I’ve been working through Jo Boaler’s “How to Learn Math” course, and it’s fantastic. It was really good until about session 5 when it became awesome. She describes a classroom activity that I believe is just as beneficial for math teachers as it is for students. She uses Number Talks as a way to develop number sense and flexibility among students. You can get a quick feel for the idea through her recent number sense video. But here’s the notion in a nutshell: You pose a question that has some potential for math flexibility but is accessible (“What is 21 x 8?” or “What is the perimeter of this rectangle with the missing corner?”) and ask students solve mentally without an algorithm. Then, you ask a student to share how he or she developed the answer. Model that student’s solution strategy. Now, ask a student who used a different approach to explain. Model that. Repeat!
Students will see the many ways numbers can be manipulated. Their own thinking in validated, but they also see and understand alternate solution methods.
When teacher see several other legitimate solution methods, they will be open to their students’ brainwork.