Mancala, Nim and the Social Aspects of Mathematics

What is math?

I asked this question to eight surprised second graders on a Tuesday in late April. “Um…numbers? Plus or minus…like one plus one equals two?” I was trying to individually interview a few of my students to better understand what they thought about math and where they saw themselves within it.

The goal of these interviews was to gather data about these students’ mathematical ideas and experiences before I started full-time student teaching, and before they embarked on our four-week adventure of playing the mathematical strategy games mancala and nim.

The logic behind this controlled structure was so that I could research how my students engaged with these games as a part of my student teaching capstone project. Here’s one of my favorite answers to this question:

“Math is where teachers like you, well assistant teachers like you who are about to become real time good teachers, it’s where they teach you numbers and stuff so like plus, multiplication, times, subtraction and other stuff using numbers and that can help you find out how to think about coordinations and stuff.”

-2nd grade student

Mathematics is often presented in school as static, objective, and independent of cultural contexts. Someone long ago discovered or invented how it works, and our job is to learn the rules and get the answers right. But this ignores the mathematics that is embedded in our daily lives, that spans across cultures and experiences.

While I am still learning how we as educators can be more conscious and inclusive of the intersection of mathematics and culture in our classrooms, I did want to at least acknowledge some of my own experiences of mathematics in childhood. I showed my students the picture above to explain that mathematics is all around us, and within us in ways we are not always aware of.

Thes rules for Nim are based off of this lesson from Dan Finkel/Math For Love.

During my time student teaching, I was committed to trying a variety of different math tasks that differed from how math was generally taught in our class, with the goal of creating a math culture that valued and was responsive to all students’ thinking. For this particular project, I wanted to focus on playing games (and these two games in particular) because:

• Games are objectively fun. Everyone can get excited to participate and play, even if they may otherwise experience math anxiety.
• These games provide a really simple entry point for all students – the rules are simple and the language demands are limited – all students can participate equally.
• They are open-ended, allow students to decipher strategies and alter the game rules. To be successful in these games requires both fluency and deeper understanding.
• They are entirely student-led, and allow teachers to step back and observe how students interact with each other, to help understand the social aspects of mathematics.
• These particular games do not require basically any money to be spent at all – games do not have to be fancy or colorful to be fun and mathematically rich.
• These games are transcultural and can be used to push back on the many ways we center White, Western culture in math class.

I decided on baseline rules for the games, generally for ease of explanation (more common forms of nim, especially, are more complicated to explain). However many students started pushing back on the rules once they got the hang of the games, and tried altering some parts to see if that affected what strategies they were using.

Students played the games in (the same) pairs of two (so four kids in a game) in an effort to push them to utilize each others’ ideas and thinking in terms of how they would play. This is a strategy I heard from multiple sources – if the goal is to promote thinking over skill, strategically pairing students creates a collaborative (and not just competitive) environment.

Half of the class each played one game the first two weeks, then switched for the next two. After two weeks of playing each game, students video interviewed each other to ask their partner what they had learned playing that game. I was particularly blown away watching what they’d done given this freedom – sure, they got a little silly sometimes, but the ways students came up with to explain their thinking with basically no direction was fascinating.

Some students decided to use the physical game objects to demonstrate what they meant as they described what they’d learned. Some wrote themselves scripts of what they wanted to say. Many mentioned how they’d learned from their partner, and what it meant to use sportsmanship. Students got really into being the “interviewer” as well, adopting a professional tone of voice and coming up with their own questions to ask their partners – “What was the biggest difference between mancala and nim?” “Which did you like better? Why?”

I thought it was especially interesting to provide multiple ways students could demonstrate their learning and engagement. Students could explain their ideas verbally in a more formal manner during their partner interviews (as well as when I interviewed them). They could also write or draw on their recording sheet whatever made sense to them, or chat more informally with their partner and group as they played the games. These multiple avenues allowed me to get a fuller picture of what each student was thinking, understanding and learning.

There was a lot of learning for me as well, going through the research process. I was trying to figure out how students engaged with the games, but also trying to see if and how students’ ideas about math were impacted through this experience. I think that is a difficult question to isolate – how kids feel about math and how they talk about it are affected by so many things – but one student did feel their definition of math was expanded because of what we had been working on. As they said:

“[Math] can also be fun, like it can also be counting and learning new ways to count, or learning new ways to play games.”

-2nd grade student

Cue happy tears!

Going forward

• This whole experience felt slightly artificial because of all the work I was doing around it to collect data and research. I am wondering how to more authentically incorporate games into math class (instead of just a special, four-time experience).
• What are other games that meet the criteria of low tech, cheap, simple, mathematically rich, either transcultural or work towards centering knowledge of marginalized students?
• I’m always a little wary of “math games”. Sometimes they just seem so flashy, fancy, or only promote fact fluency (i.e. “tricking” kids into thinking math is fun – I know that’s a cynical take, but still). What’s a good way to discern which games are worthwhile?
• How can games open up a conversation about the cultural and social aspects of mathematics often overlooked in school? And then…what do you do with that?

This blogpost is part of the The Virtual Conference on Humanizing Mathematics.