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The best thing about online communities (IMO), is the emergence of artefacts from the collected actions of many people. The online math education community (known as the MTBoS) has seen many of these collections throughout the years, most of which are aimed at supporting imaginative mathematics instruction in grade school. Personally, I have felt the community around Fraction Talks explode right under my nose, and it has been a joy to see how the prompts have sponsored amazing student reasoning. A few months ago, I had another idea for a task structure–that I dubbed #MenuMath–and began to collect examples from engaged math teachers. Since then, the collection has grown and become bilingual thanks to the translation work of Joce Dagenais. I love hearing about student and teacher creations, and you are encouraged to submit menus via my contact page if you feel inspired to do so.

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## 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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## 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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## Central Tendency: 10 Burning Questions

My intern just started a unit on statistics with my favourite starter question of all time.

(First blogged near the end of this post in 2011…)

The question is simple: floor is very low, and ceiling is very high.

Create a data set with the following characteristics:
Mean = 3
Mode = 3
Median = 3
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## 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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## Fraction Talks

Discussion is one of the organic ways through which human interaction occurs, but not all discussion is created equal in the math classroom. The tone of discussion relies on the mode of listening (Davis, 1996). Most classroom talk focuses on an evaluative mode of listening. Students are expected to share, compare, and contrast solutions to problems.

I do think that justification of their solutions gets at some important points regarding mathematical reasoning, but would like to move the discussion to center around that exact feature–the reasoning.

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## Math Class Starters

I am very distractible. Students know this; I know this. For this and multiple other reasons (including insipid tardiness on the part of my students) the first few minutes of class is often filled with retrieving forgotten textbooks, quieting down the pockets of flirtation, and acknowledging the students who show up two minutes late with a coffee.

Numerous factors have led me to the institution of class starters for grade 9s. I will do my best to summarize them here and introduce my framework, theory, and pedagogy behind them.

Why Starters? (The multiple influences)

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## The Discourse Effect

This semester, I’ve been attempting to infuse my courses with more opportunities for students to collaborate while solving problems. This post is designed to examine the shift in student disposition throughout the process.

I have noticed an increased conceptual understanding almost across the board and this is reflected in the differing solutions on summative assessments. It is also nice to see their marks  grow on these unit tests. I do not believe that paper-and-pencil tests are the best venues for displaying conceptual understanding, but it is awesome when the two intertwine.

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## Creating Communities of Discourse: Large Whiteboards

I have talked about individual whiteboards on this blog before. My school bought me supplies and I was loving the various classroom activities. While the grouping questions facilitated good mathematical talk between peers, I was still searching for a method to encourage more collegiality where my role could diminish to interested onlooker or curious participant.

So I had this brilliant idea.

Why don’t we get group-sized whiteboards created where students could work collaboratively on tasks?