# Steal Not Thy Child’s Time

My then-wife and I homeschooled two children until they reached ages 12 and 14. I’m also proud and delighted to be a grandfather, that my daughter has been home- or un-schooling her children (seven, aged 1-13 years), and that my son is very engaged with the education of his own.

Unlike most dads, I initiated the discussion of home education. My wife, having a degree in elementary education, balked at the very idea of teaching our own. She had been trained to plan and prepare, to have formal structure, and so forth – a complex task which would daunt any one person.

I view education from the perspective of the student; I ask not “how to teach,” but how to learn most productively. During 11 years of Catholic school – skipping grade 8 – I often felt that my time was being stolen from me; I wanted something better for my own – not merely in terms of “quantity of stuff learned,” but qualitatively different.

Like the top fifth of entrants, I was already above First Grade level in reading and arithmetic. The most effective way to progress would have been to actually read, to play with new ideas and interesting and challenging math problems. This is precisely what we were not allowed to do.

Instead, we spent 40 minutes or so waiting for a turn to read two lines from a “See Dick Run” book. Far better to use the same time to read interesting books at our own pace – which is what my homeschooled grandchildren do.

With math, we drilled and killed our way through textbooks, page by boring page. This is a horrendous waste of children’s time.

Lately, researchers have been discovering the value of the time spent by that top third or so outside of school. I know what I was doing outside of school – independent reading, playing with math, and otherwise teaching myself. Researchers – such as those at Reading is Fundamental – are often bewildered that children – even at the bottom of the SES rankings – often learn and improve substantially over the course of the summer, with just the slightest bit of assistance – self-chosen books, in this instance.

My wife, the degreed educator, insisted that our son go to a “gifted” first grade class at a nice suburban school. The teacher was respected by our neighbors. We actually had to push to obtain admission; the test administrators balked because his art skills, in their minds, were not quite up to snuff.

Two weeks later, he came home and asked “What is 5-7?”

“She says it’s too complicated.”

“What do you think?”

“I know that 7-5 is 2, and 7-7 is zero. So is 5-5, anything minus itself is zero. I think 5-7 must be something else, but I don’t know what it is.”

Anybody who can articulate all that is ready to advance. I briefly explained the idea of negative numbers, using a thermometer diagram to illustrate; turned the diagram on its side, making it a number line, and explained how to think of negative numbers as growing to the left versus the right, and subtraction as moving the opposite direction from addition. He understood immediately. I made sure he learned how to add and subtract all combinations of positive and negative numbers.

A few days later, I come home from work, he’s doodling on his paper, and there’s a number line. This is his own initiative, his own “work.” I asked a few questions, and he’s got the concepts perfectly, in every particular. This took minutes, not days, weeks, or months. I never had to repeat the lesson. It stuck, because it was his question; he was interested.

My wife, observing this, had an epiphany. Our son could learn without complicated textbooks and plans and so forth – a lot more rapidly than at his “gifted” class. We began homeschooling, which continued until our children were 12 and 14 years of age. They had little trouble adapting to formal education. They had some gaps (and what student does not?), but had outstanding mathematical intuition, and rapidly mastered new material.

My wife and I divided our labors; Under no circumstances was she to teach math. I was (and remain) devoted to what I call “organic learning,” and some call “unschooling,” inspired by John Holt. It was my desire to work with the nature of my children, rather than against it. Instead of “begin at page 1,” my children and I had many “random” conversations which where suited to their abilities and interests – sometimes about everyday math, sometimes about more abstract ideas such as binary arithmetic, and we conversed about myriads of non-math topics. We played many games which exercise math skills. Both became skilled mental calculators.

I must stress the role of frequent conversations, often initiated by my children. At age 3, my son asked “What is gwabbity?” (he had overheard the word “gravity” in a conversation). I could have said “gravity is what makes things fall down,” but that seemed too simple, given his state of knowledge at the time. So I went to the whiteboard, writing down the formula $F = g \frac {m_1 m_2} {r^2}$, and began to talk and draw. In a few minutes, he learned the word “mass,” had a loose idea of its meaning, was reminded that the earth is a really really big ball, was informally introduced to the idea of using vectors to represent force, and a few other ideas. I fudged very little, and built a framework which was close to what he’d want to know as his knowledge of math and physics grew.

To further illustrate the potential, let us move forward about 30 years, to a conversation with my 2nd-generation home-schooled grandson, aged 6.

I asked him to think about adding the integers from 1 to 100. The obvious but slow method: add 1 and 2, add 3, add 4, and so on. 99 additions. $1+2+3+...+100$

Or, one could write the numbers down as 1 2 3 … 50, and then write the 2nd half in reverse order:

$\begin{tabular}{ r r r r r} 1 & 2 & 3 & ... & 50 \\ +100 & +99 & +98 & +... & +51\\ \end{tabular}$

My grandson interjected “each pair adds to 101. There are 50 pairs. 5050.”  That was fast.

Could he generalize? What is the sum of the even numbers, from 2 to 100? He pondered for a few seconds, and replied “2550” – which is correct. This problem stumps most high school students. At age 8 or 9, he tested at the 18th grade equivalent in math. Does he have good math genes? Is he something of a prodigy? Yes – but a prodigy who could race at own his speed, unhindered by a governor.

And that is why we teach our own. We don’t want to hold them back, nor let schools steal their time.