Amie Albrecht retweeted this the other day over a year ago (I just came back to finish this post):
It reminded of me when I used my son to try out the first part of this NRich problem:
I’ve used this problem with middle school students before…but I wanted to use it in a math for elementary teachers undergraduate class, so I needed to see how an elementary student would think it through (he’s in 5th grade).
He attempted some mental thinking about the problem at first. But, I could tell he was going to get frustrated. I found something that could work as counters for him and asked him to represent the problem. He argued with me about it and finally said “only babies use these.”
I pushed him to use the counters…and he figured the problem out quite simply.
Using manipulatives makes problems so interesting to think about. But, I just asked him about that day and he agreed that the tool made the problem easier, but he didn’t like using them.
We need to use more manipulatives in math class!
Reflections in the Plane 
Yes! And a variety of them so students can chose which manipulative would work best for them in the particular problem they are representing!!!
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