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study plans for a future mathematician


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My 9yo, yes I know she is still really young, desperately wants to become a mathematician when she is older.

So now I am trying to work out how to best prepare her for this and also to keep up with her interests and desires.

I can't really see her changing her mind too much, all her "when I grow up" dreams her whole life have revolved around numbers, problem solving and complex calculations. And if she does change her mind, well she still loves math and she will have a great foundation in it for anything :001_smile:

 

She is 9. She should have just started 4th grade (jan-dec school year) but we call her 5th grade.

We were going to start AoPS at the start of this year however I have decided to take this first term (jan to april) to go through grade 6 australian math briefly to make sure we have not skipped any topics (2 weeks in and we will be done in another week) and also to finish up beast academy.

 

So we will be starting AoPS prealgebra once the above is finished.

She will also use alcumus.

She has been using prodigy for the last 8 months or so but has finished all the levels and topics, she maxed out the game in less than a year, damn. She still likes to play so that is good review for her but she really is done with it.

 

And then what?
Obviously my #1 plan is to continue with the AoPS books. Are there other programs I might want to consider?

Is there anything else you would recommend? Books? Online learning? Games? Activities? Anything really. What would you recommend now, or in the future for an aspiring mathematician?

If you have raised a mathematician or have an aspiring mathematician currently what are you using? How are you preparing them?

Thanks heaps :001_smile:

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I suspect you will receive lots of replies, as several of us have degrees in math, and kids who are doing well in math.  Probably the most common theme you will hear is, "don't rush, and don't try to push to some end goal."

 

Take time to explore concepts - deeply.  AoPS has a nice program here in that you can afford to spend two years on pre-algebra, two years on algebra, do number theory, probability, and so on.

 

For a mathematician, theoretical concepts are key, so spend time exploring those ideas.  Dabble in abstract algebra (just the beginnings), non-Euclidean geometries, topology, and other interesting topics.  Just make sure that she finds them interesting.  Her track doesn't need to look traditional in any way.

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That is exactly why I am asking now, I want the best ideas on exploration and "alternative" areas we might want to explore.

 

At this point I think the plan is AoPS prealgebra and then onto their introduction to number theory as this is one area she loves. But she also loves algebra and geometry... there are so many great books out there

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Love that list, too! I just thought I'd also chip in to add my own encouragement to the OP to do lots of fun stuff and explore a lot.

 

There's math everywhere, and so much if it is cool. I usually have more ideas than people actually want to hear (***needs to get better at reading social cues that she's geeking out on math***), but one idea for a girl of that age off the top of my head is (if she hasn't already) that she could watch the Bletchley Circle series (dramatized, but still kinda cool) and do a study on cryptography. Look into the Enigma. What did these ladies actually do? Look at the history of cryptography (maybe read the Code Book and other similar ones). Study modern cryptography. What is RSA and why/how does it work? Why are primes so important? Branch off into number theory. Why are large primes so hard to find? Learn basic coding and program a few of her own programs to find prime numbers or determine if a number is prime. Time them and see which ones run more quickly. Look into large of numbers her programs can actually handle - how do other people handle much larger numbers (e.g., 200 digit numbers). Introduce her to simple, but rigorous, proofs in the context of basic number theory theorems regarding prime numbers. What sorts of cryptography is used by things she uses (banks, email, etc.)? Is it all RSA or do some actually use other techniques? What does the government use or what has it used in the past? Just keep going deeper and further into any little subarea that she finds interesting! :) When you've exhausted this trail, start over with another interesting topic. You don't have to scratch very hard to find math under whatever you want to talk about in life (though some are more of them will have more interesting math than others, of course).

