Homeschooling My Daughter For My Own Benefit — Math

My kid is 7. She doesn’t need to know algebra.

I am 54. I don’t need to know it either. So why am I studying it?

It’s not that big a time commitment. I have no tests to pass.

But as I thought about my hope for daughter to grow up fully numerate and unintimidated by math-y stuff, I realized that I had to get over my own intimidation in the face of math, which (despite having a whole family full of supernumerate math-lovers) I hated in school.

So I decided to map my own ignorance, with the help of various library books and Khan Academy videos.

How much of the algebra I was exposed to in high school stuck to me? Damned little, apparently. How much of my own incompetence is due to ignorance and/or incompetence? How much of it is due to lingering emotional responses from math trauma in school?

Recently I’ve been playing with lines and slopes. I have absolutely no recollection of ever learning y-b = m (x – a) or anything that looks like it, so my engagement with the formula and its constituents doesn’t seem to have emotional content (unlike, say, quadratics, which are associated in my mind with a terrible homework fight I had with my father somewhere in 9th grade).

The first thing I notice is now many simple mistakes are available for me to make at every step of the way. It is going to take many many iterations before this process is internalized in my (so to speak) mental muscle memory. I am intellectually aware of what’s required to calculate the slope of a given line — but the actual physical process of writing the numbers down in the right positions vis-a-vis one another is fraught with complications.

As a music teacher I’ve got an advantage over some other folks: I never had any musical talent, so I had to build my musicianship from the molecular level up, making every mistake possible. It looks like the same process is happening with math.

Music teachers with “talent” are often ignorant of two key factors in developing mastery: number of repetitions and size of learning increment. It’s not enough to repeat something until your student does it right — once it’s been done right is the time to begin repetitions! And it’s not enough to increment the learning in steps suitable to your own learning style — it’s essential to figure out the increments your student requires, which may be much smaller than what you needed.

My algebra increments are very small. Fortunately, I’m patient. Yesterday I did three or four slope formulas, some several times. I made mistakes in calculating the initial slope; I transposed x and y in my head; I reversed + and – signs; I simply wrote down a 3 where I meant to write a 2. Each of these and more sent me in different wrong directions — since I didn’t figure out what I’d done until later. And that was just in the initial calculation. Once I began trying to plug these numbers into the y-b = m (x – a) formula, a whole new collection of mistakes emerged.

You know what? I’m interested in the mistakes. Getting it right is not the objective here; the “goal” is to figure out as many different ways of getting it wrong as I can.

The fact that my daughter sees me doing this at the breakfast table is a bonus for the homeschooling process. I’m doing it because I’d like to get over my own anxieties.