For real, it has changed me, as both a teacher and a mathematician. Example: I now always calculate tip in my head. (Really and truly, I was one of those folks who used the tip calculator on my phone... Not proud of it, just sayin.') Another example, I never ever tell kiddos they "can't" take a larger number away from a smaller number. Everyone know why? Because a few years later, they'll be expected to learn about negative numbers!! We'll be discouraging their mathematical thinking before it even begins. Now I say, "If you subtract a larger number from a smaller number, you'll have to work with a negative number, and you won't be learning about those for a few more years, so let's see if we need to ungroup instead."
Truly, It's the little things that make a huge difference. Like with Math Talk. Here's a link to a little freebie I used with my awesome teammate Casey last year when we were both fostering math talk with cue cards for the kiddos to refer to.
Also, I created a huge bundle of Higher Level Thinking Questions for Math Talk. Click the pic below to take a closer look and then try the preview to download 6 free cards to try in your classroom.
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To me, the concept of encouraging discourse in math is very similar to methods I have always used to promote higher-level discourse in ELA. How do you foster Math Talk in your classroom?