began with an introduction to the learning objectives
and the requirements of the course which were communicated by the instructor
and also included in the course syllabus. Students
were given a long collection of problems which would be active for the first
three weeks of the quarter. These problems were drawn from many content
areas, encompassed many problem solving approaches and methods and were
labeled for degree of difficulty from 1 to 3.
As I planned
this course I envisioned multiple sites of student learning:
- I anticipated that the need
for some mini-lectures on mathematical concepts would emerge as students
asked questions about problems which they did not understand because they
did not have the necessary resources (mathematical prerequisites).
- A second site for learning
would be demonstrations of problem solving techniques by the instructor.
These would used to
illustrate both general approaches (heuristics) and particular problem
- Yet another place where
learning was intended to take place was during whole group discussions.
- Perhaps the most important
site of learning was the work in collaborative groups during class.
- Finally, students worked
individually out-of-class on solving problems and writing up solutions.