3 ms·

My 6yo daughter has exceptional talent and interest for Math. She's already discovering some fundamental theorems for herself (number theory, algebra, geometry)

by lanna 5y ago

My 6yo daughter has exceptional talent and interest for Math. She's already discovering some fundamental theorems for herself (number theory, algebra, geometry). Does anyone here know any resources to help her development?

dharmab 5y ago
The YouTube channel 3blue1brown has some great, accessible introductions to higher level math.
- schoen 5y ago
  That's a truly fantastic recommendation. Other thoughts: * The "Exploding Dots" project came up with a creative way to present place value that leads into a lot of other concepts like number bases, algebraic structures, polynomials, and other things. (It's actually like a generalization of the abacus, with fun computer animation.) I'm not sure which presentation of this is best -- I think the original inventor has gone through like three different versions and there are several versions available online now. * I'm a huge fan of the late math journalist Martin Gardner, who wrote a lot of really entertaining stuff about math as well as puzzles and games. His books are really brilliant and cover a very wide territory. On the other hand, they were mostly written for adult audiences (originally, mainly readers of Gardner's Scientific American column) and may contain cultural references that kids wouldn't get, not least because some of them go back to the 1960s. :-( Also in some cases there have been further discoveries in the decades since the columns were published, so learning about them only from Gardner's old work may not give a good sense of where things have gone since then (e.g., he famously originally introduced both the Game of Life and the RSA algorithm to mass audiences, which then learned a lot about both topics in the ensuing decades). But maybe have a peek because they do stress the "math is fun and you can do it for fun" and also "math is all kinds of stuff and not just arithmetic" notions. * Gardner does have two math books for kids (the aha! series) that are very fun and introduce a lot of fascinating stuff about logic and paradoxes, among other topics. * Two online games that involve proof and circuit synthesis (spoiler alert: these are actually often isomorphic to each other because of Curry-Howard and stuff), which I think I heard about on HN: http://incredible.pm/ http://incredible.pm/ https://www.nandgame.com/ https://www.nandgame.com/ I totally loved both of these and I think they could conceivably be accessible for a very motivated and very talented child. Another online logic game that I also learned about on HN and loved: https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_game/ https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_g... Unlike the other two, this one uses (only) text and symbols instead of blocks and arrows. It's meant for college undergraduates, but I envision highly mathematically-talented middle-schoolers possibly being able to finish it. The user interface can probably also be improved a lot to make it clearer what you're allowed to do in each context. Maybe keep this one in mind for the future? :-) Contemporary pre-college math education is famously very weak on discrete math topics (like number theory, logic, and combinatorics). I don't know if this is due to a desire to train aerospace engineers for the Space Race, or because discrete math has radically increased its profile only in the past few decades with the rise of computer science, or as a kind of backlash against the New Math which tried (mostly unsuccessfully) to teach kids formal logical foundations through set theory. I wish I knew some more good discrete stuff for younger audiences. I haven't ever done any of it myself, but I hear Khan Academy's explanations (especially in math) are great and very self-paced.
rahimnathwani 5y ago
I was recently recommended Brainpop Jr. I signed up only 2 days ago so can't yes attest to the results.
dmnd 5y ago
Check out the iOS game "Slice Fractions"
chunky1994 5y ago
If she wants to learn math in the classical fundamental way, Spivak's calculus is actually a fantastic resource. It begins with nearly no pre-requisite number theory and has a very axiomatic approach, which while pedantic makes things much more accessible to someone without any prior training.
- Qem 5y ago
  Other Calculus book worth mention is "Elementary Calculus: An Infinitesimal Approach", by Jerome Keisler. One thing that makes learning Calculus harder than necessary is the clumsy epsilon and delta formalism, that became sort of a COBOL for Calculus. This is not the intuitive approach Newton and Leibniz used to develop Calculus, based on infinitesimals, but shunned later because it took time until Abraham Robinson made it rigorous in the 1960s. The book by Keisler showcases nicely how higher math education could improve, if academia had less inertia. The author made the entire book available for free online: https://people.math.wisc.edu/~keisler/calc.html https://people.math.wisc.edu/~keisler/calc.html See also: https://en.wikipedia.org/wiki/Nonstandard_analysis https://en.wikipedia.org/wiki/Nonstandard_analysis
gnicholas 5y ago
Probably too basic for your daughter, but check out Breaking Numbers Into Parts. [1] Also, there's Russian Math School, which is popular in some circles. 1: https://www.amazon.com/Breaking-Numbers-into-Parts-Second/dp/1727733983 https://www.amazon.com/Breaking-Numbers-into-Parts-Second/dp...
ivan_ah 5y ago
Here are some concept maps you could you could print for her: https://minireference.com/static/conceptmaps/math_and_physics_concepts.pdf https://minireference.com/static/conceptmaps/math_and_physic... https://minireference.com/static/conceptmaps/linear_algebra_concepts.pdf https://minireference.com/static/conceptmaps/linear_algebra_... The topics are more for university students, but by the sounds of it, I think she'll be able to handle ;) I find having a map of the "terrain" is always good when exploring.
alisonkisk 5y ago
Tell us more about how she explored and discovered those theorems. Sounds like you should be giving advice!