 

Another one I love talking about with kids that age would be kinds of infinity and how the numbers we usually work with are a negligibly small subset of the entire set of real numbers (compare countable and uncountable sets and classify integers, rationals, irrationals, transcendentals, etc. as one or the other), even though they're certainly not negligible in terms of their importance or usage. Ok. I'm turning off my inner geek now. :)

Edited by deanna1ynne
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Lovely ideas! A big part of math learning for DS was non-curricular but asking questions and following bunny trails. Just a small note that the Bletchley Circle series can be traumatizing for a young kid (the women also work on a serial killer case).

 

I do wish I had known to do some of the above with my kid. His preference was for me to stay out of the way although at times he needed a sounding block and someone to co-wonder and co-delight in the mysteries of the math universe ("this is so beautiful, mom!"). So do not worry at some point that she has outstripped your math *and* thinking abilities. Just keep asking questions and enabling enthusiasm.

Edited by quark
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Obviously my #1 plan is to continue with the AoPS books. Are there other programs I might want to consider? I don't know much about AoPS from experience, but I would encourage you to be cautious of jumping fully into the most rigorous/demanding (read: possibly draining) curriculum that you can with a younger-than-intended child. Also,  I have read on these forums that some students may need more repetition/straight forward practice, than AoPS offers, to build the sort of fluency that is needed, so get a cheaper secondary text to keep on hand for more problems if your child needs more practice to master some of the Algebra skills she is learning.

 

Regardless of what series you use you want an unshakeable Algebra foundation. If she can do AoPS series at 9yo then she'll build the problem solving/puzzling stamina, but at the end of it, she'll need fluency too.

 

 

Is there anything else you would recommend?

Pace yourself. Math is infinite and she can't run out, but she can burn out.

 

Books? Based on it's reputation here, AoPS is "the best" and you're already well aware of them. So my suggestions it to look for a used college level text for non-majors on discrete mathematics and a survey of mathematics to keep around for exploration and mussing about outside the curriculum. Logic Statements, Tables, and Gates are fun and accessible too anyone curious enough to go through those sections.

Start a list of biographies of Mathematicians and keep some in your house/book basket. There are dozens of them out there. You can start with Mathematicians are People Too vol 1 and 2, Women and Numbers and Headstrong: 52 Women who Changed Science and The World. There are comic books and manga guides to various topics of mathematics that she might enjoy reading, even if she can't follow everything in them. You want to really wade in concepts and sometimes the best way to see the connections is to leave the path completely behind. For example, simultaneous equations and matrices learned in Algebra 2 feed nicely into Linear Algebra, so you may take that deviation, before you get to calculus.

 

Online learning? Russian Math School offers online classes for grades 4-9. There is also Elements of Mathematics

 

Games? Chess? The Function Game? Honestly, I'm awful with being 'fun' so I'll let others recommend games.

 

Activities? Consider learning Russian, German and/or French (many advanced degrees in Math require students to read math in The Original). Maybe she'll like computer coding?

 

Anything really. What would you recommend now, or in the future for an aspiring mathematician?

 

Pace yourself. Take breaks when needed. Read, read, read, read, read about mathematicians and mathematics. Learn to write on a whiteboard/chalk board in a neat, coherent fashion. Learn how to read and study a math book. Develop the habit of copying out theorems, rules, examples and going through them so that you can teach it to someone else. Always re-explain,summarize theorems/rules in your own words. Keep a math journal. Keep a healthy mix of applied math in your studies. Keep your math foundation in tip-top shape. Look into Math Camps and Math Clubs. Does she play music? She might enjoy reading about Math-Music connection on the AMS website. Watch all the math documentaries that you can find and discuss the ideas with her.

 

If you have raised a mathematician or have an aspiring mathematician currently what are you using? How are you preparing them?

Thanks heaps :001_smile:

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I cannot stress enough how important it was to learn about mathematicians and the lives they lead/ might have lead. These stories were good brain food for mom too! We watched documentaries about them when we could. My favorites were the ones on Andrew Wiles/ Fermat and Erdos/ N is a Number. BBC's The Story of Maths was watched and re-watched multiple times.

