The Entrepreneurial Homeschool, Part 2
Part 1 covered the physical and emotional foundation. The next layer is learning to reason through difficult problems.
Part 2: Learning to Think Slowly
I challenge them with abstract thinking in its purest form. We call that math, but we usually confuse math with its notation. The syntax and the algorithms are only one aspect of “math”, the way language is only one aspect of a culture. You cannot reduce Japanese culture to the Japanese language, and you cannot reduce math to its symbols. Math is really the exercise of reasoning itself, the workout for the part of the mind that solves problems.
The trouble is that math is difficult to teach well, particularly in a classroom that must move many students at one pace. You have to go slow. Like REALLY SLOW. So slow that it’s uncomfortable to most impatient adults.
Classrooms do go slow. They just never go slow at the speed of the individual learner. For a given topic, child’s right pace is another child’s crawl. The result is one-size-fits-none: too slow for most of the class most of the time, then too fast in the exact moment when it is your turn to miss a concept. If you never miss a concept in class, it is because you went slow somewhere else, maybe at home, where someone let an idea sink in. There is always a moment where understanding has to land, and that moment is slow. Slow is smooth, and smooth is fast. We forget that we once learned “after nine comes ten” slowly, the same way we later learned a differential equation slowly.
We do not give kids room for that slow moment. It takes an educator, or an educator plus an AI, willing to sit at one child’s pace.
That is what made Khan Academy powerful: you could press pause on a good teacher and take your time. Grant Sanderson’s channel 3Blue1Brown goes further, building visualizations that let a hard idea, a Riemann zeta function or how a neural network works, actually sink in while you pause and rewatch. Go slow, but keep challenging. If you stop challenging yourself, you stop building the muscle.
A little, every day
We do math seven days a week. Five days never made sense to me. The weekend off is a leftover from when families needed a day to rest from physical farm labor and a day for the Sabbath. We do not have that constraint anymore. A little every day beats a lot once in a while, the way Kumon runs twenty minutes a day with no exceptions.
Think about how Olympians train. Not Monday to Friday. Seven days a week, rarely at one hundred percent, usually around eighty, because the total accumulated hours are what matter and going all-out daily just gets you injured.
Same idea for the mind.
The curriculum we actually use
Two things, mostly.
First, Art of Problem Solving, an American math curriculum. It is not expensive and we simply follow the textbooks: thirty minutes, an hour, sometimes two, seven days a week. I am sure China, Russia, and others have excellent programs too. This is the one I know.
Second, Code Submission Evaluation System, a sequence of programming problems. These are more abstract and harder than the pure-math ones. A tough Art of Problem Solving question might take thirty minutes. A hard CSES problem can take six or seven hours, sometimes spread across days. The description might be forty words. The solution requires discovering a great deal.
We always start on pen and paper, working numerical examples by hand. That is the whole point: structure a problem, iterate toward a solution, and let the examples push you from guessing toward a hypothesis, then from a hypothesis toward an algorithm, then toward pseudocode, and only then toward C++, Python, or Rust. We use Claude Code and AI throughout, but as a tool, not a crutch. If it solves the problem for you, you lose the discovery. You do not hand a calculator to a one-year-old learning five plus five. But you do, eventually, teach them to use the calculator.
Math teaches them to solve problems someone else chose. The next step is choosing what should exist.
Next: Part 3