It is certainly a platitude to say that learning can happen everywhere and at all times, at the most unexpected places and moments in our lives. However, that said, we also recognise that the school is a very valuable place of learning: formally and systematically in a graded way,level upon level so that we can tackle end-of-stage examinations which help us to choose our futures. But while all this is happening, a lot of undocumented and stimulating learning is going on simultaneously,
In this issue, articles on experiential learning about the environment, reading as a means of expanding horizons as well as acquiring language skills, the morning assembly as a treasure house of the learning experience- are all here. Other articles have given detailed accounts of science as a dispeller of superstition and an enhancer of a spirit of enquiry and curiosity. Sports do more than just teach the rules of the game, suggests an article: they can internalise values, inculcate inclusion and gender equality. There is an array of perspectives on the learning within learning which, paradoxically, falls outside of it.
All in all, this issue confirms what has long been felt and known — the learning that occurs outside the classroom is as vital as the formal pedagogy which takes place inside.

Explore big questions around 4 themes: black holes, the wound healing capacity of the skin, Higgs bosons, and the matrix of life. 

Use the activity sheets in ​‘A milky way to learn biology’, ​‘What do we really see’, and ​‘Trees and seasons in a changing world’ to introduce students to thinking like a scientist, the human vision, and neighborhood trees. 

Discover how astronomers measure distances in space in our new section ​‘How do we know?’ Explore how engaging students in raising an urban terrace farm can strengthen their understanding and involvement with the local environment in ​‘Pedagogy of dirty hands’. 

Try out the concept builder from ​‘Physics for closeted Aristotelians’ to find out how well your students understand motion under gravity. 

Read our ​‘Research to practice’ section to discover how to create embodied learning experiences for students in the science classroom. Or learn more about the first image of a black hole in our section ​‘Hot off the press’.

Looking for more? Enjoy our pull-out poster on human skin and booklet on identifying 10 common trees.

The July 2019 issue features Fractals on the cover — those distant and beautiful and highly mathematical creations have been brought a click away in our TechSpace section. Enjoy creating them and adding to your repertoire. We also take you through the magical tour of the beauty of mathematics starting with an article on Pentagons. Pi enters the ClassRoom section and the primary has plenty of learning — have fun joining the dots and exploring geometrical figures with different lenses. Students share their mathematical findings in two exciting articles. Our pedagogy article helps you to Understand Learners’ Thinking. And the Middle School problem corner is a Do_​It_​Yourself hands on problem solving section. The PullOut is on Ratio. 

This issue focusses on Textbooks and their significance in learning, how they are created, the ways they have been used and how they can be improved upon. The articles are based on classroom experience and as such are relevant and universal. Much thought has gone into the perceptive analyses by the authors, who have considered the full impact and importance of the power of textbooks.

The March 2019 issue is packed with articles for students, teachers and teacher educators of all classes. Striking results are not just reported, they are also explained and justified with proofs. And our sources vary from students to observations from colleagues in mathematics classrooms and mathematical tricks from websites- these are explored and explained.

Explore three ​‘Emerging Trends in Chemistry’ – new elements, metal-organic frameworks, and fluorescent tags. Read ​‘Serendipity’ & ​‘Annals of History’ to re-live the exciting jigsaw-puzzle-like process of scientific discovery – whether of a novel protein or the structure of DNA. 

Engage with the process of encouraging peer instruction in the science classroom through ​‘Students as Teachers’, or use our activity sheet ​‘Early Bird Nature Detectives Bingo’ to get students to observe (non-human) life in their backyards. 

Use our ​‘Science Lab’ section to get your students to calculate their molar masses (!) or understand pressure and volume through simple experiments with easily available low-cost materials. 

Discover the chemicals in everyday phenomenon through ​‘The Scent Orchestra of Flowers’ & ​‘The Chemistry of Life’. 

Explore the concept of energy from three very different perspectives with ​‘The Mystery of Dark Energy’, ​‘Powering (human) Life on Earth’ & ​‘Clean Energy’. Plus, enjoy our two pull-out posters on ​‘Doppler Effect’ and ​‘Some interesting scents of flowers’.

Teaching Learning Materials (TLMs) and Aids, which form the focus of this issue of Learning Curve, an indispensable part of a teacher’s bag of tricks, is a generic term that describes any material that supports and buttresses teachers’ efforts in getting a class of diverse capabilities to understand the basics of any learning. They have to fulfil some basic requirements: simplify concepts, provide the chance of practice, increase interest and motivation, help to explain complexities, concretise abstractions, enrich the course — though, of course, a single TLM may not meet all the above criteria. Thus, they are various kinds of TLMs, starting with the humble, but ever-present, blackboard (which has come in for much adverse criticism) and going all the way up to ​‘smart classrooms’, with all the advanced technology they entail. TLMs have the added value of aiding the memory — when children see how a concept/​rule of language/​experiment works, it is more likely to stay in the active memory than just learning the same thing by heart. This issue presents a wide variety of opinions and experiences with TLMs and Aids.

