Teaching Science -- especially mathematics -- by T. V

There have been recommendations making rounds especially from policy making institutions and educationists with regard to radical changes like new kinds of teaching strategies and bringing in technology aids in the teaching of Mathematics

In this blog we try to sum up the thoughts of some of the prominent decision makers. An analysis of the same seems to be significant especially for K-12 teachers keeping in mind the abysmally lowered enthusiasm towards the subject of Mathematics.

It has been seen that a lot of importance is given to activity based learning and on thought provoking ``try and discuss" segments in the curriculum. Also wherever possible flow charts and simulations are being recommended to understand the concepts especially where mathematical abstraction is involved.

Another commonly stated fact is that teachers at the school level need to be ‘adequately trained' to make math interesting.It is important to understand the gist of this aspect - Teachers need to acquire “mathematical common sense". The elegance and power of mathematical reasoning needs to be communicated drawing analogy from real life situations. Also it is of utmost importance that teachers teaching at high school grades need to take an extra effort and try to connect material taught in schools to the one seen in freshman courses in college. For instance topics like `limit concept', `trigonometric ratios' have to be dealt with a lot of care.

Looking at ourselves and introspecting our teaching strategies leads to the fundamental question as to what are we conveying to students. Especially when it comes to abstract mathematics involving sets, binary operations and various structures, one must believe and convey that it is about ideas and patterns that make a universal aesthetic appeal, rather than a collection of motiveless rules. The universal aesthetic sense leads to ideas that can build confidence in problem solving ability in varied situations .

Finally to end, we look at words of wisdom - A quote by Hyman Bass

points out that one doesn't learn culinary art by eating out at fancy restaurants, one does not learn how to sing opera by attending performances, and one does not learn how to play tennis by watching the US-Open-- you actually learn by doing. So a workbook culture is required where we as educators can supervise the practice of mathematics, done through problem solving and proof writing through mathematical reasoning.

Wave phenomena

We shall start with some very simple facts about light waves. The wavelength and frequency are closely related, in fact they are inversely proportional to each other viz, the higher the frequency the shorter the wavelength. This simple fact is given by
The equation for electromagnetic waves : λν=c , where λ is the wavelength, ν is the frequency and c is the speed of light.
The analysis of wave phenomena fits properly in the mathematical topic of non-linear analysis. Ever since physicists Huygens and Hertz began to understand light waves there is an ever increasing apetite to understand waves better.This is partly due to the practical considerations of image processing and VFX and also partly for pure mathematical fascination.
 The details of how rainbows form are fascinating, too. Light is refracted upon entering and exiting raindrops, and reflected within raindrops, sometimes more than once. The angle of refraction and thus the position of the rainbow--not a fixed place but at an angle of elevation of about 42 degrees from the line connecting your eye to your head’s shadow--can be figured out using trigonometry. Because different colors of light have different wavelengths, they are refracted at different angles, which produces a rainbow (or two).
If you look closely, you’ll see lighter colors inside the inner violet band (inset), which appear because of the interference of light waves, with some waves reinforcing each other. The explanation for these bands isn’t obvious and they weren’t accounted for in early theories about rainbows. Proving that these lighter bands should appear required the wave theory of light and their precise description involved an integral, (the Airy integral) that was numerically evaluated using infinite series. Curiosity about rainbows has led to many other discoveries in mathematics and physics, including “rainbows” formed by scattered atoms and nuclei.