A Newsletter from Azim Premji Foundation For Private Circulation only Issue XIV, March 2010 8 12 14 2 10 6 4 9 16 Special Issue on School Mathematics A The Broad Picture D The Role of Assessment B Some Perspectives E Personal Reflections on Mathematics C In the Classroom F Book Review and Resources In this issue In Also inside: Trivia, Logico-Math Brain Teasers and more.... Editorial Team D D Karopady, Madhumita Sudhakar, Neeraja Raghavan, Nidhi Tiwari, S. Giridhar and Umashanker Periodi Advisors to the Issue Hriday Kant Dewan, N. Venu and Rohit Dhankar Cartoons by Balraj KN Email : [email protected] Design Dhanesh, Prajeesh, Shubhangi, Sam Adroit Human Creative Services Pvt. Ltd., Email : [email protected] Printed by Pragathi Prints Bangalore - 560 103 Please Note: All views and opinions expressed in this issue are that of the authors and Azim Premji Foundation bears no responsibility for the same. From The Editor t is a pleasure to bring you this Special Issue of We found it immensely Learning Curve on Mathematics. It is the third enriching to read the essays Iin the series to be devoted to a particular of students to understand theme or subject, the previous ones being on what goes through their minds and souls as they comes Science and Language learning. to terms with Math? Putting together this special issue on Mathematics Nearly 20 years ago in Delhi, I accompanied my has been a precious learning experience for us. daughter for admission to kindergarten class. The Unlike the issues on Science and Language, one head mistress after the usual ice breakers, asked realized that one must address all the extreme the child, whether one is bigger or two is bigger. The emotions that surface at the very mention of Math: child immediately said one. To which the kind lady fear, hate, terror and absolute love and ecstasy too. opened both her palms and asked the child whether Topics that we thought were obvious turned out to she wanted one chocolate or two. The child took be not so obvious. In the very process of discussing two and the lady repeated her question. Is one and finalizing the menu, our own perspective about bigger or two? One repeated the child firmly. To the the subject grew visibly. eternal credit of the head mistress, she promptly admitted the child. Over the years nothing seems to As always, we reached out to a distinguished panel have changed because last week as I flipped of contributors and as usual we have run up a huge through the cartoon strip in a newspaper I saw a debt of gratitude. Each one of the contributors person presumably a teacher ask a child, "If I had responded to our unreasonable deadlines with four apples in this hand and four in the other hand, tolerance and enthusiasm. One contributor, what would I have?" To which the child answers very correctly "Really big hands!” unfailingly humorous at all times told me that I might as well sign my letters as "naggingly yours" Your views on this edition of Learning Curve are instead of the customary "sincerely yours". Prof H. most important. While your encouragement has Subramanian ignored ill health and wedding duties been the tonic, your candid feedback helps us to in the family to submit his article in time. With that continuously improve subsequent editions. one gesture he has forever a special place in our hearts. It is only such support that enables us to S. Giridhar bring out Learning Curve. Head - Programs & Advocacy We are hopeful that every article will strike a chord in you; for instance while one article discusses the very nature of Mathematics the other traces the history of the subject; similarly while one describes the pedagogy of the subject the other shares insights and the practical perspective of the teacher. And so on. Pg No: 3 CONTENTS Mother's Math and the Art of Estimation 40 - Nat Ramachandran Issue XIV : March, 2010 Special Issue on School Mathematics What Ails Mathematics Teaching? 42 - D D Karopady SECTION A: The Broad Picture Ancient India and Mathematics 48 - Sundar Sarukkai A Culture of Enjoying Mathematics 7 - Shashidhar Jagadeeshan How Sound are our Mathematics Teachers? Insights from the SchoolTELLS The Nature of Mathematics and its Survey 52 Relation to School Education 12 - Amitabha Mukherji - Geeta Gandhi Kingdon & Rukmini Banerji Pedagogy of Mathematics 16 Section C: In the Classroom - Hriday Kant Dewan Computational & Mathematical Concepts in Arts and Sciences 23 - Krishnan Balasubramanian Meaningful Teaching of Mathematics 57 - Vijay Gupta & Devika Nadig Culture in the Learning of Mathematics 26 - K Subramaniam Section B: Some Perspectives Concept Attainment Model 60 - Arun Naik Number: The Role of Pattern and Play Dialogue in Math Teaching: Realities and in its Teaching Challenges - Shailesh Shirali 30 - Ekta Sharma 63 Mathematics and the National The Role