A short summary of the goals and the content of Math 010

The course is intended for undergraduate students who are preparing or are hoping to prepare for elementary teaching. The course cannot be used as part of an honours program in mathematics, that is, a ` mathematics major'.

The course meets three times a week for one-hour lectures. In addition, the students go out once a week for ten weeks, in pairs, to a local elementary school assigned to them, to provide an enrichment class to a group of students from grades 7 and 8. This enrichment class forms part of the StepAhead enrichment program. In most cases, the two grades are combined, and the schools are expected to select the students who may take the enrichment. We recommend to the schools that they select the top 1/4 or 1/3 of the class.

I try to accomplish the following things in this course:

1. Prepare the student teachers (and potential student teachers - not all are in the faculty of education) to teach the enrichment material they will present.
   
2. Have them present the material, relate their lessons to the Ontario curriculum, and to submit reports on all their school visits.
   
3. Discuss elementary mathematics with the students with a view to understanding the connections between mathematical topics, at a depth that will enable them to make informed judgments in teaching situations later on. The topics discussed include number patterns, prime factors, divisibility tricks with explanations, fractions, place value, decimal expressions (repeated and terminating), rational and irrational numbers, word problems, the Theorem of Pythagoras (with explanation), polyhedra, Euler number, angles, areas. In all cases the stress is on looking behind the formulas to the logical understanding that gives rise to them. At the same time I try to present material in the context of imagined teaching situations, so that the questions combine logical elements with pedagogical elements. For example, when you want to introduce fractions you not only stress the fact that there has to be a clearly understood unit (the thing you are taking a fraction of) but you also ask yourself what pictures or concrete materials are least likely to distract elementary school students from the central idea you are trying to teach.

The enrichment material is presented in a two year cycle, so that students in the elementary schools do not get a repeat in grade 8 of what they saw in grade 7. The material is written up in two booklets I have written for the purpose. These serve as "text" for the course.