Make my child a math genius
January 17, 2013 7:45 PM   Subscribe

My son is now 15 months old, and I would like for him to have the best possible mathematics education. What should I be doing now and what sort of long-term plan should I have in order to help him both to learn and to love mathematics? (He doesn't have to be a mathematician when he grows up, but really knowing mathematics is non-negotiable.)

I have a BS in mathematics and an MA in statistics, but I have never felt like I had a really good mathematics education. Things went too slowly, and then they went too quickly. I've often felt like I'm missing something about how to really think like a mathematician. I would like my son's experience to be better than mine.

I am perfectly willing to teach him myself if it comes down to it. But since I am a complete ignoramus with respect to child development, I don't know when or how to start. Are there things I could or should be doing now to help him develop number concepts or better spatial reasoning skills? How young is too young for dedicated math tutoring? Is there an optimal way to make mathematical thinking a way of life? A way of life that you really enjoy?

I know this question is pretty vague and potentially far-ranging, but I'd really like to hear whatever it prompts. If you are a mathematician and have a story about how you came to love math or how you came to think like a mathematician, great. If you hate math and have a story about how that came to be and how you think it could have been avoided, great. Specific programs of study that you like or hate, great.

If it helps, this question from a few years back is in a similar direction (and had some great answers), but it is a bit narrower than what I'm looking for.
posted by Jonathan Livengood to Education (48 answers total) 60 users marked this as a favorite
Don't be uptight about it. When he gets older, enroll him in Kumon. Have fun with math.

If you're kind of a type A person who is too invested in this or your disappointment in mistakes can be sensed, learn to loosen up. Encourage the kid. Don't judge mistakes. Practice makes perfect. That can't be emphasized enough.
posted by discopolo at 7:51 PM on January 17, 2013 [6 favorites]

And my mom was a math teacher who was often disappointed that it took me practice to learn things at a young age. She wanted desperately for me to be a prodigy and it really disappointed her that I actually needed to study to learn things. (Yes, weird, I know.)

I totally agree with you, BTW. An excellent foundation in math can open all kinds of doors. Not being scared of math allowed me to change careers. The other career changers in my physics class (in their 20s and 30s) were so math anxious that I really doubt they truly got to choose what they wanted to do with their lives. It's really sad.

Also, remember to tell the kid to consult other texts when their teacher doesn't make sense. Learning on your own and being able to teach yourself is truly the way to success.
posted by discopolo at 7:56 PM on January 17, 2013 [1 favorite]

Look into Montessori teaching methods for math. Beginning lessons are totally hands on so it isn't so abstract. He'll be able to start a lot of it soon and each work has lots of room - they start simple and get more and more complex as the child masters each objective.
posted by dawkins_7 at 7:57 PM on January 17, 2013 [2 favorites]

I may get slammed for this but my son has been doing math apps since about that age and now, at 5, he is phenomenal at math for his age. You have to make it fun for a young child and one on one teaching only goes so far...Find games, apps, patterns, age appropriate work books that you can do together....but do look at the apps, there are some great ones. And when he's older....Team Umi Zumi is probably one of the best educational (math) programs out there.
posted by pearlybob at 7:58 PM on January 17, 2013 [3 favorites]

I love math -- always have.

What I loved about it when I was a kid was that they used physical objects to teach us. They had blocks that we would count and add and subtract, and when we got older multiply and divide. It's important to make math relevant to something kids can actual experience, even more so the younger they are.

But keep in mind, no matter how much you want your kid to think a certain way, how people's minds work is something they're born with. Some people have a better natural ability to think with math, just like some are naturally better at creative pursuits. So yeah, do what you can to help your kid. But also watch for what his natural aptitudes are and encourage those -- even if they aren't what you would want in your ideal child.
posted by DoubleLune at 8:01 PM on January 17, 2013 [8 favorites]

Richard Feynman (I think? Could be someone else) wrote an anecdote about his father, who would play a game with him as a child about spatial relationships: How many couches do you think would fit in this room? How many __ would fit in __? That kind of thing, and then helping him reason through it. I can't track down that anecdote, but I did find this fun interview which is related: Richard Feynman on his father.

A kid I knew in middle school was assigned extra-curricular math by his parents. Which seems like it could backfire, but he's got a mathematics from Harvard now, so I guess it worked.
posted by qxntpqbbbqxl at 8:05 PM on January 17, 2013 [5 favorites]

Keep high expectations in your household, combined with compassion and patience. Make sure your child understands that being proficient in math is not an option, it is something that your family does. Keep with it from a young age, and make sure you never let him believe that he can quit or stop. While doing that, understand that it may be difficult, and you will have to help out a lot along the way, as well as allow him to make breakthroughs on his own.

Education games nowadays are pretty advanced, so as soon as he reaches an age where you feel electronic games are acceptable, start him on the education games. I would suggest not showing him any other games for a while, and just do the educational ones. As time goes on, with a solid background in the basics, he should be able to slowly progress without reaching any severe road blocks.

Making sure that he fully understands things as he goes forward is extremely important. A lot of education is focused around passing a test and moving on, so that after a few years, the building blocks are really not as solid as they should be. It will be up to you to identify which things are not covered well enough in school and to help strengthen those points.

I think the most important thing of all though is going to be high expectations (within realistic limits). In school everyone in my family did well and went to college, but we were raised being told that we were all going to college through our whole life, and also told that an A was a good grade, and anything less meant we needed to work harder. We were not punished when we didn't get A's, though. Our parents would just spend more time with us to help us understand things. All of our victories were celebrated (ice cream if we got good report cards or did really well on a test), and failures were taken as an opportunity to do better. I never felt like I was being forced to work hard, but rather I thought that everyone works hard, and couldn't really understand a world where you didn't do your homework and study until you did well.
posted by markblasco at 8:07 PM on January 17, 2013 [4 favorites]

I think this is a great goal, but one to be treated delicately. Kids can be rebellious against things simply because it's "imposed" on them.

