowledge in teachers of mathematics about Mathematics Laboratory.

6. Improper evaluation and assessment techniques.

A Mathematics Laboratory is a place where some of the mathematical activities are carried out and is akin to any other science laboratory. The way students get hands-on experience in a science laboratory, even in a Mathematics Laboratory, students should get hands-on experience and scope for new innovations. Further Mathematics Laboratory should be a learning environment where many young minds decide that mathematics is more than practicing “sums” that the teacher assigns. It is exactly what is not happening in India, in spite of Laboratories being set up in some schools. As per the recent survey of laboratory activities followed in schools, it is realized that, there are a few prescribed activities to be carried out by students using manipulatives and make record work. On the basis of the record work and other influencing factors assessment is done. Does this kind of activities, which are prescribed and being done under the influence of a teacher enable the main goal of mathematics education? No, because it opens up once again, Teacher Centered learning rather than Learner Centered learning. So, instead of focusing on a few selected activities, students should be given a freehand to act independently to work and discover new ideas. NCF – 2005 has been insisting for Mathematisation of Child’s mind, but the system in so called Mathematics Laboratories already opened and working are not providing a platform which enables the child to articulate logically and develop reasoning ability that is what is precisely called by NCF – 2005 “MATHEMATISATION OF CHILD’S MIND.”

So, a Mathematics Laboratory set up in any school should be a formal environment where Mathematical concepts are made fully explicit and environment should be such that the user can create and explore mathematics and learn on his own and make his/her own assessment.

An ideal Mathematics Laboratory is a milieu where the following components are seen.

1. Context management

2. Online Library or Virtual Mathematics Library for reference

3. Software that deals with different mathematics branches

4. Graphical software for carrying out both symbolic and numeric computation

5. Conceptualization of mathematical ideas to stimulate the growth of analytic thinking

6. Instantaneous assessment worksheets so as to assess the degree of learning

7. Prescribed curriculum with mandatory credits to be completed

8. Virtual evaluation and assessment tool to give immediate feedback to the child

9. Teacher’s role must cut short to facilitator and he/she should ensure a stress free learning atmosphere in a Mathematics Laboratory

10. Exercises in non-routine problems suited to the maturity level of students could be made available on all topics to all grades. This will help children to develop problem solving abilities which are a must. Such exercises will also give a “taste” for the students to go beyond the peripheries prescribed.

11. Mathematics Laboratory timings should be wide open till late evenings in any school so as to enable the learner to cope with mathematics at his pace but not in accordance with running syllabi.

12. Instead of selecting a few activities, there must be a mandatory credit that must be completed by students right from classes I to X and assessment should be on the basis of continuous comprehensive evaluation of all the credits completed.

Research Perspective:

For the research purpose, the author has happened to visit various Mathematics Laboratories located at (i) NCERT, New Delhi; (ii) Ramanujam Institute of Mathematics Learning, Chennai and two schools affiliated to CBSE governed by a Mysore based Education trust functioning in & around Bangalore, (iii) Mathematics Laboratory, Kendriya Vidyalaya, INS-Hamla, Mumbai; (iv) Mathematics Laboratory, Homi Bhabha Science Education Centre, Mumbai and (v) A Conference on Technology use in Mathematics Education (TIME – 2007) held at IIT, Bombay

The author had discussed with the teachers working at the above specified Mathematics Laboratories about the methods of teaching Mathematics in Laboratories and how they find those methods as compared to classroom methods. Majority of teachers have expressed the following.

(i) Teaching Mathematics in a Laboratory is a time consuming process and syllabi completion in Indian curriculum is a time bound process as they are followed by term-end examinations to assess the students.

(ii) Teaching Mathematics in a Laboratory using plastic moulds or paper cuttings create interest to a moderate extent amongst students and full learning process is not achieved.

(iii) Lack of embedded infrastructure, besides teachers are not trained in using the embedded environment to teach mathematics.

(iv) A Mathematics laboratory period is more or less akin to classroom teaching of mathematics.

