Memory is the residue of Thought!!!!

Response to the Jane Keiser article and an Article from the American Teacher by Daniel T. Willingham.

It seems that the main point from Jane's article is that students need to produce their own definitions first. The concise definitions that we have for terms may not and in most cases do not register with the students. It is very possible that there are words in the definition itself that they don't understand. However, I think the idea goes beyond just definitions. The key is that the students are working with and idea and making discoveries. They aren't being feed definitions and examples. My experience has been that if students discover something themselves they are much more likely to remember the definition, concept, or procedure in the future.

"What Will Improve a Student's Memory?" In this article by Willingham there is a statement the supports the thought of students struggling with an idea, making their own conjectures, and then revising. His statement has nothing to do with mathematics, but definitely applies.
"..., the first principle for students is that memories are formed as the residue of thought." If are students are just given a definition and are not asked to think about the concept or make their own definition there most likely won't be a memory. If a student creates a definition and then defends the definition he or she has definitely devoted thought to the definition. Then as the created definition receives praise or is revised the student is engaging in thought.

Therefore, (sounds like a proof) it make sense that we give students opportunities to think about mathematics through activities and investigations.