R.K. NAYAK

D.M.S, R.I.E, BHOPAL-13

nayak.rajakishore@gmail.com

Mobile no. +91-9098304004

A Critical Analysis towards Making Constructivist Approach in Mathematics a Reality:

The Role of Stakeholders

Abstract After repeated successful experimentation of Public and Private Partnership (PPP) in several core sectors of development, it is suggested to carry out the same in our school education. It is high time to recognize the contribution of private tutors in teaching mathematics to school children and refine their natural traits as per established scientific teaching practice. Latest innovations in mathematics teaching practice must go out of four walls of education planners and philosophers to the major segment of ground level informal education practitioners.

In absence of any well framed guideline rather regulation for private practitioners imparting education to our school children, school education is in chaos. Schools are turning to be middlemen receiving contract and bypassing the responsibility on the shoulder of somebody else i.e. the private tutors and parents.

This paper throws light on the dark side of genuineness of the claim made by our so called well known reputed schools regarding their academic contribution to the nourishment of their students. Simultaneously, it analyses how the limited academic nutrition provided by school fails to meet the academic hunger level of our students; thus making them prone to academic malnutrition in mathematics.

This paper also reflects on how the desperate attempt of parents to get their children out of this academic malnutrition forces them to fall prey to these private untrained education practitioners. This paper reflects on the dimensions of healthy scientific collaboration between teacher, taught and private tutor who may be parents providing academic help to their kids.

It provides quantitative analysis of the engagement of the child in school , private tuition and self study. It gives a picture of the number of academic hours dedicated in practice in a calendar year to finish the mathematics syllabus with reference to constraints and flexibilities provided in NCF 2005.

It exemplifies how ill planned activities and projects in mathematics are proving a bane rather than boon for academic growth. It also analyses the scope for digital intervention in our class room.

It shows us the path to induce our traditional values and scientific temperament in children by integrating these at appropriate places in our regular classroom activities. It triggers the mind of our school teachers towards refining their management skills. It shows us new outlook for smooth and timely conduction of daily routine academic work by the concerned teacher. It reflects on the poor reporting habit of our mathematics teachers.

Introduction

Common phrases like how do you perform in mathematics, what is your score in mathematics are the societal pressure on the child. This lopsided attitude of society needs to be changed keeping in mind the aesthetic part of our daily life. We need not give disproportionate weightage to mathematics. Developing trust on proposed research designs like constructivist approach or any other depending on the suitability is the need of the time

Before introducing anything new to ease the process of mathematics teaching one must get double sure about the feasibility of the implementation part keeping in mind the Indian scenario.

Cost effective monitoring systems for academic management of disadvantaged groups of our schools must be set. Persons having established and well proven managerial skills in the school academics must be role models for other school principals. School principal’s management skill plays a pivotal role in shaping the academic environment of the school. At local level continuous refining of the skills of teachers is needed. Best teaching practices can be induced in our own settings provided the correct inclination is at place. The hunger for improvement in teaching practice must be there. Teaching is an art.

It is quite common to see only one or two good mathematics teachers in a radius of 5km to whom one would prefer to send children for private tuition. What makes these teachers different from others? It may be their natural traits combined with acquired skills. Over exaggeration of work load by most of the teachers and the psychological support they receive makes the process of imparting education inefficient. Although in theory end number of teaching models are available, but on ground level there is a scarcity of understanding at the time

We need trouble shooters for our academic problem management the way we provide A.M.C. for our hard ware set up. There is a problem of mismatch of academic nourishment received by students from school and their need. It evaluates in general the success of school as a social institution in meeting the basic mathematics needs of a secondary school going child. It sensitizes people to look for a replacement of traditional pattern of mathematics teaching.

This paper analyses the approximate time for which the child receives training in mathematics in school and private tuition. This paper looks at different perspectives of making constructivist approach in teaching of mathematics a reality in our classrooms. How the quality of the mathematics teaching can be improved by taking the help of home tutors?

