# CC BY-NC-SA

## Understanding Learners' Thinking through an Analysis of Errors

In this article, I have argued that it is important not to bunch all the students’ errors as “careless mistakes” or “over-generalisations”. We can classify the errors to understand – (a) what is their mathematical source and (b) what could be the student’s thinking underlying such responses. This will help us in designing appropriate interventions for handling these errors in classroom.

## A path to π

Consider the following situation. A regular polygon of n sides is placed symmetrically inside another regular polygon of n sides i.e. with corresponding sides parallel and with a constant distance between them. We now have a 'path of uniform width' running around the inner polygon. Now the following is asked: By how much does the perimeter of the outer polygon exceed that of the inner.

## Radii of In-circle and Ex-circles of a Right- Angled Triangle

In this article, I provide a relation connecting the lengths of the tangents from the vertices of a right-angled triangle to its incircle and ex-circles, in terms of its inradius and ex-radii. I give a geometric proof as well as an analytic proof.

## Circles Inscribed in Segments

As I was going through Evan Chen’s Euclidean Geometry for Mathematical Olympiads, I came across in this remarkable problem.

## A Counter-intuitive PYTHAGOREAN SURPRISE

Imagine a tightly stretched rope from one end of the field to be 100m; so the length of the rope is 100m. Now replace this rope by one that is slightly longer, say by 20 cm. There is some slack in the rope, so we should be able to lift the midpoint of the rope to some height. Imagine pinching the rope at its midpoint and raising the rope till it is taut. Question: To what height can you raise the midpoint?

## From Regular Pentagons to the Icosahedron via the Golden Ratio - Part 1

This series of articles will explore an amazing connection between three different objects in mathematics: the regular pentagon, the Golden Ratio and the icosahedron. Obviously, if the Golden Ratio is involved then the Fibonacci sequence can’t be far behind and, if the icosahedron is, so is its dual the dodecahedron!

## Teacher Lead Science Fair at Malpura, Rajasthan

I am sharing my experience of seven Science Fairs which were held in different schools of Malpura block in 2019 and which was inspired by one Science Fair held in 2018 (Malpura). The best part of these fairs was the deep involvement of the Science teachers from all these schools.

## π Enters the 5th Class

I write this to tell myself that it was not a dream...

This year I taught a bunch of fifth standard kids in Sahyadri School KFI (Krishnamurti Foundation India), who, like all others of their age, were high-energy kids; they were willing to explore but found it difficult to sit down in one place. I had a great relationship with them. The air in the classroom was of love, trust and wonder!

## Evolving Perception of Teaching and Learning Materials

Materials can be important for helping children learn. The very young child learns in interaction with and acting on the objects around her. In the beginning, the senses, motor abilities and subsequent causal analysis develops through their observations of the things around and their behaviour in different circumstances. This interaction with materials is spontaneous and directed by the child. The manner of interaction is decided by her and often their explorations do not meet with the approval of the adults.

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