Volume 7 Issue 3: The November issue has beaten the nay-sayers at their own game with articles that celebrate the joy of doing mathematics through games, stories, applications of mathematics and activities on line and in the classroom. 

Explore the ​‘Evolution’ of stars, the Earth, life, and humans through three articles for our adult readers and one short story written for young adults. 

In ​‘Annals of History’ relive the contentious process of arriving at the unexpected mathematical pattern that has become key to our understanding of the diversity of life on Earth. 

Read ​‘Research to Practice’, ​‘The Science Educator at Work’ and ​‘Teaching as if the Earth Matters’ to see how complex concepts related to energy, evolution and soil can be taught through metaphors, art and real-world experiences. 

Learn more about Lynn Margulis’s ​‘controversial’ ideas and life in science in ​‘Biography of a Scientist’. If you’d like more, try some simple classroom experiments from ​‘The Science Lab’ to understand foundational principles in Physics. 

Use the seven activity sheets from ​‘Life in your Backyard’ to introduce your students to the fascinating world of spiders. Plus, enjoy our nine pull-out posters on themes as diverse as ​‘Benthic Fauna’, ​‘The Hard Problem of Consciousness’, and ​‘Ocean Acidification’.

Education initiatives are part of governments all across the globe, guided by a much-deliberated system of principles influencing decisions that are aimed at achieving pre-determined outcomes, which, in turn, are perceived to be beneficial to a particular country’s goals. Much thought goes on behind creating initiatives: they are statements of intent and, equally, the task of implementation is a very complex one. Not just that, innovative education initiatives have the huge additional responsibility of creating and shaping future generations, who, in turn, are any country’s future. The initiatives have to keep in mind the cultural and social norms of the country, while creating the atmosphere for salutary change. Another aspect that has to be taken into account while designing innovative government initiatives in education is the changes in society and its demands, both locally and globally, and rethink their strategies in order to benefit a new and contemporary scenario which will equip children to face and handle challenges of current times.

Volume 7 Issue 2: And it’s out! Most of you would have already received your copy of the July issue of At Right Angles, here’s the official announcement and the link with the welcome news that AtRiA is finally a whole school math resource! The shift all the way to Primary is marked with several new sub-sections in ClassRoom: from Sense-Making in Mathematics – the cover says it all- to TearOut- where all a busy teacher has to do is to tear out a ready made worksheet – complete with facilitator notes- and use it to challenge students to think in fun mathematical ways. As always, PullOut shares strategies and tips on a specific theme, this time we continue our series on Algebra.

And to top it all, we have not one but two students contributing articles to the Features section, no less! Enjoy a great read!

Volume 7 Issue 1: This issue of AtRiA welcomes you to the Math Village. Where house numbers, rangoli patterns, piles of fruit and even a child’s amusement device speaks to the instictive mathematician in each of us.

Read about these in Triangular Numbers in Features and the House Number Problem in ClassRoom. Appropriately, many of these problems were prompted by Ramanujan in his village. The Review is of a book which was used to teach a pre-course at the School of Arts and Sciences, Azim Premji University and it syncs perfectly with the theme of finding mathematics in the most unexpected places.

Hone up on how to create a Conjecturing ClassRoom or generate Elementary Cellular Automata! Misconceptions in Fractions and an analysis of common errors in Algebra give an insight into students’ struggles with mathematics and the PullOut, too, focuses on Algebra and how to make a seamless move from Arithmetic to Algebra.

It is different for each one of us which is why when people reminisce about their school, opinions can differ about the same subject or teacher. The teacher, for her part, also has unique relationships with the class she goes to. It is a dynamic, organic process. The same concern, involvement and thoughtfulness that was evident in the experiences recounted in the first part are present in the narratives of this Issue too.

What happens within the classroom has the power to change lives — for the better or for the worse. We ourselves know from our own school experiences of transactions which empowered or disabled or left us unmoved, according to the atmosphere in the classroom. This is not quite the same as the relationship between teacher and student, vital as that is. In this issue, we have a number of articles which explore the boundaries of the classroom and its importance as an investment for the future.