I remember a quote about someone who fell in love with books not because his parents forced him to read, but because his parents simply had a huge library open to him that he was free to explore on his own.

I think pearlybob is on to something for making it fun. I'm a great typist today (110+ WPM) because in school we would go to the computer lab and play a space-invaders-esque game where you shot down the enemy by typing. To be quick, you couldn't look at the keyboard, and I wanted to be quick.

I was also a great mathematician in 4th and 5th grade because we had a program called accelerated math. It was a computer program that used scantrons. Each kid at their own profile, and would work on their own, and at their own pace. So kids wound up on totally different math subjects. There was a tad bit of competitiveness to this as well, but mostly I think it had to do with the "freedom" of being able to advance at my own pace.

DoubleLune also has a great point. Just be watchful of your kid, and be there to support him however he wants, however he needs, and however it looks where his talents currently lie.

markblasco also has a good point about not showing him any other sorts of games than educational ones. I don't know how it was when I was growing up because computers were still new, but the only games I have remembrance of were educational ones. I don't know if my parents forbade any other sorts, or there really weren't any other sorts at the time. Yet I still had lots of fun with them. I hope that the market for educational games is still strong.

(I go back and forth on how much to impose "education" on a child. It worked out great for John Stuart Mill, but I think that's only because his father also secluded him from every other child. Mill must have been shocked when he found out that other kids weren't fluent in Latin and composing sequels to The Iliad in plot and poetic form. I think today once a kid realized how "easier" the other kids had it, they might rebel and the whole plan would backfire.)
posted by SollosQ at 8:13 PM on January 17, 2013 [2 favorites]

Just as a sort of random data point, I never thought of myself as a "math person" despite always being in gifted/honors/advanced courses throughout school, and always being at least a course or two ahead of grade level in math.

As an adult, I truly started thinking of myself as a math person because of my hobbies: cooking, knitting, sewing, home projects that involve measuring and calculating and geometry, working on our finances, etc.

Make sure your child has a solid understanding of how mathematics is involved in daily life. The general understanding of most math disciplines is that it's "not necessary in real life", but that's not true. You can't figure out how to adjust a sleeve to fit in the sweater you're knitting, you can't figure out how to make half again as much soup, you can't figure out how to build shelves just right, if you aren't good at math.
posted by padraigin at 8:16 PM on January 17, 2013 [2 favorites]

I am a big math and statistics fan. Probabilities. I have worked with my kids from a young age. Part of it was by doing things with them they did not realize was math until we discussed it afterwards. I taught my kids a lot of card games. Especially poker and black jack. We would figure out the odds. Even playing board games like monopoly helped them with numbers.

I try to explain to them constantly that every decision they make is math related. Mostly probabilities and risk reward. Even crossing the street is a risk reward problem.

We also talked about the consequences of not knowing math skills. 18 months is young, but my kids went to Montessori when they were young and learned basic math at an early age.

I think doing puzzles helps. Brain teasers. Even Encyclopedia Brown books lead me to understand math and figuring out logic.

Check out this book. It talks about math so that even my mother who has a T-shirt that says, "I majored in English, you do the math" can understand it.

My kids are now late high school or early college and while I doubt any of them will be math majors, they are certainly math literate.
posted by JohnnyGunn at 8:18 PM on January 17, 2013 [2 favorites]

I don't know when or how to start

Your child will tell you! Have confidence in yourself and have confidence in your son. (On a basic level, though, start now; it is never ever too early to introduce concepts for anything. Also, consider purging number board books that don't bother with 0...)

My father was a college math prof and sat down with me and did the intro stuff for the courses he taught when I was in very early grade school. It was interesting, interesting stuff and I remember being quite pleased with the (not overwhelming) challenge. School math classes were terrible.

Then I got older and school math classes still sucked and I did little else with math. I notice I am generally slightly better than the average grown-up at math -- but certainly nobody would guess my dad's career from looking at me; 'better than average' is damning with faint praise, most people suck at math.

My advice would be to steer clear of what the schools are doing; there are reasons math is a widely hated subject among kids.

A cursory Google for "unschooling math" brings up some thoughts on how it might be handled outside of standard classroom pedagogy. I am (surprise) an "unschooling" homeschooling parent; my 5yo writes out lists of basic addition and subtraction for kicks, understands negative numbers and base 10 (get some base 10 blocks...), and tax; when she wants something she has to make the purchase herself and we work on her being able to understand all parts of the receipt. Just making it a part of everyday life = no math loathing or anxiety at all.

Lots of homeschoolers like Life of Fred Math, which I have browsed and found enjoyable and useful.
posted by kmennie at 8:23 PM on January 17, 2013 [2 favorites]

Don't discount the value of music in learning mathematical principles, either.
posted by empath at 8:33 PM on January 17, 2013 [3 favorites]

Also, I think its always best to teach by example. Find a hobby for the two of you that includes a lot of measuring, weighing, estimating, etc.
posted by empath at 8:35 PM on January 17, 2013 [2 favorites]

I majored in computer science but minored in math as an undergrad, then did basically the same thing for the time I spent in grad school. In my ideal life, Project Euler would have been around when I was 8 or 9 years old. I would also have wanted a good tutorial in how to use Python or Ruby, so that I could understand how to solve the problems fairly easily. Unfortunately I don't have pointers for the latter.
posted by A dead Quaker at 8:39 PM on January 17, 2013 [1 favorite]

Praise efforts made, not 'intelligence' per se: not "you're so clever" but "you worked really well".
posted by anadem at 8:42 PM on January 17, 2013 [12 favorites]

Sets and set theory are concepts that you can cue in on with color, or shape and only later reveal as basic concepts in number theory. Sorting algorithms can be fun, and you can actually demonstrate some pretty neat things with dance. Blocks help spatial relations. Teaching recusion can be fun (though it can also accentuate ocd behaviors)
posted by Nanukthedog at 8:46 PM on January 17, 2013 [1 favorite]

Pattern recognition. Use of logic and problem solving skills. Analog clocks and watches. Let him help pay when you use cash and talk to him about how much change you're getting back. Pattern recognition. Family game night where the games require strategy and aren't displayed on a screen. Encourage a love of reading (reading for fun improves academic achievement in ALL subjects). Let him solve his own problems as often as possible. Did I mention pattern recognition?

