I disagree with you assertion on creativity in maths. Maths allows creativity and is very open ended. You can do things that are not required but are creative - leveraging identities and properties to vastly simplify a problem, reframing the problem to make it more tractable etc. And programming is very useful to learning maths. Any topic that requires some form of calculating to build familiarity will benefit greatly from playing by programming.
Consider complex numbers. You usually first meet them with imaginary numbers and polynomial equations. But they are extremely obtuse. But if you look at operations on them in terms of vectors, lateral extension of the reals to make the picture in terms of solvable polynomial equations complete, or in terms of polar coordinates, rotations, trigonometry, and e you start to get a fuller picture. But if you really want to get them you program a simple system (scaling and rotating triangles for example) that allows you to leverage all those properties. You build in the identities and operations. And then you experiment. Play with it. Play is vital to learning. With that, you get motivation and a fuller understanding than a mere that is just the way it is. With that deeper more intuitive understanding you are able to remember and internalize it better. Making the future topics easier but more importantly, developing the ability to draw connections rather than merely leaving each concept in isolation.
That is why maths is so hard. So much of it is completely divorced to how they were originated and completely unmotivated and magical. With no intuition future learning is further crippled, building apprehension via a negative feedback loop.
You are confusing learning math with the field of math.
Again I am a big proponent of Seymores work but that is not the point here.
The point is that Kahn Academy allows you to learn math in your own tempo and that is the future of education. That doesn't mean that other things wont be important too but to say that it's not the future of education is simply missing the greater point IMHO.
People who have never been able to understand it before now suddenly do. We don't all need to be math wizards.
I was arguing your assertion that maths is not creative, even in the basic level. I completely agree that non uniform pacing is a really great breakthrough and do not argue the efficacy of these videos. Nor their impact on the future of education. But saying there is no creativity in maths is the type of thing that hurts the education of the subject - with teachers punishing kids for doing things unlike the book says.
I also think, especially for learning kids maths, not to underestimate how powerful learning as playing is in motivating concepts. I do think such a thing done right, where you would replace a bunch of videos with one game would be even better than the videos as the future of education. As that type of active learning allows not just variable pacing but also variable exploration and creativity. And by building a repertoire of stories for concepts, it counters how alien and not straight forwardly relatable to real life experience more abstract maths is. A fact that makes learning maths hard.
As a first test of this idea I hope to someday make or see a game where kids program little battling bots and in the process learn concepts from high level physics and maths. as a side-effect. without realizing they are learning. I guess based on personal experiences, I feel there is still a class of kids that the khan academy style won't reach.
I think I know what you are getting at but I think we are talking about two different things.
That kids learn concepts from high level physics and maths does not mean they learn formal math.
I am not saying that they need to learn formal math (in fact there are plenty of arguments against spending so much time trying to teach kids any math)
But it's important to understand that if everyone have to learn concepts in their own way they will loos the ability to communicate with each other.
The ability to transfer metaphors from something we understand into the world of Mindstorms and through that develop conceptual understanding of various areas does not necessarily transcend into understanding of math.
It might though create something else and quite wonderful. But formal math it probably wont be.
This might be semantics but after reading your comment it makes me feel like Kahn Academy is an improved version of the present of education. The future of education, in my mind, is still a world where we kids get to be apprentices of real mathematicians, engineers, doctors, biologists, artists, etc.
Comments
I disagree with you assertion on creativity in maths. Maths allows creativity and is very open ended. You can do things that are not required but are creative - leveraging identities and properties to vastly simplify a problem, reframing the problem to make it more tractable etc. And programming is very useful to learning maths. Any topic that requires some form of calculating to build familiarity will benefit greatly from playing by programming.
Consider complex numbers. You usually first meet them with imaginary numbers and polynomial equations. But they are extremely obtuse. But if you look at operations on them in terms of vectors, lateral extension of the reals to make the picture in terms of solvable polynomial equations complete, or in terms of polar coordinates, rotations, trigonometry, and e you start to get a fuller picture. But if you really want to get them you program a simple system (scaling and rotating triangles for example) that allows you to leverage all those properties. You build in the identities and operations. And then you experiment. Play with it. Play is vital to learning. With that, you get motivation and a fuller understanding than a mere that is just the way it is. With that deeper more intuitive understanding you are able to remember and internalize it better. Making the future topics easier but more importantly, developing the ability to draw connections rather than merely leaving each concept in isolation.
That is why maths is so hard. So much of it is completely divorced to how they were originated and completely unmotivated and magical. With no intuition future learning is further crippled, building apprehension via a negative feedback loop.
You are confusing learning math with the field of math.
Again I am a big proponent of Seymores work but that is not the point here.
The point is that Kahn Academy allows you to learn math in your own tempo and that is the future of education. That doesn't mean that other things wont be important too but to say that it's not the future of education is simply missing the greater point IMHO.
People who have never been able to understand it before now suddenly do. We don't all need to be math wizards.
I was arguing your assertion that maths is not creative, even in the basic level. I completely agree that non uniform pacing is a really great breakthrough and do not argue the efficacy of these videos. Nor their impact on the future of education. But saying there is no creativity in maths is the type of thing that hurts the education of the subject - with teachers punishing kids for doing things unlike the book says.
I also think, especially for learning kids maths, not to underestimate how powerful learning as playing is in motivating concepts. I do think such a thing done right, where you would replace a bunch of videos with one game would be even better than the videos as the future of education. As that type of active learning allows not just variable pacing but also variable exploration and creativity. And by building a repertoire of stories for concepts, it counters how alien and not straight forwardly relatable to real life experience more abstract maths is. A fact that makes learning maths hard.
As a first test of this idea I hope to someday make or see a game where kids program little battling bots and in the process learn concepts from high level physics and maths. as a side-effect. without realizing they are learning. I guess based on personal experiences, I feel there is still a class of kids that the khan academy style won't reach.
I think I know what you are getting at but I think we are talking about two different things.
That kids learn concepts from high level physics and maths does not mean they learn formal math.
I am not saying that they need to learn formal math (in fact there are plenty of arguments against spending so much time trying to teach kids any math)
But it's important to understand that if everyone have to learn concepts in their own way they will loos the ability to communicate with each other.
The ability to transfer metaphors from something we understand into the world of Mindstorms and through that develop conceptual understanding of various areas does not necessarily transcend into understanding of math.
It might though create something else and quite wonderful. But formal math it probably wont be.
Don't know why you've been downvoted I have upped you again.
This might be semantics but after reading your comment it makes me feel like Kahn Academy is an improved version of the present of education. The future of education, in my mind, is still a world where we kids get to be apprentices of real mathematicians, engineers, doctors, biologists, artists, etc.