Good Math, Bad Math had an entry recently, titled, “Teaching Multiplication: Is it repeated addition?”.

There ensued a lively discussion on math fundamentals and pedagogy, where the usual points were brought up.

But what really caught my attention was an anonymous, autobiographical account of a PhD’s struggle with mathematics.

Reproduced here:

In the preface of “The road to reality” R. Penrose talks about a girl who could not “get the hang of cancelling”. That and all this bring bad memories to me. I learned multiplication as repeated addition and then I figured out how to extend them to rational numbers.

I was good at math. I was in fact the best student at my class. A few years later I learned about square roots and suddenly everybody was adding, subtracting and multiplying strange things like square root of 2. I remember that my mind was clearly messed up about math in high school.

I yet had the best GPA of my class but I didn’t feel I understand math at all. While I knew the problems involved logarithms or roots at that level are supposed to be very easy, I could not understand what I’m really doing. I guess somehow in my mind, I made axioms in arithmetic that worked well for integers and rationals but I could not extend and generalize them to real numbers.

As a results, I never learned trigonometry in high school. I could not understand why everybody in the class could so easily just add or multiply trigonometric functions of x and mix them with all other functions while I could not understand what even adding or multiplying a number by a irrational number means. This lack of understanding of math hunted me all the years in the university. I passed my math courses with B- and Cs. I could not understand anything as I would always get stuck in the basic definitions that did not work out.

I did not get to clear my mind about it till years later during my PhD in engineering when I had the opportunity to study, on my own, and finally get to learn axiomatic set theory, peano numbers and such. I feel all my years at the high school and university was ruined because I never learned the basics of mathematics from the beginning.

Maybe it was my teachers’ fault, but probably they didn’t know much about math themselves. Maybe it was my father’s fault that kept repeating not to move to next step until understanding everything correctly and truly.

I’ve started to learn math on my own, from scratch. I am 36 now. I hope this year I can finally finish basic calculus and understand it.

So honest, so poignant… and so sad, because it’s happy ending is so rare…

I can only imagine how many students have been through the same struggles, but without the final triumph, and all because of some fundamental error of understanding that was not corrected (or worse, was propagated) in their foundational years.

on July 27, 2008 at 6:37 am |Myrtle Hocklemeier“I’ve started to learn math on my own, from scratch. I am 36 now. I hope this year I can finally finish basic calculus and understand it”

It’s been said that real analysis, the class that follows all the engineering calculus, is “calculus taught correctly”

Pure math, the theory behind the algorithms, isn’t usually taught to anyone but math majors.