Watch out for his learning style (auditory, visually, or physically is the simplest breakdown.) When he's old enough make him aware of how best to help himself learn.

But most importantly, cultivate the family culture that anything can be learned if you practce it and keep trying. You might have to work twice as hard as your neighbor before you "get" a math concept, but the goal is to "get" it, not to get it first.
posted by rakaidan at 8:55 PM on January 17, 2013 [3 favorites]

I can't answer how to make someone with a less-mathematical mind into someone with a more-mathematical mind, because I do think to some extent it is a matter of nature and not nurture. Of all the things my parents did wrong, I think they did schooling mostly right; we were (all seven of us) homeschooled, and given a pretty rigorous basic reading- writing-'rithmatic core, and allowed to develop and delve into our particular topics of interest on top of that. The only thing we were NOT allowed to do was study nothing. The result of this was that I studied politics and linguistics, one brother (the true mathematically-minded one) just got his master's in engineering from a top university, a second brother quit college to work in local government administration, and a third is currently teaching English in Japan. None of us are bad at math, exactly (we all had excellent grades in college) but the engineer brother was the one counting the tiles in the Sunday-school room at church as a toddler and doing calculus for fun in his spare time as an adolescent. I suppose, as a parent, you could try to force this sort of thing via constant exposure/extra tutoring/high expectations, but to some extent your child's personality is going to shine through as well. You don't want to miss the chance to have the world's next great artist or governor or whatever because you were too busy focusing all your energy on one subject.
posted by celtalitha at 9:28 PM on January 17, 2013 [3 favorites]

Don't despair if your kid isn't a prodigy. The vast majority of the people who employ mathematics at a high level in engineering, finance and other practical disciplines were on the regular honors track - calculus in 11th or 12th grade, not 5th or 6th grade. Plenty of people of high attainment in theoretical disciplines (math, physics, economics) were non prodigies too, although probably not many Field Medalists.
posted by MattD at 9:30 PM on January 17, 2013 [3 favorites]

Buy him good textbooks. Feynman and Einstein both taught themselves higher math from textbooks. Nearly all math is done alone, with a book (or paper) containing hard problems. Buy the textbooks currently used in the current best university math department, and always be ready with the next textbook or other equally-good literature when your kid wants something new to read. The best teacher you could find for your kid cannot explain nearly as well as the best professor whose textbook you could buy for your kid.

No TV, videogames or internet in the house. (There's a lot of good stuff there, but much much more distracting crap. You should supply endless books instead of internet.)

If you really want to make him a math genius, homeschool him with the kids of other achievement-driven parents. Talk to professors who have children your kid's age, and parents who take their kids to skill-based competitions for piano or chess.

Read with the kid until he loves to read by himself. Buy him flashcards when appropriate. Don't expect the local public school to be competent.

As a kid I was a "brilliant student" who read nonfiction for fun, because my parents started out reading to me and steered me toward trying to be the smartest student. I wasn't homeshooled with professors' children and I'm not quite as successful now as the people I know who were. I and all the other driven nerds I know have good technical jobs or PhDs at this point. I regret getting into computer games, news and popular music -- it's ok to keep your kid away from some stuff. I also wish I had realized earlier that most textbooks are written by committee and grade school teachers don't necessarily like their subjects. In the end, the nerds will inherit the Earth, and rare technical skills pay really well.
posted by sninctown at 9:45 PM on January 17, 2013 [2 favorites]

I want so badly to be proficient in math and statistics, but I am not. If you give me the formula I can plug in the numbers and go, but I cannot do math in my head (I must see or visualize objects to use in solving problems) nor can I explain to you why the formula works or why you would use a specific one. I am not strong in math, and I know of one reason why.

I have always been an advanced, prolific reader. I'd read anything I could get my hands on just for the sheer joy of seeing words on paper. So while my brain is naturally geared that way, the teachers discovered it in 1st grade and decided that I needed to go to the next higher grade to get in some advanced reading. So for an hour a day I'd do that. From first grade to fourth grade I did that. The unfortunate part is that my extra hour of reading somewhere else meant I missed the math lesson for my grade. Starting in second grade I was simply expected to stay in at recess to get the math assignment done if I didn't get it done during free time or whatever. That was fine until we hit multiplication and division...and my math skills fell apart and I never recovered. I cried for weeks being the only kid staying in at recess because I couldn't do 100 multiplication problems in 60 seconds (which led to a whole other hang up about being watched and judged).

I'm 37, and almost 30 years later this still gets stuck in my craw. To this day I have to mentally add 4 "8"s instead of knowing what 4x8 is automatically. By God, I can read like a maniac though!

You asked if any of us hated math, and why. For me, it's because I was denied those lessons in order to advance a gift I had. Be careful that you don't cause a similar problem, or allow it to happen in your child's school. I think the combination of the stigma of being not only the "advanced" kid, but also the one who had to stay in because she was always "behind" instilled a fear of math in me that is unshakeable. I do my best to figure out ways to not be the person everyone else watches trying to figure out how to add the tip so the total come out to an even number...heck, half the time I probably over tip because its an easier number to handle while everyone else is watching and waiting for me. Don't focus so much on math that your child is afraid of reading or speaking in front of others, or misses other lessons that are vitally important. Find that balance somehow.

posted by MultiFaceted at 9:48 PM on January 17, 2013 [3 favorites]

I can't recommend Kate Nonesuch's Family Math Fun! enough [link to free pdf download from this page]. I was lucky enough to attend a math ed workshop with her (my area is literacy, but I tagged along with the numeracy people and it was great). Be sure to read the introduction--it gives lots of examples of practical things you can do with kids every day, incorporating math into their daily lives so that it seems only natural to be comfortable with various mathematical principles and applications. Some of these will be better when your kid's older, but some of them you can probably start doing with him right now, or very soon.

