# Reflections: Can I do more than totem poles in math?

Reflections is a monthly column for teachers, by teachers on topics of interest to mathematics educators: lesson plans, book/resource reviews, reflections on classroom experiences, and more. If you are interested in sharing your own ideas with mathematics educators in the province (and beyond), consider contributing to this column! Contact us at thevariable (at) smts (dot) ca.

Can I do more than totem poles in math?
Sharon Harvey

“A totem pole casts a shadow that is 15 m long. The angle of depression of the sun is 43°. How tall is the totem pole?” Or perhaps this one: “The following beading pattern has a ratio of black to red beads of 4:7. If there are 35 black beads, how many red beads are there?” FNIM content – check.

This was me. This is me. This has been me for 8 years. Is it better than nothing? Maybe. Is it good enough? Definitely not.

I’ve always known that I struggle with incorporating FNIM (First Nations, Inuit, and Métis) content in math. It’s something that shows up in my Professional Growth Plan year after year, because I am never okay with what I am doing. I know I need to do something more. Something that makes students think, question, and respond to FNIM content while still focusing on mathematical concepts. But I’m a full time teacher, and with all the time commitments that this involves, I don’t have time to develop something fabulous – so instead, I totem pole and bead pattern.

In November, I attended the SUM conference in Saskatoon. A group of teachers and consultants for Saskatoon Catholic Schools presented a statistics unit for grade 9s that was rooted in FNIM material. This was exactly what I had been looking for. They had collected the statistics and the ideas, and they put them in one place where I could take what I needed. And I did. I took parts of their plan and molded it into the unit that I share below. Does it still have room for improvement? Of course it does, but I’m excited enough by what I saw and did with my students to want to share it, even in its rawest form.

I broke the unit into two big topics: Games of Chance and Interpreting Statistics.

Games of Chance

The FNIM Games of Chance unit began as a group lesson. We watched the PowerPoint from the SUM unit around chance and why certain FNIM communities played games of chance. We all made and played the game “Stick Dice”.  In this version of the game, players alternate tossing four decorated sticks (see example below). The goal of the game is to collect 10 counters (choose your favorite manipulative), which players earn when certain events occur (see below). (Counters are taken away from the other player when none are left unclaimed. For example, suppose each player has 5 counters. If Player 2 earns 2 points on his or her turn, he/she takes two counters from Player 1, so that Player 2 now has seven counters and Player 1 has three.)

The points are allocated as follows:
Only one design facing up (4 identical designs) – 2 points
Two of one design facing up, two of the other design facing up (see left) – 1 point
Any other combination – 0 points
We discussed the frequency of scoring tosses to blank tosses that we had observed in the game. Then, I asked what the chance of scoring was each time that I tossed the sticks. Depending on how your students approach this question, it leads to a variety of probability conversations. Some of my students quickly resorted to theoretical probability (though they couldn’t have labelled it that) and started writing down all the possibilities, and which among these would win. Other students tossed sticks and recorded what happened. Of course, they came up with different probabilities of scoring, so I asked who was correct. This was likely the most brilliant question I’ve ever asked in my math class (give me a break – I’m still new…ish). I have never had students so invested or defensive of their answer.  It took way longer than I expected for students to come to realization that what should (theoretically) happen doesn’t always happen – oh, to be young again! After discussion, we decided that, at some point in time, the theory and the experiment must match – otherwise, according to my grade 9’s, “what’s the point of the theory – why even have it?” So I asked them to figure it out. Was 20 tosses enough? 40? 60? So. Much. Fun. We did other math stuff too, like determining the formula for theoretical probability, talking about subjective judgment and good old hunches.

Following our experiments, I asked students to research a FNIM game of chance and present their findings to the class. We collectively made a list of requirements (see below), and I gave them 3 days to complete a presentation.  I also made a sign-up list with the games from the SUM unit so that there weren’t more than two people signed up for a game. (Nobody wants to learn the same game 7 times, no matter how awesome it is.) There was also an ‘other’ category for those who wanted to explore a game of chance that wasn’t on the list.

Project requirements:

• Game origin (Which nation? Where?)
• Why it was played (entertainment, wagers, dexterity, etc.)
• How to play
• Sample of the game with a chance for others to play later
• Original materials and adapted materials (What was originally used to play the game, and what can we use today? e.g., popsicle sticks instead of bones)
• The “math,” including the experimental and theoretical probabilities if possible, and an explanation if not possible (the explanation came later, when they were sure there was absolutely no purely theoretical probability about, for example, getting a piece of bark with a hole in it or not)

Interpreting Statistics

Following the presentations each day (I limited it to 5 presentations per day), the students participated in a Gallery Walk, which are similar to “stations” in that they involve students walking around the classroom to visit different activity centers, but involve statistics found in newspapers or websites. I presented them through PowerPoint. The GSCS unit plan included 6 “walks” to choose from, and I chose four among these: Top 10 Stats (a YouTube video), Educational Funding, Credit Completion at Oskayak, and Traditional Languages. During each walk, students were required to fill out a graphic organizer that asked them to identify what in the data they found surprising and interesting, what they already knew, and if they had any questions. It looked like this:

We did the first Gallery Walk as a class, during which I had students watch the video “10 Extraordinary Statistics,” which you can find here: https://www.youtube.com/watch?v=BE54mDs6St4. We watched it twice, and only during the second time did they record anything on their graphic organizers. We discussed what in the video surprised them, what was interesting, and things they already knew. Then we discussed the questions that they had, such as: Is it outlandish to state that coconuts are 15 times more dangerous than sharks? Why or why not? What does “conceive” mean? Are zoo animals considered privately owned?

This led to a great discussion on the use of statistics: Why do we use them? How can they be misrepresented? How do we know where the statistics are from? This initial conversation about coconuts and IKEA made it easier to illicit a similar discussion when looking at data about course completion for First Nations students, the loss of traditional languages, or the difference between educational funding for public and on-reserve schools.

After each gallery walk, we had a whole-group discussion. We talked about the validity of the statistics, as well as the history that led to the statistics. As much as we talk about FNIM history and culture in schools, there is so much more to discuss. About 30% of my class is made up of EAL students who don’t know the history of First Nations in Canada. They asked amazing questions, such as: (Regarding traditional languages:) “Why did people force First Nations people to not speak their own language?” (With respect to educational funding:) “Why do we get more money than them?” (Regarding history:) “Were they the first people in Canada?” The students posed questions, discussed, and learned together. Finally, we finished up our unit by looking at sampling and collection methods.

It was new. It was exciting. I can’t wait to do it again.

For the full unit plan, or for questions or comments, you can contact:

Sharon Harvey at harveys@spsd.sk.ca
Diane Sproat (GSCS Math Consultant) at dsproat@gscs.sk.ca

Sharon Harvey has been a teacher within the Saskatoon Public School Division for eight years. She has taught all secondary levels of mathematics, as well as within the resource program. She strives to create an inclusive and safe environment for her students.