(v) Lack of appropriate teaching strategy to be adopted in a Laboratory set-up to teach mathematics

The author had attended 2nd conference of Technology in Mathematics Education (TIME – 2007) at Indian Institute of Technology, Bombay. During the conference the author had discussed with eminent personalities from the field of Mathematics about Mathematics Laboratory.

From the above visits and discussions made with teachers of mathematics, it was realized that infrastructure as required for a Mathematics Laboratory may not be in the hands of teachers, however, use of Mathematics Laboratory and an appropriate method or strategy to disseminate knowledge of Mathematics through Mathematics Laboratory is very much in the hands of teachers assuming that they have fully equipped with Mathematics Laboratory. Therefore it is necessary to develop an appropriate Method or strategy for using it in the Mathematics Laboratory set-up. The author is doing Research on this subject and is he expected to evolve a good strategy. The strategy will be published for all after the finalization of strategy for the author’s research work.

Conclusion

Doing some prescribed limited activities of mathematics without proper evaluation and assessment techniques yield hazardous results. Hence, it is preferred to have a professional outlook for a Mathematics Laboratory, which interacts with students to conceptualize the mathematical ideas that stimulate the growth of analytic thinking and develops research attitude amongst. Furthermore, a Mathematics Laboratory equipped with latest technological aids is sure to provide a platform to students develop the higher-order thinking skills that include reasoning, proof, solving complex problems and making connections that enable one to see mathematics as an integrated whole, and communicating clearly and effectively about one’s own and others’ mathematical thinking.

References:

1. Busha, Charles and Stephen P. Harter. Research Methods in Librarianship: techniques and Interpretations. Academic Press: New York, NY, 1980.

2. LoBiondo-Wood, G & Haber, J 1994 Nursing Research (3rd Edition) St Louis, Mosby. Pp 221 – 225.

3. www.aera.net/uploadedFiles/Publications/Journals/Educational_Researcher/3406/Boote.pdf

4. www.sceincenews.com/articles

5. www.lcc.com/mathlab/ – For syllabus and to interact with Mr. Cary Rhode, a Mathematics Instructor

6. Schulman, L. S. (1999) professing educational scholarship In E. C. Lagemann & L. S. Shulman (Eds.), Issues in education research: Problems and possibilities (pp.159–165). San Francisco: Jossey-Bass.

7. http://www.aera.net/uploadedFiles/Publications/Journals/Educational_Researcher/3406/Boote.pdf

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

9. Buch M.B., Fourth Educational Survey (1988-1992), published by NCERT, Ministry of Human Resources Development, Government of India, New Delhi

10. www.valencia.com: University of New Mexico

11. http://cerme4.crm.es

12. Sholomo Sharan, David W.Johnson., Handbook of cooperative Learning Methods (1994); Westpost Publishing House; Connectuit, London

13. Augustine B. Mascuilli (2000) “Effectiveness of Teaching Mathematics online; ALN Magazine 4 (2)

14. Watt. S (eds.); Computers and Mathematics, Springer – Verlag ; New York ( p215 – p277)

15. Sidhu Kulbir Singh; The Teaching of Mathematics; (1994) Sterling Publishers Private Limited, New Delhi; (p17 – p205)

16. Sunitha E; Sambasiva Rao R and Bhaskara Rao Digumarti; Methods of teaching Mathematics (2006); Discovery Publishing House; New Delhi

17. National Curriculum Framework 2005 (NCF – 2005) – A Paradigm Shift – Mathematics ( 2005); NCERT publications, New Delhi

18. Yixin Zhang; “An Experiment on Mathematics Pedagogy: Traditional Method Vs Computer Assisted Instruction” (2000); McNeese State University Lake Charles, U.S.A

19. Kenneth A; Handbook on Collaborative Learning (1999); (p80 – p100); The Johns-Hopking University Press, Baltimore, London

20. Atkinson.R.C & Suppes. P (1986); Program in computer assisted instruction; Final report, Washington, DC, Office of Education (DHEW)

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.

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