Chapters from the table of contents: Songs and Rhymes; Math at Home; Math in Nature; Playing with Shapes; Things To Make; Card Games; School Math (e.g. times tables).

Good luck!
posted by hurdy gurdy girl at 9:53 PM on January 17, 2013

The biggest thing will be how you and his teachers respond when he plateaus, burns out, or struggles with a particular skill set. Patience, patience, patience, and faith that he'll persevere eventually, with support and effort.

Why do I hate math? I was in an advanced program for arithmetic in 2nd and 3rd grade--working at a 6th grade level. In 4th grade, we jumped to middle-school level work and I hit a wall. After bad grades (C's) on a pair of quizzes I was promptly demoted, along with 2 others, to a kind of math purgatory taught in the hallway by an aide.

I remember asking when we'd be let back into regular math, and being told, "you'll never catch up to them, you're just bad at math." It was humiliating, and you better believe I never seriously pursued it again. And in fact I still think of myself as "bad at math" and absolutely dread it, although I never got a math grade lower than a B+ in my entire life, university calculus included.

(luckily there were things at which I was much more naturally talented and, for the most part, they remained unsabotaged...)
posted by like_a_friend at 9:54 PM on January 17, 2013 [1 favorite]

Internalize the Exploratorium's stuff for teachers.

I am perfectly willing to teach him myself if it comes down to it. But since I am a complete ignoramus with respect to child development, I don't know when or how to start.

Stuff he learns through play is fun.

Stuff he learns from you standing over him with a worksheet may not be.

better spatial reasoning skills

Montessori blocks - especially if you make them yourself.
• Make his furniture out of gridbeam.
• Lego
• Fischertechnik or Meccano / erector set
• Origami
Fermi problems
Cartoon Guide to Physics
Flying Circus of Physics book
Family Scientist - Let him notice you making the demo appratus; he'll think "This is what grown-ups do!".
• Draw a huge Voronoi Diagram on his wall. Do other tilings and fractals on the other walls with removable vinyl tape or with him and tempera paint and cut sponges. Save the starchart for the ceiling.
• Find a local hackerspace or lasercutter jobshop and do up tesellation puzzles out of acrylic or plywood that can be tidied into in a frame. Stain the wood yourself.
Ball of Whacks
• Do Generative Art projects with him. Like this, compass and straight-edge stuff, and so on. Physical stuff you can hold in your hands, not just apps and screen stuff.

Revisiting the "make the demo apparatus" bit - if you turn this into a hobby for yourself, and a fun parent-kid activity, he'll think it's fun and normal that he helped his dad paint some blocks or that he and his mom wear a cyantotype t-shirt of the fractal he helped draw on the wall. Any toy or demo you make with him from scratch is worth a dozen prepackaged kits.
posted by sebastienbailard at 9:57 PM on January 17, 2013 [3 favorites]

Try to raise a science genius, not just a math genius. The science will give him context for the math, and he'll get used to asking you a question about the world and having you work him through the idea.
posted by sebastienbailard at 10:03 PM on January 17, 2013 [2 favorites]

Why do I hate math? Partly because there was so much pressure, screaming, and ridicule associated with my elementary school math career, and partly because I have a terrible time with counting things that I see. I can count things I hear with zero effort. I can easily count things that I touch. But it is terribly difficult for me to keep track of how many things are in a particular visual field. Or, say, how many places are after the decimal. It's just a weird blind spot that I've learned to work around.

If your kiddo turns out to be wired a bit differently from you, you might just try approaching math in a different way (music! manipulatives! dance! geometry!) than whatever way worked for you. I can pretty much guarantee that it will work better than yelling and shaming and whatever bullshit passed for teaching in the 1980's.
posted by corey flood at 10:14 PM on January 17, 2013 [1 favorite]

What corey flood said. If it's that awful be willing to back up or slow down or take a break altogether - they may need another 6-12 months (or more!) in order to process. Algebra at 13 vs. Algebra at 14 can make a big difference. I took it at 13 and shouldn't have (being in "all the other honors classes" is not a reason!), but that got the ball rolling to taking everything a year or two early, and I never really caught up. Always passed, but it was always awful (crying, fighting, mediocre teachers, peer pressure from fellow nerds etc.)

Any education system that lets you move at your own pace sounds like an absolute dream*. The Trachtenberg system of mathematics, Physics, and studying for the GRE as an adult made math okay.

Make it okay if he turns out different... make it painfully clear that it's okay. Make a point of encouraging whatever it is he's interested in and passionate about and good at - even if it's not math. Especially if it's not math. If he wants singing lessons and you're sending him to Kumon instead, he will hate it - he gets both, or gets to sing (say, as long he maintains an A in his math class at school or whatever)...

*I went to an overcrowded, underfunded public school in California where most of the students didn't speak English... it wasn't good for anybody.
posted by jrobin276 at 11:08 PM on January 17, 2013 [1 favorite]

When I was a tiny kid I absolutely devoured Math For Smarty Pants. That is a good book.
posted by value of information at 11:20 PM on January 17, 2013 [4 favorites]

corey flood: "I can count things I hear with zero effort. I can easily count things that I touch. But it is terribly difficult for me to keep track of how many things are in a particular visual field."

Which is why I think a lot of this comes down to an investment in early childhood education. I recall my mom made me some number game cards using 9x5 notecards and a boatload of circular dot stickers. At first it was just counting, and identification, but it eventually grew into addition and subtraction.