Volume 6 Issue 3: The word ​‘heuristics’ has always left me fumbling for the perfect definition. Rule of thumb seems adequate but too informal, as a teacher trainer, I’ve always preferred to illustrate rather than define this word. And the first article in the November issue does just that- Gaurav Bhatnagar, leads you gently into the Exponential Series- a heuristic definition! The relaxed tone continues with V. G. Tikekar setting the stage to arrive at formulae which are usually given and proved using mathematical induction. He, on the other hand, uses the narrative mode to set the context which explains and then proves the sum of squares and sum of cubes formulae. From story we move to song, V. Ramprashanth’s article Tonic Ambiguity is a delightful depart from our usual articles and it explains very simply, using just the concepts of ratios, how two hearers can place the same tones at different positions on the musical scale. CoMaC and then Shailesh Shirali, wrap up the Features section with a bouquet of proofs.

ClassRoom opens with Prithwijit De’s trademark investigative style – the title simply says A Triangle Problem – read on to find out more. Student Corner is our happy space and this time, we have Vinay Nair’s students talking about Happy Numbers and Bodhideep Joardar Investigating Pi. Next, we have Naveen Yadav combining Set Theory, Geometry and Combinatorics in Scalene Triples and Ujjwal Rane follows up on his previous article on Fagnano’s Theorem with a very visual, very practical alternative proof. A video of this result has also been uploaded by him on YouTube, it is available at https://​youtu​.be/​5​M​r​N​M​-​VxXd8. Low Floor High Ceiling features a modification of an investigation into triangles having the same area and perimeter and conditions for congruency. Learn about G numbers in Hara Gopal’s article. We’re particularly delighted to bring in yet another new sub-section to ClassRoom – Course Correction features vignettes from pedagogical experience, ways in which pitfalls leading to misconceptions can be addressed and used to advantage to strengthen student understanding. This time, we feature the solution of a problem from a traditionally ambivalent topic- Combinatorics.

On to TechSpace, we have not one but two articles this time. Thomas Lingefjard describes the use of technology to introduce concepts in Calculus and Sangeeta Gulati describes changes in the Desmos software and how it can now be used to build activity kits. Problem Corner is a treasure trove of interesting problems in addition to the usual Middle School, Senior School and Adventures in Problem Solving articles.

Review features an old classic – R. Ramanujam takes us through a lovely guided tour of Hardy’s A Mathematician’s Apology. And there is an unexpected bonanza, with this issue, we will feature a mini- review, it may be of a video clip, a game, a story…………..all things mathematical in essence. This time, J. Shashidhar talks about Marcus du Sautoy’s Story of Mathematics. Read the facing page to know more about this fascinating mathematician.

Pullout has graduated to Upper Primary – with this issue, we bring you a compendium of information about teaching Integers- surely the point when students begin to have negative thoughts about mathematics. I’m sure you’ll enjoy reading how to combat those tendrils of fear.

Education policies have resulted in several enduring legacies in keeping with the ever-changing society, as well as its political manifestos. Because of the dynamic nature of society in general, and the speed with which the world changes, bringing with it changes vis-a-vis every aspect of socio-economic-political change, national education policies from 1968 have seen changes in 1986, 1992 and now a draft policy in 2016. It is expected that each policy, when introduced, will take into account the demands of the day while preserving the central core of its goals. National educational policies are, or at least should be, the consequence of a clear understanding of the socio-cultural beliefs of India, and at the same time having clarity in introducing a system that is aligned to the goals enshrined in our Constitution and has the avowed purpose of creating a democratic society of enlightened citizens. In this Issue, we have articles which examine education policies from 1968, which was the starting point chosen for this issue. The draft policy of 2016 has been closely examined, as have the ways in which language and literacy have been addressed. Another article is an examination of the history of educational policy documents. Other articles have been written about specific aspects such as CCE and the Midday Meal Scheme. This is only a sampling and we hope that readers will find this Issue interesting.

Volume 6 Issue 2: It is a pleasure to share with you, our readers, the collection of articles in this, the July 2017 issue. The (un)popular view of mathematics being a terrifying subject takes a completely new twist with the first article in which a mathematician takes on a terrorist threat! The hunt for answers to a mathematical problem is usually an absorbing one, at least to aficionados of the subject but Arun Vaidya’s fascinating story I M Code makes it a matter of life and death.

Following this, we have an article on another application of mathematics: Interpolation by Sankaran Viswanath. You will see again how mathematics is a tool for prediction, and how data can be fitted into mathematical expressions which then provide a mathematical model. From here, we move on to card tricks; yes, fun and mathematics can go together — and At Right Angles shows you how in Suhas Saha’s Ternary Base Magic Trick. A quick peek behind the magic reveals patterns based on the ternary base, it’s not as complex as it sounds, read on to find out. Our Features section ends with Shailesh Shirali’s exposition on Quadrilaterals with Perpendicular Diagonals, a nice bouquet of Arithmetic, Algebra and Geometry for you.

