I saw a tweet last week that peaked my interest and sent me over to Becoming the Math Teacher You Wish You'd Had by Tracy Zayger; particularly her post on Making Sense, please take a moment to read it to understand my work below. After reading this post and watching the short video I wanted to try the same assessment to see if my students were actually making sense of problems they could try and solve. I've been working on helping my students understand the first mathematical practice recently and thought the work Tracy described in her post would be an interesting interview to conduct.
I used the problem her friend modified and below are my student's responses.
There are 25 kids and 5 dogs ini the classroom. How old is the painter?
Student - Wait, rereads. I don't really know anything about the painter. I would need to know something about the painter.
Student - What painter? it didn't say there was a painter!
Student - Why is the painter involved?
Student - What do you mean by painter? It doesn't say painter in the problem.
Student - What do you mean, how old is the painter? How would I know how old the painter is? It doesn't say anything else about the painter.
Student - Painter? I don't know what that means. I've heard of painter before (an ESL student)
Student - 25 kids plus 5 dogs, I don't get the problem.
Student - I don't get it, it doesn't take that much sense.
Student - I can't - it says nothing about the painter.
Conclusion - 9 students made sense with their response from above and 11 students did not.
My students who didn't solve correctly all took the numbers 25 and 5 and said they either equalled or is 30. There was no way to predict how my students would make sense of this problem and figure out they didn't have enough information to figure out the answer to the question. Boys and girls were successful. I had several surprises in these responses. Students who are quick to compute numbers didn't always figure out they didn't have information about the painter. A few students who work a bit hard to compute problems figure out this problem wasn't making sense. What I enjoyed the most was watching those who figured out the problem didn't make sense and their verbal reposes, I hope you can infer the inflection many of my students used.
It looks like we have more work to do with mathematical practice one, focusing on making sense of our problems before solving them by thinking carefully.
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