of Concrete Experiences in Curriculum Framework 34 Learning Primary School Math 66 - Indu Prasad - Meena Suresh Important Concepts in Primary School The Value of Drill and Practice in Math: A Mathematics 37 Perspective 69 - Kamala Mukunda - Uma Harikumar 2 + 2 = ? A Case for Early Identification Learning to Add: Are we Subtracting the of Dyscalculia 72 Importance of the Home Environment? - Sulata Shenoy - Amita Chudgar 114 Fold Paper and Learn Mathematics Confessions of a Victim of Mathematics - V S S Sastry 77 - Indu Prasad 117 Broomstick Tables 81 - Arvind Gupta The Elusive “Mr. Math” 120 - Shwetha Ram Section D: The Role of Assessment Math for the Non-Mathematical Soul 122 Lessons from the International PISA - Devika Narayan Project 84 - Ross Turner Unsung Heroes: What is it that makes them Stand Out? 124 - Anant Gangola Response Analysis: Understanding Children from their Frame of Reference 88 - Abhishek S Rathore & Falguni Sarangi Engineers, Accountants and Mathematics 126 - V S Kumar Insights about Student Learning from an Adaptive Learning Math Program - Sridhar Rajagopalan 93 Section F: Book Review and Resources Section E: Personal Reflections on Mathematics Two Books Worth a Read 130 Ten Great Mathematicians 101 - Neeraja Raghavan - Hari Subramanian Digital Resources for Mathematics The Hypocrisy in Math 109 Teachers 133 - S C Behar - S N Gananath Resource Kit Math Missionary - P. K. Srinivasan 111 136 - Arvind Gupta - Nidhi Tiwari & Madhumita Sudhakar s e c t i o n A T H E The Broad B R OPicture A D P I C T U R E 1 A Culture of Enjoying Mathematics Shashidhar Jagadeeshan Introduction and teachers have about Mathematics? And perhaps t appears that whether we like it or not, Mathematics most importantly, what are the pervades all aspects of our lives. Whether you are a factors that motivate humans to farmer or a techie, a comfortable relationship with I learn? In this article I hope to Mathematics, and competency at the level at which one begin such an exploration by first uses it, is a requisite in an equitable society. Some will argue describing the various ways in which Mathematics is viewed that even if the content of Mathematics learnt at school is and experienced, and how these views might affect forgotten, students will retain the ability to think clearly and curriculum if applied in isolation. I then go on to look at logically (an essential life skill) because of their exposure to curriculum design and pedagogy and see if we can truly mathematical reasoning. The tacit assumption here is that create a culture of enjoying Mathematics not just for a elite learning Mathematics will not only help us in our daily lives few but for all. but will also enhance the quality of our life. How ironic that for a vast majority their experience with Mathematics is so The Blind Men and Mathematics contrary to this assumption. Enough has been written We are all familiar with the famous Jataka tale about the bemoaning the state of Mathematics education the world blind men and the elephant. Each one makes tactile contact over, and the term 'Mathphobia' has become part of with a different part of the elephant, and comes up with common parlance. A major reason for school dropout is the descriptions ranging from a wall to a rope! Mathematics too inability to cope with Mathematics; it seems to be a suffers from partial perceptions. Perhaps the mystery, universal phenomenon that many students fear and dread depth and richness of Mathematics is revealed in the fact Mathematics. Sadly, this feeling often persists into that it can be seen in so many different ways. Let us look at adulthood. some of these perceptions and how they impact curriculum There have been many attempts to reform Mathematics design and pedagogy. education, and huge sums of money have been dedicated Mathematics as accountancy: For a large majority of to this cause. Unfortunately, the motives for reform are people, Mathematics is synonymous with accountancy. suspect and, in my opinion, this is part of the problem. Perhaps it is not unreasonable to say that the bulk of Advanced nations want to improve their citizens' humanity uses Mathematics to compare prices, make sure Mathematics competency out of a fear that citizens of rival they are not being cheated of the correct change, perhaps nations are outperforming them. Emerging nations want to calculate interests, discounts and rebates; some may even improve their Matheducation so that they can create a calculate areas and volumes. The more advanced may use 'knowledge society'. Humans empowered with knowledge it in book keeping. It is also true that many discoveries in are seen as a great asset in the market place. Reforms arithmetic probably came from the need to keep records of based on these motivations do not seem to have made land and accounts of trade.