Tuesday, September 21, 2010

 

Fractions and Slope

I just read a great article in last month's NCTM journal, Mathematics Teaching in the Middle School. It describes how algebra teachers can use the properties of slope to clarify student understanding of fraction operations. If you are an NCTM member, you can access the article here.

The article got me to thinking about several different ideas. First of all, the ability to work with fractions is critical for student success in upper levels of math. High school teachers are constantly providing remediation to students who are having trouble with fractions. I would dare say that fractions are to pre-algebra and above as basic facts are to arithmetic. I hear 5th-8th grade teachers saying, "My students struggle with what I am trying to teach because they don't know their basic facts. " I hear 7th-high school teachers saying, "My students struggle with what I am trying to teach because they don't know how to work with fractions." Each year in math builds on the previous years' work. If students are missing crucial pieces of their mathematical foundation, they cannot build upon that foundation and acquire the new knowledge they need. The longer this is allowed to continue without repair, the more unstable the structure becomes.

I am not saying that we should neglect the required content for a grade and just reteach skills from earlier years. The second thing I want to share from this article is that we should be constantly looking for connections in the content we teach. There are many ways to embed skill practice in grade-level contexts. In fact, the new context may be what certain students need to see in order to master content that has been troubling them. As the author of the article says, making a connection between two math concepts may help "students develop a richer understanding of both (Cheng, 2010)." Where are other places that we can embed fraction understanding?

Reference

Cheng, Ivan. "Fractions: A New Slant on Slope." Mathematics Teaching in the Middle School 16 (August 2010): 34-41.

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Comments:
Hi Jeanne,

Your statement referring to students missing pieces of their middle school math foundation coupled with "we should be constantly looking for connections in the content we teach" got our attention at Imagine Education! This is THE issue we strived to address in developing Ko's Journey - www.kosjourney.com - a rich, story-based middle school math game. Please check out our website and let us know if you are interested in reviewing Ko's Journey!

Thank you for your dedication to improving math education and re-discovering technology!

Jennifer Harris
Co-Producer, Ko's Journey
www.imagineeducation.org
 
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