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.

Music at home…

…Daughter and I have exchanges about music theory. She calls them “wacky questions,” and enjoys it when I give her puzzles about harmonic relationships. “If A is ONE, then what is the TWO chord? The FIVE chord?” “Spell a G major triad.” Etc., etc.

Recently we began moving into questions about harmonic sequences. “In the key of C, what is a I-IV-VI-V-I progression?”

She’s seven. I don’t have any huge expectations about this; it’s just a fun game we play. This is way out of her league.

Or is it?

At tonight’s guitar practice I was coaching her into a D-minor chord (the standard one at the bottom of the neck). She started playing a sequence, not too adroitly…and when I tried to steer her in the direction of something I had planned, she said, “Stop! I want to play my own progression!”

Then she dictated: “D minor, A minor, C, A minor, D major, G, A major, D.”

I did a little on-the-spot voice-leading to make two harmony parts and we sang through them. Cool. My daughter’s composing her own chord patterns.

Then she told me to “write it down, so we don’t forget it.”

I think it’s time to show her more about notation.

What Did You Learn In Unschooling Today?

Daughter and I had breakfast this morning, and she asked me some random addition questions. “Dad, how do you make twenty-seven?” It turned out she was thinking about a series of dance moves her Kathak classes had introduced, in which a group of nine turns is done three times. Her teacher had only shown the first two repetitions, so there was some confusion in her mind.

We worked it out; I was inspired to play some more with groups of nine, so we began adding up columns of 9s. All the fun of early math tricks started to come back for me — add up the digits of the sum of any group of nines, and they always add up to nine; etc., etc., etc. We kept adding nines together and exploring what the results looked like. Eventually I drew a 9×16 matrix on a piece of paper and filled in each cell as she counted up to 144.

She asked for some other numbers, and we played with 5s and 3s, examining the patterns they created as their sums built up. It was a fun way to prolong our breakfast.

Eventually she finished her oatmeal, and asked me to do more numbers. And I said, “I’ll give you a rhythm lesson.” She responded, “I don’t want a drum lesson now!” and I said, “Not drums. Rhythm and numbers.”

Whereupon I started showing her Reinhard Flatischler’s “TA-KI” and “GA-ME-LA” syllable groups.

We sat facing one another in two chairs. I said, “I’m going to say some magic rhythm words, and you say them back. The first word is TA-KI. Try it.”

She did. So we traded groups of recited TA-KIs back and forth for a while until she was comfortable with them. I began patting my knees on the first syllable of each TA-KI, and she imitated me happily.

Eventually I said “Great! The second rhythm word is GA-ME-LA. Try it!” and we repeated the process.

Then we started mixing up the syllables, while patting our knees on the first syllables of each “word.”


TA-KI / GA-ME-LA = 5 beats, accented 2+3

TA-KI / TA-KI / GA-ME-LA = 7 beats, accented 2 + 2+3

TA-KI / TA-KI / TA-KI / GA-ME-LA = 9 beats, accented 2 + 2 + 2 + 3

GA-ME-LA / GA-ME-LA / TA-KI = 8 beats, accented 3 + 3 + 2

She was getting it! While there were frequent glitches in the knee-patting, she recovered nicely.

Eventually we decided to do patty-cake. She really took the initiative at this point, deciding which syllable groups should have knee-pats, which should have patty-cake claps, and which should have spoken syllabic recitation. At this point I was just along for the ride.

The last few minutes were spent jamming on an 11-beat sequence, divided 3 + 3 + 3 + 2:

GA-ME-LA / GA-ME-LA / GA-ME-LA / TA-KI.

She decreed that we would pat knees for each of the GA-ME-LA groups, but not recite; on the final TA-KI, we’d clap each other’s hands and speak the “word” out loud. There we stayed for multiple repetitions, gaining confidence and competence.

Eventually we stopped and went upstairs, where she got dressed and ready for the next part of our day.

Which was spent in the woodshop. We’ve been making a stringed instrument together, and today was to be devoted to using my newly acquired drawknife for the shaping of the third tuning peg. The previous two had been very time-consuming, requiring chisels, surforms and a disc sander to achieve the right shape. But this tool, terrifying though it looks (a 10-inch knife sharpened to a razor edge in the hands of a six-year-old?), is designed beautifully. Harming one’s self is virtually impossible, since holding the handles prevents the blade from getting near arms, fingers, wrists or any body part.

And she loved it. “Dad! This is a wonderful tool!” She didn’t want to stop removing wood, and her hands grew steadily more intelligent with each stroke. “Can you give me some other pieces of wood so I can practice some more with the drawknife? Look! I’m getting to be really good at drawknifing!” (a wonderful verb, I think).

And soon the tuning peg was shaped correctly; a little rounding on the disc sander and it was just about the same shape as the others, which had taken easily four times longer to make. Sometime later this week we’ll finish stringing her “tar,” and start lessons.

And then we got on our adult-and-kid tandem bike and had a long ride, including a visit to Mom at work, a trip to the library, lunch, an ice-cream cone, Daddy getting a cappucino, a playground visit and a return home about four hours later.

A good day of homeschooling.