Comments on the Adler Article

There were a few quotes in the Adler issue that I found interesting and would like to comment on:
In reference to Helen’s reflection she indicated that she had “gone on too long.” I find that whenever I discuss the vocabulary associated with a concept the pacing is really important. If I stay on a subject too long then I lose the attention of a large portion of the class. For example, when discussing slope with relation to any given linear relation and graph, it’s important for me to recognize when it’s time to move on and come back to the concept at another opportunity. I realize that slope is an important idea but there is always a point when the students tune out.

“some mathematical ideas are difficult for pupils to verbalize precisely and with meaning”
I find that some students hate verbally communicating what they are working on. I was like that. Sometimes the concepts are hard to put into words, and a student will make the argument that in showing the work mathematically they are still ‘communicating’ what they are doing, just not verbally. I still believe that communicating using words is an important activity, but only when appropriate. In addition, I sometimes feel that because much of the math is often out of any context, communicating what is happening is made that much more difficult.