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Five-Year-Olds Can Learn Calculus (2014)
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Re: Five-Year-Olds Can Learn Calculus (2014)
#92Jason Roberts has been doing an awesome job rolling out a high level math program in the Pasadena school district. 6th, 7th, 8th graders learning Calculus. They even have an anual competition at CalTech called Solve. Info and video of kids in action here: https://www.mathacademy.us/solve/ Direct link to video: https://vimeo.com/224720563
Justin - when are you guys going to put out another Techzing episode?
Re: Five-Year-Olds Can Learn Calculus (2014)
#93Earlier quoted context omitted.
Thats the kind of BS math they shouldn't bother teaching. Most of math is about concepts, and if 5 year olds can grapple with super-basic calculus how about teaching 10 year olds proof-based math and concepts (closer to college level) than memorization? Its kind of dumb how arithmetic is seen as a precursor to math when its really not. You could do an ENTIRE college-level course in linear algebra or calculus or graph…
Being able to recognize that 11 * 15 = 10*15 + 15 may be related to success in higher level math courses like linear algebra and calculus.
I never learnt my times tables when I was little I just learnt how to do the multiplications in my head on the fly.
Years later when I worked in a shop I used to cost complex print jobs in my head and co-workers though it was magic.
The way maths is taught in the UK is largely how and very rarely why.
Re: Five-Year-Olds Can Learn Calculus (2014)
#94One of the best curriculums I've seen for children (grades 2-5) learning math is the Beast Academy series: https://beastacademy.com/ They have challenging problems that emphasize basic and advanced concepts in a variety of ways, often posed as games or puzzles.
I can second this, with a minor caveat. My daughter (third grade) loves these books, and we get a lot of good problem-solving into the curriculum as a result. The caveat, in my opinion, is that they don't provide enough cyclic review in their default configuration. Each chapter includes 80-100 problems, divided in to usually between 4-8 sections. The problems are great, but once a section is complete they're weak on…
Are you home schooling? If not your daughter must be bored out of her mind at school.
Re: Five-Year-Olds Can Learn Calculus (2014)
#95Earlier quoted context omitted.
There are some aspects of doing math that isn't fun, because it is grinding. Learning the time tables for example - you just have to do lots of exercises to get used to multiplying. No way around that. Just like in sports, where you must also do a lot of basic practise to get good. Making the practise like a game can be done to done degree, but ultimately, a kid is going to see through that after a while, since it ge…
Thats the kind of BS math they shouldn't bother teaching. Most of math is about concepts, and if 5 year olds can grapple with super-basic calculus how about teaching 10 year olds proof-based math and concepts (closer to college level) than memorization? Its kind of dumb how arithmetic is seen as a precursor to math when its really not. You could do an ENTIRE college-level course in linear algebra or calculus or graph…
> Thats the kind of BS math they shouldn't bother teaching. Most of math is about concepts, and if 5 year olds can grapple with super-basic calculus how about teaching 10 year olds proof-based math and concepts (closer to college level) than memorization?
The times tables are BS math? The thing I've used IRL literally hundreds (thousands?) of times more than I've ever used anything from, say, calculus? The thing that yes I could use a calculator for but damn would it get annoying because I use it so often? That's what we should stop teaching?
Math things I use a lot in actual real life: basic arithmetic (drilled skills/knowledge!), basic algebra, factions/percentages (converting one to the other, and scaling other numbers by them—the basic arithmetic stuff is also vital here), and generally how triangles work. That's... almost all of it, actually. Some high-school-level stats stuff from time to time, I guess.
Re: Five-Year-Olds Can Learn Calculus (2014)
#96I have no doubt they can. There's so much negative cultural conditioning towards mathematics by eliciting negative emotions that it's ridiculous (i.e. math is scary, math is hard, math is for smart people, etc.). I believe kids who excel at math is not due to them being smarter but due to the bypassing of the cultural conditioning. The bypassing can be due to the parents, teachers, some mentor, or their particular fa…
They bypass conditioning because they are smarter and are good at it. Who do you think are the people who espouse anti-intellectual drivel like "math is scary" or "math is uncool"? Hint: not the smart people.
