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My son really loves math (so do both his parents, for that matter), and does well at it in school. I will give him math puzzles or tricks now & again, as well as introducing him to Khan Academy and some similar sites.

But I was trying to think of some advanced mathematical concepts that are typically introduced much later, simply because fewer people study them, but not because they inherently require a huge amount of previous knowledge. I wanted to ask this community for some ideas. Let me give some ideas of the sort of thing I was thinking of at potential ideas:

  • graph theory
  • set theory
  • combinatorics
  • sequences & series
  • etc.

I don't mind if the concepts are tough, per se, I just don't want topics that require a huge amount of prior knowledge. E.g., I'm a statistician, and matrices, Bayesian inference, etc. all require quite a bit of prior understanding. Whereas, on the flip side, my son loved learning things like fibonocci sequence because it didn't require a huge set of previous knowledge.

If it matters, he is now in 4th grade, but maybe has the math knowledge of a 5th or 6th grader.

I plan on taking one concept that seems to make the most sense (and that he sounds excited about), and drill down into that one. I don't want to hit him broadside with 4 or 5 different topics that we just cover in a cursory manner.

Thanks!

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  • $\begingroup$ Once again I suggest How to Prove It: A Structured Approach, by D.J. Velleman. $\endgroup$
    – Git Gud
    Nov 16, 2013 at 21:57
  • $\begingroup$ Some cities have math circles where kids (elementary through high school) meet once a week to learn interesting math topics like you are talking about. A good example is the Towers of Hanoi puzzle, which is accessible to children. If your child can't attend a math circle, maybe you can get copies of the worksheets used at math circles and work through them together. Also check out the curriculum at artofproblemsolving.com and their Beast Academy which is aimed at elementary school students. $\endgroup$
    – littleO
    Nov 16, 2013 at 22:06
  • $\begingroup$ @littleO Thanks! I will check out some local groups. We're in the Bay Area, so there are plenty, I'm sure. Even at his school. But now I'm thinking maybe I just set something like this up with him & his friends. $\endgroup$ Nov 18, 2013 at 18:54

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From teaching and from this site, what is clear is that today's student has limited ability to visualize in three dimensions, little ability to even draw the graph of a function on xy axes on graph paper. all that has been relegated to computer screens.. My actual advice, which is what i did for my friend who had middle school and grade school children, was to get construction toys. I like Zometool, http://zometool.com/ , I like those sticks-with-magnets sets. And i really like compass and straightedge with thin cardboard for making Platonic solids. i think a fourth grader can handle a real compass without injuring himself, i did.

Anyway, from the experience with Marty's children, i do not really know what kids will do with toys if you do not guide them much. Plus, Marty's kids are all in college and going into computer science anyway. I just know, very well, what today's kids cannot do. Surely an architect needs to be able to visualize in 3-D, preferably with lots of experience building models? Plus, perhaps more to the point, what are purely visual aspects of probability and statistics? In dimension $n,$ if a point is uniformly distributed in the cube with all coordinates $-1 \leq x_i \leq 1,$ what is the likelihood that it is in the (inscribed) unit ball?

Let's see, stacking spheres. I would use ping pong balls, fewer uncertainties than oranges, less weight than billiard balls. Why does it not really change anything whether we start with the bottom layer arranged in a square or an equilateral triangle?

Probably enough. Write to me if you like. My site profile has enough information to get my email addresses, phone number.

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  • $\begingroup$ Thanks! We already have Zometool. I'm happy getting & using toys with him, but he actually wants something a bit more in the realm of "solving": puzzles, and puzzle-like things, etc. So I'm looking for ways to encourage creative problem solving. $\endgroup$ Nov 18, 2013 at 18:53

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