reflection theory

Thirteen Days

A huge piece of my identity is invested in being a mathematics teacher.1 This week I began a new and interesting challenge as a university faculty member preparing pre-service elementary and secondary mathematics teachers. This provides me more time to think deeply and openly about the entirety of the mathematics education enterprise, and put some of those ideas into public circulation through speaking and writing opportunities. I am really looking forward to that.

It also means that I am charged with orchestrating the formative experiences with mathematics teaching for about half of my province’s new teachers. That fact is terrifying. I am given just thirteen days in each course with which to shape the impressions, experiences, and ambitions of the future teachers of my province, city, school division, and (quite possibly) my own children. Thirteen days.

The following is the introduction from my course outline. It is designed to introduce the students to myself and the lofty ambitions contained in each and every one of those thirteen days. While it is beyond verbose, I believe it captures my hopes for each of my students, their students, and the thirteen days that we will work together.

It has been suggested that “fanaticism consists in redoubling your effort when you have forgotten your aim” (Santayana, 1905/2011, p. 8), and while I am tempted to wear the label of Math Education Fanatic with pride, I do feel that understanding a purpose is important for any learning ecology. Therefore, in order to avoid being labeled a fanatic (albeit, begrudgingly), the contents of this course (e.g. readings, writings, discussions, presentations, etc.) have been designed with three general outcomes in mind:

  • to build empathy for your future students
  • to be applicable to the work of teaching
  • to develop appreciation for the possibilities of mathematics education

Stated globally, the goal of this course is to provide opportunity for you to situate yourself with-and-in the ever-evolving climate of mathematics education in Saskatchewan, Canada, and abroad.

That is a significant legacy to tackle, and one that (locally) has undergone a significant philosophical change—at least to the extent that policy documents (e.g. Common Curriculum Framework for K-9 Mathematics 2006, Common Curriculum Framework for 10-12 Mathematics 2008) and the renewal of curricula (see can constitute change. But change is not legislated into being, it is intentional and informed by both theory and experience—by research and practice. Here, you will be expected to show evidence of an open, reflective, insightful, and critical stance toward the teaching and learning of mathematics. By doing so, you will begin to build the skills and agency necessary to enact mathematics lessons that align with the vision proposed in policy and curriculum documents.

Teaching and learning mathematics in Saskatchewan is changing, and while Newtonian physics would have us believe that objects in motion tend to stay in motion, the opposite seems to be true for transformative change in mathematics education. Perhaps, then, just a touch of fanaticism is required, lest we fall prey to another compelling aphorism: The more things change, the more things stay the same.


Alberta Education. (2006). Common curriculum framework for K-9 mathematics: Western and northern Canadian protocol. Edmonton, AB: Alberta Education.

Alberta Education. (2008). Common curriculum framework for 10-12 mathematics: Western and northern Canadian protocol. Edmonton, AB: Alberta Education.

Santayana, G. (2011). Introduction. In M. S. Wokeck & M. A. Coleman (Eds.), The life of reason (Vol. VII, pp. 1-19). Cambridge, MA: Massachusetts Institute of Technology. (Original work published 1905)


  1. Maybe more than is considered “normal” or “healthy,” but my obsession with my profession is not nearly as unforgiving as my undying devotion to the Toronto Maple Leafs.

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