During the COVID pandemic, I finally had time and opportunity to sit and develop a curriculum for the twins (who are 6 now). Bryan Caplan wrote a few blog posts once on home-schooling and I found his success inspirational. So in the same spirit, here are some notes from my own experience, maybe they will be of use to others.
The kids are bilingual (English/Hebrew), with the dominant language being English. They are now fairly fluent readers in English (they read Dr. Seuss books by themselves). They can also read basic texts in Hebrew. In Spanish, they are just picking up some early vocabulary, so progress here is quite minimal (we only started two weeks ago).
Perhaps their biggest progress is in Math. We have now covered >80% of the multiplication table (up to 11). They can do calculations like 13×3 in their head. They can also add up long numbers–e.g., 1231+4582. And they can also solve equations like x-3×8=4. We have covered this material in roughly 2 months.
Method and Methods:
Every day at the same time, we sit for math. Afterwards, they will have an online class with the Hebrew teacher. They get a one hour break, and then they have their Spanish class, again online. A few hours later, they will sit and read a short book to us in English. Each class duration is ~30 minutes.
I taught them how to read in English using this wonderful, incredible book. It looks cheap and it is cheap, but it is of tremendous value. The kids could read, without undue effort, when they were 5. (we started working on this a little before they turned 5)
Teaching how to read requires some effort. At first, the kids were reluctant, and as we were doing this at the end of the day, they were a bit tired. But every day I’d give them a star for good performance (half a star otherwise, but that was rare), and we had a conversion system of stars to candy and present. So this system moonshined as an introduction to delayed gratification and the value of saving. I won’t belabor the technique, as the book does a great job of explaining it.
Teaching math requires much more creativity. My general approach is that everything is custom made; we don’t use worksheets or the such. That means that I will give them questions that I write on the spot and are well within their reach, but always pushing a bit. The occasional exercise will get a special asterisk next to it, denoting that it is a ‘head-scratcher.’ They are told, repeatedly, that they are not expected to be able to solve the headscratchers, and they take immense pride in cracking them.
We started with the most basic addition. They used fingers, bananas, and dolls to help them add things up. After establishing the basic mechanism of addition (e.g., 3+4), we started playing the game ‘What Makes Ten?” In this game I will give them random numbers, from 1-10, and ask them what other number would be needed to make a ten. Their answer must be complete (If I ask ‘4’, they must answer ‘4+6 make ten.’ Simply answering 6 is not enough). This took a little bit of practice, but they finally had it.
Then we moved to adding numbers that exceed ten, e.g., 6+8. Here I taught them the trick that you can transfer some of the first number to the second number, to make it ten. So in this example, the six will ‘give’ 2 to 8, thus making ten, and the 6 will become 4. Adding up 4 and 10 is easy and they grasped it incredibly fast. In fact, after a few tries, they were already able to do this in their head (not perfectly)
Our next step was to play ‘What makes 11′, and then ’12,’ and then ’13.’ At times, I would employ a fairly rigid, but super effective, mnemonic device I call ‘the pyramid’. Basically, we would have cards, with all the numbers from 1-10 listen on them in random order. When presented with the card for, say, 6, they have to answer 5 when we play the 11 game. The pyramid is built on the (frustrating but effective) idea that every time they get the answer wrong, I tell them the right answer and then flip the cards all the way back. I used the pyramid system in law school and I know how painful it is; but I was also able to treat close book exams as if they were open book exams, which gave me a lot of edge.
Now it was time to do multiplication. I gave them a fairly vague description of multiplication at first. I told them that 3×4, means that we write 4+4+4 and we see the second number (4) three times. At this point they could add up the numbers, but they only had a flimsy grasp on the concept of multiplication. But that was fine. Our next step was to learn 2x(1-10) by heart, using the pyramid method. It took time and effort, but we nailed it.
When we got to learn 3x(1-6) I came up with the ‘Monster game.’ They stand 10-14 floor tiles away from me. They are monsters and I am their victim. My weapon is the questions I ask, and every-time they get it right, they get to take one step forward–until eventually, they devour me. This game added some excitement to the otherwise very boring exercise of learning 3×3.
At this point, I got a little bored with multiplication. So we moved to play ‘mirror land’. The idea here is that if they see something like ‘x-3=4’, the equal sign is the ‘mirror’. All the numbers want to move to mirror land, to be with their friends. As the numbers move to mirror land, they bring their sign with them–only that, just like a mirror, the sign flips. This concept was fairly easy to understand, but they did ask me what ‘x’ was doing there. So I just told them we call it ‘the mystery number’ and our task is to find out what the mystery number is. This seems to have added a little bit of excitement to our game.
A final method we learned is the ‘Tummy Method.’ How do you do 13×3? I wanted to show them that you can split, in parenthesis, the 13 into 10+3 and then multiply each element by three and add them up. But they hated the word parenthesis. So I told them that it is like a tummy. When we open parenthesis, we open up the number’s tummy. Silly, I know, but I don’t argue with success. Very quickly, the kids could do this in their head, so when I ask them 12×4, it takes them a moment or two of reflection but they tend to get it right.