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Communicating Advanced Mathematics to Kids

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Re: Communicating Advanced Mathematics to Kids

#31

Post by dbcurtis »

DoreenMichele wrote: post #14

A good place to promote this would be with secular homeschoolers. Those homeschooling for nonreligious reasons are often dealing with a bright kid interested in advanced subjects. They often need lay explanations that make advanced subjects approachable without dumbing it down. A lot of stuff is intentionally overcomplicated. My oldest was furious when I finally explained to him that algebra is basically renaming the…

I'll add to that. We fell into the secular homeschooler camp. At some point, it takes less effort to just homeschool than to spend endless time arguing with school administrators to challenge your child appropriately. "We can give them extra worksheets for homework." Oh wow, thanks.

A great resource for "mathy" kids is Art of Problem Solving. https://artofproblemsolving.com There are free resources, their math books are outstaningly excellent (well, they could use more excercizes, but the exposition is superb), and they have online classes. The online classes are run with a live chat room that typesets LaTeX. The pace of the classes is blistering, so not for everybody. But you can buy the same books for cheap and use them at home at a pace that is right for your kid.

We used AoPS as the main spine of our child's math curriculum. At the time, it topped out at about AP Calculus, I'm not sure if they go beyond single variable calculus yet. Anyway, after that a local university let our kid take multivariable calculus along side the freshman engineering students. We were lucky to have that resource. Next problem: when your kid completes multi-variable calculus at age 13, what next? We did discrete math and freshman engineering physics, and counted them toward the high shool transcript.

Which is another problem homeschooler's face -- the so-called "mommy transcript". When it comes to college applications, it's good to have somebody in addition to mom posting grades to your transcript. The Uni grades in math and physics and recommendation letters from university profs helped the college application package a lot. For that matter, AoPS is well ennough known now that it is good on a transcript.

While I'm on math resources, http://www.mathpath.org is a truly wonderful summer math camp for kids in the 11-14 age range. Great faculty, great staff. Now would be a good time to think about applying for 2018. Just so you understand the scale here: My kid spent all of their spare time for two weeks on the quailifying quiz, attempting 5 of the 7 questions, a couple of those attempts were a bit weak. (A good solid attempt at 2 or 3 will get you in.) If you think your child might like MathPath, I'd encourage you to download the quiz now and let your kid start pondering the questions.

Re: Communicating Advanced Mathematics to Kids

#32

Post by DoreenMichele »

colomon wrote: post #17
DoreenMichele wrote: post #14

A good place to promote this would be with secular homeschoolers. Those homeschooling for nonreligious reasons are often dealing with a bright kid interested in advanced subjects. They often need lay explanations that make advanced subjects approachable without dumbing it down. A lot of stuff is intentionally overcomplicated. My oldest was furious when I finally explained to him that algebra is basically renaming the…

I've actually been trying to explain that exact concept (algebra variables) to some advanced third graders. It's been surprisingly hard to get them to grasp it.

I think it helped my son for me to explain that letters were just short "names" in place of the phrase "mystery number." Or something along those lines.

Like "We are just going to call it X or Y instead of the unknown number we are trying to figure out."

Re: Communicating Advanced Mathematics to Kids

#33

Post by victor106 »

laderach wrote: post #20

My son is now 4 years old, he has been showing a great deal of interest in playing with numbers and puzzles, so I have been thinking quite a bit about this lately. The other day I ran across an issue of Scientific American from the late 70s ( http://flowcytometry.sysbio.med.harvard.edu/files/flowcytome... ) and I was super impressed by the quality and educational value of the content. Much superior to its current ver…

I glanced through the Scientific American link you pasted and it looks awesome.

It’s not just the content but the ads and the copywriting is just incredible. In this age of 140 chars You don’t see such long form copy anymore...

Re: Communicating Advanced Mathematics to Kids

#34

Post by mathgenius »

briandear wrote: post #7
mathgenius wrote: post #5

Earlier quoted context omitted.

> far outside what they see in school There's so much cool mathematics out there that school kids can understand given a good enough teacher. It's really disappointing to me the crud that gets taught in school, but then i remember that a big part of this is the teachers just aren't that inspired. All it takes is one or two good teachers to really change a kids outlook on mathematics.

You also have the problem (at least in public schools,) that teachers are obliged to “stick to the curriculum” and much of a teacher’s time is spent catering to the lowest common denominator lest the test scores fall to an unacceptable level. I might argue that kids should get a double period for math, especially earlier in their school careers — one class to teach the fundamentals, another class to simply explore. T…

I hated learning the multiplication table when I was 5. Basically, I boycotted the whole thing. It occured to me recently, why don't they talk about the holes in the multiplication table? These are the prime numbers! So easy to mention this and may have inspired my 5 year old self to dig a bit deeper.

My first real mathematical experience was in second grade. My teacher had some hoops on the floor, and was putting coloured shapes inside. Red shapes in one hoop, and triangles in another hoop. But then the problem arose: what to do with the red triangles? It was total magic when she dragged one hoop to overlap with another hoop and placed the red triangle in the overlap. Venn diagrams for six year olds.

