If there is one discipline that is associated with the terms “question” or “problem,” it seems to be math. When preparing to write this I thought, “Well, I have some ideas, but let’s see what’s out there on the web.” When I used my trusty search engines to look for “mathematical questions” or “student questions in math” or anything similar, the results were consistent. I found lots of pages of math worksheets, activities, and assorted math questions and problems, all designed to help teachers ask good math questions. That’s fine, and useful, but didn’t help me think about students asking questions about math.
Fortunately, I’m persistent. Sometimes searching is a matter of finding the right words. In this case, the critical term is “problem posing.” Advocates of problem posing want students to ask their own questions about math, not just seek out the answer to a presented problem. Problem posing mirrors the mathematical curiosity of mathematicians and helps students envision math as an environment for exploration rather than a never-ending series of calculations. While it helps students take responsibility for their inquiry, it can also give teachers a clearer window into students’ mathematical thinking—win win, it seems.
A problem-posing session typically begins with the presentation of a mathematical stimulus . This might be a shape, a situation, even a game that uses logic. Once you have a stimulus, there are two steps. Listen to Annie Fetter from The Math Forum.
Noticing. Wondering. Do these sound familiar? They might have different labels, maybe “observing” and “questioning” or “inquiring.” But as I’ve written this series of posts about questioning in different disciplines, I’ve been struck by the way we keep coming back to the same two queries: What do you observe? What do you wonder? Some of us might not think of questioning that way in mathematics, but it works–and it is central to mathematical thinking.
If, after noting their observations, students aren’t sure about the kinds of questions they might ask, English (1997) suggests prompts like:
What are the important ideas in this problem?
Where else have we seen ideas like these?
Do we have enough important ideas to solve the problem?
How might you change some of these ideas to make a different problem?
What if you were not given all these ideas: What might the problem become then?
What if you were to add some new ideas? What new questions might you ask?
If you are looking for stimulus problems for problem posing, you could start by browsing Annie Fetter’s blog at the Math Forum or the Forum’s Puzzles and Problems section. You also might want to explore some of Dan Meyers’ materials, particularly his 101 Questions site. That site is particularly helpful if you want to dip you toe into problem posing in your warm-up activities.
Whitin (2006) calls problem posing “an adventure waiting to happen.” Do your students think of math as an adventure? If not, perhaps the problem-posing journey might be a way head in the right direction.
English, L. D. (1997). Promoting a problem posing classroom. Teaching Children Mathematics, 4, 3, 172-179.
Whitin, D. J. (2006). Problem posing in the elementary classroom. Teaching Children Mathematics, 13, 1, 14-18.
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