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classroom structure factors routine tasks theory

Going with Your Gut

I teach university courses in mathematical problem solving at St. Francis Xavier University during my Summer break. The classes involve initiating numerous problem solving episodes and then interrogating and filtering our collective experience through the lens of current theory in the field. This structure provides plenty of opportunity to workshop new ways to launch tasks, and this year, I began experimenting with a new sort of launch routine that had pleasant results. This post is an attempt to reflect on why that may have been the case.

First, however, you must indulge me by responding to a prompt in five seconds or less.

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assessment classroom structure

The Interview Quiz

I love creating curious tasks for my students. I love anticipating their thinking, observing their milestones of thought, and then posing new, interesting wrinkles to sustain their problem solving. It really is what fuels my practice. Honestly, interacting with students keeps me coming back for more–day in and day out. It’s what I enjoy most about the job.

I think that’s why I’ve always hated assessment events. They always seemed disconnected from the students.

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classroom structure factors games play projects reflection technology

Report on a Math Tournament

**This post contains the materials and advice you’ll need to run a distanced math tournament with your district, division, school, province, state, classroom, family, coworkers, neighbours, etc., etc., etc.**

Honestly, the more math love, the better! (IMHO)

In mid-October, I designed a math provincial math tournament open to all middle school teachers in my home province of Saskatchewan, Canada. After writing up a blog post that served as a formal invitation, the tournament (which I affectionately called the Saskatchewan Mathematics Invitational Tournament–or #SMIT2020 for short) has been running for just over a month with over 80 classrooms from across the province playing Federico Chialvo’s delightful game MULTI. (see here for more information).

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classroom structure factors games numerical flexibility play technology

A Math Tournament

**Update: Nov 23, 2020: Follow along on Twitter with some of the thinking at the hashtag #SMIT2020

COVID has created a global (and now chronic) pressure on all teachers in all classrooms, and the shifting, local realities have made teacher collaboration a precious commodity. It’s hard enough to find time to confer with colleagues under the best of situations, and now our major professional muster points are not currently viable–adding further value to any sense of connection that can be generated.

Bummer, right?

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classroom structure questioning set theory

Expecting Questions

I have mixed feelings about student questions.

We (as teachers) act like we want students to ask questions; however, there are plenty of implicit messages about teaching that tell us that good teachers don’t need students to ask questions. One of the oldest pillars of teaching tells us to provide adequate wait time for students to formulate and ask questions, but there is a sense of relief when time passes without the need for clarification. This feeling essentially equates clarity with quality. Wait time becomes an emergency procedure to be used when we feel an awkward imbalance in the room.

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assessment classroom structure collectivity

Using Visible Random Groups in Assessments

Since the onset of my career, I have been keenly interested in how students work together in the contexts of school. We know that students (and humans in general… actually animals in general) form collectives to accomplish elaborate tasks. These traffic jams of human interaction transcend individuality to the point where the level of activity is so dense that groups begin to synchronize into a sort of group mind. However, we have a school system built on individuality and (unfortunately) competition, and triggering these collective structures is extremely difficult in part because students know that, when push comes to shove, they will be weighed and measured as an individual.

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classroom structure discourse integers linear functions numeracy

Counting Circles Brainstorm

Let it be known that Sadie Estrella is a Hawaiian treasure.

She made her way north for SUM2015 in Saskatoon and I got the opportunity to learn from her about counting circles (as well as share an eventful dinner). 

It is probably good to understand her work on counting circles before reading a couple of ideas I had during her session. 

I went to her blog and searched for #countingcircle, and the results can be read here

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classroom structure discourse fractions integers numeracy trigonometry

Clothesline Series

I joined a middle years math community organized by my school division. I have a growing interest in the transition of students from middle school to high school because many of the tasks I use or create get at middle years content. I’m wondering what knowledge students come to my room with and what atmosphere it was learned in. Both have huge impacts on how students operate in my room.

I was surprised to hear that middle years teachers lamented that students could not use number lines. I use number lines as a support in my high school classes because I (ignorantly) assumed that this was an accessible tool from their elementary days. As it turns out, what I thought was making things easier for kids to conceptualize, probably was causing cold sweats and night terrors.

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classroom structure collectivity discourse fractions

Navigating Collectivity: Grade 9 Fractions

Today an amazing thing happened; students put aside the endemic disdain for rational numbers and had a conversation. I’d go further, they weren’t discussing their views on fractions, they were collectively conjecturing–the moves of the room enacted each other. I don’t think that a written document can capture the movement of the body of learners, but I have to try something. Think of it as less of a remembering and more of a re-membering, a reconstruction of a living learning event from the past.
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classroom structure graphing quadratics theory

On Collective Consciousness and Individual Epiphanies

I would like to begin with a conjecture:

The amount of collective action in a learning system is inversely related to the possible degree of curricular specificity. 


The mathematical action of a group of learners centred on a particular task gives rise to a unique way of being with the problem, but also reinvents the problem.

In short, what emerges from collectivity is not tidy.