Fascinating piece on the Atlantic:
“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.”
Pushback has come primarily from two very different (and usually opposing) camps. One is the “let kids be kids” cohort, which worries that legitimizing the idea of involving toddlers with algebra and calculus will tempt Tiger Mom types to push their kids into formal abstractions in these subjects at ever younger ages, even though that would completely miss the point. Other critics fall into the “back to basics” camp, which contends that all this play will prevent kids from becoming fluid in traditional calculation skills.
Droujkova views these criticisms as indicative of something much bigger: “They reflect rather deep chasms between different philosophies of education, or more broadly, differences in the futures we pave for kids. When we assign a lot of similar exercises, we picture kids in situations that require industrial precision.” Giving children logic puzzles or open projects, on the other hand, indicates aspirations of them growing up to become explorers or designers. “It does not work that directly,” she concedes, “but these beliefs dictate what mathematics education the grown-ups select or make for the kids.”