[[https://www.edweek.org/teaching-learning/teachers-nurture-growth-mindsets-in-math/2015/09][Teachers Nurture Growth Mindsets in Math]]
Stanford University math education professor Jo Boaler explains the concept in a video included in the course: In a traditional problem, a teacher may give students the dimensions of a rectangle and ask them to find its perimeter. In an open problem, a teacher may ask students to draw three rectangles with a certain perimeter and explain their work.
Exploring Concepts Mariel Triggs, who teaches math at a private high school in San Francisco, said her students unpack open math problems step-by-step to explore a concept.
For example, she will ask them how many baseballs it would take to fill a room, and then allow them to determine all of the information they need to solve the problem. After they arrive at the answer, she will ask them how the problem would change if they expanded the dimensions of the imaginary room.
“I get these students and they will say, ‘I am not good at math,’ and I began to realize that what they were really saying was, ‘I don’t know how to do the problem in front of me,’ ” she said. “I frame it like a fun puzzle.”
Teachers said those strategies dovetail nicely with the Common Core State Standards’ emphasis on sense-making, abstract reasoning, developing strategies to use math concepts, and critiquing the reasoning of others.
And open problems allow students to understand how math concepts relate to each other, rather than merely understanding how to use an algorithm the teacher prescribes, they said. It’s not that getting the correct answer doesn’t matter, Montoy-Wilson said. But open problems emphasize that the process of arriving at the answer matters too, she said.
This is why math class always felt preparatory and not like the real thing - because it never was real in the important sense. I never had application. and application can be a tight loop, a present-moment thing, it doesn't have to be Out There in the complex once-we're-an-expert universe. You can look at the water right now.