Some educators are calling for reform in the way mathematics are taught in our schools. The goal? To capture a progression truer to how children think; to grow the big concepts throughout their education, rather than introducing them after most students have already abandoned an interest in mathematics as a subject, via The Atlantic.
But this progression actually “has nothing to do with how people think, how children grow and learn, or how mathematics is built,” says pioneering math educator and curriculum designer Maria Droujkova. She echoes a number of voices from around the world that want to revolutionize the way math is taught, bringing it more in line with these principles.
The current sequence is merely an entrenched historical accident that strips much of the fun out of what she describes as the “playful universe” of mathematics, with its more than 60 top-level disciplines, and its manifestations in everything from weaving to building, nature, music and art. Worse, the standard curriculum starts with arithmetic, which Droujkova says is much harder for young children than playful activities based on supposedly more advanced fields of mathematics.
“Calculations kids are forced to do are often so developmentally inappropriate, the experience amounts to torture,” she says. They also miss the essential point—that mathematics is fundamentally about patterns and structures, rather than “little manipulations of numbers,” as she puts it. It’s akin to budding filmmakers learning first about costumes, lighting and other technical aspects, rather than about crafting meaningful stories…
The idea isn’t to create a generation of baby geniuses but to layer the learning in a more integrated, natural way:
“You can take any branch of mathematics and find things that are both complex and easy in it,” Droujkova says. “My quest, with several colleagues around the world, is to take the treasure of mathematics and find the accessible ways into all of it.”
She started with algebra and calculus, because they’re “pattern-drafter tools, designer tools, maker tools—they support cool free play.” So “Moebius Noodles” includes activities such as making fractals (to foster an appreciation of the ideas of recursion and infinitesimals) and “mirror books” (mirrors that are taped to each other like the covers of a book and can be angled in different ways around an object to introduce the concepts of infinity and transformations). (Another book in this genre is “Calculus by and for Young People,” by Don Cohen.)
“It’s not the subject of calculus as formally taught in college,” Droujkova notes. “But before we get there, we want to have hands-on, grounded, metaphoric play. At the free play level, you are learning in a very fundamental way—you really own your concept, mentally, physically, emotionally, culturally.” This approach “gives you deep roots, so the canopy of the high abstraction does not wither. What is learned without play is qualitatively different. It helps with test taking and mundane exercises, but it does nothing for logical thinking and problem solving. These things are separate, and you can’t get here from there.”
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