How the school teacher and tutor should work cohesively to complement each other? What is the present academic standard of the tutors? How lower middle class section do not get access to good tutors? How the child simply go and waste his /her time in so called unorganized tution classes? It demonstrates the method of changing the traditional way of teaching mathematics to value oriented teaching strategy.

It integrates the teacher, taught, parents and society for knowledge construction and use. It tries to put a design which bridges the gap between home and school text book.

Experimental Methods It is a qualitative Case Study of perception and practice of mathematics in our schools from Class 6th to 10th. This experiment was carried in last summer vacation in D.M.S, Bhopal for 43days from 8th May to 26th June 2013. It probes deeply and analyses interactions between factors that explain present status or that influence change or growth to establish constructivist approach in teaching mathematics. It is a longitudinal approach, showing development over a period of time.

Here an attempt is made to organize social data for the purpose of viewing social reality. It is about the kind of system, a prototype for a category of individuals. Data has been gathered by a wide variety of methods, including : 1. Questionnaires, opinionaires and interest inventories. 2. Interviews with the students, tutors, parents, relatives, friends, other teachers and experts. 3. Recorded data from news papers, school, government agencies and other informal sources.

Results

It is found that students get about 100 hours i.e. 140 to 160 periods of group teaching in a academic session. Learning through smaller groups in informal way is found more suitable. Here the career profile of the tutors imparting coaching has also been provided. Qualitative idea about the money spent by different classes of parents for mathematics tuition has been provided. Students need direct observation for their mathematical skills getting developed. Here one to one contact between teacher and student is preferred. Teacher should club up students with almost similar attitudes and aptitudes under one group with a maximum of 6 to 8 students. Tutors teaching students were also called

. Most of the tutors were found continuing their education or preparing for competitive examinations. They were part time tutors. They did not have any B.Ed. training. They use to take nominal amount like Rs. 200 to 400 per month for 5 days a week. It is also found that the most of the students hardly find 3 to 4 hours a week for self study. The tutor’s method of teaching was mostly superficial paper-pencil type.

Developing deductive and analytical skills of students while working on the solution of the problem was hardly attempted at. While students paying a hefty amount like Rs.2000 to 5000 per month for mathematics coaching at home by established and matured working teachers of public schools are at advantage.

Discussion

Most of the students receiving coaching from established coaching classes also do not get proper attention from their tutors because of large class size. Timing of the coaching classes is too long. The average spending on coaching classes Rs. 20000 to 50000 per year. Although faculty is very good at coaching centers making 50 to 70 students of class 10th sit in one class makes it difficult for the child to get personal doubts cleared.

Most of the coaching classes only concentrate on solving the problems through short cut easy to remember methods. Mostly procedures are restricted to the history of solution. Inherent process of development is found missing. Coaching classes are found not evaluating student’s routine worksheets. Again the students turn up for personal tuition in which one to one contact happens.

Discussion

The crux is disadvantaged group cannot purchase readymade mathematics from market nor they can cook mathematics at home. To make mathematics of substantial quality affordable to them the school teacher needs to provide informal training to their tutors on core and current aspects of teaching mathematics.

. The established coaching classes should recruit more faculties and impart coaching in smaller groups. A school teacher interacting with more than 150 students everyday i.e.4 to 5 different classes makes it almost impossible to provide complete academic nourishment to all the needy. The average child needs 400 to 500 hours of academic guidance.

Here is a deficit of 300 to 400hours in a academic year. This deficit forces the parents to send their children to private tuition. The problem is despite attending private tuition the result does not improve. Forget about development student is found to lack in basics of mathematics.

First step is having a common copy for tuition and class work. Maintain day , date and class number, title in chronological order. Let all the effort by the child, classroom teacher, taught and/or private tutor get reflected here. This reflects how big the claim is.

Second step, do not be in a hurry to finish the course. Go to the under current theme of the content. Come down to the level of the child and gradually pick him up to the level expected. Do not get frustrated over failure of the child.

