In this Mathematics Teacher article, teacher/consultant/author Marian Small says “too many students sit in a mathematics class where the material being taught is just not quite at the right level for them” – either too easy or too difficult. The best way to engage all students, Small believes, is asking open-ended questions. Some examples:
- Instead of asking fifth graders to multiply 42 x 37, pose this problem: You multiply two numbers that are 5 apart. What could the product be? I hope some of you use small numbers and some larger numbers. Some students might multiply 3 x 8 while others multiply 92 x 97.
- There are ___ students in one school and ___ in another school. Choose values that make sense to you for both blanks and tell how many there are in both schools together.
- You multiply two numbers and the tens digit of the product is 8. What could you be multiplying? One student might multiply 40 x 2 while another multiplies 140 x 2 and the class discusses the connections.
- A number is a lot like 50. What might it be? What’s a number that you think is very different from 50? The teacher follows up by asking what 25 and 50, for example, have in common, or how 49 and 50 are different.
- You evaluate an algebraic expression. If you increase the value of the variable just a little, the value of the expression increases a lot. What might the expression be?
- The answer to a question is the word quadratic. What could the question be?
- More students are engaged because there will be a variety of unique answers. - Because it’s easier to be right, students’ confidence increases.
- A variety of responses produces a richer mathematical conversation.
- There’s the potential to change students’ beliefs about the nature of mathematics.
Please Note: This summary is reprinted with permission from issue #1046 of The Marshall Memo, an excellent resource for educators.
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