>Read a social sciences academic paper and see what I mean for a quick example.
I have actually done some graduate-level work in sociology and history, and the papers and books I read were mostly examples of very good statistical work and well-thought-out process analysis. You can put your STEM-master-race badge away.
>Beyond arithmetic, students have almost zero examples of why they should bother learning anything else.
When I say "for no reason," I don't mean "for no day-to-day practical reason." Playing with abstract concepts is and should be its own reward; that was the whole point of TFA. Mechanically memorizing how to take the derivatives of polynomials is neither a fun abstract concept nor a boring-but-necessary practical skill.
>If we can turn Mathematics education into a kind of "game", then fill in the details and formal bits as they age, they'll at least be able to relate to it even if they don't understand the application or relevancy.
"Gamification" as a cynical ploy to get kids to sit still long enough memorize their times tables may or may not work. But even if it does, it's only gotten them to play the game long enough to pass them to the next level; it has deliberately shifted their interest away from the joy of learning for its own sake. That is not what the article is about, and it's not helpful in the long run.
>Approaching it from this sense "two points make a line, we only have one point, so take the limit" is the method today and with all respect, it's been a terrible terrible failure...even if it is "correct".
No... no, it isn't. The approach today, for the majority of students, is to learn the bare basics so that you can plug them into an equation and find out what the marginal cost of widgets will be next year given a certain set of equations. And in any case, it comes so late that kids have been taught that "math" is something that actually is boring and useless.
> Playing with abstract concepts is and should be its own reward
I'm sorry, but you're just simply wrong on all points. Promoting the status quo in math education, as you are doing, has been, is, and will continue to be a failure that drives kids away from learning. There are now decades of evidence of the failures of k-12 education to address this need and I find it unbelievable that you haven't gotten the picture yet.
I'm not saying that what I'm proposing is correct, but continuing the very poor pedagogical approach that you support is not going to solve the educational failures that we're experiencing today. What we need are fundamentally new approaches to Math education. You are not providing any insight into what those approaches should be.
I'm sorry, but in a discussion to fix and change what is obviously utterly broken in k-12 maths education, suggesting to just continue the course is not a helpful contribution and is simply part of perpetuating the problem.
This has been recognized for so long, that it has finally percolated out of educational establishment, which has failed to address the problem with undereducated and unqualified teachers, student motivation, repeated failures in curriculum development (Common Core is simply the latest joke of a curriculum), and has reached levels as high as the White House for targeting. You have to know that the current approaches are failing if the President has to get involved.
"Schools often lack teachers who know how to teach science and mathematics effectively, and who know and love their subject well enough to inspire their students. Teachers lack adequate support, including appropriate professional development as well as interesting and intriguing curricula."
"As a result, too many American students conclude early in their education that STEM subjects are boring, too difficult, or unwelcoming, leaving them ill-prepared to meet the challenges that will face their generation, their country, and the world."
"Put together, this body of evidence suggests that grade-school children do not think as simplistically about STEM subjects as conventional curricula assume. They are capable of grasping both concrete examples and abstract concepts at remarkably early ages. Conventional approaches to teaching science and math have sometimes been shaped by misconceptions about what children cannot learn rather than focusing
on students’ innate curiosity, reasoning skills, and intimate observations of the natural world."
"The first principle of How People Learn emphasizes both the need to build on existing knowledge and the need to engage students' preconceptions -- particularly when they interfere with learning. In mathematics, certain preconceptions that are often fostered early on in school settings are in fact counterproductive. Students who believe them can easily conclude that the study of mathematics is 'not for them' and should be avoided if at all possible."
I differ from this report in that they continue to promote a bottom-up approach to maths education. I think math should be taught from a top-down approach, like nearly every other discipline. You don't learn to bake a cake by first spending 10 years learning about chemistry, agriculture, nutrition, animal husbandry, distillation etc. You say "I want to bake a cake" and you start with a simple cake recipe. Then the next time you say "I want to bake a different cake" and you use a more complicated recipe. And so on and so forth until you don't need a recipe and are putting together your own cakes from scratch.
The "cake" I'm proposing is calculus...and I believe, from experience teaching basic calculus to kids under 10, that this is realizable and beneficial.
I have actually done some graduate-level work in sociology and history, and the papers and books I read were mostly examples of very good statistical work and well-thought-out process analysis. You can put your STEM-master-race badge away.
>Beyond arithmetic, students have almost zero examples of why they should bother learning anything else.
When I say "for no reason," I don't mean "for no day-to-day practical reason." Playing with abstract concepts is and should be its own reward; that was the whole point of TFA. Mechanically memorizing how to take the derivatives of polynomials is neither a fun abstract concept nor a boring-but-necessary practical skill.
>If we can turn Mathematics education into a kind of "game", then fill in the details and formal bits as they age, they'll at least be able to relate to it even if they don't understand the application or relevancy.
"Gamification" as a cynical ploy to get kids to sit still long enough memorize their times tables may or may not work. But even if it does, it's only gotten them to play the game long enough to pass them to the next level; it has deliberately shifted their interest away from the joy of learning for its own sake. That is not what the article is about, and it's not helpful in the long run.
>Approaching it from this sense "two points make a line, we only have one point, so take the limit" is the method today and with all respect, it's been a terrible terrible failure...even if it is "correct".
No... no, it isn't. The approach today, for the majority of students, is to learn the bare basics so that you can plug them into an equation and find out what the marginal cost of widgets will be next year given a certain set of equations. And in any case, it comes so late that kids have been taught that "math" is something that actually is boring and useless.