And every year, I find that I'm still fighting the pull of traditional learning in math.
In the past few days, I've been pondering these questions. How do you get them to ditch worksheets? And this afternoon a colleague stopped by asking simply, How do we get them to try?
These questions are separate, yet related. The textbook and the worksheet are compelling in their comfort - they are straightforward and, even if the math is hard, they are easy for our brains to figure out.
Doing something different is difficult - not just for students, but also for the teachers who craft learning experiences. While there are abundant tasks and learning activities available on-line, it takes effort and thought to design a unit that balances conceptual understanding with meaningful practice and a compelling enough project that aligns to both. It's a sweet spot that I occasionally hit.
A few weeks ago, I made up a game. A colleague was planning to drop by that day to see how the kids collaborated around math. We had just learned to multiply fractions, which is easy enough from a procedural standpoint, but it takes thinking to understand why the product is smaller than the the factors.
Armed with some dice and a grid, I decided to have the kids create fractions by rolling two different colored dice and multiply them. If the product was close to zero, you got no points. If the product was close to a half, you'd get half a point and if the product was closer to 1, a player got a whole point. The player with the highest score after six rounds wins. The players must decide in advice which color should represent the numerator and which the denominator.
As the first class of the day played, they developed a few questions:
- If my product is closer to a whole number greater than one, can I have that number of points?
- Can I decide which digit should be the numerator, rather than leaving it up to chase?
The class decided that the answer to both of these should be no. Even though improper fractions, some of them large, were a big part of the game, assigning points greater than one made it nearly impossible for the opponent to catch up. Likewise, choosing your own numerator and denominator could mean a runaway in terms of points, assuming the player had figured out that improper fractions will help you win the game.
Subsequent classes grappled with new questions:
- What if you added up all your products to obtain your score? (too cumbersome given the diversity of denominators)
- Is there a way to know you will win the game or is it merely chance? (the latter)
- How would the game change if we had dice with numbers beyond 1-6? (more complicated computation, not necessarily higher scores)
- What would happen if both players used the same numbers? (there would be an unbreakable tie)
- What should we name this game? (after much debate, we settled on Slicin' and Dicin')
Slicin' and Dicin' made for a fun day of thinking and competition, but it also helped students appreciate what happens when we find a fraction of another fraction. Students questioned the rules and components of the game, which deepened their understanding in a way that a traditional worksheet might not.
While I will not presume to suggest that this one activity has forever solved the comfort of worksheets or a reluctance to try, I will say that it did have a positive impact on:
- the understanding of the concept
- the ability to sustain attention and effort with problems
- curiosity around what was happening to the numbers
- inquiry around how to make the game more winnable
- overall engagement, even from the more challenging pockets in the room
I hope to find some additional impromptu games that can meet these same goals and move us all a little further away from practice that feels both comfortable and boring. In the meantime, I hope to try the game with a new set of students to see what questions they can generate.
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