I’ve been silent on the writing front recently. It’s been a struggle to think about formulating my thoughts, or to entertain the notion that what I might have to say is important enough to write about. January has been a struggle for me, in and out of the classroom. But what it comes down to is this — I firmly believe in my approach to mathematics education, in my philosophy as an educator around assessment, around what learning is, around what my role as an educator is. In recent days, however, there have been a lot of little voices popping up though — maybe I’m wrong, maybe I’m doing it wrong, maybe I’m leading my colleagues astray, maybe I’m learning my students astray….so. many. maybes.

But what I have come to see is that, just like for my students, the struggle makes me stronger. It causes me to pause and reflect and to learn and ask questions and debate and discuss. Sometimes, that struggle means that I need to be willing to think differently, and sometimes that struggle means that I am affirmed in my thinking and given the courage to press on, despite opposition. I need to hold the line for my students.

We’ve been working a great deal on making our thinking visible. Recently, we’ve been working on combining our understanding of fractions, decimals, percentages and area. In order to do this, we’ve been working on Steve Wyborney’s Tiled Area Problems. (check out this awesome resource here: http://www.stevewyborney.com/?p=836 here.) Students are required to use their understanding of area, fractions, adding fractions, and proportionality and relationships in order to determine the area of the shape and then share their thinking. Students need to add fractions in a meaningful context, and then make conversions to percent and decimals to share their thinking in different ways.

After we work on problems like this, I then post them on the wall outside my classroom. Every one’s work gets posted — not only the ‘best ones’. I do this to celebrate and share everyone’s thinking, but also to show and share this type of activity with my colleagues. To me, this is working with fractions in a meaningful context. It’s not a word problem. It’s not a story. It’s not a task that says, “Add the fractions.” But it is a task where students designed their own problem, and then decided how they wanted to tackle it. They were involved from the very beginning — they did the math, they shared their thinking in whatever way made sense to them. Math is more than word problems in a textbook. It’s more than isolated practice of skills. It’s about making the best decision for the situation you’re in. It’s about embracing the struggle.

Thanks so much for sharing these examples of the thinking of your students making sense of the area of the tiled shapes. I’ve shared this with other teachers at my school and they were quite interested in the talk that it will promote. 🙂

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Thanks, Janice! I appreciate hearing your thoughts and would love to hear about how your colleagues use Steve’s resources.

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