>not the smart people.
Sometimes it is smart to embrace this. Find a grade school student struggling with math, tell them it is easy, and they'll think themselves a failure. Instead, I find it better to tell them that math can be easy or hard, and it depends upon how one is taught. Let the student know the failure to understand math isn't due to something inherent in them, but something that can be changed. (I am assuming a student who tries or has tried in the past, if they don't try at all, that takes a different approach).
Math, as taught in school, is hard.
Re: Five-Year-Olds Can Learn Calculus (2014)
#97Earlier quoted context omitted.
TBF "what calculus is" -- i.e., the level of rigor at which topics are taught -- varies a lot even among college courses called "calculus"... In particular, IMO the distance between AP calculus and honors calculus at an ivy is larger than the difference between this material and AP calculus.
Up to a point, but does it not all grow out of the concept of limits?
I would say that the fundamental idea to understand is the concept of changing ratios.
Limits seems to me to be more a tool in order to calculate the ratios than a fundamental concept.
Re: Five-Year-Olds Can Learn Calculus (2014)
#98Earlier quoted context omitted.
There's plenty of research on the "entity theory" bias, mostly applied to gender. I.e. if you tell girls that they're bad at math, on average, they will act as if they are. Unfortunately, framing math as hard or scary only serves to reinforce stereotypes and bar people who do not have the keys to defuse that framing from advancing. It's not the rich male kids who are told math is hard and scary.
> There's plenty of research on the "entity theory" bias, mostly applied to gender. Junk science if there ever was any. The effect sizes for these treatments are tiny, if they even replicate it all. It seems like every day now there's a new rebuttal of stereotype threat, implicit association tests, priming, etc. Just from today: http://www.tandfonline.com/doi/abs/10.1080/09515089.2017.135... http://internal.psycholog…
How do you call it junk science?
From your second link, conclusions section:
>Nonetheless, the evidence overwhelmingly supports the tripartite pattern: (1)Although errors, biases, and self-fulfilling prophecies in person perception, are occasionally powerful, on average, they tend to be weak, fragile and fleeting; (2) Perceptions of individuals and groups tend to be at least moderately, and often highly accurate; and (3) Conclusions based on the research on error, bias, and self-fulfilling prophecies routinely overstate their power and pervasiveness, and consistently ignore evidence of accuracy, agreement, and rationality in social perception.
Namely point 1, which points out it is valid science. Point 3 is the criticism that it is vastly overstated, and personally I would add it is used as a political tool far more than it should be. But the science isn't junk.
Re: Five-Year-Olds Can Learn Calculus (2014)
#99Jason Roberts has been doing an awesome job rolling out a high level math program in the Pasadena school district. 6th, 7th, 8th graders learning Calculus. They even have an anual competition at CalTech called Solve. Info and video of kids in action here: https://www.mathacademy.us/solve/ Direct link to video: https://vimeo.com/224720563
Justin - when are you guys going to put out another Techzing episode?
Jason is doing show notes as we speak!
Re: Five-Year-Olds Can Learn Calculus (2014)
#100Earlier quoted context omitted.
Hard and scary carry differently meanings in those contexts though, surely? Video games are safe e.g you can always try again, you can do incrementally well. Video games are scary in an exhilarating way, you blood will pump and your pupils will dilate but at the end you can put it down, turn the lights on and watch funny cat videos to recover. Math (at school) is hard because you get one shot. Finite lives. After eno…
Nicely illustrated. As you imply, the scariness is a property of schooling rather than of mathematics itself. And where game play is scary, it's at a level chosen by and controlled by the player, for optimal learning I suspect.
Not only that, but with "GPA" provides a running historical average that serves as a sign that:
"No matter how good the student is now, they sucked at one time and they can never escape this eventuality".
Imagine a game that's tough, full of oft-used rules, failure potentialities everywhere, limited lives, and punishes failure/learning cycle. That's School.