 

One of the things I forget to mention here is how much I helped to scaffold DS's math learning. A lot of the scaffolding was in the form of writing/ scribing help. Here are some examples:

  1. Working on algebra 1 side by side throughout the coursework. AoPS was not as accessible to us then and there was no AoPS Prealgebra yet so we found a tutor who was good with gifted kids and followed his suggestion to use Dolciani. It was perfect for a first pass for an 8yo. DS did all the assigned problems, but I did not insist he write everything down. I did work on the problems right next to him (without him seeing my work). We slowly added the step by step writing but not for every problem. We chose maybe 3 out of 10 to write down while DS solved the rest in his head. Then we moved on to every other problem and only a few months later, writing each one down. This transition was so gentle and so well paced out that when DS moved into geometry at 9yo and about 3+ months after finishing algebra 1, he could write all his proofs on his own, for every single assigned problem!
  2. During geometry, DS would keep all the theorems/ axioms etc in his head. I bought an index card notebook and wrote them down for him and labeled them to match the Jurgensen textbook so that he would always have the  concepts at his fingertips. After a while, he did not need that booklet and it now sits on our bookshelf as a very precious memento of those initial proof writing days.
  3. DS is very mathy but he was also very often stuck on problems or had growth spurts that caused lots of angst/ anxiety in other areas. I was worried all the while but trusted my gut instinct to put math or something else on hold to give him time to process. We had many days of unschooling/ non structured learning where we just spent time watching cool documentaries/ lectures and following those bunny trails. About a week later, whatever was bugging DS was usually resolved with a brand new cognitive leap of some kind taking place. Things that were difficult a day/ week before suddenly became so easy/ self explanatory.
  4. We had whiteboards wherever we could place them. It started off with a small 8"x10" lapboard, then we found a 2x3 whiteboard (later, a 3x4) whiteboard cheap and mounted it at the right eye level/ writing height. Now we have 2 large whiteboards in his room and 2 glassboards in our hallway for his math scribblings.
  5. I buy LOTS of graph paper notebooks, loose refillable paper and pens for scribblings. DS never leaves for classes without his bag of colorful markers for math.
  6. No matter what people say, you don't need to worry about learning to use a graphing calculator when they hit algebra 2. There are many free online tools (Geogebra and Wolfram's are favorites here)
  7. Similarly, don't worry about LaTeX (I did!). It becomes second nature for kids who start loving the AoPS forums.
  8. Never sacrifice thinking time. I allowed DS to sacrifice curriculum time but I made absolutely sure he always had thinking time (except for this senior year which has been crazy busy but he still has thinking time in the car where we spend hours and hours).

All I can think of for now. :001_smile:

 

ETA: oh, "teach it back to me as if I am many years younger than you". If you were a fly on my wall, that's what you might hear most often. Also, "can you show it to me on paper kiddo? Draw it out for me?" :laugh:

Edited by quark
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Your post made me think of the Math Prize for Girls talks given by Richard Rusczyk of AOPS. Here is the transcript of one of them, which is a bit on the older side, but has a lot of information in it:

 

http://mathprize.atfoundation.org/archive/2009/Rusczyk_Problem_Solving_Presentation_at_Math_Prize_for_Girls_2009.pdf

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For extracurricular reading, Martin Gardner has some really nice books and I've heard good things about just being able to read through a college math for liberal arts book (jacobs is one of the best) and enjoy the small intros to advanced topics. 

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My middle was aimed at mathematics until she veered into aerospace at the end. :D I think encouraging a future career in mathematics is great, because even if it changes, strong math skills can help in many fields. And at least you'll have a girl who knows she can excel in that area. :)

 

She did accelerated math (calculus in middle school, up through college diffeq in high school) but more importantly, we rolled around in mathematics.... MathCounts and other challenges, every book in three library systems about math and mathematicians, math games and research, etc. When she was young, we did multiple programs, not simultaneously. We came at math from every angle.

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