Doc Running at Everything Ed has organized another great blog hop, this time on strategies to help students who struggle in math:
Gaming is such an integral part of today’s culture that it can be hard to remember that in the early 80’s, video games were still a novelty one step away from pinball machines. Today, the graphics and audio as well as the complexity of the narrative have advanced to cinematic proportions, and today’s online multi-player games allow extensive social interaction and coordination. But my 20th century adventures with the pixelated worlds of Atari and Nintendo 64 were nearly as compelling. How is that possible?
It’s not just that I was younger then. It’s that one big part of gaming is learning and creatively applying algorithms precisely to get a desired result. It’s worth remembering that despite the mind blowing sophistication of gaming today, the player’s actual interaction with many games has hardly changed since the early days—you are often trying to solve spatial puzzles by pressing buttons in the correct order at the correct moment. It’s deeply satisfying to master algorithms and make progress with increasingly complex puzzles. But it takes resilience in the face of repeated failure. We love that process.
But why is it that many students shy away from complexity when its presented in a high school math class? In literature students wade into Shakespeare to understand the best of the English language. In science, students must do experiments, and we don’t dumb down the periodic table or the Kreb’s cycle to avoid complexity. It would be obscene to treat every historical event as a simplistic, perfectly resolved narrative of good and evil. And yet, math has a reputation for being utterly algorithmic, solvable like the simplest video game from the 80’s. In fact, many students expect that most math problems actually have a cheat code, and beg the teacher to release them so everyone wins the game.
Why is it relatively easy to embrace the struggle in other disciplines but frequently hard for students to do so in math? The short answer is that the game of math looks like Pac Man when actually it’s more like Minecraft. The objective of the game of math isn’t just to crack levels, but to build worlds. Sometimes you’ll be a construction worker following a set of instructions, but often you’ll be an engineer, coming up with the procedure the construction worker will use. Sometimes you’ll be the architect, designing something that is both beautiful and functional. The more your world mirrors the real one, the closer you are to winning the game.
So how do we make a real game of math for students?
1) Give students a steady diet of open-ended but do-able problems grounded in the real world for which they don’t yet have the cheat codes. The first time you played any game, you died pretty quickly. Also the second time. You knew this would happen, and you responded well to the experience, because you knew that the game was designed for you to learn by experimentation, failure and restarts. Students may come to you expecting a cheat code and hoping to play perfectly from the start, but they need to learn that the game doesn’t work that way. Many students are unaccustomed to working without a rehearsed algorithm pre-placed in their hands and will need time to engage with problems creatively.
2) Give students guided experiments which help them develop the tools to solve the real world problems you’ve given them. Traditionally we have given students hammers and nails and told them to practice incessantly, with the promise that one day they would build a house. Instead I suggest students try and build a dog house with what they’ve got on hand. Then, just as they are asking for better tools, we help students develop the tools they need to build a better dog house. In this way students have a deeper understanding of and greater ownership for the algorithms in their toolbox. A great example is a linear function: an awesome tool whose efficacy resonates really well when introduced after a real-world problem that can be modeled with a line.
3) Have students work together in pairs and small groups. Students who lack basic skills or the confidence to engage creatively with problems can fade into silence unless they are continually challenged to interact. Small group work pushes weaker students to remain involved and gives you regular feedback. Advanced students learn to articulate ideas intelligibly for their peers.
4) Go back as far as you can reasonably go. Students who are accustomed to using cheat codes will often lack a real understanding of basic concepts and procedures. The cumulative nature of our world-building means we can’t leave these skills behind. Revisiting fractions, order of operations and so on pays dividends later.
5) Create problems which can be answered using a variety of tools. The diversity of abilities in the classroom means that we have to create problems and experiments which allow everyone to contribute at their level. There are many problems whose solution can be achieved through approximate measurement, graphical estimation, guess-and-check with a table, or algebra. Creating scenarios which can be approached from multiple angles engages students at different levels, offers a method of checking results and demonstrates the open-ended nature of the game of math.
6) Allow students time and space to struggle. Given the time and curriculum constraints of the school year it can be challenging to allow students to grapple with problems and experiments. Students need time to make mistakes and try again, and if they are not accustomed to that experience in math they will need even more time.
The game of math is not won on points or time, but on the complexity of the world constructed. If we want students to build real world models and solve open-ended problems, they must reach beyond cheat codes to become not just construction workers, but the engineers who design the algorithms and the architects who design the models. The struggle will require repeated failures and restarts, but that’s what makes gaming fun.
Check out the other great post in this blog hop below!