This ended up having two effects: firstly, it had a sort of snowball effect; I was placed in a gifted education program very early. Where they continued to feed me more math topics. The grade system also build a bit of personal pride in my math abilities relative to peers. I also got a lot of math puzzle books as a kid, and so on. I recall a neighbor sold us some slightly old math textbooks that were above my gradelevel, which I suppose help kept me above pace. In 6th grade I remember there was a public chart of math worksheets progress, and I was way behind. So I spent a couple of recesses catching up and ended up pretty much blasting way ahead. Maybe it was just me but I don't recall the teacher paying attention to it all for anyone after that.
posted by pwnguin at 11:25 PM on January 17, 2013 [1 favorite]

Nearly all math is done alone, with a book (or paper) containing hard problems. Buy the textbooks currently used in the current best university math department, and always be ready with the next textbook or other equally-good literature when your kid wants something new to read. The best teacher you could find for your kid cannot explain nearly as well as the best professor whose textbook you could buy for your kid.

Most math is done alone but you also spend a lot of time talking to other people about your ideas. And even the best departments use terrible terrible textbooks for 1/3 of their classes (who knows why). You should encourage him to teach himself, but interaction with peers and more knowledgeable adults is absolutely critical to developing a love of and ability in mathematics.
posted by matildatakesovertheworld at 11:38 PM on January 17, 2013

This isn't so much about getting started but what is it that you feel you missed out on? Why not take the opportunity to explore those areas yourself - get a tutor or take a class of your own. Once he's older and up to speed on the basics you can share the things you're finding out, so it's not so much you teaching him but you learning together (or rather him learning how you learn). He's a bit young for it now but when he's old enough you'll be actively demonstrating the joy of exploring and expanding your math knowledge.
posted by freya_lamb at 2:33 AM on January 18, 2013

I came in here to recommend Math for Smarty Pants, too. Loved that book. I also loved Square One Television if you can find it anywhere - it might be a little too '80s for modern kids, but you never know.

Essentially, look for fun things that have a math component. Especially toys or other hands-on activities. For example, I loved these blocks as a kid; each little block represents 1, and there are larger blocks representing 10 and 100, and whee, blocks! They're small and therefore not toddler-friendly, but that's just an example.

And look for ways to point out the math in everyday activities. If he wants to help you with cooking, that's a great time to teach him about measurements and fractions. And money is just math you can buy candy with!

Also, since math and science are closely related as mentioned upthread, expose him to cool science stuff early. Start with the kid-friendliest subjects: dinosaurs, space, and bugs.
posted by Metroid Baby at 4:39 AM on January 18, 2013 [1 favorite]

"Pick a number from 1 to 10. Double it. Add 8. Divide by 2. Subtract your original number. You got 4." I got interested in math because I wanted to know how my mother did that trick.
posted by Obscure Reference at 4:41 AM on January 18, 2013 [5 favorites]

Husbunny is a mathematician and he always says that the west sucks at teaching mathematics.

One thing that makes Asian kids so much better at math is that their language has a very systematic method of NAMING numbers. Basically the mathematics are built into the language!

My advice is to have a native Mandarin speaker teach your son Mandarin, counting and Abacus. That would be the easiest, most natural way to do it.
posted by Ruthless Bunny at 7:01 AM on January 18, 2013

I'll provide myself as anecdata in support of Montessori schools and educational games. I started off in a Montessori school (where I kicked ass in the stamp game, thank you very much), and the first computer game I loved was Operation Neptune, and now I'm midway through a Ph.D. in math. (And we all know that correlation implies causation, right?) I don't remember exactly the extent to which my parents filtered out non-educational games and TV (internet was not such a serious issue at the time), or how old I was when they stopped, but I know they did. It's probably a bit harder to do that these days than it was in the early 90s, but I suspect it's worth it.

Remember, also, that there are many roads to mathematical thinking; pure math is only one of them. I found my way to math through physics, and I got to physics through model rockets and airplanes. My brother, who is not a mathematician but definitely has the 'mathematical thinking' you are talking about, got there through programming and computer science (and a healthy dose of natural sciences, too). Even now, when I've been neck-deep in mathematics for years, my mathematical thinking is deeply linked to my physical thinking, and I'm a better mathematician for it. Honestly, I think that science may be a better path to this kind of thought than pure math is.

The last thing I'd suggest is to try to instill the general principle that hard work is more valuable than innate intelligence. When your child succeeds, praise him for his efforts rather than his enormous brain. There's been some research lately showing that kids who are told they are really smart are actually discouraged from trying difficult things--when they meet a task they can't solve right away, they conclude that they're just not smart enough, instead of realizing that it will just take some work to figure out. So, I know your title was a bit tongue-in-cheek, but maybe avoid terms like "math genius" in favor of something like "math expert," that connotes skill rather than talent.
posted by Aquinas at 7:32 AM on January 18, 2013 [2 favorites]

Things you can do right now, with your toddler:

Put a few decks of cards in his toybox and let him get familiar with them. Let him use the cards to build houses or make tracks for his cars, whatever. Sometimes, you play with him and sort the cards into red/black or suits, or people/dots. Count them out into piles. Don't worry about any cards that get lost or broken - the whole 52 is not the point, just worry about the individual cards.

Count everything you do with him: putting toys away, cheerios on his high chair tray, spoons in the dishwasher, etc. If the things you are counting go too high, just push those aside and start over. I still remember when Sesame Street graduated from always counting 10's up to counting 20's. I'm not sure that going any higher at this age is worthwhile.

Other things to pay attention to: sorting, grouping, sets. The idea of "more" and "less" when comparing groups of things, graduating to "lots more" or "just a little more" as he gets better at it.

Once he knows some of the numbers, have a "Two Day" (for example) where you feed him 2 pancakes with 2 forks and give him 2 juice boxes (you both can laugh as you drink the other one because having 2 juice boxes is silly). Find groups of 2 things at the park (2 swings, 2 rocks, 2 water fountains, 2 kids in the sandbox, etc), everywhere you go, point out things that you can see which are in sets of 2; see if he can find some on his own. Do that for a week or so, then change to another number. Come back to Two Day at some other time in the future just to reinforce.

