It’s the time of year we celebrate scary things: ghosts, goblins, clowns, pumpkin spice (whatever that is). There is one creepy thing with the power to raise the hairs on necks everywhere and which rarely gets celebrated: math. This is a shame. Because the fear of math is not inherent in the subject. Rather, it’s a result of growing up in a school environment based on four terrifying myths about math:
- Math is applied computation, and being good at math is about memorizing increasingly complex incantations done with arcane symbols.
- Math achievement comes from implementing quality programs “with fidelity.”
- Problem solving is the last in a long series of teachable math skills.
- Some people just aren’t math people.
So let me turn on the lights and pull off the rubber mask to reveal the truth behind the myths.
Math is the language of problem solving
The point of learning math is to understand how to make sense of problems and communicate with others about them. The structure, vocabulary, and grammar of a language shape the way people think. The rules of math are not just recipes we must blindly follow in doing computations. They are a precise and sophisticated way of structuring ideas and understanding solutions. Learning math is therefore far more than just memorizing the vocabulary and grammar. It’s about becoming fluent in the idioms and subtle features of math, which leads us directly to the next truth:
Language is learned best by immersion
If we treated world language instruction the way we teach math, we’d have students drill on grammar rules and vocabulary for several years and the only sentences they would hear, read, speak, or write would be in isolated, contrived situations. There would be no conversations, no discussions, and no need to come up with your own thoughts in the other language. Now imagine one of those students was dropped into a foreign city for a week: that’s the annual state math test.
A better way to learn is to spend most of your time immersed in an environment where the language is used naturally. You still have instruction in the grammar and vocabulary, but it’s always done in the context of the way the language is really used by native speakers. In math, this means all skills, content, and structured algorithms are taught in the context of problem solving. Students solve problems every day, and they have abundant opportunities to collaborate just as adult problem-solvers do.
Problem solving is a complex collection of learnable skills and habits
We often treat problem solving as just another isolated skill, as if it’s a simple checklist we can give students. “Understand, Plan, Solve, and then Check,” we tell kids. Just follow the recipe and you’ll solve every problem.
Just like communicating in a foreign language, problem solving is actually a complicated and sophisticated collection of skills and habits of mind. The power is not in accumulating all of the isolated problem solving techniques, but in being able to use them together in interesting and often messy ways. Like learning a language, learning how to solve problems is something that students do over a long period of time, and there is always more depth to discover from new and different kinds of problems they can encounter.
Everyone can be a “math person” if given the right environment
All of this presupposes that students are regularly encountering the right kinds of experiences to be immersed in problem solving. This doesn’t happen automatically or by accident. It has to be systematically designed. Ideally, a district team will create structures and provide resources to enable this, but an individual classroom teacher can also do this. The 5 Principles framework is a guide for developing aspects of your classroom and school culture that supports problem solving and innovative thinking:
- Conjecture. Promote student inquiry and critical thinking. Never end with an answer, and always follow up with questions like, “How do you know?” and “Are there other ways you could solve that?”
- Communication. Students learning a language need to use it. A lot. So give them opportunities not just to do rote computations but to express their reasoning verbally and in writing. Let them translate from the math language of symbols into English and back again.
- Collaboration. Few problems are ever solved by one person working alone. More often, people work together to generate ideas and build on each others’ solutions. These are skills in themselves, and students can learn a lot about how to solve problems themselves when they see how others attack a problem.
- Chaos. Let’s face it: there are few problems in life that are neat, organized, and prepackaged with exactly the right information needed to solve it. Students need to experience messy, complicated problems as often as they do the more straightforward ones we usually present them in math class.
- Celebration. Yes, this means finding ways to make math enjoyable. But it is also about recognizing the positive value of mistakes and letting students celebrate the growth that happens afterwards. Students should have plenty of opportunities to recover from failure and show new learning.
Building the Culture
Every educator has an obligation to create the right conditions for learning how to solve problems. Even if you don’t teach math, you can create a classroom culture that promotes the 5 Principles. Encourage your students to ask questions and communicate clearly, to work together and tolerate the messiness of real problems, and to celebrate not only the right answers but the learning that comes from mistakes.
What’s one thing you can do today to change the culture of your classroom? Share your ideas in the comments, and join the discussion at http://www.geraldaungst.com/5cmath. To learn more about creating a classroom culture that promotes problem solving and innovative thinking, check out my new book 5 Principles of the Modern Mathematics Classroom.