"Bear in mind that the wonderful things you learn in your schools are the work of many generations, produced by enthusiastic effort and infinite labor in every country of the world. All this is put into your hands as your inheritance in order that you may receive it, honor it, add to it, and one day faithfully hand it to your children. Thus do we mortals achieve immortality in the permanent things which we create in common." - Albert Einstein

Thursday, December 5, 2013

Colors: Help in Algebra

Algebra can be quite abstract. Yet, its equations present themselves in real life on so many occasions. For instance, the number of minutes from 11:56 pm for any time at the hour of the following day can be represented by an equation like y = 60 x + 4. Algebra not only attempts to condense a real life situation into a mathematical equation but also demonstrates a particular way of thinking.

To illustrate, here are sample problems (These are copied from "Algebra Connections Parent Guide"):


Now, here is one way of thinking in algebra made obvious by colors:


Here, the tiles in each figure that are present all throughout the series is coded blue, what is changing from figure to figure is coded red. Thus, in the first series, the number of constant tiles is 5, and for each figure, 2 tiles are added. Thus, for (1), the number of tiles in each figure is 2x + 5, where x is the figure number. For (2), there is only one blue coded tile and for each figure 4 tiles are added, hence the number of tiles in each figure x is 4x + 1. Here are the answers:


This technique of helping students make their thinking visible is nicely shared in following Teaching Channel video:


When I was in high school, I had a classmate who liked to use pens with different color inks. And it was indeed very helpful to look over his notes. Color coding was not just randomly using any color. It was actually thinking in progress....

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