Third step, there is always a scope for the concrete understanding of the abstract or verbal problem. i.e. always opt for the child to read the problem at ease. Let the child prepare his own mental picture. If the child finds difficulty, let us go step by step together to comprehend the problem. Let the child feel the problem in his own surroundings. Let him compose the problem in his own words and use diagram to simplify the situation.

Insist the child to be the subject of the problem and be the creator of the movie related to the problem. Let everybody have their unique way of presenting or modifying the problem. When the problem becomes the child’s creation then he/she would be more personal in looking at every aspect of the problem carefully, calculate minutely and present appropriately. Initially they may be guided for presentation of solution, later on they pick up. The way the world has gone for the miniaturization, the same way the problem solving is a miniaturizing skill.

Fourth step, let the child explore the value or societal aspect of the problem . Always the teacher should be there to help the child relate problem solving skills with his daily life. The teacher should help the child view the honesty, sincerity, punctuality, generosity in problems. This way the social science aspect of mathematics can be of interest to students. How this presentation is affecting or shaping their personal traits should be explained to them . Let the child feel that the problem is meant for his aesthetic, intellectual and social development, the same way one undertakes physical exercises in a gymnasium. Time and again the value aspect of us can be induced in class room mathematics.

The researcher while teaching ratio proportion to class seventh students of D.M.S cited the following example. A daily labor donated Rs.10 from his daily income of Rs.400. where as a business man having Rs.5000 as his daily earning donated Rs. 50. Who is more generous?

Here both the ratio can be compared and value related judgment can be formed. They can be explained what constitutes a proportion and need of such comparison. Simultaneously for a break from calculation the teacher can tell them the provision of donation in ratio form from the religious dictates. Again they should be instructed to find their family income and determine their responsibility for a donation to the poor. Fifth step, to sensitize people about costly affairs of mathematics

Fifth step, to sensitize people about costly affairs of mathematics. Let us make mathematics affordable. Grow mathematics everywhere. If we would be successful in growing mathematics in our home and back yard then that would be our greatest achievement. This is the constructivist approach which is helping us in shifting from traditional literature mathematics to practical mathematics. Little theoretical knowledge is needed to start with practical, and then the practical leads to deepen and establish the abstract theoretical knowledge.

The democracy for the people, by the people and of the people. To establish mathematics theoretical formula or short cuts out of drastic need for the same should be the norm. Mathematics formula as far as possible should be like

Sixth step, administering trivial mathematics projects should be stopped. Mathematics in need is indeed. One model project may go as follows. This is a model project on Surface Areas and Volume for Class 10th student. E.g. our government needs to fix the minimum daily labor charges for digging job in your district. As a consultant what advice would you give for fixation of minimum daily wages?

The teacher would explain or create an informal discussion forum to discuss about the pathetic social and financial situation of our daily wagers engaged in different construction activities of society. How they help us beautify our country? What is our responsibility towards them? How to mathematically view the situation? Students can be encouraged to visit and interact with labor supervisor or labor at any site in their neighborhood where construction work or related digging work for underground water tank or foundation of a building is going on.

Tell the students to prepare a questionnaire for interview. If it is not possible for them to visit any site, let them collect data through inquiry method from their parents, neighbour or anybody else found suitable. One format of questionnaire may be 1. Proposed capacity of underground water tank(in litre) 5000 litre or ____c.c. or ___metre cube or ___cubic feet. 2. Length and breadth of available area under which it is to be dug. Length=____ m breadth =____m. 3. What should be the depth of tank to contain 5000litre water? ____ m or ___feet.

4. Wages or Cost of digging 1 cubic feet Rs.____. 5. Wages for digging the above tank Rs._____. Then this project can be further taken ahead like single or double layered brick work to be carried over along all sides. Let the child and teacher together develop further another questionnaire for getting the tank ready to use condition.