In ClassRoom, we have the second part of the Inequalities series started in the March 2017 issue, again, both Algebra and Geometry are used to first prove the arithmetic mean- geometric mean inequality and then apply it in several situations to illustrate the power of this relationship and also view its implications in graphs, geometric figures, functions􀀿􀀿􀀿.the list of connections seems endless! Moshe Stupel and David Ben-Chaim appear next with their article Three Elegant Proofs, the name says it all, we promise it lives up to its title. CoMaC, as usual, provides an indepth analysis of an often-asked question, now increasingly appearing even in WhatsApp forwards: What’s the next number? Is the answer really unique as the question implies it to be? More on numbers with Swati Sircar and Sneha Titus, writing on the Sums of Consecutive Natural Numbers; mental mathematics becomes visual all of a sudden, and this Low Floor High Ceiling activity is sure to appeal to a variety of learning styles. Vinay Nair takes up the theme of Divisibility by Primes and provides some powerful tests using an ​‘osculator’. Students are sure to be intrigued. ClassRoom concludes with a Proof Without Words on a property of the Orthocentre of a triangle.

For some time now, we have been featuring articles by students and we are particularly happy when they write in with their own discoveries. So much so, that from this issue onwards, we have devoted space to Student Corner in the ClassRoom section. Featured this time are Bodhideep of class 6 and Parthiv of class 11, you are sure to be impressed with their discoveries.

Our cover this time, features Golden Quadrilaterals and the illustrations have been provided by Michael de Villiers, who continues his series on constructive defining. These beautiful quadrilaterals have been defined by investigation and are an interesting activity for students who believe that everything in mathematics is pre-defined and that there is nothing new in mathematics to be discovered.

Problem Corner has seen some changes over the last few issues. In a deliberate attempt to avoid a ​‘camp’ approach to problem solving and to make this section more inclusive, we have a wide variety to interest our readers. Prithwijit De sets the ball rolling with his article on ProblemPosing. This is followed by Middle and Senior Problems addressed to different age groups. CoMaC presents a theorem about a triangle and a problem about a rational number; the titles are deliberately bland but these are as fun as Shailesh Shirali’s Adventures in Problem Solving.

The Review this time will certainly have you leaping to order this book: The Cartoon Guides to Calculus and Algebra, a series whose name says both all and nothing. Can such a serious subject be illustrated with cartoons? With mathematical rigour? Read the Review and I’m sure you’ll be convinced.

Our issue concludes with the PullOut — Padmapriya Shirali focuses on Large Numbers and how students can grasp this concept. I am sure that adults too will enjoy this refresher course and pick up tips on how to make this topic child- friendly and approachable. So it’s over to you now! Happy reading.…

Volume 6 Issue 1: The Art of the Matter — can a picture be a powerful pedagogical tool? At Right Angles believes it can, and if you read the write up on the facing page, I’m sure you will agree with us. Going to the heart of the art is key to mathematics and there’s more of the same inside this issue. We begin with Ramya Ramalingam, a sixteen-year-old school girl, unravelling the mysteries of Knot Theory for us. And Haneet Gandhi picks up where her series on Tessellations stopped, with a fascinating article on tiling and the pictures we can create with different combinations and permutations of polygons.

In the Classroom section, Khushboo Awasthi opens up the Square Root Spiral with a series of investigative questions; Ujjwal Rane proves Fagnano’s Theorem in several innovative ways. CoMaC describes an unusual way to bisect an angle and also manages to pull yet another 3−4−5 triangle which has long connected math with art pops up in Kepler’s triangle — read more about it in Marcus Bizony’s article. And in How To Prove It, Shailesh Shirali uses Ptolemy’s theorem to reveal all kinds of fascinating relationships in cyclic quadrilaterals.

Tech Space features the first part of a two-part series on constructive definitions; Michael de Villiers shows you how to do so with a GeoGebra activity centered on the golden rhombus. Truely cutting edge math pedagogy!

Our review this time is by Kamala Mukunda who shares her views on Liping Ma’s classic Knowing and Teaching Elementary Mathematics. This is a must-have for every school library and a must-read for mathematics teachers of all classes.

Finally, it’s Time — this Pull Out by Padmapriya Shirali will give you several new ideas to introduce this all important concept and help students quantify something which impinges on their consciousness long before they come to school.

