At the workshops, I asked participants to choose between two activities:
I asked them to go to one side of the room if they wanted to write a recipe and the other side if they were interested in writing equations/diagrams/algorithms. After they separated into these two large groups, I asked them to divide themselves into smaller groups to do the activity, or to work alone if they wished. Only one person chose to work alone; the others worked mostly in groups of two or three, occasionally in a group of four or five. Many of the groups using math symbols made several equations, or elaborate flow charts. As a whole, the recipes, equations, and diagrams take up the importance of various intellectual aspects of math instruction equally with the emotional aspects.
At each workshop I gave participants a sheet of questions: What did you hear that you didn’t already know about? What did you hear that confirms your own experience? What seems to go against your own experience? What findings would you most like to implement in your own situation? If/when you try to implement these findings what gets in your way? Eighty people turned in these questionnaires to me at the end of the workshops; I discarded answers from four people who did not teach math (from the Fundamentals Articulation Committee, which includes both English and Math instructors) and who indicated on their sheets that they were not math teachers.
As I thought about writing this manual, I was especially interested in the answers to the final two questions: "What findings would you most like to implement in your own situation?" and "If/when you try to implement these findings what gets in your way?" I knew that the answers to the first question would guide me about what to write about, and the answers to the second would shape what I had to say on the topic.