In the typical learning pattern for math concepts, kids first get the fundamentals of numbers—counting, adding, subtracting, sequencing, etc.—then they learn multiplying and dividing. Usually around the third grade, they are ready to memorize the basic 1-12 multiplication table.
My daughter was different. She was very interested in numbers from a young age and mastered most of the concepts that would be taught in K-2 with no problem. But she was much more interested in what people consider “advanced” math: she loved learning about tesseracts, pi, and the Sieve of Eratosthenes. As a kindergartener, she made us a googol dollar note. Then third grade came around, and I thought maybe she would be ready to start memorizing the multiplication table.
It was then that I found out that my daughter was different, but not unique, in her learning pattern. Despite how easy elementary math had been up to that point, she absolutely freaked out at memorizing. So I started asking around and found out that there’s a whole group of these kids and many of them end up being very good at math. But they end their elementary years thinking they’re “bad at math” because what seems simple to other kids is beyond their grasp. School math is obviously very frustrating to these kids, but since we homeschool, we could do things differently.
At the advice of other homeschoolers, I decided just to drop it and go on. Some parents report that their kids resist memorizing until they get to algebra, and then they get sick of looking up the numbers. Others report that they are adults who still suffer from this problem—often in STEM fields, they still figure out 8×7 through skip counting. In my daughter’s case, it came down to swinging.
One day recently we were outside and she asked me to push her on the swing. I told her I would if she’d answer a math problem, so I started shooting her multiplication problems that I knew she hadn’t mastered yet and rewarded answers—right or wrong—with pushes. When the answers were wrong, we figured out the right answer before the pushes were received.
Since that day, she’s been requesting “swing math,” and it occurs to me that I should have thought of this earlier, much earlier. When she was a preschooler and having trouble controlling her behavior, our occupational therapist recommended swinging—lots of swinging—as therapy. Swinging has always made her a happier person, but even more, she seems to come in from swinging inspired and full of ideas. The movement obviously stimulates her brain.
Little by little, “swing math” is helping us overcome her block. I’ve extended the types of problems to include fractions with unlike denominators and other computational challenges. They all go much better when she’s moving. I don’t have a report on how it’s affected her ability to do math on paper yet, but I suspect after a while it will start to creep in and become automatic.
Now if only I could somehow get her to make her bed while swinging, our household would be a lot more peaceful!
I love how the swing helped!
But memorizing isn’t the important part to me – make connections and understanding conceptually are much more important. If you really get the connections, 9’s are easy to figure out, 6*9 is 6 less than 6*10 (which, understanding place value, you’ll know is 60). 7*8 is hard for lots of folks, but square numbers are usually easy. 7*8 is 7 more than 7*7, so it’s 49 plus 7 or 56.
You might like the Math In Your Feet blog, especially this post: http://mathinyourfeet.blogspot.com/2012/10/a-small-moment-of-multiplication.html
I totally agree that the memorization is not the most important aspect. But it’s the key to what’s frustrating to her: she is hampered by getting stuck on 6×7 instead of enjoying the actual math that she’s doing. She actually knows all the concepts and when no actual calculation is involved, she can understand them. But the second she has calculation in front of her, it all goes away. So for example, we have a catchphrase we use: “9’s are easy!” That’s our shorthand for remembering that 6*9 is 6*10 (which is easy) minus 6. But put into context, that understanding just goes out of her head. So the memorization becomes easy because the answers start to be automatic and thus calculation is must less frustrating… All of this is hopeful thinking so far – I’m just amazed that she’s finally remembering math facts!
For 9’s, I used the fingers method to help me remember. e.g. If you bend your left middle finger, it stands for 3×9 and you have 2 fingers to the left of the middle finger, and 7 fingers to the right, and that gives you 27.
For the others, I think my mother made me memorize and recite them when I was young. There are other mnemonics.
Thanks – One time my husband and I exchanged notes on how we do mental math, and it turns out we use completely different methods. So I figure everyone should just use the one that speaks to them…. whatever that may happen to be!