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. *****Use this time to read Sadie’s work*****A couple things struck me while she was talking: She is so honestly passionate. You can tell that she cares when she talks. I immediately …

Continue reading »## 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 …

Continue reading »## WODB: Polynomial Functions

If you haven’t experienced the conversation stemming from Which One Doesn’t Belong? activities, you are missing out. As far as I can decipher (#MTBoS feel free to correct me), this all began with Christopher Danielson’s Shape Book centered around this structure. From there, a crew of tweeps (headed up by Mary Bourassa) established WODB.ca (YES! Canadian) to curate a collection of problems of this format. My unit on polynomial functions (either in Foundations of Mathematics 30 or Pre-calculus 30) requires students to decipher attributes of polynomial functions from their graph and vice versa. These include end behaviour, sign of …

Continue reading »## 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 During the teacher rotation between groups, I picked up on some lines of reasoning. (Not being directly responsible for the teaching of the lesson, allows me to sit back, be inspired, and follow the lines of inspiration). Student justifications for their data sets were very …

Continue reading »## Navigating Collectivity: Grade 9 Fractions

“I hate fractions” – Everyone 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. My intern and I have worked at fostering a spirit of collectivity …

Continue reading »## Integer War

Math 9 poses the specific challenge of pre-assessment. The wave of administrative details (lockers, fees, photos, textbooks, tryouts, etc.) creates a logistical whirlwind for teachers. On top of that, you have no clue who (most) of these new students are, or what their mathematical history is. Our department gives a short pre-skills exam to help with this process, but I like to use the first week to work on integer tasks to really see how the newbies move mathematically–beyond a number on an exam. One such task was stolen (read: borrowed) from Timon Piccini. I decided to place focus on the idea of …

Continue reading »## 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. Dear Mr. Banting, You called me a “genius” in math class once, and that night I went …

Continue reading »## 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. Rather than piecing together the pieces of isolated reasoning (which I still think has value), I want to see a collective …

Continue reading »## 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.Now there are certainly battle lines drawn, but would it be possible to distill the highbrow mudslinging into a succinct cause–a common denominator?The recent tweet conversation between Dan Meyer and Robert Craigen (storied by @MathewMaddux here) serves as …

Continue reading »## The Scale of Coffee Cups

A colleague is a religious McDonalds’ coffee drinker. One day she showed up with a medium coffee and a cream on the side. It was in two separate cups: I asked her for her cups when she was done. (She is also a math teacher so understands that this is not a creepy request. It is no weirder than the time I bought 400 ping pong balls, or 1500 bendy straws). I then made her a request to buy a large and small coffee in the future and save me the cups. The result was a family of coffee cups …

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