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Why are we worried that elementary school children might misunderstand arithmetic? This is the problem with the Common Core math standards, that they think you
by j2kun 12y ago
Why are we worried that elementary school children might misunderstand arithmetic? This is the problem with the Common Core math standards, that they think you need to have a perfect understanding of something before you can move on, and if you have moved on then you have a perfect understanding of everything that came before it.
That's just not how math works at any level! Understanding counting and arithmetic and numbers is a continuously evolving process. Children should be exposed to these things: the difference between a number and its representation, alternative ways to understand counting, etc., but to require every student understand all of them before moving on is ridiculous. And likewise, in later grades (even in high school!) one should revisit the concepts they thought they mastered from the different perspectives that their more mature coursework allows them to. There are important things to say about counting and arithmetic from first grade all the way through a PhD.
- hga 12y agoTo take this further, isn't one of the most consequential bits of math done in recent times Gödel's (in)famous incompleteness theorems (https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...), which are based on the natural numbers?
- j2kun 12y agoNot to mention the myriad of open problems in number theory, and the fact that "combinatorics" (the mathematics of counting) is a huge field all by itself.
- j2kun 12y agoMy favorite example is this one, in which a man tries to teach the binary number system to third graders http://www.garlikov.com/Soc_Meth.html http://www.garlikov.com/Soc_Meth.html The point is he focuses on challenging their understanding of numbers vs representations of numbers, despite the fact that they thought they mastered simple counting in first grade. They come away from this not with a mastery of binary arithmetic but with a better understanding of their usual decimal counting system.
- hga 12y agoI'm now remembering even more of the New Math that was remaining in my elementary school education (1966-72): I always remember set theory in 3rd grade (not particularly motivated as I remember, but very neat, a useful way to help describe the world), 4th grade as I recall is where non-decimal bases were introduced. And of course it had that obvious effect (at least for me). This was in Joplin, MO, one of the reddest Red State parts of the country, albeit in a school district famous after the 1955 publication of Why Johnny Can't Read for still being able to teach its students how to read. But the language arts were always very capably taught in the district, generally better than math.
- basch 12y agohttp://www.theatlantic.com/education/archive/2014/03/5-year-olds-can-learn-calculus/284124/ http://www.theatlantic.com/education/archive/2014/03/5-year-...