BCAMT Conference 2011

Here’s the list of puzzles & games from my session at the BCAMT Fall Conference.

Together, we brainstormed some ideas about connecting games to mathematics. I listed some of these ideas in an earlier post.

Also, I attended a couple of sessions in the morning…

“It’s the most interesting thing a graphing calculator can do and we don’t even have kids do it.” Dan Kamin was talking about creating a scatterplot to determine the linear, quadratic, or exponential regression equation. While lines/curves of best fit are no longer in the curriculum (regression functions were in Applications of Math 10 & 11), it is expected that students will solve problems by analyzing linear, quadratic, and exponential functions. This provides opportunities to have students use technology to answer questions such as:

  • Is the data best modeled with a line or with a curve?
  • What is the equation of the function that best models the data?
  • How does your best fit line/curve compare with the those used by experts?

As a person inhales and exhales, the volume of air in the lungs can be modeled with a periodic function. Dan asked his students to write the equation of the sinusoidal function. They couldn’t. It wasn’t a Ferris wheel. “No one had asked them to create something before.”

I’ve had difficulty making domain and range relevant to 15-year-olds. David Wees shared an interesting activity at his presentation. Have students draw a picture of an object using line segments. Then, for each line segment, have them write the equation and determine the domain and range. Finally, have them enter this information using GeoGebra and compare the result with the drawing.

A reminder… the 2012 BCAMT New Teachers’ Conference will be held on February 11 at Queen Elizabeth Secondary School in Surrey.

How come we’re playing games today? I thought this was math class.

Inspired by reading the tweets & blogs of Surrey teachers over the summer, I thought I’d resurrect my blog.

In his blog, Richard deMerchant writes about how games, in addition to being fun, can help develop conceptual understanding of mathematics (http://rvdemerchant.wordpress.com/2011/08/31/count-down-part-two-games/). He also writes about the impact that debriefing strategies (“Why did you make that move?” etc.) has had on his son’s thinking.

I have seen this in my daughters as well. My 6-year-old loves the game/puzzle Camouflage. The challenge is to place polar bears on ice and fish in water while also having the game pieces fit on the board (see http://www.smartgamesandpuzzles.com/inventor/Camouflage.html for a better description). As she was playing, she went to place a piece down and then stopped herself saying “That can’t go there. It’ll make a square”. I asked her to explain this to me. She had figured out that if a move created a blank one-by-one square, then she would not be able to fit all the pieces on the board. (The game pieces are one-by-two dominoes or L-shaped triominoes). She developed this strategy on her own. As she completed the increasingly more difficult challenges, I could see her develop problem solving and reasoning skills (as well as spacial sense).

This year, I’m excited by the inclusion of the games learning outcomes in the Foundations and AWM pathways. This one comes from FoM 11:

But games/puzzles can also be used to address/enhance other learning outcomes in the math curriculum. For example,
  • rotations in Pentago
  • translations in Rush Hour
  • combinatorics in Mastermind
  • area in TopThis!
  • isometric drawings & volume in Block by Block
Each secondary school in Surrey will be receiving a games kit in the fall. Here’s the list: Secondary Games Kit
At a workshop in June, I asked teachers to play Blokus. Immediately, one teacher asked “What’s the point? Why are we doing this?”. It didn’t feel like math for him and it probably won’t feel like math for our students. However, aside from the strategy aspect, think of the possible connections to traditional math topics. For example,
  • transformations (when determining the number of game pieces, or ‘free polyominoes’)
  • area/ratios/percent (when determining the winner)
  • square roots (If the 4-player game board is 20-by-20, what should the dimensions of the 2-player game board be?)
In defining math, most of us math teachers will probably use words like ‘problem-solving’, ‘reasoning’, ‘patterns’, ‘estimation’, etc. (Would our students use these words or would they use words like ‘memorize’, ‘rules’, ‘formulas’…?) Compare a lesson in which students play (and discuss!) Blokus to one in which the teacher shows students how to divide rational expressions (1. factor numerators/denominators, 2. invert and multiply, 3. cancel) and students practice questions similar to the examples. In which lesson might you see the words listed above? In which classroom are students doing math?