Once he knows what a group of each number looks like, see if he can do it fast. Put a small number of pennies or rocks in your hand and flash it open and then closed. See if he can tell just by sight what that number is, without actually counting each one. The idea of this is to get used to the idea that groups of numbers have shapes - 3 is a triangle, 4 is a square, 8 could be a rectangle of 2x4, etc.

At some point, you'll be able to start operations with the numbers that are all around you. As long as you do it with concrete things, you can do all kinds of things. Especially work with the idea of "half".

But the idea at this age is to get him familiar with the idea that the world is quantifiable and there are some rules that we use when we organize those quantities.
posted by CathyG at 7:36 AM on January 18, 2013 [2 favorites]

I am a mathematician, and I've been very involved with math since I was a young child, and I thought a lot about how to answer your question, but I don't think I have very good answers. I have a story, though. When I was little I remember staring at a rectangular array of holes in my parents' stereo speaker -- it was a 5 x 6, and I was just kind of gazing at it and contemplating it and then I was like, holy crap, it's 5 columns with 6 hole each, but it's also 6 rows with 5 holes each, and that's why 5 x 6 and 6 x 5 are the same, not because somebody told me that, but because that's just how it is.

Moments like that made me a mathematician but I don't know how you make moments like that happen.
posted by escabeche at 8:23 AM on January 18, 2013 [6 favorites]

Like corey flood, I can't count objects unless I can touch them. My mother saved my kindergarten math worksheets, I think initially because she saved everything and she keeps them now to threaten to embarrass me with them. I'm a PhD student in math. Flashcards with circles on them would have done me no good. Moving blocks around, probably. (I honestly have no memory of how I learned to add.)

Unlike Aquinas, science didn't really do me any good mathematically. People kept telling me how much I would love physics, since I liked math. Got to (calculus-based) physics in high school and hated it. Sure, I did well. I got As and a 5 on the AP test. But, basically, I fumbled about and stuck some stuff into a formula having little real understanding of why I was doing it. (My physical intuition kind of sucks.) It dawned on me years later that had someone said the words 'Riemann sum', it would have all made sense. If you make something rigorous, I'm way more likely to understand you.

The theme here is, I guess, that it depends on your kid. I like being right and being good at things (who doesn't), which means I'll do flashcards and worksheets until the cows come home if they're at the right level of difficulty. (I'm still bitter about how those of us who could read in first grade (my mother taught me in the summer) were sent to a table to do worksheets about synonyms and antonyms during the reading lesson. We could read. We knew what the words in the problems meant. We didn't know what synonyms and antonyms were.) My brother is not so enthused by being good at things and wouldn't volunteer to do worksheets. He was super into Playmobil and Lego. But that's a good excuse to teach him about history. (My brother is mathematically adept. He's not as inclined towards pure math as I am. I don't remember what he did math-wise as a small child.)

I was banned from watching things that weren't PBS (not too hard when your TV doesn't receive much other than PBS). For years I wanted to be a structural engineer because there was a structural engineer in the documentary about the Chicago Flood who had a cool calculator on his desk and a cool graphic to go along with his explanation. But, mostly, watching a lot of PBS is a way to be bored in social studies--I think I'd already seen 90% of the documentaries we watched in school. I mean, I guess I endorse raising your kid on PBS and without video games. I think it did me good. But I don't think it'll make your kid good at math. That said, I liked watching TV. I would watch Wall Street Week with Louis Rukeyser on Saturday mornings, for heaven's sake. Watching 'adult' PBS likely did me good. I did get books from the library to learn about stuff I saw on TV. (Also, holy crap, don't limit your kid to checking only three books out of the library. I spent a summer volunteering in the children's library in high school and this just blew my mind. Some kid wants five books (or whatever) and their parent only lets them have three. If your kid can't keep track of five books, let them have five and make a 'one library book off the shelf at a time' rule at home.)

One thing that makes Asian kids so much better at math is that their language has a very systematic method of NAMING numbers. Basically the mathematics are built into the language!

I think this is oft-repeated, but isn't particularly true. There are lots of languages where the numbers work in a similar fashion. German basically does. The multiples of 10 follow an obvious pattern (n-zig, though zwanzig for 20 and siebzig for 70, not siebenzig) and everything else is x-und-n-zig. Heck, this is what's happening in English, too. (The '-ty' is coming from some kind of Germanic root. 10 in Norwegian and Danish is, in fact, 'ti'.) And Norwegian. And Swedish. Between 40 and 100, Danish gets into a system based on multiples of twenty, but I don't think Danes are freakishly good at multiples of 20. (Though, interestingly, Danish uses a system based on 10s for dealings with other Scandinavian countries. I think because that's a big place the similarities between the languages break down, so Danes are probably a bit better at 20s than the Swedes, say.)
posted by hoyland at 8:28 AM on January 18, 2013 [2 favorites]

I am not a math person, and these will not suit your child now, but two things that actually made math appealing and comprehensible to me as an older child were Donald in Mathemagic Land and Square One. In particular, watching how Square One tries to render abstract concepts concrete might give you some ideas (if you can find it, which I hope you can!).

Square One speaks to applying math concretely, which was big for me. I did pretty well in stats because I could see the practical applications. Algebra was wretched, and it was only well after school that I found ways to apply it. A friend posted on Facebook recently that her son was helping out with dinner, and as he chopped vegetables, he observed "I'm making fractions!" Those were the kind of moments that made the slog of maths worthwhile for me.

