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## Re-Constructing Shapes

For the first time in a decade, I am not reconvening with a high school staff to begin preparations for the school year. (I’m preparing to work with pre-service teachers on a university campus). It feels weird–very weird. It is a day that I look forward to because optimism is a constant across the building. Staff feels fresh, materials are crisp, and possibilities are endless. It sadly belies what’s to come.

Bummer, right?

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## Experiencing Scale in Higher Dimensions

A colleague and I have often bemoaned our attempts to teach the concept of scale factor in higher dimensions. A topic that has such beautiful and elegant patterns and symmetries between the scale factors consistently seems to sail directly past the experience of our students. I have tried enacting several tasks with the students including some favourites from the #MTBoS (Mathalicious 1600 Pennsylvania and Giant Gummy Bear). Each time, the thinking during the task seems to dissipate when new problems are offered. It just seems like students have a hard time trusting the immense rate that surface area and volume can grow (or shrink). In the past, I had used digital images of cubes growing after having their dimensions scaled by 2, 3, 4… etc.; students seemed to grasp the pattern yet under-appreciate the girth of 8, 27, 64… etc. times as many cubes.

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The progression followed by most teachers and resources during the study of surface area and volume is identical. Like a intravenous drip, concepts are released gradually to the patients so as to not overdose them with complexity. Begin with the calculation of 2-dimensional areas, and then proceed to the calculation of surface area of familiar prisms. (I say prisms, so a parallel can be drawn to the common structure for finding the volume of said prisms. That is, [area of base x height]). In this way, surface area is conceptualized as nothing more than a dissection of 3-dimensional solids into the now familiar 2-dimensional shapes.

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Surface area is intuitive. Intuition is a natural hook into curiosity. When you think something might (or should) be the case, it begs the question, why? It just seems as though textbooks haven’t gotten wind of that.

Perusing the surface area chapter of the assigned textbook for my Grade 9 math class offers a steady diet of colourful geometric solids all mashed together (at convenient right angles) in various arrangements. Without fail, the questions ask the same thing:

Find the surface area of…

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## CCSS: Support from the North

I can’t–for the life of me–understand why someone would argue to eliminate high level mathematical reasoning in favour of memorized tricks, but that seems to be the case with those arguing against the Common Core State Standards. I cannot fathom how this can be the case except to chalk it up to a case of “he-said-she-said”. Change (especially in something as resistant to it as mathematics education) breeds ignorance. And Ignorance breeds fear.

Let’s face it: The public is scared of reform efforts and most teachers aren’t far behind.

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## Project Work Scaffold

There are two schools of thought when it comes to PBL:

1. Start with a large-scale project and fit the specific outcomes within it, or
2. Build toward a larger project with smaller tasks.
I love the idea of large projects, but also aim to make my work as accessible as possible for those who want to take it and improve on it. I just don’t see option one working within my traditional classroom of 35 students for one hour a day. The existence of an overarching curriculum only further decreases its accessibility.
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## Soft Drink Project Part 5: The Show

This is the finale of a series of blog posts detailing a student posed project. To get the full picture, begin reading at part one:

Soft Drink Project Part 1: The Framework
As the project drew to a close, students began to place a valuation on their work. Very seldom did the topic of grades come up during the process, but even students know they are playing a game. They asked me how I would be grading, and I told them we would be using our self/peer/teacher model as always.
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## Soft Drink Project Part 4: The Math

This is the fourth in a series of posts detailing a student-posed math project. To get the full picture, please read the previous posts beginning with:

Soft Drink Project Part 1: The Framework
This post is designed to dampen the fear of math teachers. I know, because I was very afraid that the project had missed the mark until students moved into this phase. For some reason, teachers feel like they have more ability to complete a list of outcomes if they dictate the exact way, pace, and form that the learning will take. My division states they want to create life-long learners; in this model, the only lifelong learners are teachers because they must continue to do all the learning for their students day after day.
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## Soft Drink Project Part 3: The Design

This post is the third in a series of posts detailing the happenings of a math project. To better understand the whole story, please start reading at the beginning:

Soft Drink Project Part 1: The Framework
The next few classes after the brainstorming class were a blur. Students would come into class, grab their previous work, and get down to business. It was the best I could do to have supplies waiting for them. I learned quickly that students can become pretty demanding when it came to their learning.
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## Soft Drink Project Part 2: The Brainstorm

This post will make a lot more sense if you read the framework for the project in “Soft Drink Project Part 1: The Framework“.

I left the classroom energized; I could not remember a time that I was more pleased with a lesson that I had taught. In fact, I wouldn’t even call it teaching. I was observing. The process of brainstorming began organically. I had my doubts that it would continue the following Monday. Typically, students can’t even remember where they sit after a weekend–let alone what task they ended on.