12 = ?
If 12 is the answer, what might the question be?
When I first asked this question to my Year 3 class, the response was a room full of blank stares. But, after a term of weekly variations on this question, it became a total success. Every child could come up with a different response, show a range of maths skills, and work together to share and check their ideas!
This specific strategy reflects a philosophical approach to mathematics – exploring the process of reaching an answer and understanding the relationships and patterns between numbers. It is not a new approach. Plato explored and taught the subject of mathematics this way and elite European scholars continued to learn this philosophical approach through the 16th century (Harouni, 2015).
Because it was good enough for Plato, I was interested in how it would work for my class. I started by working this strategy into the starter or plenary of my daily maths lessons and there are several reasons why I really value this approach.
This strategy:
1. Is differentiated!
The more math you know, the more questions you can come up with and the more challenging the questions can be.
2. Engages students.
After the initial shock of being asked to do something so different (gasp!), they enjoyed the control of making up their own questions and having a classmate solve and check them.
3. Allows for quick assessment.
By posing this question in the middle of a unit or the end of a lesson, I could quickly assess what skills students understood and could apply, and what needed more practice.
4. Is adaptable.
I have asked students to show me more specific skills through answer-question strategy.
For example, it has been very useful to teach and practice word problems. Give the students a number and ask them to write their own word problem.
Areas in which I have found this strategy to be particularly useful is to practice word problems and to emphasise reverse operations. You could also give children an area or perimeter and ask them to create different possible shapes, explore adding and subtracting fractions for a specific amount or show students a 2-D shape and ask what 3-D shapes it could create.
This ‘here’s the answer, what’s the question?’ strategy has worked successfully in maths lessons across a range of ages. However, it does take practice. My class really struggled the first time, but after modelling the thought process, sharing countless student examples and repeating it each week, it became a popular class activity – and my favourite math toolbox strategy.
(If you’d like to read more about the philosophical approach, as well as other approaches to teaching mathematics, this Harvard dissertation by Houman Harouni is an interesting read.) https://dash.harvard.edu/bitstream/handle/1/16461047/HAROUNI-DISSERTATION-2015.pdf?sequence=1
Ashleigh Johnson shares her brilliant expertise with us again this week. Let her know if you try out her tactic @davisan09
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