by lanna 5y ago

dharmab 5y ago

The YouTube channel 3blue1brown has some great, accessible introductions to higher level math.

schoen 5y ago
That's a truly fantastic recommendation. Other thoughts: * The "Exploding Dots" project came up with a creative way to present place value that leads into a lot of other concepts like number bases, algebraic structures, polynomials, and other things. (It's actually like a generalization of the abacus, with fun computer animation.) I'm not sure which presentation of this is best -- I think the original inventor has gone through like three different versions and there are several versions available online now. * I'm a huge fan of the late math journalist Martin Gardner, who wrote a lot of really entertaining stuff about math as well as puzzles and games. His books are really brilliant and cover a very wide territory. On the other hand, they were mostly written for adult audiences (originally, mainly readers of Gardner's Scientific American column) and may contain cultural references that kids wouldn't get, not least because some of them go back to the 1960s. :-( Also in some cases there have been further discoveries in the decades since the columns were published, so learning about them only from Gardner's old work may not give a good sense of where things have gone since then (e.g., he famously originally introduced both the Game of Life and the RSA algorithm to mass audiences, which then learned a lot about both topics in the ensuing decades). But maybe have a peek because they do stress the "math is fun and you can do it for fun" and also "math is all kinds of stuff and not just arithmetic" notions. * Gardner does have two math books for kids (the aha! series) that are very fun and introduce a lot of fascinating stuff about logic and paradoxes, among other topics. * Two online games that involve proof and circuit synthesis (spoiler alert: these are actually often isomorphic to each other because of Curry-Howard and stuff), which I think I heard about on HN: http://incredible.pm/ http://incredible.pm/ https://www.nandgame.com/ https://www.nandgame.com/ I totally loved both of these and I think they could conceivably be accessible for a very motivated and very talented child. Another online logic game that I also learned about on HN and loved: https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_game/ https://www.ma.imperial.ac.uk/~buzzard/xena/natural_number_g... Unlike the other two, this one uses (only) text and symbols instead of blocks and arrows. It's meant for college undergraduates, but I envision highly mathematically-talented middle-schoolers possibly being able to finish it. The user interface can probably also be improved a lot to make it clearer what you're allowed to do in each context. Maybe keep this one in mind for the future? :-) Contemporary pre-college math education is famously very weak on discrete math topics (like number theory, logic, and combinatorics). I don't know if this is due to a desire to train aerospace engineers for the Space Race, or because discrete math has radically increased its profile only in the past few decades with the rise of computer science, or as a kind of backlash against the New Math which tried (mostly unsuccessfully) to teach kids formal logical foundations through set theory. I wish I knew some more good discrete stuff for younger audiences. I haven't ever done any of it myself, but I hear Khan Academy's explanations (especially in math) are great and very self-paced.

rahimnathwani 5y ago

I was recently recommended Brainpop Jr. I signed up only 2 days ago so can't yes attest to the results.

dmnd 5y ago

Check out the iOS game "Slice Fractions"

chunky1994 5y ago

If she wants to learn math in the classical fundamental way, Spivak's calculus is actually a fantastic resource. It begins with nearly no pre-requisite number theory and has a very axiomatic approach, which while pedantic makes things much more accessible to someone without any prior training.

Qem 5y ago
Other Calculus book worth mention is "Elementary Calculus: An Infinitesimal Approach", by Jerome Keisler. One thing that makes learning Calculus harder than necessary is the clumsy epsilon and delta formalism, that became sort of a COBOL for Calculus. This is not the intuitive approach Newton and Leibniz used to develop Calculus, based on infinitesimals, but shunned later because it took time until Abraham Robinson made it rigorous in the 1960s. The book by Keisler showcases nicely how higher math education could improve, if academia had less inertia. The author made the entire book available for free online: https://people.math.wisc.edu/~keisler/calc.html https://people.math.wisc.edu/~keisler/calc.html See also: https://en.wikipedia.org/wiki/Nonstandard_analysis https://en.wikipedia.org/wiki/Nonstandard_analysis

gnicholas 5y ago

Probably too basic for your daughter, but check out Breaking Numbers Into Parts. [1] Also, there's Russian Math School, which is popular in some circles. 1: https://www.amazon.com/Breaking-Numbers-into-Parts-Second/dp/1727733983 https://www.amazon.com/Breaking-Numbers-into-Parts-Second/dp...

ivan_ah 5y ago

Here are some concept maps you could you could print for her: https://minireference.com/static/conceptmaps/math_and_physics_concepts.pdf https://minireference.com/static/conceptmaps/math_and_physic... https://minireference.com/static/conceptmaps/linear_algebra_concepts.pdf https://minireference.com/static/conceptmaps/linear_algebra_... The topics are more for university students, but by the sounds of it, I think she'll be able to handle ;) I find having a map of the "terrain" is always good when exploring.

alisonkisk 5y ago

Tell us more about how she explored and discovered those theorems. Sounds like you should be giving advice!