Teach the process of learning math (or other subjects) without using numbers.
Project a picture of Einstein on the overhead and ask your students to draw it as well as they can in 10-15 min. Note their approaches and comments. Students will regularly use their erasers. When they are done, collect their work, finished or not.
In debriefing, ask how many students used their erasers. Ask why they used erasers. Ask if that is an admission of failure or a sign of improving an outcome.
At this point, I relate this to learning math... that it is alright to make mistakes, as long as we correct them.
After a couple of weeks, hand the students back their drawing and ask them to identify two things they really like and two things that they think they could improve. If you feel that it is safe, have them offer one positive comment and one respectful critique of another's work. When they're done, ask them to try again, focusing on improving the two areas they thought they could improve. Once again, collect the students' work.
This time, in debrief, ask students what it would take to improve if they could do this again. I have consistently found that students comment that they need more time and some instruction in how to draw.
Relate this to their approach to math. Focus on their ability to self assess and how this improves future attempts. Relate it to their ability to think critically about their work and the work of others. Ask them if they spend the time necessary to produce quality work. Ask them how well they take advantage of the instruction they are being given.
At this point, I contacted students from the University of Oregon Art Department to come to my class and give instructions on drawing. This time it was a full class period, and students were allowed to take the drawing home and work on it. The results are that students can put all three drawings in sequence and see the progression of their success. Now is the time when I reflect on learning as a work in progress, mistakes are valuable, receptiveness to instruction affects the effectiveness of instruction, etc.
Submitted by: Stan Mercer