And I still can't multiply six times eight! I have to work it out every time...

Re: Communicating Advanced Mathematics to Kids

#35

Post by iak8god »

DoreenMichele wrote: post #14

A good place to promote this would be with secular homeschoolers. Those homeschooling for nonreligious reasons are often dealing with a bright kid interested in advanced subjects. They often need lay explanations that make advanced subjects approachable without dumbing it down. A lot of stuff is intentionally overcomplicated. My oldest was furious when I finally explained to him that algebra is basically renaming the…

> A good place to promote this would be with secular homeschoolers. Those homeschooling for nonreligious reasons are often dealing with a bright kid interested in advanced subjects.

I don't see any reason to restrict this to those homeschooling for nonreligious reasons. There are plenty of bright homeschooled kids interested in advanced subjects regardless of their parents' primary motivation for homeschooling.

Re: Communicating Advanced Mathematics to Kids

#36

Post by nileshtrivedi »

laderach wrote: post #26
todd8 wrote: post #25

Earlier quoted context omitted.

I grew up in an inner city Detroit neighborhood. The junior high school that I attended was pretty rough so, to avoid the gangs that formed after school, I quickly ran over to the near by public library and stayed there until it was safe to walk home around dinner time. A friend showed me a magazine at the library; it was Scientific American and it completely hooked me. This was 1963 and SA was then a great magazine.…

Thank you for sharing your story! I am going to google Martin Gardner's Mathematical Games later this afternoon!

A book that is based on many of Martin's articles is: "Symmetry, Shape & Space".

Re: Communicating Advanced Mathematics to Kids

#37

Post by DoreenMichele »

dbcurtis wrote: post #31
DoreenMichele wrote: post #14

A good place to promote this would be with secular homeschoolers. Those homeschooling for nonreligious reasons are often dealing with a bright kid interested in advanced subjects. They often need lay explanations that make advanced subjects approachable without dumbing it down. A lot of stuff is intentionally overcomplicated. My oldest was furious when I finally explained to him that algebra is basically renaming the…

I'll add to that. We fell into the secular homeschooler camp. At some point, it takes less effort to just homeschool than to spend endless time arguing with school administrators to challenge your child appropriately. "We can give them extra worksheets for homework." Oh wow, thanks. A great resource for "mathy" kids is Art of Problem Solving. https://artofproblemsolving.com There are free resources, their math books…

My son is actually math challenged and also a science nerd. This is a whole other mind-boggling challenge.

I bought math books full of words off the bargain table for as little as a dollar and, after sorting things out with his father, just gave my son the stack of books to read. No tests. No written work. No problem solving. Just read these books. That finally worked and he has a good grounding in math, though he can't crunch numbers. He is, as they say, calculator dependent. But he absolutely understands important concepts. To my mind, this is vastly better than a kid who can estimate to 8 decimal places in their head, but can't grasp GIGO (garbage in, garbage out).

Re: Communicating Advanced Mathematics to Kids

#38

Post by DoreenMichele »

iak8god wrote: post #35
DoreenMichele wrote: post #14

A good place to promote this would be with secular homeschoolers. Those homeschooling for nonreligious reasons are often dealing with a bright kid interested in advanced subjects. They often need lay explanations that make advanced subjects approachable without dumbing it down. A lot of stuff is intentionally overcomplicated. My oldest was furious when I finally explained to him that algebra is basically renaming the…

> A good place to promote this would be with secular homeschoolers. Those homeschooling for nonreligious reasons are often dealing with a bright kid interested in advanced subjects. I don't see any reason to restrict this to those homeschooling for nonreligious reasons. There are plenty of bright homeschooled kids interested in advanced subjects regardless of their parents' primary motivation for homeschooling.

I am in no way restricting it, merely suggesting fertile ground to find enthusiastic early adopters who can help it flourish.

Re: Communicating Advanced Mathematics to Kids

#39

Post by jxcl »

laderach wrote: post #20

My son is now 4 years old, he has been showing a great deal of interest in playing with numbers and puzzles, so I have been thinking quite a bit about this lately. The other day I ran across an issue of Scientific American from the late 70s ( http://flowcytometry.sysbio.med.harvard.edu/files/flowcytome... ) and I was super impressed by the quality and educational value of the content. Much superior to its current ver…

The style of writing may well be very attractive, but it's important to remember that you're reading scientific articles written about forty years ago, and above that, in fields that are both advancing very quickly.

I don't have the opportunity to read the linked magazine right now, but I wouldn't be surprised if much of the research cited in it has been disproven.

Re: Communicating Advanced Mathematics to Kids

#40

Post by colomon »

burp3141 wrote: post #29
colomon wrote: post #17

Earlier quoted context omitted.

I've actually been trying to explain that exact concept (algebra variables) to some advanced third graders. It's been surprisingly hard to get them to grasp it.

I've always translated "x" to "?" (the value to be discovered) as a mental shortcut. The "?" symbol might be easier to interpret for third graders.

I think they are used to seeing empty boxes for mystery values.
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