I remember who was perhaps my best math teacher in my undergraduate schooling. It was his first semester at BYU, teaching ODEs. He had a very good method of teaching, including emphasizing that it really doesn't matter what the variable is called. He had some variables called ":D", or "sassy," or something random like that. This way, he helped us look a little more at what we were actually doing. His teaching was effective enough that once in a while, we would talk about the subject for 20 min, and he would tell stories for the other 30 min. Some could argue that this was a waste of time, but we found it effective. To this day, ODEs is still one of my favorite topics in mathematics.
But the thing I learned from Dr. Humpherys was the use of "the buffer." When we came to a part of a problem where we needed to calculate something, he wouldn't clutter up the board. Rather, he would go to the extra board on the side of the room (which he called a buffer, after the idea in computer programming where you store some temporarily important information and then delete it when you're finished). Then when he finished, he would go back and put what we calculated into the equations.
I am currently helping the USU Physics faculty as they interview candidates for the Physics Education Research position. Last week, as I was summarizing some student feedback, I read a lot of comments on how they liked how he put the important equations on the side. Or, in Dr. Humphery's terms, he used "the buffer." So, it's not just me. There's extra space on that board--use it!
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Ha! My board is usually more full than not. I have resorted to using different whiteboard marker colors to help my kids tell where one explanation starts and ends.
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