Analyses of the Indian labour market have been been characterized by the lack of recognition of one major fallacy or myth, two looming crises, and a silent tragedy resulting from unrealized expectations. The fallacy is that 12 mn join the Indian labour force every year, looking for work. The first of the two looming crisis is that millions need and wish to agriculture behind in search of non-agricultural work, but at least since 2011-12 they are not finding enough work to pull them away from agriculture. The second looming crisis is that youth are joining the age group of 14+ in growing numbers, each year with higher and higher levels of education, and are not finding nonagricultural work – despite their aspiration being only for such work. The final concern, which is simmering rather than reached the ​‘ready-to-boil-over’ stage, is the sub-group of the second looming crisis of youth who are getting better educated, is for girls who have reached gender parity in secondary education, and hence aspire for nonagricultural work. All three categories of workers have plenty among them who are disheartened workers, for whom there are too few non-agricultural opportunities.

Author:

• Santosh Mehrotra

The Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA) provides 100 days of work in a year for every rural household at a minimum wage. Because of MGNREGA, for the first time in the country, a transaction-based management information system (MIS) has been made available in the public domain, a feather in the cap of transparency. An essential safeguard in MGNREGA is delay compensation to be paid when workers do not receive wages within 15 days of completion of work. Despite several attempted measures, payment delays are rampant and the method of calculating delay compensation is flawed leading to massive under-calculation of the true payable compensation. By analysing over 90 lakh transactions for the financial year 2016 – 2017 across 10 states, we observe that only 21% of the payments were made on time and the central government alone was taking an average of over 50 days to electronically transfer wages. On aggregate, in our sample, while the true total delay compensation payable is about Rs. 36 crores, only about Rs. 15.6 crores is being calculated in the MIS. The Ministry of Rural Development (MoRD) has acknowledged the correctness of the findings and the Supreme Court of India has also issued Orders to the MoRD based on these findings.

Authors:

• Rajendran Narayanan
• Sakina Dhorajiwala
• Rajesh Golani

The policymakers, particularly on the right side of the aisle, have traditionally stigmatized any form of environmental regulations, as being a detrimental practice, which raises the cost of production, disproportionately affects the small businesses, and imposes expenses on the economy that tend to stifle economic growth and cut levels of employment (Murphy et al. [2015]). So, what this argument does is to essentially juxtapose environmental regulations against the growth and job opportunities in any economy. In the specific context of developing countries, this raises serious concerns about any environmental regulations as these economies are already reeling under problems of severe unemployment and poverty. Therefore, any discussion on clean energy in the context of a developing economy is usually taken with a grain of salt since it somehow tends to generate a feeling among the politicians as well as the policymakers that it will inflict hardships on the economy.

Authors:

• Rohit Azad
• Shouvik Chakraborty

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.

There has been substantial recent interest in the decline of labour shares across countries. For the most part, attention has been focused on developed countries. We examine the evolution of India’s labour share in its formal industrial sector from 1983- 2016. Using two datasets corresponding to sectoral aggregate data and plant-level data respectively, we document a secular decline in the labour share across all sectors from 1983, with a stabilisation at very low levels (around 8 to 10 percent) starting around 2005. We then use the plant-level data to identify correlates that illuminate reasons for the overall decline in the labour share. We find strong evidence to support multiple causes: increased capital intensity, greater informalisation, greater privatisation, and productivity increases in larger firms. As such, we suggest that the declines in labour share experienced are due to a composite set of factors. Conversely, other potential explanations (e.g. regional variation in the labour share) have less explanatory power.

Authors:

• Arjun Jayadev
• Amay Narayan

The challenge of employment in the Indian economy, especially after it growth acceleration since the mid-1980s, relates to its quality rather than its quantity. While employment growth has kept pace with the labour force over the long run, what has grown is informal employment. The coexistence of rapid capital accumulation, robust output growth and lack of growth of formal employment can be understood using the well-known Harris-Todaro model of a dual economy. This framework highlights the key role of the wage gap between the modern and traditional sectors as a determinant of urban informal employment. Hence, one of the most effective and egalitarian ways to address the employment problem is to adopt policies to increase agricultural productivity and income, which can reduce the wage gap. Since crop yields in India are far lower than many other countries in the world, including China, Brazil, and Bangladesh, there is ample scope for land-augmenting and labour-absorbing technological change in Indian agriculture. Efforts to ramp up industrialization should be taken up in earnest only after the wage gap has been narrowed significantly.

Author:

• Deepankar Basu

India’s overall economic performance over the last fifteen years has been outstanding, with the economy growing at an average of over 7% p.a. Growth has been service-led with the services sector accounting for over 60% of GDP growth over the period. Importantly, India’s structural transformation has been marked by a shift straight from agriculture to services led growth, leapfrogging manufacturing. The problem with this pattern of growth has been that it has generated relatively fewer opportunities of employment generation. The role of the manufacturing sector, ordinarily considered to be an important engine of growth and job creation for low and middle income countries, has been rather limited. Its share in total GDP and employment has continued to hover around 15% and 12% respectively for the last three decades.

Author:

• Radhicka Kapoor

Understanding the nature of work performed by women in India requires rest of all that we broaden our understanding of what is work, and recognize the different kinds of socially necessary as well as other work. The nature of work and how to capture it in empirical data have indeed been among the most complicated and debated issues in social sciences. This is particularly so in societies where much work occurs in informal, often even very private, settings that can be very hard to identify, let alone measure. The fact that international de nations of work and of economic activity have themselves been changing over time only adds to the complexity.

Authors:

• Bidisha Mondal
• Jayati Ghosh
• Shiney Chakraborty
• Sona Mitra

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:

The starting point of this Issue is Mahatma Gandhi’s Nai Talim which he envisaged over many years and made available in 1937. Children learn by making and doing, and it is by relating these two to the larger context that the understanding of the whole picture emerges. It is this larger picture that this issue has attempted to present. This issue also explores the relevance of Nai Talim in the India of today. The explorations are on the idea of Nai Talim and the overall visions of a ​‘good society’, rethinking Nai Talim in the light of the NCF of 2005, as well as in the present context.

Volume 4 Issue 1: The lead feature in the March 2015 issue of AtRiA is based on the theme Proof Without Words. In the Review section, Mark Kleiner discusses Edward Frenkel’s Love and Math — the Heart of Hidden Reality. Thomas Lingefjard, in his article Learning Math with a DGE system, addresses a pressing need of teachers using technology in the classroom. This issue features a new author Ali Hussen whose article weaves in algebra, geometry and arithmetic. It also introduces a new series on Low Floor High Ceiling activities.The pullout continues on the Teaching of Geometry (part ii).

Volume 3 Issue 3:

Learning Curve decided to devote this issue to Inclusive Education as a theme. In this issue, readers will find articles on literature for children particularly emphasizing inclusion, on gender stereotyping and an article on RTE and inclusion in schooling, among others. The issue also has an article on teaching language to include, caste as a barrier to education and upward social mobility and, finally, teacher preparedness in curriculum development.