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The problem involved mathematical equivalence (i.e., 4+5+7=__+7), which is known to be critical to later algebraic learning. In the speech-only videos, the instructor simply explains the problem. In the other videos, the instructor uses two hand gestures while speaking, using different hands to refer to the two sides of the equation. Students who learned from the gesture videos performed better on a test given immediately afterward than those who learned from the speech-only video. Another test was given 24 hours later, and the gesture students actually showed improvement in their performance while the speech-only students did not.

The consideration of cord length is very important in a bungee jump—too short, and the jumper doesn’t get much of a thrill; too long, and ouch! In this lesson, students model a bungee jump using a Barbie® doll and rubber bands. The distance to which the doll will fall is directly proportional to the number of rubber bands, so this context is used to examine linear functions.

I have started this blog to document, revisit, and hopefully improve upon many of the approaches that have helped me the most over these years. Some of the postings are “mini-lectures” that most of my tutees have probably heard (cue the eye-rolls). Others are musings about the variations in how math seems to be understood or taught.

Did you ever read a book called “The Number Devil”  by Hans Magnus Enzensberger? If you ever see a copy of it, grab it and have a look. In chapter one, Robert, the hero of the story, meets the Number Devil. The Number Devil explains to Robert that knowing a little bit of arithmetic, such as addition and subtraction, is quite useful for when the batteries of your calculator run out but really it has little to do with mathematics. How often do teachers fail to grasp the distinction? How often do we overstate the importance of the “skills” that we fail to recognize the importance of their application? It’s like a football team that focuses so much energy on their training sessions that they forget to turn up to play their game.