Avenues of Thinking

Three of the math practices described in the Common Core State Standards for Mathematicsreason abstractly and quantitatively (MP2), look for and make use of structure (MP7), and look for and express regularity in repeated reasoning (MP8) –  describe three different avenues of mathematical thinking that provide entry into and through all kinds of math problems (see graphic). Click on the table for an overview of what a math doer pays attention to, the questions they ask themselves, and the subsequent actions they take when using a particular avenue of thinking. Click on the video for an engaging five-minute presentation describing the three avenues of thinking.

Use our routines for reasoning to develop these avenues of thinking in your students and they will become powerful math problem solvers!

Avenues of Thinking Routines for Reasoning

Routines for Reasoning, Heinemann 2016

Appendix A

Routines for Reasoning, Heinemann, 2016

Grace Kelemanik ignites the 2015 NCTM audience with a framework for the Standards for Mathematical Practice,
When does 2+7+8=1?

Watch a five minute overview of a framework for the Standards for Mathematical Practice.  Pause when you’d like to spend more time considering the mathematics and the student work.


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