What stands out for me in Donald in Mathemagic Land is the beauty of math: proportions in music, art and nature. Fractals are beautiful and amazing. Things like that impart a sense of wonder with respect to math in me that made me curious about it, though rather too late in life to really become a math person.
posted by EvaDestruction at 8:35 AM on January 18, 2013

You know that thing that went around a few years ago about how kids need to be encouraged for hard work instead of being smart? Poster child here. I have next to no ability to sit down and focus on working through things, and I grew up with a hatred for math, despite having a math teacher for a mother.

Part of it was that my parents never encouraged me to sit down and work through problems (math and otherwise) when very young, and as I was smart enough to grasp concepts and regurgitate them at an early age, that meant by the time I hit the point where I needed to sit down and work through problems and to practice them, I had neither the ability to make myself sit down and do it nor the patience for repeated failures on the way to a solution. I started getting Bs in math in the 7th grade, and by the time I took highschool calculus, I scraped by with Cs, and that only because if I did any worse, my parents would have punished me. (As it was, I got interminable lectures for Cs, but at least I wasn't grounded or worse.)

So you can see that there's no joy associated with math, either, just tedium and bad memories.

Nowadays, if I'm interested in something I can often work through whatever it is if I can see that it's directly applicable to the eventual solution. I do web design and development now, and I'd never have considered myself able to program if you asked 15 years ago. But I cannot sit down and do algebra for the sake of doing algebra, because I can't make the connection between what I'm doing there and any other point of my life. If I end up with a programming problem that needs an algebraic solution (and is not a "Write a program to solve this equation" thing), then I'll be able to teach myself that one thing, but I'm not going to be able to force myself to expand that just for the sake of doing math.

So: encourage your kid whenever he works hard, and for repeated failures on the way to success. And start that early. It doesn't have to apply just to math, but to anything.
posted by telophase at 8:42 AM on January 18, 2013

The best place to start is to have accepted, before you even do start, that you child may not be at all interested in math. They may have no natural talent for it they may find it all a terrible boring slog they are only doing to please you and to spend time with you and that they would much rather paint or colour or run or write stories or read books and you need to be alright with that. If you go into it with an OMG YOU WILL LEARN ALL THE MATH mentality your kid will end up hating maths.
posted by wwax at 8:48 AM on January 18, 2013

Math at the elementary school level is a completely different animal than math once you get past algebra, in a way that a lot of people don't even realize, and you yourself may have forgotten. You love math, but you probably have a bit less affection for arithmetic.

Getting him a private tutor to learn to memorize times tables isn't going to impart him with any desire or ability to work through mathematical problems logically, and I could see teaching him algebra and up leading to a lot of frustration when he hits elementary school and finds out this class they call "math" is just really boring baby stuff.

Try to ease off of the idea of knowing a great deal of math being non-negotiable, don't make it into something you'll feel hugely disappointed every time he looses interest in math and gets into something else. Think of it as something that's really wonderful and enjoyable that you can share with him as he grows up, and don't let it become that thing that he'll be a disappointment to a parent if he fails at -- in the short run that can work, but it tends to lead to a real dislike of the subject over time.

For your long term plan, you need to know what he'll be doing in elementary school. If he's going to be in an ordinary pubic school where years are spent on memorizing and drills, it's going to feel even slower than it did for you if he knows anything already. If you are planning on private school or a magnet school, start finding out how they deal with math and arithmetic education -- a good starting point for this is to see if any teachers there have math degrees, but you'll need to see what educational philosophy the school follows as well since the teachers may change.

Depending on how devoted you are to this, you might want to move or do homeschooling, perhaps with a group of like-minded parents. You say you know nothing about child development, which gives you a chance to model lifelong learning for your son while you take some psychology and child development classes. Now is a perfect time to get started on this, assuming you are interested in other aspects of his development other than mathematical ability.
posted by yohko at 1:16 PM on January 18, 2013

I was a gifted child. My mum taught me to read at two; by three, I was reading at secondary school level. I had to take separate English classes from the rest of the class all through primary because they weren't sufficiently advanced enough. I read voraciously, I read my sister's CSE exam text when I was six because I was bored, I read broadsheet newspapers at an age when I had to spread them out on the floor as they were too big for me to hold, and I read extremely quickly (people think I'm lying about having read things) because I figured out how to use Teletext when I was seven and you had a short period of time before the pages changed. I have never needed to revise for an exam in my life because I am very, very good at recalling things I have read and often verbatim.

I am terrible at maths. I got a C grade at GCSE only with hard work. I would ask my dad for help only to end up in tears because he couldn't see why I couldn't understand what to him were simple sums and would get annoyed. I can't remember all my times tables, and sometimes when I add up in my head I have to 'count out' the numbers by tapping my finger or pencil nib on the table quietly. I have bought furniture too big for my room because I can't visualise what a metre looks like as a side of a solid object. The only thing I showed aptitude at was quadratic equations as to me they were like code breaking (I later went on to do a linguistics degree).

So I guess what I'm saying is that not every child can have a natural aptitude for maths. My mum is I'm sure dyslexic, but she taught me to read, and I loved it. I got some pride from being given long strings of numbers and being able to add them together in infant school, but I'm not sure whether I began to find it dull or find it difficult first - I always believe that if you're not interested in something, it will always be a lot harder. My dad was an architect and very mathematically capable, but he wasn't able to understand why I didn't find things as easy or interesting as he did, and that made it a difficult experience and probably put me off a little more.

One big reason that I wish I was better at maths is that I have been learning to crochet - crochet, especially in the round, is mathematical - you are adding or subtracting stitches at intervals to create the pattern and this means you are always counting and working out where the next increase or decrease goes. Small children can learn how to do it easily (I'm going to try knitting properly at some point this year on the same principle) so it might be worth a try as a hobby that works as stealth maths - it makes me visualise numbers in a way I didn't before.
posted by mippy at 1:50 PM on January 18, 2013

I started explaining simple addition to my son as soon as he understood the concept. Then he would sit in my lap and I'd give him problems aloud. Then it was subtraction, multiplication and so on from there. It was fun for him when a lot of typical boy things weren't. He isn't a math prodigy now but he is two years ahead in school and it is his favorite subject.

