Gifted Issues Discussion homepage Forums General Discussion How my math skills improved dramatically

In Gifted children could learn math much earlier I suggested that children of IQ ~145 can learn math 5+ years ahead of schedule. Those of you who have children in this IQ range but who are not currently working grade level may wonder how one goes about doing this. It’s not necessarily a matter of trying to plough through the material more rapidly.

My own experience here may be illuminating. When I was a freshman in high school, I was a mediocre math student: I earned a D in second semester geometry and had to repeat the course. By the time I was a senior in high school, I was one of the strongest few math students in my class of ~600 students at an academic magnet high school. I went on to earn a PhD in math. Most people wouldn't have guessed that I could have improved so much, and the shift that occurred was very surreal to me. It’s all the more striking in that the bulk of the shift occurred in a single year.

I thought I’d share what strategies facilitated the change. Because I was at the high school level, the particulars of my experience may not be relevant to your own child’s situation, but some of the general principles will be.

I became motivated to learn more:

I took a course in chemistry my sophomore year, and loved it so much that I thought that I would pursue a career in the physical sciences. I knew that understanding math is essential for a career in the physical sciences, and so I became determined to learn it well.

I immersed myself in math:

At the start of my junior year I started learning calculus on my own. I didn’t have the “official” prerequisites for calculus, for example, I didn’t know trigonometry. But I didn’t need to learn trigonometry to get started: I just skipped over the parts of calculus books involving trigonometric functions. Because I was behind a semester, I didn’t have the “official” prerequisite for analytic geometry during my junior year, but I gained permission to sit in on a course (not for official academic credit) while taking trigonometry at the same time. I also took a course in honors physics that used a lot of algebra at the same time.

I learned these subjects better simultaneously than I would have had I learned them sequentially. A lot of times students don’t spend enough time learning math per day to imprint the material in their long-term memories. They end up forgetting the techniques that they learn in short order, and have to relearn them repeatedly as a result. Learning them thoroughly the first time around would save them a lot of time later on. Because there was substantial overlap in the algebraic techniques utilized in the different subjects I was studying, my exposure to them per day was higher, so that when I learned them, they stuck in my long-term memory.

I learned from multiple expositions:

This is related to the above point, but is worth highlighting on its own: I read textbooks on the subjects that I was studying aside from the assigned textbooks. Often a given textbook won’t explain all of the topics as well as possible, and when one has difficulty understanding a given textbook’s exposition of a topic, one can find a better one if one consults other references.

I learned basic techniques in the context of interesting problems:

I distinctly remember hearing about how it was possible to find the graph of a rotated conic section from its defining equation. I found it amazing that it was possible to do this. Similarly, I found some of the applications of calculus to be amazing. This amazement motivated me to learn how to implement the various techniques needed, and they became more memorable when placed in the context of larger problems.

Art of Problem Solving materials supply a rich source of interesting problems. (Disclosure: I teach for Art of Problem Solving.)

I found a friend who was also learning math in a serious way:

It was really helpful to have someone who was both deeply involved and responsive, who I could consult when I got stuck, and with whom I could work through problems. This was helpful both from a motivational point of view (learning with someone else can be more fun than learning in isolation) and also from the point of view of having easier access to knowledge.

What in inspiring turnaround!

If I understand correctly, becoming aware of how the math was relevant and would be utilized was key to fueling the motivation to learn the math?

Knowing how math would apply seems to be the antidote to many kids' view that a subject may be irrelevant. There seem to be a number of teachers who are unable to answer the common question, "When am I ever going use this?"

Thanks for sharing a great BTDT anecdote.

I can't thank you enough for posting this. I could tell a similar story about math and science, only it took me until my junior year of college to "find" my inner scholar this way. From then on-- it was, er-- well, it wasn't that it was easy exactly, but it was more engaging, more flow-state, more of the time.