The teacher is central to the teaching — learning process, whatever a school’s policies, whether private or public, whatever board it has chosen to adopt. The teacher is an essential component of the success of the process. This being the case it is essential to consider what ​‘creates’ a good, effective teacher and what sustains her and , through her, the framework of the school. This Issue is aimed at not only teachers and teacher-educators, but also policy makers and observers, in short, anyone with an interest in education. The focus articles deal with the policy and practice of teacher development and suggests alternatives while two more examine gender sensitisation and pre-service teacher preparation discussing in considerable detail the curriculum and its realities. This is followed by articles from practitioners across the field, from both private and public institutions. Teachers have recounted their experiences on the ground. There are critiques of the present system holding up practices against the light of theory, while some teachers have described their positive encounters, testifying to the dedication of colleagues working with enthusiasm and vigour in remote areas, without the help of sophisticated teaching aids.

Engage with 2 themes — ​‘Emerging Trends in Physics’ and ​‘Indian Science Facilities’ — by exploring methods & processes defining future research in areas as fascinating as the discovery of black holes, understanding dark matter, using radio-astronomy to probe the universe, enabling space travel, the search for exoplanets, & establishing human settlements on Mars. In ​‘Origins’ & ​‘Annals of History’, piece together current understanding of our shared history through the beginnings of space-time & planetary worlds, the notion of elements, or that of life. Discover simple classroom activities to reveal & challenge mental models of force in ​‘The Science Lab’, encourage the use of art to study ecology in ​‘The Science Teacher at Work’, or integrate social justice in the science curriculum in ​‘Research to Practice’. Also discover little-known aspects of ​‘The Origins of Composting’ & ​‘Ocean Microbes’ in our pull-out posters!

Volume 5 Issue 3:

Volume 5 Issue 2: 

In ​‘Interactions’ & ​‘Emerging Trends in Biology’, explore articles on chemical ecology, the common cold, fundamental forces, gut microbes in health & disease, & memory. In ​‘The Science Lab’, discover simple classroom activities to teach photosynthesis & daytime astronomy. In ​‘Annals of History’, trace the journey of microscopy from the simple magnifying glass to the powerful electron microscopes & easy-to-assemble foldscopes available today. Discover the writer & physician Oliver Sacks through his fascination for the human brain, bikes and stories in ​‘Biography of a Scientist’. Enjoy our pull-out poster on ​‘Ten things you didn’t know about – Bones’ & nature-based activity sheets – ​‘Chirp Chirp’, ​‘Hibiscus Tales’, ​‘Bark Bites’ & ​‘All about Ants’! Or browse through our pocket-size pictorial guide to common butterflies!

Volume 5 Issue 1:

The theme of public education is one that affects every society across the globe. All over, there has been fundamental dissatisfaction with the systems, though the idea itself is intimately linked with a democratic society: one in which the individual is taught her place in the larger society. In India there has been disaffection with both public and private schooling, especially in urban centres, where private schooling flourishes at exorbitant cost, many times with inadequate space, facilities and less than adequate teaching. Every single person in the country is crucially involved in what form education takes, since it matters to us what the future of our society is going to be. It reveals too the tremendous hope that we all have that there are solutions, elusive perhaps, but they exist and it is for us, and others who follow, to find these solutions. This hope is all the more attenuated when we hear stories, as we do, of our public schools in the remotest of places, where teachers are doing a wonderful job, coming to school braving the weather, working under very challenging circumstances, their enthusiasm unabated.

Volume 4 Issue 3: Two themes dominate this issue of AtRiA: Archimedes & Magic Squares — an unlikely combination! Both are exceedingly rich topics to write about, with histories that go far back in time. Who can’t be both charmed and thrilled by the story of Archimedes?

Explore ​‘Inter-disciplinary Science’ with 5 articles that connect knowledge, methods, & perspectives from across the natural sciences. Trace the exciting history of familiar science concepts in ​‘Serendipity’ & ​‘Annals of History’. Enjoy reading about the quirky & brilliant J.B.S Haldane in ​‘Biography of a Scientist’. Re-discover the wonders of the world within us (Macrophages) & in outer space (Mars Orbiter Mission) in our section ​‘In here/​Out there’. Prepare to be surprised by the colourful life of the humble fly in the section on ​‘Nature in your Backyard’. Check out our ​‘Science Online’ section for a step-by-step introduction to an open access software tool for understanding Time. Also enjoy our pull-out posters on ​‘Experiments with Water’ & ​‘Ten things you didn’t know about – Blood’!

Volume 4 Issue 2: