“MY numbers!” (On the ownership of knowledge)

The other day, I presented some students with the following game:

Last cookie is a game for two players. In this game, a number of cookies are divided between two cookie jars, and each jar has at least one cookie. Each player can take cookie in one of two ways:

  1. By taking any number they like from just one jar or
  2. By taking the same amount from both jar.

The winner is the person who takes the last cookie(s).

Some of you may recognize this as Wythoff’s game; on the NRICH website, which has a great online version of the game, it’s called Last Biscuit (I modified the name for a Canadian audience). If you aren’t familiar with the problem, I highly encourage you to give it a go – very easy to understand and play, but the optimal strategy is not particularly obvious.

I assigned this game as homeplay (get it?? because it’s a game… terrible, I know). Then, the other day, we picked it up again after about a week of rumination.

https://i0.wp.com/alexmakarski.com/wp-content/uploads/last-cookie.jpg

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My math elevator pitch

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Last week, some incredibly talented students at our high school put on an evening of one-act plays. I was particularly excited to see A Charlie Brown Christmas,  and I was not disappointed – I was so impressed by how well the kids brought the classic cartoon to life. However, the play that really gave me some food for thought that night was A Straight Skinny: a story about a high school algebra class that had been caught cheating on a midterm exam.

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On McNugget math (and being less helpful)

Another great Pi Club (still a working title) meeting.

Today, we worked on the McNugget problem (a case of the Frobenius/coin problem), which goes something like this:

Chicken McNuggets come in packages of 6, 9, and 20. Assuming money is not a factor and that you can only buy full packages, what is the largest number of Chicken McNuggets that you cannot buy?

mcnuggets

(Of course, I brought McNuggets for the occasion. You know, as manipulatives…)

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Pi Club: Round 2

First things first, Pi Club has a new member – and SHE is a wonderful addition to the group! WOOP WOOP, girl power!

Today, we worked on two problems. First, the lightbulb problem (found here):

There are 100 light bulbs lined up in a row in a long room. Each bulb has its own switch and is currently switched off. The room has an entry door and an exit door. There are 100 people lined up outside the entry door. Each bulb is numbered consecutively from 1 to 100. So is each person.

Person No. 1 enters the room, switches on every bulb, and exits. Person No. 2 enters and flips the switch on every second bulb (turning off bulbs 2, 4, 6…). Person No. 3 enters and flips the switch on every third bulb (changing the state on bulbs 3, 6, 9…). This continues until all 100 people have passed through the room.

What is the final state of bulb No. 64? And how many of the light bulbs are illuminated after the 100th person has passed through the room?

They didn’t take too long to work this one out. Great conversations were had.

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I think I started a math club

It began with one student. I noticed pretty early in the semester that grade 9 math was old hat for him and that he needed a challenge, so we started to meet once a week or so to talk math and work on some interesting problems. (During our first meeting, we proved that the square root of 2 is irrational.)

Then, he brought a friend. Who eventually brought two more friends. (If you’ve been doing the math, you might expect 8 students at our next meeting; alas, there were only 5. But wait, that’s five students who want to do math outside of math class!) We did a few problems, but mostly spent time discussing the idea of doing independent projects that the students would present to the class on the last day before Christmas break.

Today was the first session that really felt math club-y: I ordered some pizza, gave the students the Crossing the Bridge problem (thanks, Sadie!) and some white boards, then set them loose.

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Relationship is key

In comparison to majority culture students ([…] primarily of European descent): the overall academic achievement levels of ____________ students is low; their rate of suspension from school is three times higher; they are over-represented in special education programmes for behavioral issues; enrol in pre-school programs in lower proportions than other groups; tend to be over-represented in low stream education classes; are more likely than other students to be found in vocational curriculum streams; leave school earlier with less formal qualifications and enrol in tertiary education in lower proportions.

Sound familiar? I suspect that both Canadian and American educators can easily fill in the blank in this quote, which actually comes from a study addressing educational disparities facing Maori students in New Zealand (see Bishop, Berryman, Cavanagh, & Teddy, 2009).

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How to eat an elephant

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Before I began my internship, I thought that the experience would provide me with answers… fortunately or unfortunately, as I near the end, I find that I am left with even more questions than when I started. How do you cultivate an environment where mathematical risk-taking – and making mistakes – is encouraged and valued? What is the value of homework? What constitutes a truly rich task? What is the difference between a 78% and a 79%? Random or mixed-ability groups? How long can I continue to function without coffee and a full night’s sleep?

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