Continuing my last post, here are some updates (9.22)
School resumed, online, which greatly limited our progress. In some ways, school is for the time being less education and more entertainment.
We now have roughly 40 minutes per kid for education + 20 minutes to practice reading Hebrew in the afternoon.
In the 40 minutes, the kids use Spaced Repetition to cover multiplication, division and reading. Some thoughts.
- I may’ve noted, but we use Anki Droid, and we call it the “Honesty Game.” The idea here is that we are developing the critical ability to judge your own progress honestly. At first, one kid either marked everything as easy or, at a later stage, marked all the easy questions as hard (so he would get them the next day, instead of doing harder problems). But after “playing” together, they have developed a good sense of how to mark the difficulty of answering questions and will sometimes mark things as hard.
- The labels on Ankidroid are not great. The kids didn’t like the “hard” label which conveyed a sense of failure. We simply go by colors (How was it? Was it red or grey? Oh, that one was easy, is it a green or a blue?)
- I LOVE ANKI
- We started with multiplication, but quickly added division. The kids don’t remember division by heart, nor do I encourage them to. In fact, I intentionally try to get them to get the right answer by trying different answers. They get to practice multiplication by the backdoor. There’s an old idea in spaced repetition that you should only cover what you’ve learned , but I think this is a valid exception.
- Another faux pas I committed was to reset their progress in multiplication. This was their first deck and their responses were not very well calibrated, so I wanted to make sure they redo everything. It was the right call.
- I added a deck called 4000 words in English. This surprised my spouse, who thought it would be better to have them just read text. But we both think now that reading + anki is a much superior approach. Early reading books expose the kids to limited vocabulary in the interest of telling a story. But it is good to get some early exposure to ‘difficult’ words intentionally (merge, scholarship, approach). The kids make substantial progress this way and surprise me with their reading. Another perk is that this exercise is entirely autonomous, because Anki will read the word to them.
The kids are very different in thinking styles and so their paths diverge. One likes to solve everything without writing anything, the other dislikes mental calculations. I’m very accommodating, although I will occasionally insist on doing things the other way (usually I will have them fail doing things their way).
Another rule is that if you can ‘cheat’ your way to the answer, you are not made to answer the question in the ‘proper’ way. So I wanted to teach them long addition, but one kid did everything in their head, so I didn’t ask them to do it again by writing everything down. It makes my life a bit harder (and I will definitely act annoyed to encourage the sense of outsmarting me) , but it seems like the sort of thing math teachers should encourage.
Rounding was relatively a breeze. We can now do long multiplication (e.g., 23*2), but we are still a bit hazy on when to use the standard method (by writing top bottom and adding the results) and when to use the ‘tummy method’ (20+3)*2. We need to do some more work in this area.
We started doing fractions and order of operations with one kid. It went surprisingly well, but I haven’t attempted it with the other kid who is less interested in money.
Excitingly, we covered the reading of graphs. I just used a few easy examples, including one which marks each person in the house and how much of a dummy (‘toomtoom’ in our household slang) s/he is. Much to my chagrin, the kids erased their own bars and marked my the highest.
I’m still looking for math riddles and puzzles. One kid really enjoys them and wants more. The other one is more receptive to questions that are easier for me to reproduce. We got a kick out of a question that asked: “Mark paid $3 for a chocolate bar, and $4 for a candy bar, he got $5 in change, how much money did he pay?”. It may not come across as interesting to an adult, but it was unexpected and fun.
We have now went up a level in “mirror land”– my term for algebraic manipulation. It was fairly easy to explain that numbers jump the equal sign and then their sign changes (+4 becomes -4 after jumping). It was harder to explain the meaning of adding up Xs (3*x+2*x), so we drew boxes with the letter X on them, and then tried to figure out how many balls we would have, if each box held 3 balls, or 5 balls. That was fairly effective.
Then I told them that instead of mirror land, we have two countries. The X land and the numbers land. The X’s think they are better than the numbers, and the numbers think they are better. In reality, however, they are equal to each other. This means that we want all Xs to be in their own country and all the numbers in their own country. Every time they jump over the = sign, their own sign changes. It may sound silly, but it was fairly effective: We finished today with the following exercise– Solve 50x-20=80-50x.