Teacher Development

The emphasis in the books is on the process of science - observing, asking questions, trying to find the answers through further observations and experiments - rather than on information that chil- dren are expected to memorize without any real understanding. Needless to add, it would be difficult to use this book meaningfully without doing the activities.

The aim of the Homi Bhabha primary science curriculum is to engage students and teachers together in a joyful and meaningful learning experience. The curriculum is built out of simple, thematically organised, activities and exercises. The TextBook, WorkBook and Teacher’s Book for each Class are meant to promote active learning in every sense. To use these books, students must get out of the mind-set of copying the correct answers from the blackboard or from other students. Small Science should not be just read, it should be done.

Primary school students, particularly in rural areas, have rich, interactive experiences of the natural world. But lacking systematisation and clear expression, their observations and skills do not contribute to school learning. Urban students from literate homes, on the other hand, are often encouraged to ignore their natural surroundings, and to concentrate on meaningless bookish learning.

Small Science Class 1 & 2 deals with the broad area of environmental studies. This Teacher's Book illustrates a few of the almost unlimited learning opportunities offered by our immediate environment. In these first two classes we should remain unconstrained by a definite set of topics; the idea is to simply open up possibilities for learning in everyday contexts.

It was during lunch on a pleasant day that I was told about this popular book on Mathematics called “Mathematician’s Delight.” I was chatting with a professor who said that his choice to become a mathematician was influenced by this book. The story went like this: When the professor was a teenager, just after high school, during the summer vacation, he found this book and wanted to give it a try. He could follow most of it without much difficulty, and solved most of the exercises which led him to ‘experiment’ with mathematical ideas on his own.

In this edition of ‘Adventures’ we study a few miscellaneous problems, some from the PRMO and some from the AIME (the ‘American Invitational Mathematics Examination’). As usual, we pose the problems first and present the solutions later.

We know that Pythagorean triples are infinite in number, and the most common formula for generating triples is to take two relatively prime odd numbers s and t, where s > t ≥ 1, and produce the triple (st, (s2−t2)/2 , (s2+t2)/2 ). However, can we generate all possible triples from just one triple? Can we generate infinitely many triples from just one triple? These might be questions worth investigating.

There is another class of semi-regular 3D shapes - the Archimedian solids. In these the faces are again regular polygons but they are not all congruent, i.e. they differ in the number of sides. One such Archimedian solid is the truncated  icosahedron.

On the web page [1] belonging to A2Y Academy For Excellence, there appears a curious method to find the square root of a four-digit number if it is known that that number is a perfect square. We describe the method here using two examples and then consider how to explain it.

A classroom observation. A colleague a shared an observation that had come up during an exploratory class he was taking at the middle school level. The topic being discussed was Pythagorean Triples, i.e., triples (a, b, c) of positive integers satisfying the relation a 2 + b 2 = c 2 . If the three integers also happen to be relatively prime to each other, i.e., share no common factors exceeding 1, then the triple is called a ‘Primitive Pythagorean Triple’ (PPT for short).

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