![]() And knowing what to do with them still requires a great teacher.ĭragonBox Numbers could change all that. But these are just basic virtual versions of the classics. This site from Houghton Mifflin Harcourt School Publishers offers tons of digital manipulatives. Luckily there are now free digital versions of almost all the world’s great math manipulatives. But these things are rarely within the financial means of underprivileged schools. LEGO Education actually sells some fantastic “ MoreToMath” products that come with all the bricks you need, plus a comprehensive curriculum. ![]() Some even use LEGO bricks, which also work well. ![]() The world’s wealthiest students already have brightly colored math manipulatives they’ve been using them for decades. This kind of learning requires manipulatives, which turn real-world mathematical concepts into flexible playful experiences. The necessary skill these days is not solving equations, but rather, understanding math well enough to know how to translate real world experiences into complex calculations that can be assigned to the machines. In fact, that’s precisely what matters now that computers do most mathematical procedures. Anyway, what we really want is graduates who have sophisticated number sense and thorough mathematical thinking/comprehension. Let’s forget rigor the word is an obstacle to developing pedagogy and improving education for the next generation. I suspect most parents would prefer accuracy and meticulous precision over the “stiffness” or “cold shivers” that are implied by a fastidious definition of the word “rigor.” And to anyone who argues that our current usage is adequate because we all understand what the word means, I’d say: you’re hardly being rigorous with your use of language. Check out the Oxford English Dictionary and you’ll discover that the word has more to do with obedience-in both its negative and its positive connotations-than it has to do with the sort of accuracy and thoroughness with which we associate it in the context of education. The word “rigor” literally has to do with hostility, severity, or harsh inflexibility. They also understand that at some point, parents (most of whom have very highly developed number sense themselves, but still understand very little about it) will inevitably walk into conferences demanding that their children stop playing so much and start receiving a “rigorous” mathematics education. Which is why any kid who isn’t driven by obedience alone will eventually ask, “why do I need to know this?” Starting with manipulatives, on the other hand, can teach children “number sense.”Īll good (and many bad) elementary/primary school teachers understand just how essential manipulatives are to learning math and number sense. Starting math education only with Hindu-Arabic numerals just teaches kids to follow directions-they are taught to memorize a symbolic code and use it according to a set of rules that must seem completely arbitrary to them, seeing how as there’s no way for them to know that those rules are grounded in physical reality. Mathematicians and educators refer to this kind of understanding as “number sense.” The hard part of math is not using the code, but rather learning to think about your world in mathematical terms, learning to understand what the numbers actually mean, learning to speak “math” fluently. That’s all mathematics is: a complex and extremely useful language through which we organize and categorize our experience. The numbers themselves are just symbols that represent an abstract philosophical conception of the human experience in the world. Although most of us think of math as “numbers.” Our numbers-the Hindu-Arabic numeral system-is really just a kind of code.
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