Category: reflection

On Scalene Triangles

[Update Nov 4th, 2021: Since this initial post, I have intentionally backgrounded the term “#FreeScalene” because I am now at a place where I feel that facetiously couching a classroom activity in this language treats the work of important social movements with too little respect. I leave this post here (complete with this addendum) because this blog is a place to archive my professional trajectory, and I feel this update is an important piece of that growth.

If you want to read my thoughts on the merits of debating geometric definitions (especially triangles), portions of this post are expanded upon here.]

[Original Post: Published March 2020]

This past weekend I was invited to Toronto to give the 2019 Margaret Sinclair Memorial Award Lecture at the Fields Math Ed. Forum at the Fields Institute for Research in Mathematical Sciences. While the layers of the organizational hierarchy can be a mouthful, the bottom line is that I was given the great honour of presenting my thoughts on the teaching and learning of mathematics–as they are formulated at this time of writing. I broke the day into three distinct sections: The recipient’s lecture, a poetic provocation about hotdogs and mathematics education, and a gallery walk composed of some of my favourite invitations from my career to date.

(Link to the video archive of the invited lecture.)

probability reflection

An Improbable Run at the Rosenthal Prize

Post author By natbanting
Post date January 11, 2020
2 Comments on An Improbable Run at the Rosenthal Prize

In early December, I found out that my submission had been selected as the winner of the 2019 Rosenthal Prize for Inspiration and Innovation in Math Teaching. At the time, I had zero reference point to understand what that meant, but have since experienced first hand the hospitality of the international math education community. This post is not a summary of the winning submission; that detailed lesson plan has been posted on the MoMath website. [UPDATE April 2021: Rachel Welbourn a gracieusement traduit les documents de la tâche en français.] Here, I want to take the time to reflect aloud on how this whole thing happened–a process, I think, might be of value for math teachers. I’ve attempted to distill my take-aways into four categories, but, in actuality, they still exist (for me) as a tangled heap composed of equal parts disbelief, gratitude, and empowerment to pursue the next challenge.

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.

equations logic reflection

On Brilliance, Relevance, and Impotence: A Classroom Example

Post author By natbanting
Post date February 5, 2018
1 Comment on On Brilliance, Relevance, and Impotence: A Classroom Example

Everyone knows that you can’t wish for more wishes, but no one says you can’t wish for more genies.

According to the binding rules of genies (as published by Disney in the 1992 film, Aladdin), there are a few restrictions on what can and cannot be wished for. Probably the most famous restriction is that there is unequivocally no circumstance in which one is permitted to wish for more wishes. This is grouped with three other limitations stating that genies will not kill people, make people fall in love, or revive people from the dead. Other than that, the wishes are limited only by the imagination of the master.

inequalities infinity reflection

Second-hand Student-ing

Billy: “Banting, I have a question for you.”

It was 5-minute break between classes and I was trying to reset the random seating plan, open up the electronic attendance system, and load the image that would serve as a starter for the day’s lesson. During this small window of time, questions are usually about missing binders, requests for future work due to mid-semester holiday plans, or updates on my ever-present pile of grading. In short, I usually do not want to deal with them. Begrudgingly, I obliged.

Billy: “I need a piece of paper and a pen”

reflection

Real-World: An Attack on “Relevance”

Post author By natbanting
Post date November 1, 2016
6 Comments on Real-World: An Attack on “Relevance”

**deep breath**

Last week, I caught myself saying something to a pre-service teacher as we planned a Grade 1 lesson for the making of 10s. I asked her,

“Why would the students need to know how to make up 10s?”

When she was auspiciously silent, I filled the space with a statement said entirely tongue-in-cheek. It was only upon reflection, that I kicked myself for not being able to shut up and allow her to think. I said,

“…because my job is to convince teenagers they need logarithms, and that is much more difficult.”

equations estimation games pattern reflection stations tasks

TDC Math Fair 2016: A Summary

Post author By natbanting
Post date June 29, 2016
3 Comments on TDC Math Fair 2016: A Summary

Background:
On June 15th, my Grade 9 class and I hosted our second annual math fair. What started out as a small idea has grown into a capstone event of their semester. This year, we had 330 elementary school students visit our building to take part in the fair’s activities. Several people (following the hashtag #TDCMathFair2016) commented that they would like to do similar things with their student transitions. This post details the rationale behind the event, how we structured it, what stations we had, and feedback/advice from our exploits.

reflection

Mathematics Is: Student Impressions

Post author By natbanting
Post date June 20, 2016
4 Comments on Mathematics Is: Student Impressions

I have taught the second half of a Math 9 Enriched course for the last three years. The students generally finish two-thirds of the curricular outcomes during the first semester (with an different teacher). This alleviates the perpetual nemesis of time, and leaves me with no excuse to stretch the boundaries of what is possible in a classroom.

I spend most of the time developing a classroom ecology focused around conjecture, community, and curiosity. The result is a constant focus on problem shaping, solving, and re-posing.

At the end of the semester, I ask students to respond to a simple prompt. They have ten minutes to answer:

What is Mathematics?

reflection

Classroom Clean-Up

No more students for this year. I’ve spent a full day cleaning up and re-arranging my space for my incoming intern (for whom I’m very excited for).

Amidst the broken calculators and stray linking cubes, I found a note that a student wrote me from my first year of teaching. It served as a brief reminder of why I attempt to curate a community of mathematical action with my students. It isn’t the easiest way to teach, but has a limitless ceiling.

math wars reflection theory

Math Wars North

O Canada!

The debate about best practice in Canadian math education has exploded once again. This time attracting high profile combatants.

This post is not meant to resolve deep-seated values, but rather provide a perspective that gets lost in the partisan arguments. It wouldn’t take a long time to place me in a camp, but that would be assuming that there are two camps that want drastically different things.