I only wish I had thought to do it with our first child.
posted by Requiax at 2:35 PM on January 18, 2013

Response by poster: Lots of interesting and helpful answers, everyone! Thanks very much.
posted by Jonathan Livengood at 7:46 PM on January 18, 2013

The things I am about to write are from my myopic point of view as someone surrounded by people who love mathematics.

Lockhart's Lament tells truth about the state of the teaching of mathematics in America. It tells an awful truth of despair.

The Art of Problem Solving is how a lot of kids learn the math problems that get them to do well on USAMO or Putnam every year. Contest math is the mathematics most like actual math which actual mathematicians do, and the higher contest math tracks are feeders for mathematics departments at universities, especially the American Mathematics Competition (AMC) to the American Invitational Mathematics Examination (AIME) to the USA Math Olympiad (USAMO) to the International Math Olympiad (IMO).

The AoPS people also have an entire mathematics curriculum which may be of interest later. They stress creativity and the ability to prove things. The textbooks are remarkable: you can actually read them and they will try to make sense. Of the USAMO participants I knew, most of them had some significant involvement with them. A traipse around their forums would also be enlightening. They also have a line of textbooks for smaller kids.

I feel kind of bad, being such a partisan for the AoPS (Pepsi Green?) people, but they are badasses and I didn't see any mention of them in this thread.

The other high-level contest (Putnam, USAMO, IMO) participants I knew cobbled together their education from a long list of other great math books. Euclid's Elements rewards study. How to Solve It and How to Prove It, by Polya and Velleman respectively, also come up. Enderton's Introduction to Logic comes up, although in my honest opinion, it's mostly a 500-page lump of symbolic notation. Linear Algebra Done Right is the most-recommended linear algebra book. Here's a reading list. Here's another reading list which seems alright.

The discrete math book I liked most was this one, which is neither finished nor a book yet. Keith Schwarz is one of the best teachers I have ever met, and I think he's turning twenty-five this year.

Of course, these are all college math textbooks. In my experience, most people could have done college mathematics in high school, if they were willing to be as stressed and work as hard as college undergraduates in math. My friend who did mathematical research in middle school was willing, and so was the friend who finished Stanford's physics curriculum in fifteen months, but most people weren't. There is no foolproof way of instilling that will to study. I know too many parents who tried and failed.

What you can do is love math yourself, as my father did, and show your kid cool stuff and let him understand it. Of the people I know who love mathematics, I can't recall a single one whose parents didn't love it also. Of the people I know whose parents hated mathematics yet loved the idea of their kids loving mathematics, I can't recall a single one who didn't wretch at the sight of figures.

But as for the idea of mere innate genius, let me quote from the eminently quotable Ted Orland's book, Art and Fear:

Talent in a snare and a delusion. In the end, the practical questions about talent come down to these: Who cares? Who would know? and What difference would it make? And the practical answers are: Nobody, Nobody and None.

Let us finish with a complete digression.

Discrete math is the study of the discrete: about things which are not continuous, but separated into distinct values. This is a field which includes combinatorics, probability, number theory, set theory, logic, algorithms, and graph theory.

I don't think that I need to convince you that schoolkids need more education in probability and logic. The modern human being is drowned daily by specious argument and specious data. The modern human being is also sometimes replaced by algorithms. It is also true that schoolkids need to learn more about algorithms and graph theory. Consider the amount of time you spend mucking about with formalisms in calculus, and consider that the foundations of formalism itself are discussed in discrete maths.

I also found it to be true that you could better build foundations for a dedication towards mathematics on discrete mathematics, because it has more of the foundations -- set theory and logic. You look at a purer mathematics. I went to high school with someone who fooled around in calculus class by doing discrete mathematics. He ended up going to the USAMO.
posted by curuinor at 9:29 PM on January 18, 2013 [7 favorites]

I'm surprised more people haven't mentioned music. Math was by far my favorite subject all through school, partially because it came really naturally — and I chalk a lot of that up to taking music and music theory lessons from a really young age. (I started taking piano lessons when I was five, after begging my parents for a year. Lisa Simpson is my patronus, basically.) When you're little, just the repetition of counting and numeral literacy winds up being important. Fractions? Well I already knew about whole notes, half notes, quarter notes, and time signatures, so it was easy peasy. When learning about logs, most people are taught to think about a clock — but it always reminded me of an eight-note scale. Because I had already been rolling these ideas around in my head, by the time they came up in math class, they seemed really organic and obvious to me.

The best math teacher I ever had (the best anything-teacher, honestly) used to give "coming attractions" of concepts we'd say later in our math careers, stuff that was outside of our skills at the moment. I think piano was full of coming attractions for math, so to speak. It definitely helped me connect different concepts to each other, to sort of "see" math in my own ideas and not just in the ways my teachers explained it. Sometimes we think about drawing inferences and making wild connections as more of an artsy/literary skill, but it's an essential part of mathematical thinking. And it's, you know, really intellectually rewarding, even at a young age.
posted by Charity Garfein at 5:50 PM on January 19, 2013 [1 favorite]

A few suggestions:

- Consider putting your son into Montessori at a young age ( He'll get a good start and foundation in math there.

- Sing and play music that has counting components (One Two Buckle My Shoe, The Ants Go Marching One by One, Twelve days of Christmas, etc.).

- Play a lot of number games like counting backwards (make it fun with "ignition, blastoff!), skip counting, etc.).

- Do a lot of counting and measuring of things in front of him so that he sees that as just a normal and natural part of everyday life.

- Check out Singapore Math and if you are interested buy some of their materials (I did that with my daughter starting at age 3+).

- Very important: don't push too hard because if a child is not developmentally ready for something, it will be frustrating and stressful for him if pushed too hard to try to learn it.
posted by Dansaman at 3:32 PM on January 25, 2013 [1 favorite]

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