1. Size of pit (l×b×h) _____ 2. For double layered brick work, volume to be occupied by the bricks. _____ ft3or ____cm3 or___ m3. 3. Does it reduce the net capacity of the tank to contain 5000 litres? Yes/ No 4. What will you do to keep the net volume 5000 litre? Increase the depth or length or breadth. 5. Does it reflect lack of initial farsightedness in computation of net volume excluding the volume of the bricks?____

6. Would you face problem of getting a digger for such a small piece of work? ____. 7. Does the digger charge comparatively more money for this work? ____. 8. Calculate the money that you could have saved, had you correctly calculated the volume to be dug at first go. Rs ____. ( here the teacher can show the role of correct calculating skills in our daily life).

9. Number of bricks required.______10. Cost of the bricks. _____. 11.Labour charge for brick work and plaster per 1 ft2. ____. 12. Total labour charge Rs ______. 13. Any other expense not added. Rs _____.

At the end of the project the student would be enlightened on several aspects of the problem. Once the concepts are well established the student can compose theoretical problems on his own and solve those. Similar things to be carried on Algebraic Expressions, Pair of Linear Equations, Real Numbers, Height and Distances, Statistics and Probability. The researcher connected Tsunami with height and distance of trigonometry to make this chapter interesting. There is ample scope for linking most of our bookish mathematics to our daily life. When it is linked, the process of linking helps introvert or otherwise dormant children to open up.

At the local school level informal training cum discussion sessions involving interested potential parents and tutors can be held. This shows us the way to switch over from repetitive sort of working in mathematics to construction of knowledge in mathematics.

It also addresses different personal traits of learning by doing or experiencing i.e. pragmatism. Here is an opportunity to make mathematics child centered from being curriculum centered or teacher centered. It needs collaboration between classroom teacher, taught, parents and tutors. It is one person’s responsibility. It is high time to dissuade the way coaching classes have made the end product of teaching mathematics their sole aim.

Conclusion To

Conclusion

To partially sum up the critical analysis of Mathematics learning phobia in common learner’s mind and how to introduce innovative constructivist means into the teaching learning process , still there is a lot to be thought in this area by all the stake holders and to carry out rigorous work on them. Let us take this herculean task of rewriting our Mathematics Text books in the prescribed pattern of NCF- 2005. The psychological aspect of classroom teacher is needed to be taken care of.

Working techniques need to be provided to our classroom teacher. Their attitude towards taught needs a change that each time the child fails it is our strategy and efforts fail. Simply to save ourselves, getting the child passed is not the moral. Several creative ways to deliver the message to our large segment of teacher is need of the time. Unemployed tutors can be provided training on such construction aspect of knowledge. It can be started with creating a group of similar minded people using both print media and digital media to convey the new way of working with mathematical process.

Gradual shifting of our attitude towards a constructivist curriculum pattern and related evaluation system can certainly take us ahead. This would be only possible by replacing our existing artificial Mathematics problems mentioned in our text-books with the practical problems available in our surroundings. It will lead the curriculum to be more students oriented which is a long nourished desire of all the Mathematicians and educationists of our country.

Consequently, it will also revitalize our existing laboratories and also lead to the correct implementation and understanding of CCE. This would be possible only when all the stakeholders play their active role towards concrete enrichment of child’s experience.

Acknowledgments and References

1. NCERT (2005). National Curriculum Frame Work. 2. Hidi, S.,&Harackiewicz, J.M.(2000). Motivating the academically unmotivated: A critical issue for the 21st century. Review of Educational Research,70,151-179 3. Kim, J.K (2005). The Effect of a Constructivist Teaching Approach on Student Academic Achievement, Self concepts and learning strategies. Asia Pacific Education Review,6(1),7-19. 4. UN. (2012). Retrieved from http://www.un.org/millenniumgoals/education.html

5. Zeynep Basci & Mucahit Dilekmen. (2009). An Analysis of Classroom Teachers Attitude towards Corporal Punishment from the Aspect of Several Variables. World Applied Sciences Journal, 6(7),933-938. 6. Dillip Thakore.(2013). RTE ACT 2009:Confusion Confounded. Education World, 5(1),38- 50