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March 26, 2014

Generating intuition in algebra (1) : Geogebra : introduction

We had worked on one variable algebra with puzzles and looking at abstracting something real and taking an abstract equation and interpreting it in real terms. I introduced geogebra as part of this effort to get an intuitive feel of what two variable algebraic equations look like.
On the resource front computers were available for all the students of 7th grade a couple of days a week which could be used for some unique learning.

To get comfortable with the tool I worked through practical geometry. I had worked with one grade for 2-1/2 weeks to construct 90, 60, 30 degree angles. After a demo (only geometry) in one class their first assignment was to draw an equilateral triangle for a line segment they drew, measure the sides (to see if they are equal), measure the angles (to see if they are equal) and label the vertices.

I noticed how quickly the children become comfortable with a tool that is marginally intuitive and how differences like lines and line-segments become quite clear as they try out different menu options. The references of constructions become obvious e.g. for a circle what was the center and which point was used as reference for radius. 
The measurements add a self-check so the children notice something is incorrect and try to figure out what could have gone wrong.Perhaps, if I had introduced practical geometry this way I would have saved a lot of paper from having holes and trying to make sure everyone had compass, scale, protractor, etc.

Not everyone was interested in trying out geogebra and in the first class I focused on the early adopters and allowed the rest to work on mathlab (computer games that are based on math concepts) . By the second class everyone was in and some of the students who had been able to complete their assignments well were paired to support the ones who were doing it for the first time.

For those who had completed I asked them to make a square with each side 4 cm using arcs and lines. It was a fun challenge and one child claimed that he did it. Most others were able to get squares, but not of the same length as their original line segment. 

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