Posted by: Gary Ernest Davis on: February 14, 2011

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Michel Paul teaches mathematics at Beverly Hills High School in California. One of his students, Hannah, recently completed a GeoGebra

Hannah had never used GeoGebra before, and had recently arrived in the US from China.

Below is a screenshot of her GeoGebra project (click on the image for a larger version):

And **here** is a version of Hannah’s dynamic GeoGebra application.

Hannah explained how she came to create this GeoGebra applicaton:

“I am Hannah, the project “fish” is my works. Now, let me introduce how I create it.

Before I did it on the GeoGebra, I would draw my ideas on the paper.

Afterward, I would make a list of all the functional images and geometric images, then I would have a clear idea to choose which images could constitute to my work.

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After that, I began to create it on the GeoGebra.

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Every one of the functional images and geometric images have their qualities; I needed to know how the images would change when I changed their qualities.

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I tried many times to get a appropriate one.

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I would learn it when I attempted to make it better.

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This is a good way for me to learn math because I like Art.”

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And here is Michel Paul’s comment on Hannah’s work:

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“Interesting that she says she sketched it out first and then experimented with ways to implement it.

When I initially congratulated her on such a great project and asked her how she did it, she just laughed and said it took a long time.

I like her last statement, “This is a good way for me to learn math because I like Art.”

I had the kids in the lab on Friday, and I was watching what she was coming up with on her own while I was trying to help the others get up to speed. She was spontaneously creating all kinds of cool stuff.

This is an FST class (Functions, Statistics, Trig). The class is designed for students who have completed Algebra 2 but might not be ready for Analysis.

Hanna transferred to the school and was originally put in Analysis but was switched to FST because of language issues.

She had not been in the class more than a week or two when I assigned the project to do over winter break.

I had used GeoGebra previously with the other students, but Hanna had never seen it before, so I was hoping she wouldn’t feel overwhelmed. But she clearly took to it like … a fish in water. : )

The instructions for the project were simply to use GeoGebra to illustrate any of the concepts we had been studying about the various types of functions, such as quadratics, exponentials, step functions, transformations of functions, even and odd functions, and so on. Typical stuff.

I showed the kids how they could import pictures and create text boxes and sliders. I told them that they could be as creative as they wanted and to above all have fun with it.

The interesting thing is that we had not yet studied any trig – we are doing that now. So Hanna clearly had some prior background in trig in order to create this.”

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Both Michel and I are impressed by the level of creativity students show when they are :

- allowed and encouraged to follow their interests.
- given appropriate technological tools to help them.
- given time to complete longer projects.

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We are vitally interested in delineating and making quite explicit the means by which we would assess creative projects such as this. The reason is that some people devalue this sort of highly creative work in mathematics because they cannot easily check it right or wrong and/or assign a number to it.

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1 | dwees

February 14, 2011 at 9:23 am

This is a really good example of what happens when you set children on a task without much guidance. If you give too many instructions on what to expect, you can’t get creative stuff like this back.