This is a continuation of my previous blog post, where I recounted what I learned from this past year’s National Council of Teachers of Mathematics conference in Washington, D.C. In the first post, I compared my NCTM experiences to a nearby museum. In this one, I compare them to an opportunity granted to HMH employees.
Not knowing what it would involve but craving a classroom experience, in late 2017 I signed up for an HMH class titled “Learning Creative Learning.” It was a survey that extended over six weeks; it covered Mitchel Resnick’s research at the Massachusetts Institute of Technology focusing on “creative learning” and was planned around his just-published book Lifelong Kindergarten.
His central thesis is this: we teach kindergarteners by having them play and explore in playgrounds and classrooms and on computers—and we should teach everyone, even adults, using the same general approach. Playgrounds are replaced with electronics, art supplies, and public spaces, but the principles and benefits of open-ended play remain the same. This way of framing education was new to me. Resnick’s research expands on these ideas. In particular, he lists four Ps as guidelines for developing creative learning:
- Projects
- Peers
- Passion
- Play
Projects and Peers
I lump the first two Ps together because projects—especially classroom projects—are rarely developed or completed in isolation. This was clear throughout the NCTM conference, where I noticed a variety of sessions offering different perspectives on how students can best work together on projects:
- One session examined the difference between using patterns and using structure in math. The speakers—an assistant professor and a public school teacher outside of Boston—described a subtle theme between them: They both eschew the answer and focus on the process. The learning benefit of a project comes from an effortful attempt, especially if it’s a failure.
- In another session, an Illinois high school teacher explained how he has learned to best help a group of students who are stuck on a task: give the smallest amount of instruction possible, then walk away.
- The same teacher made another claim that surprised me: Only give examples for a math idea when it’s necessary. He argued that when we give examples, we focus the learner’s framework of the math in too narrow a way.
Passion
The third P, passion, can be a very elusive creature in a math classroom. Part of fostering creative learning and getting students to explore independently requires latching on to topics the students do care about. Some care about math—don’t get me wrong—but an awful lot don’t. Nearly 50 percent of first and second graders report at least medium levels of math anxiety, according to one 2014 study. At the conference, I kept an eye out for ways to connect math with topics the learner is passionate about and noticed two major trends.
Wide-Open Math Problems
One session discussed a class simulation where one team is a store looking for a vendor; all other student teams are vendors who have to make the pitch that their company is the best. These are my favorite types of math problems. There is no one answer, and different students’ passions can influence how they approach the problem. Consider the different math approaches students could viably pursue:
- Diagramming a store layout
- Documenting market research
- Visiting stores or websites to analyze competitors’ prices
- Creating a spreadsheet to document sales and profits
Sometimes, the feeling of wide openness comes from a problem that’s deceptively hard and has many valid ways of thinking about it. One woman at the conference showed me a math problem that blew her mind: “Is 5.6 even?” To a mathematician, sure, the answer is no. (Well, to a mathematician, I suppose “evenness” could be thought of as a 2-adic valuation…) But to students fresh off learning about decimals, it forces them to confront what it actually means to be even. A child interested in history or reading is free to explore that avenue of solving the problem.
Highly Engaging Contexts
I attended another session where the speaker, a math education professor at University of Nevada, Reno, cited contexts that were measurably high-interest to children, especially girls. I was pleasantly surprised to learn that 10-year-old girls love books, especially series books or chapter books. Consider these passions, along with ways to build them in a math classroom.
For better or worse, it’s not true that everyone will use algebra and beyond in their jobs. But all jobs still benefit from mathematics, whether or not their practitioners care. Teaching a child to solve math problems now will pay dividends later once they have one of the most versatile tools in an intellectual toolbox at their disposal. Mathematics empowers a creative learner to be even more creative.
Play
And now the final P: play. I learned at the conference that British Columbia incorporates play into its math standards. They have performance standards for K–7 that require different play activities, such as “Use spinners, dice, or coins … and play simple games.” Their grades 6–9 math standards nail the point down even deeper: “Use logic and patterns to solve puzzles and play games.” It struck me as an omission in U.S. standards that I never realized was missing.
And so, I will finish by putting theory to practice. Within each paragraph of this blog, I hid at least one animal in the paragraph. Each animal is at least four letters long and crosses over at least two words (e.g. “...a term I tested…”). Can you find them all? (Bullet points don’t count, making for 10 in all including “termite.”)
***
Watch for more from the author on incorporating play into your math classroom. And for math classroom solutions that inspire passionate learners, check out our K–12 math solutions.