Anyway. I could have written it, but my DD14 (who thinks she is "bad" at STEM, btw) wouldn't have taken it so much to heart.

She read your post and exclaimed; "Yes! Exactly! He learns the way that I learn. I need to have all of those pieces to put together or I feel frustrated that I'm not truly understanding what I'm doing, and I feel inadequate that I don't really have mastery of the material. I need to see how it fits together and work hard problems that mean something."




When she has all of those things working together, it is flatly ASTONISHING how much ground she can cover per unit time. It's really remarkable. I so wish that she'd had the experience of a similarly able peer to work with.

@ indigo — Yes, that's correct. I could already see math being useful in chemistry, which was my initial motivation. Reading a non-technical book about mathematical research like Fermat's Enigma or The Music of the Primes could also help.

@ HowlerKarma — Glad to help . You speak in past tense in writing "I so wish that she'd had the experience of a similarly able peer to work with," — it's not too late! She's younger than I was when I got seriously interested in math. What math is she currently studying? What science?

It is so nice to have you here as you REALLY seem to "get" gifted kids. JS, you sound gifted yourself!

Puts some new perspective on what seemed like stupid things i did in college on my way to get a BA in math. (I sort of fell into it after deciding against other majors.) For example I decided to take the Quantum Physics for Chemestry majors my sophomore year that didn't require the Differential Equations class. I just though Quantum Mechanics sounded fun. I struggled so much in the first half of that class. But it turns out that so did all those junior Chem Majors. But I had an advantage, I was enrolled in Differential Equations concurrently and by the end of the Quantum class I realized how stupid it was to try and learn the subject without the necessary math.

What really frustrates me with my son's Alebgra II class this year is that he really ENJOYED Alegebra I & Geometry. He had enthusiastic and good teachers. But his currently class just seems like a chore. Perhaps he will have new perspective on these things when he gets to Chemistry.

I didn't really see how beautiful math was until I took Differential Equations, honestly. Which I took in order to meet my major's math requirements without taking that very last quarter of calculus. {ahem}

My advisor thought that I was crazy, incidentally, and I never worked so hard for a B in my life, never having seen any linear algebra (which I had to teach myself along the way)...

but that's when it hit me that this stuff was AMAZING, and that I enjoyed working that hard on interesting problems. OMG, the take-home exams in that class. They were comprised of a part A (vicious in-class midterm on Fri) and part B (take-home extended problems, often 3 of them, due first thing Monday morning).

Think of it as a 4-day, non-stop math marathon, with completely untested problems made up by the prof. Surreal-- sometimes they were problems that didn't HAVE solutions.

Still. After that, I voluntarily took math every quarter until I graduated, and I was then the go-to girl in my grad school lab for advanced stats and for non-linear modeling. I am the mathy person in about 95% of the professional settings I've been in since I got my B.S. Which is surreal for a kid that flunked algebra II and calculus I and II the first time through (really, not kidding). I never saw the point in Algebra II concepts until dealing with some advanced applications work later, honestly. To be fair, though, I also had a horrible high school teacher for that class.

That mathy way of looking at problems was completely transformative for me in every way. It flipped the switch for me into "growth mindset" and ultimately broke my perfectionistic inner voice.

If I could bottle that, I'd give it to every HG+ kid in America.


When I say past tense here, I mean most recently in trigonometry where my DD was attempting to learn in a vacuum due to an AWOL teacher, and no contact with classmates in a virtual setting. Not working. She's a high school senior this year, and that's where I have regrets-- one of her dearest friends would have been an AMAZING study partner, if only they'd lived closer to one another over the years. Sadly, they also plan to attend colleges 2h apart, too. But we've routinely used the other strategies outlined by JS, and I can attest to their efficacy.

It's the same pedagogical framework that I tried to set up for my own students in upper division analytical chemistry-- give them HARD problems to work, and let them work together on them over an extended (and self-determined) period of time each week.

Agreed.

Jonah, I hope you stick around here.