This article gives a great deal of background information but no clear direction for the pedagogy of teaching Mathematics. I find that disappointing in this day of reducing numbers of students in senior Mathematics classes. I notice that we frustrate students by our process. I also notice the stumbling blocks faced by students in senior classes, when they have not been used to showing some steps in order to gain an answer.

As every student processes Mathematics differently, we need to have a multitude of approaches. I certainly do not want to frustrate them. After all, we want understanding to foster competence. These are the key considerations, not procedure.

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