Evaluating Statements about Enlargements

11 May

We recently used the Mathematics Assessment Project formative assessment lesson on Evaluating Statements about Enlargements.

I had just returned from NCSM where I heard Tim Kanold’s session “Beyond Teaching for Understanding: The elements of an authentic formative assessment process”. In the session, he suggested that no more than 35% of class should be the teacher leading from the front of the classroom. I was determined to figure out how this played out in my classroom when I got back to school. I also found a blog post where he talks about leaving the front of the classroom behind.

We started with Candy Rings.

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When I got the results from the first poll, I knew I was in trouble. Why did you choose “correct”, Amber? Two of the small rings has the same total circumference as one of the large rings. Why did you choose “incorrect”, Ryan? Some of the pieces on the larger ring look broken. Those on the smaller ring are closer together.

Against my better judgment, I asked the next question. After all, construct a viable argument and critique the reasoning of others is how we are learning math, right?

If the price of the small ring of candy is 40 cents, what is a fair price for a large one?

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About half of the class used proportional reasoning, deciding that 80 cents was fair. The other half used business reasoning. Some included tax. Some decided that the larger portion should have a bit of a discount. All of them had an argument for why they chose what they did.


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No one thought that Jasmina reasoned correctly about the amount of pizzas.

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And only a few insisted on using business sense to come up with a fair price for a large pizza.

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Students then worked with their teams to determine whether their cards with statements about enlargements were true or false. I gave each team 6 cards to evaluate. They reasoned abstractly and quantitatively. They constructed viable arguments and critiqued the reasoning of others. They even had a good time.

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This particular class clocked in at exactly 65% peer-to-peer discussion. Even then, the 35% whole group discourse wasn’t just one raised student hand at a time. I used the Quick Poll results to selectively call on students who don’t always raise their hand. They presented their argument and the class decided whether to buy it or not. I was there to facilitate the conversation and move it forward. I’m not sure whether that only counts as “leading from the front of the classroom”.

Either way, the journey to leave the front of the classroom behind continues …


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