Luba Vangelova reports on a group that believes it may be better to introduce certain elements of, say, calculus to young kids before more route ideas like multiplication tables:
Finding an appropriate path hinges on appreciating an often-overlooked fact—that “the complexity of the idea and the difficulty of doing it are separate, independent dimensions,” she says. “Unfortunately a lot of what little children are offered is simple but hard—primitive ideas that are hard for humans to implement,” because they readily tax the limits of working memory, attention, precision and other cognitive functions. Examples of activities that fall into the “simple but hard” quadrant: Building a trench with a spoon (a military punishment that involves many small, repetitive tasks, akin to doing 100 two-digit addition problems on a typical worksheet, as Droujkova points out), or memorizing multiplication tables as individual facts rather than patterns.
Far better, she says, to start by creating rich and social mathematical experiences that are complex (allowing them to be taken in many different directions) yet easy (making them conducive to immediate play). Activities that fall into this quadrant: building a house with LEGO blocks, doing origami or snowflake cut-outs, or using a pretend “function box” that transforms objects (and can also be used in combination with a second machine to compose functions, or backwards to invert a function, and so on).
“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.”
Full Story: The Atlantic: 5-Year-Olds Can Learn Calculus
The book Moebius Noodles attempts to put these ideas into practice.