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, …

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FractionTalks.com

I have been thinking about extending the Fraction Talk love ever since I wrote this initial post in June 2015. I have used them with my grade nine classes as the starter during units on rational numbers. I have taken the larger questions (such as “What possible fractions can be shaded using this diagram?”) as the prompt for entire lessons of student activity. I have used them to create great conversations with grade 7 and 8 students at our school’s annual math fair. I finally found the time (honestly, I found the tech guy… many thanks to @evandcole) to begin a collection …

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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.  *****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 …

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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 …

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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 …

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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. How can I justify curating a collective of learners, when school is so interested in individuals?Learners commerce on a central path of mathematical learning while acting on a problem, but each take away personal, enacted knowings from …

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The Review Day: Unit Analysis and Scale Factor

There seems to be three sacred cows in mathematics education: the worksheet / exercise set the review day the exam It is not surprising that these three feed off one another, and make up the bulk of assessment in the typical mathematics classroom (including my own). Here’s my disclaimer:While I have been known to slaughter a few of the sacred cows of the instructional process, I have lagged severely behind in my attention to assessment. I value the complexities of learning that occur when student ideas encounter perturbations, curiosities, and other conceptualizations. The type of assessment that comes out of these …

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Large Whiteboard Project

Group whiteboarding has changed how I teach mathematics. It has also changed how students operate as a community of mathematicians.  Since ordering my first set of large whiteboards, our department has ordered four times again, and given workshops to the division’s mathematics teachers. (For a tour through my whiteboarding history, start here: mini whiteboards) My running motto has become,  “Whiteboards give me more than eight-and-a-half by eleven ideas” This, coupled with the assertion that you can’t expect limitless ideas with limited innovation space, caused me to think bigger. This is the result.  Whiteboard paint from the HomeDepot coupled with ebay’d …

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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) Success with my Enriched 9 class last semester …

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“__BL” : Education’s Obsession With Labels

Last week there was an interesting twitter discussion on the nature of projects versus the nature of problems. @dandersod @samjshah @k8nowak @leslie_su76 How is Mega M&M a project rather than a problem? — Dan Meyer (@ddmeyer) July 17, 2014 It occurred with specific reference between the differences of PBL (project-based learning) and PrBL (problem-based learning). If you follow this blog or scan the provided tags you will find PBL does occupy some space here. There is also a large amount of posts detailing “tasks”. This is a rather artificial term I use to refer to a piece of mathematical work …

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