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Students are given a statement and then they justify if it is always, never or sometimes true. They use examples, counterexamples, and/or algebraic reasoning.
Students are given a statement and then they justify if it is always, never or sometimes true. They use examples, counterexamples, and/or algebraic reasoning.
Always, Sometimes, Never increases depth of understanding. It connects to the mathematical idea of counterexamples and encourages critical thinking. This structure also creates mathematical discourse in a debate style to critique other's reasoning. Here are some general questions. Fawn Nguyen also has a blog post on this with some more resources.
Always, Sometimes, Never increases depth of understanding. It connects to the mathematical idea of counterexamples and encourages critical thinking. This structure also creates mathematical discourse in a debate style to critique other's reasoning. Here are some general questions. Fawn Nguyen also has a blog post on this with some more resources.
Tips for implementation:
Tips for implementation:
Give individual think time before asking students to collaborate. Use questions to encourage a first step. Can you find an example where this is true? What if you try actual numbers? Would graphing help (thank you Desmos!)
Give individual think time before asking students to collaborate. Use questions to encourage a first step. Can you find an example where this is true? What if you try actual numbers? Would graphing help (thank you Desmos!)
Listen to student conversations. Use this to help decide who to call on based on students who need to increase their mathematical status.
Listen to student conversations. Use this to help decide who to call on based on students who need to increase their mathematical status.
If students are needing a movement break, have them gather in corners of the room based on their response. Then have the always group go first, then the never, then sometimes tease out the learning. Return to whatever group is true at the end to see if you can justify a response as a class.
If students are needing a movement break, have them gather in corners of the room based on their response. Then have the always group go first, then the never, then sometimes tease out the learning. Return to whatever group is true at the end to see if you can justify a response as a class.
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