“Students may not understand what they see, rather, they see what they understand.” Awesome Aaron.

This comment led me to

“… mathematics as a practice seems to be mainly in the service of economics and warfare. I am calling for a radical reimagination of mathematics, a version that embraces the body, emotions, and harmony.

Where is math as a human process being created by human people ­ creating versus redoing what others have done.” – Rochelle Gutierrez, p. 45
http://www.msri.org/workshops/836/schedules/21847/documents/3077/assets/28783

Amen. 10/10. Thank you Rochelle.

Reminds me of the distinction between Conceptions vs. Misconceptions; Windows and Mirrors (In Lak’ech)

Or is it okay in this case to say you did a great job of understanding and you recognized what I wanted you to recognize but you simply made a calculation error?

Right. If I’m confident that students didn’t do what they meant to do, I don’t have a problem making that observation, telling them that their intent makes a lot of sense to me, that they just need to make sure they enacted it correctly.

I feel that this is a great thing to think about when looking at and responding to student work. It will feel like more work and might be more difficult on the teachers part, but it should have a valuable impact.

Roberto,
Ain’t that the truth! I feel like a of of my energy gets spent on trying to “ignore” that test-oriented culture that is far to prevalent in our district and feeder schools. Healthy attitudes towards assessment are just as important as healthy attitudes towards “mistakes”.

I love the line in Principles to Actions that says, “support the learning of important mathematics and furnish useful information to both teachers and students” and that it should motivate, support, and improve math learning.