MATH 4100

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Table of contents


For this year, the material will be on the Moodle Site:

The material below is form a previous year (2007)

Basic Information on the Course

Mathematics 4100 Topics in Mathematics Education will meet in Ross S525 (the MathStat Lab, near my office ;-) ) Thursdays 4-7 for the winter semester.

The rough design is as a 'capstone' course for people with an interest in teaching mathematics. It will be run roughly as a seminar, with an emphasis on group discussions and presentations by students in the class. The details of what materials we read and discuss will be worked out during the semester, depending on the interests and questions expressed in the class.

One theme of current research in Mathematics Education is work on Mathematics for Teaching (MfT). In this work, people look at core areas to achieve a profound understanding in order to recognize the variety of approaches which can work, the possible gaps which certain approaches will create, the misconceptions that may underlie student responses, etc.

Here is the Course Outline

Here is Assignment 1 Your Math Ed Autobiography

An update: I am going to modify the marking scheme to combine the Portfolio and the Project. I am suggesting that there are a number of smaller writing / reflection / engagement activities which you can do and combine into a porfolio, in smaller chunks. I will talk more about those in class, and post a revised outline after that discussion. I also think the portfolio may be of more value to you, after the course.


I have some visitors lined up for the class.

  • the author of the paper on the Evolution of the Concept of a Function, Israel Kleiner, will come to the class, but not for a few weeks [This got displaced - sorry].
  • January 25, Shirely Dalrymple, a teacher in York Region, a former president of the Ontario Association of Mathematics Educators, and a secondee at the Ministry of Education working on materials for the revised mathematics curriculum, came to the class. Among other things, she helped lead a discussion of the 'functions thinking problem' I posted on the phorum on the weekend. She has sent some links which are on the links pages. February 1, we will follow up some of the issues raised, included an effort to fully explore the alternative approaches to the original problem (see the Phorum).
  • Shortly after that (February 8?), Anthony Azzapardi, a teacher with the Toronto District Catholic School Board who has been seconded to the ministry and has been leading the revisions of the mathematics curriculum for the last four years will come and lead a discussion about this revision, what needs have been driving it, and what issues are still not solved!
  • Margaret Sinclair (Faculty of Education) lead a session on Technology in Mathematics Education on March 22. Margaret is a lead investigator in a large Texas Instrument project on the use of TI calculators in high school classrooms. Here is a GSP Sketch bundling some of her examples together
  • There were two session on Ethnomathematics / History of Mathematics in early March.
  • Michael Szeto and I are leading an exploration of some optimization problems, using more direct reasoning than 'calculus'. The initial problem was to maximize the area of a triangle with vertices on a unit circle.

Here is a GSP sketch to explore this: GSP Sketch to Explore Here are two more sketches: GSP Sketch on maximizing area with fixed perimeter with a fence along the river and GSP Sketch on maximizing area with fixed perimeter.

Upcoming Fields Institute Mathematics Education Forum meeting: January 20, 10-2. (A number of people in the class attended - there will be two more sessions this semester.)

From the January 18 class, there is an Assignment I as well as a handout of the program objectives for the Mathematics for Education program, that can assist you with your reflections towards the portfolio.

Assignment 3 and Portfolio Information is available here.

For a week, from March 29, the Education Week Special on the Digital Decade is available free at:

I don't know the quality of the material, but there is a lot there, primarily in the US context. One quote: students use technology more outside of school than in school.


Some Links and Resources for the Course. I am continuing to post new material there, including a link to some nice examples of 'functions based' problems developed by Peter Taylor (Head of Math at Queen's, and a text book author).

Link to 4100 Phorum (|Math)

Link to Links and Resources for summer Spatial Reasoning projects