Multiplication

Every day, my 5 year old and I experience something scary but exciting. Out of nowhere, a MONSTER starts chasing us! We hear its footsteps and heavy breathing, give each other a wide-eyed look, and quickly run for cover: under a table perhaps, or a bedsheet. There we do 5-10 minutes of multiplication flash cards and the monster goes away.

This game has been great fun over the last few weeks, but sadly it’s coming to an end. G has almost mastered multiplication now, both conceptually and with good recall.

For what it’s worth, this isn’t meant to be possible for a few more years. For instance Kate Snow in the introduction to her popular Multiplication Facts That Stick book advises that:

While it’s fine to use this book to introduce your younger child to the multiplication facts, don’t expect thorough mastery of the multiplication facts until your child is at least eight years old. Most children’s brains aren’t developmentally mature enough to memorize all the multiplication facts until this age.

In addition, the spaced repetition cards we used—the very thoughtfully and beautifully made Multiplication by Heart—are intended for ages 8+, and Beast Academy covers multiplication in level 3 (typically grade 3 or 4). I didn’t set out to teach multiplication early, but it’s been interesting to reflect on how this transpired.

I worry when I spell out what worked for us that it might be interpreted as a set of suggestions. While some ideas might happen to be a fit for you too, what I’m most trying to convey is actually a style of education that involves getting to know your kid, developing your own language of games, jokes and rituals that generate high yielding experiences more or less opportunistically. This will surely look very different from one kid to another.

Incidentally, both Katherine and I are excited about AI, in fact Katherine runs a business that would have been impossible without the current generation of large language models, and I helped her build it. Some people believe these same breakthroughs may dramatically accelerate early childhood education. This I think is silly, considering that early childhood education is already accelerated for many kids, mostly through thoughtful, playful interaction with somebody who loves them (so, not a large language model).

Anyway, here is that worked for us.

Firstly, we have Cuisenaire rods at home, originally intended to be used with a program called Miquon. The program itself didn’t stick, but the Cusisenaire rods became a common toy, and somehow they had a tendency to arrange themselves into patterns that raised questions about multiplication.

In retrospect, a lot of random creative play with the Cuisenare rod must have helped with intuition building, but it was still important for Katherine or I to be there to ask a question or provide a well calibrated next challenge. Most children will play and build something like a pyramid, say, but most won’t necessarily think to calculate the number of units in the 5th layer, and to wonder if it’s the same with 5 rows of 5 almonds each, and what happens if dad eats one of the rows, and whether this is more like having four yellow rods now or five purples, and so on.

So through the rods, we had some budding intuition for multiplication. A handful of times subsequently, a simple multiplication problem would arise, such as everyone in the family having a certain number of strawberries say, and we would “skip count” together to make the calculation. These were all incidental opportunities, but valuable, in retrospect.

One day when we were visiting my parents, G found a pair of dice. I’m not sure why, but I decided to suggest a game where we would roll the dice and calculate the product of the two numbers. This is not a naturally fun thing to do, but the mood seemed to call for it: often G just seems to have had enough of her own play and is ready for a little challenge from an adult. It doesn’t take much to learn the techniques for multiplying up to 6x6, so she mastered this corner of the times table in perhaps ten minutes. Somehow this random moment with the dice was the highest yielding time spent on multiplication.

Later when G was playing Matific, the “adaptive learning” “algorithm” goofed and served up some multiplication problems without much preparation. Luckily they were geometric in nature (count the number of tiles required to cover a rectangle) and small enough to do by skip counting. Since we tend to be with our kids during ipad time, I was able to jump in and teach a couple of the multiplication techniques for larger numbers (such as multiplication by 8 as three doublings, or 9n as 10n - n).

Somehow I still hadn’t noticed at that point that we were on the cusp of having learnt multiplication. The Multiplication by Heart cards I bought mostly to take advantage of free shipping while in the US, and because everything from Dan Finkel and team has been great (see for instance Katherine’s love of Tiny Polka Dots). G happened to open the package and wanted to try it, so we did, fully expecting that we’d just shelve them for a year or two. But, we found fun little ways to do the cards on most days, and really hit our stride running from the monster. We are road tripping at the moment, and some days we’ll have spent hours driving, show up tired at a new motel, and G in opening up her suitcase and seeing the box would light up and squeal “I hear a monster!”

I’ll miss this game, and these days, but thankfully there’ll be many more.