Route 66 (2020)

During the coronavirus crisis in NYC, touring and gigs have been cancelled, and a good part of my day is taken up with homeschooling (kids age 7 and 10). Our 18 year old is figuring out what it means to graduate high school without every going back to class. Although I was a “good” student, I never much liked the format of the segmented day, switching between subjects and listening to teachers drone on in front of a class. One-on-one with a mentor was (and still is) the way that I like to get information. Also, I got a lot more satisfaction out of using my hands (music, sports, building, art) than doing paperwork. 

If I were to design my own curriculum (which is basically what’s happening now), I’d skew towards a non-linear learning method — dive into what’s interesting to you for as long as possible to get deeply into a subject, and don’t worry about the fact that one subject is getting advanced and another is getting neglected — it will even out over time. The most important things are curiosity, focus, and deep engagement. If you don’t dig it, it won’t stick. Harness the natural impulse to explore, rather than forcing everything into an artificial grid. But this isn’t to say that everything can just be freewheeling and creative — some things just have to be memorized and hard-wired through repetition. Spelling is one, and the multiplication tables are another. As a functional person, you don’t have much option but to proficient in these areas. There are a lot of things like this in music as well, repetitive muscular and mental actions that have to be automated so you don’t stumble when inspiration calls. You just have to slog through these fundamentals, and the challenge as a teacher is how to be rigorous without killing the joy of learning. 

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Over the years I’ve tried a lot of different ways of teaching the times tables. Since there’s no “fun” way to do it, the best way is probably to get it over with as efficiently as possible. The problem with doing them sequentially (3 x 5 is 15, 3 x 6 is 18, etc.) is that they become a kind of pattern. More like adding and counting than multiplying. Randomization (flash cards) can remedy this. Another problem is redundancy (3 x 5 and 5 x 3, etc.). Double-sided flashcards with inverted versions of the same problem on both sides can fix this. Once you eliminate redundancies (and take out anything with a “1,” which nobody needs to practice), the times tables up to 12 are reduced from 144 to 66 unique combinations. You can easily write these on cards, but I already did it for you. Download and print out the two PDFs below (on thick paper if you have it) and cut off the border of the paper, along the black lines. Glue the two pages back to back so that 2×3 is on the back of 3×2 and so on. If you’re just using regular paper to print, you can sandwich a sheet of construction paper or posterboard between the two sheets when you glue them, to make the cards thicker and more durable. Let the paper dry, and cut it up into cards along the black lines. At home we do the game like this:

1. Warmup round: Kid sits across the table from the parent with the pile of cards. Doesn’t matter which side of the cards are up. Parent starts a timer, and kid picks up the cards one by one and says the answer, tossing it to the parent. Parent checks the answer and throws it back if it is wrong. In the beginning stages, the parent gives some tips and tricks for various ones, whatever comes to mind. The dots on the cards can be used to visualize the concept so it’s not all just abstract numbers. During this round, the parent takes any cards that were answered wrong or took a long time to remember and puts them aside from the rest.

2. Second round: Kid looks through the pile of trouble cards and practices them until they can do them more quickly. They are allowed to start the next round with those cards. Parent starts the timer, goes through all 66 again, starting with the trouble cards. The 2nd round should be a lot shorter than the first one. Usually the kids have had enough at this point.

Here are the levels:

More than 5 minutes: novice (still figuring out how to multiply)

3–5 minutes: egg (rote learning stage)

2–3 minutes: caterpillar (moving slow, but getting there)

1–2 minutes: cocoon (transitional stage, might be in here a while)

Less than a minute: butterfly (done: you are free to fly away!)

I think these can be done at any age range. Currently my 7 year old is a caterpillar, and the 10 year old is in the cocoon. The 18 year old made it to butterfly a while back and graduated. This format is a good start, but maybe you can think of ways to make it more fun with your family. And if you come up with a good way to remember 7 x 8, let me know.

Family video here, PDFs below that: