Number talks#
See also: teaching-mathematics, number-talk-examples
References: QCAA Number talks fact sheet, Math for love
Boaler (2015) identifies this as the "best strategy" she knows for teaching number-sense and math-facts at the same time. Apparently perfect as a lesson starter or for parents at home.
Example problem given is \(18 \times 5\) which, in one application, resulted in six different ways to solve it. Blog post includes video of an individual student being asked \(36 + 9\) and using an interesting approach. An addendum talks about another method where students note that \(36\) is \(4 \times 9\) and so the answer is \(5 \times 9\).
Method#
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Teacher poses a problem
Often a mental arithmetic problem, but can include other types (visuals etc.)
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Students mentally solve the problem
Indicate they have an answer by holding a thumb - or additional fingers for additional methods - to their chest. To allow others to proceed without time pressure.
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Students share their answers
Teacher records all solutions, no comment on correctness.
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Students explain their thinking.
Students explain and teacher writes the steps on the board
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Discussion and consensus
By the end have multiple methods and a consensus on the correct answer
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Followup - if appropriate
Suggestions#
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Draw upon and share visual methods. Aim being to open possibilities.
Number talk images 2. Scaffold the introduction of the approach 3. Low floor 4. Be explicit about the protocol
Impacts#
Changes - Students and teachers#
Following tables (adapted from Parker & Humphreys, 2018) summarises what changes for students and teachers during number talks
For students
From | Towards |
---|---|
Remembering | Reasoning |
Focusing on the answer | Focusing on how they get their answers |
Doing a problem “the teacher’s way” | Doing a problem in a way that makes sense to them |
Expecting the teacher to tell them whether their answers are right or wrong | Expecting their teacher to ask them to verify the answers for themselves |
Trying to avoid mistakes | Seeing mistakes as opportunities to learn |
Seeing confusion as bad | Getting comfortable with cognitive dissonance |
Reproducing their teacher’s method and asking the teacher when they get stuck | Listening to their classmates’ methods and asking them questions |
Thinking there is one way to solve a problem | Knowing there are many ways to solve problems |
Relying on the teacher to direct discourse | Jumping in to share responsibility for discourse |
For teachers | FROM | Toward | | ---- | ---- | | Asking questions you already know the answers to | Asking questions you're genuinely curious about | | Focusing on answers | Focusing on reasoning | | Being the "primary explainer" | Letting kids do the thinking | | Listening for a particular response | Listening to students | | Demonstrating how to solve problems | Finding out how students solve problems | | Verifying correct answers | Expecting students to verify their own answers | | Knowing ahead of time where a lesson will go | Responding flexibly to where students' thinking leads | | Being in charge of classroom discourse | Sharing responsibility with students for classroom discourse|
References#
Boaler, J. (2015). Creating Mathematical Mindsets: The Importance of Flexibility with Numbers. In Mathematical Mindsets: Unleashing Students' Potential Through Creative Math, Inspiring Messages and Innovative Teaching (pp. 33--56). John Wiley & Sons, Incorporated.
Humphreys, C., & Parker, R. (2023). Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding, Grades 3-10 (1st ed.). Routledge. https://doi.org/10.4324/9781032681573
Parker, R., & Humphreys, C. (2018). Digging Deeper: Making Number Talks Matter Even More, Grades 3-10. Taylor & Francis Group. http://ebookcentral.proquest.com/lib/griffith/detail.action?docID=5584097