Introduction to Mathematical Thinking

"How I taught the course MAST 217 - Introduction to Mathematical Thinking at Concordia University in Montreal in the years 2016-18" by Anna Sierpinska, with the assistance of Vinicius Gontijo Lauar.
Lecture notes from an undergraduate course, available here.

Lectures on the Theory of Didactic Situations

Lectures on the Theory of Didactic Situations

These lectures were given in the program, "Master in the Teaching of Mathematics", at Concordia University in Montreal, as part of the course MATH 645, in the fall of year 1999. Guy Brousseau's book "Theory of Didactical Situations in Mathematics" (Kluwer, 1997) was used as a textbook in the course.

TDS-Lecture 1      TDS-Lecture 2      TDS-Lecture 3      TDS-Lecture 4      TDS-Lecture 5     

TDS-Lecture 6      TDS-Lecture 7      TDS-Lecture 8      TDS-Lecture 9     

History of Mathematics Education

Materials for a graduate course on the history of mathematics education: Readings and written assignments

Popularization of Mathematics

A course on Popularization of Mathematics

The course was offered in the program "Master in the Teaching of Mathematics", at Concordia University in Montreal, in the fall term of 2010. The course outline is available here.

There were three assignments in the course. Students agreed to have their responses to the assignments published.

Assignment 1 - Images of mathematics conveyed by various popularization of mathematics works.

Students' responses to Assignment 1 are available here.

Assignment 2 - Comparison of two popularization works

Assignment 2 was given as follows: "Describe your criteria of 'good popularization'. Take two examples of popularization, belonging to the same category (e.g. both from the category of recreational mathematics, or both from the category of popular writing, or two web sites, or two works of art, etc.), one that you would qualify as 'good popularization' and the other - as 'poor popularization' and justify your assessment."

In class, the lecturer (A. Sierpinska) presented students with an analysis and evaluation of two popular lectures in mathematics proposed by Klara Kelecsenyi in her doctoral thesis (see link in the section "PhD Theses" on the Home page). Klara Kelecsenyi used the Duval-Jakobson model of functions of language to analyze the means the lecturers were using to communicate their messages. This framework was therefore presented extensively in class.

In their responses to Assignment 2, several students used the Duval-Jakobson model to analyze the popularization works they chose to compare. Students' applications of the model revealed discrepancies in their interpretations of the categories of language functions in the model. This led to classroom discussions that led to sharpen somewhat the definitions of the categories in order to arrive at some agreement on our understanding of the categories of the model. Those definitions can be found here.

Some students used the Duval-Jakobson model not only to analyze the works they were comparing but also to evaluate them, although the model was not initially developed for the purposes of evaluation. This led to classroom discussions that resulted in adapting the Duval-Jakobson model for the purposes of comparative evaluation of popularization works from the point of view of their uses of language. We called the adaptation "The D-J scorecard" and it is available here.

Examples of Students' responses to Assignment 2.

Four examples are given. One of the students whom I asked for permission to publish his work agreed for publication but asked not to publish his name. His name appears therefore as "Anonymous Student".

[Anonymous Student] - "Comparison of Two Popular Works in Mathematics [on fractals]"

Carol Beddard - "Popularization of Number Theory - A comparison of two books"

Sujata Saha - "Which one is better? A comparison of two works that popularize fractals"

Maria Tutino - "Popular Works to Promote Mathematics as the key to Success and Advancement"

Assignment 3 - Design and implementation of a popularization activity in mathematics

Assignment 3 was given as follows: "Design a popularization activity (a workshop, a lecture, a website, etc.). Explain your thinking behind the design; justify the choices you have made. Implement the activity with an audience of at least two people without university degrees in mathematical sciences. After the activity, ask participants questions such as, a. what the activity was about; b. what he or she liked about the activity; c. what she did not like. Based on this feedback, explain how you would change the activity for repeating it with another audience."

Examples of students' responses to Assignment 3

Anonymous Student - "A work of popularisation of mathematics - From design to practice (The Monty Hall Problem)"

Abdulsalam Alreshidi - "The non-political independence of mathematics"

Carol Beddard - "A Series of Quests. Design and implementation of an activity to popularize mathematics"

Nicolas Boileau - "Popularisation of mathematics at a week-end science and mathematics popularisation event in a local Cultural Centre - Flipping coin triangles upside down"

Sujata Saha - "Towers of Hanoi - A simple puzzle that can't be ignored"

Megan Tremblay - "Popularisation of mathematics at a week-end science and mathematics popularization event in a local Cultural Centre - Making squares on a geoboard"

Maria Tutino - "The Math Puzzle Relay!"

Lee Zentner - "Popularization of Mathematics: Making Slime"

Last Modified: 01/23/19 05:42