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From the Editor S Desk From the Editor�s Desk . The quintessential �maths master� of folklore has since been often replaced in the Indian classroom by the equally legendary �math teacher�- that stern but loving disciplinarian who has inflexibly drawn many a student to success in mathematics (and very often, in study skills and perhaps even life skills). Gender has often played a role in the field of mathematics with studies being conducted on whether boys are better than girls in mathematics, and why there are so few female mathematicians in the field. Which is why At Right Angles has chosen to focus on the theme �Women in the field of math education� in this issue. Both Jill Adler and Jo Boaler are important figures in the field of math pedagogy. In Features, we bring to you an account of the sterling work done by Jill Adler in South Africa. The write up is by Ravi Subramaniam, HBCSE, who has interacted closely with her work. In Reviews, Prabhat Kumar has described Jo Boaler�s latest book and the trendsetting work that she, along with Carol Dweck, has done on mindsets. Closer home, Parvin Sinclair who has been involved in preparing the B.Ed material for mathematics in the IGNOU B.Ed course. and Geetha Venkatraman, a well-known figure in college level math education efforts and our very own Jonaki Ghosh who has done sterling work in the field of technology in math education have all contributed significantly to the Indian mathematics education scene. May their tribe increase! Also in Features, Shailesh Shirali wraps up his series on 3, 4, 5; J. Shashidhar talks about the concept of multiple infinities and Prithwijit De will take you on a fascinating journey in his succinctly titled article �An Eye on Eyeball�. In ClassRoom, we have two articles on the Digital Root of a number, and Anant Vyawahare describes how it was used by accountants to tally their figures long before calculators were invented. We feature two groups of writers from outside India who talk about �Three Means� and �Inequality for the Area of a Quadrilateral�. Tech Space features the uses of a graphics calculator, increasingly being used by students to quickly generate graphs and study abstract concepts such as the derivative of a function. And we have an article sparked by the work of Agnipratim Nag, a class 8 student of Frank Anthony Public School, Bangalore; look for an unusual take on the �Difference of Two Squares�. Students are clearly reading our articles with great interest, Jayaram Chandar not only provided an answer to our question on the smallest number which does not divide 1 × 2 × 3 × ....... × 99 × 100 but also devised a Java program which gives the smallest number which does not divide any input number. The link has since been uploaded on our FaceBook page AtRiUM. We conclude the article with Padmapriya Shirali�s exciting PullOut on Area and Perimeter. Do try out the suggested activities. As always, we look forward to hearing from you; mail us at [email protected] and don�t hesitate to send us articles for publication. Sneha Titus Associate Editor A Publication of Azim Premji University together with Community Mathematics Centre, Rishi Valley and Sahyadri School, Pune Contents Features ClassRoom Our leading section has articles which are focused on This section gives you a 'fly on the wall' classroom mathematical content in both pure and applied experience. With articles that deal with issues of pedagogy, mathematics. The themes vary: from little known teaching methodology and classroom teaching, it takes you proofs of well-known theorems to proofs without to the hot seat of mathematics education. ClassRoom is words; from the mathematics concealed in paper meant for practising teachers and teacher educators. Chief Editor Associate Editor folding to the significance of mathematics in the world Articles are sometimes anecdotal; or about how to teach a Shailesh Shirali Sneha Titus we live in; from historical perspectives to current topic or concept in a different way. They often take a new Sahyadri School KFI and Azim Premji University Community Mathematics Centre, developments in the field of mathematics. Written by look at assessment or at projects; discuss how to anchor a Rishi Valley School KFI practising mathematicians, the common thread is the math club or math expo; offer insights into remedial joy of sharing discoveries and the investigative teaching etc. Editorial Committee approaches leading to them. Athmaraman R Sangeeta Gulati Tanuj Shah Tanuj Shah Association of Mathematics Sanskriti School, Delhi Rishi Valley School 38 A Diagonal Investigation Teachers of India, Chennai Giridhar S Padmapriya Shirali Ravi Subramanian Prithwijit De Sahyadri School KFI Azim Premji University 05 Anant Vyawahare Homi Bhabha Centre for Science Jill Adler - A South African Mathematics Swati Sircar 42 Education, Tata Institute of Shashidhar Jagadeeshan The Digital Root Azim Premji University Education Researcher Fundamental Research, Mumbai Centre For Learning, Bangalore K. Subramaniam CoMaC Hriday Kant Dewan DD Karopady Geetha Venkataraman Homi Bhabha Centre for Science 11 45 Azim Premji University Azim Premji University Digital Roots of Perfect Numbers Education, Tata Institute of Through the Symmetry Lens_Part II Jonaki B Ghosh A. Ramachandran Fundamental Research, Mumbai Lady Shri Ram College for Women, Formerly of Rishi Valley School KFI Shashidhar J Marcus Bizony Ramgopal Vallath University of Delhi 17 50 Azim Premji University The Magical World of Infinities-Part_II Three Means Addendum 24 54 CoMaC and Agnipratim Nag Design Print Georg Cantor The Difference of Two Squares Formula - Please Note: Zinc & Broccoli SCPL All views and opinions expressed in this issue are those of the authors A New Look [email protected] Bangalore - 560 062 Shailesh Shirali www.scpl.net and Azim Premji Foundation bears no responsibility for the same. Shailesh Shirali 27 3, 4, 5... And Other Memorable Triples 58 - Part IV How to Prove It At Right Angles is a publication of Azim Premji University together with Community Mathematics Centre, Rishi Valley School and Prithwijit De CoMaC Sahyadri School (KFI). It aims to reach out to teachers, teacher educators, students & those who are passionate about mathematics. It 34 63 provides a platform for the expression of varied opinions & perspectives and encourages new and informed positions, thought-provoking An Eye on Eyeball A 80-80-20 Triangle points of view and stories of innovation. The approach is a balance between being an �academic� and 'practitioner� oriented magazine. 66 CoMaC Addendum to a 20-30-130 Triangle.
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