Last month, I got really into wanting to find out how children learn/remember. The impetus was wondering if Anki would help Thumper learn her addition facts. Anki is a program that many people use to learn a second language. It’s basically a flashcard system. But it shows you the flashcard based on spaced repetition. Cards you deem as easy to recall won’t be shown to you as often as cards whose content you haven’t mastered. That got me to wondering about spaced learning so I borrowed a huge stack of books. I managed to read about 2 books out of the 10 I borrowed. One was How We Learn. Another was on children and memory. I shall put in a review about what I learned later.
In researching Anki, I came across a website which reviewed the use of Anki specifically for 4th graders and up in learning their math facts. The author found some issues with the app. One reason I remember was because children can’t quite tell you whether or not they know or not know a concept. Another was that it was hard to scale/implement for a classroom of children. They recommended Reflex Math instead. Since the app has a 14 day trial period, I decided to check it out.
The short verdict is: I LOVE IT.
Relay Math is an iPad game where children answer math facts until their answer time is fast enough to be considered a “reflex”. There are 2 modes in the app, addition/subtraction and multiplication/division. In each mode, the child starts with two games and can unlock additional games after a certain number of days has passed. One game has the child answer math fact questions so that the ninja can hop on successively higher wooden branches, dodging birds and what not. The game starts with some assessment of your knowledge and reflex time. The problems progress with higher and higher numbers. So for example, maybe for multiplication it tests you on adding 1 to a number or adding 10 to a number first. After awhile, it also teaches you about the fact families (5+2=7, 7-2=5, 7-5=2). You’re shown facts to solve based on what you know or don’t know.
There is a teacher mode so you can see which math facts your child is working on, which one is unassessed, which one they’ve mastered. You can see the progress they make day to day in graphs and charts. It has a classroom mode so you can add multiple students. I created two accounts for Thumper, one for addition/subtraction, one multiplication/division. There is a timer on the app. After 45 minutes or an hour it will disallow the child from playing more. Because the thinking is that more frequent practice is better than playing a long time each day.
Thumper loves the app because it’s a game. I put in a limit of 20-30 minutes max each time she uses it, in addition to the daily limit imposed by the program. She likes the fact that there are new games to unlock (she gets bored and likes trying new things) and loves earning tokens to accessorize her avatar. We don’t allow her to use other games on the iPad, which I think is important as it would otherwise distract her from wanting to use the app.
At $35 per year per child I think it’s a worthwhile and cheap investment. Given her rate of progression I think we only need it for one year.
How We Used Relay Math
I’m not really following the Montessori philosophy in doing facts memorization. Partly because Thumper finds the concrete work tedious. Partly because this is the way I learned math and I really have no problem with it. I have fond memories of doing worksheets in first grade at night, sitting alongside my mother while she did piece work; and having that aha! moment when, after doing many problems on one worksheet, having answers come to me fast. Especially for multiplication, where memorizing the multiplication table is very rhythmic in Chinese, it’s just as fine to memorize the table then memorizing them doing concrete work. Of course, Thumper already has done some of this work at her Montessori preschool. So it isn’t as if we’re just doing abstract work from the beginning.
Beginning in November we started with the addition tables. We ended up with the routine of doing two 5 minute timed worksheets daily. I would do table of 2, then 3, then mixed of 2 and 3. Eventually by the time we got to 5 & 6, it was one worksheet of whatever number we worked on that week plus a review of all the numbers. I introduced new worksheets based on how many questions she got right. So if she consistently wasn’t making progress in number of problems solved, I knew it was time to move on. Learning from the “How We Learn” book, I also tried to switch it up a bit by constantly adding new material and reviewing old ones. So that is why some days we did addition and some days multiplication. Math-aids.com is great for generating these worksheets. I would log how many answers Thumper got right on a worksheet in Google Docs to track her progress and know when to move on. We did 2, 3, and 4 in November and 4, 5, 6, in December for addition.
For multiplication, we first memorized the table in Chinese orally. We’d work on about 3 numbers a day (e.g. 2×2, 2×3, 2×4). Sometimes this was done in the 15 minutes driving to swim practice. Once I knew Thumper had it kind of down, we started on the worksheets. She did 2 and 3 in November, reviewed mixes of 2 and 3 in first two week of December, then 4 and 5 last week of December. This was partly because she really didn’t want to memorize multiplication (or do work in general in December), and I didn’t push her on it as long as she did 10 minutes a day of math memorization.
Near the end of November, I added Reflex Math to the mix. We only did addition/subtraction. From the records, it seems that her fluency in the math facts are slightly behind the worksheets we’re practicing. So maybe we’re doing 5 & 6 right now in addition, but according to Reflex Math, her fluency is at 3 and 4 and maybe she has a few of the 5s down.
But, I feel the app has helped. We were doing 2, 3, and 4 for quite awhile, all of November. She was getting better each time but it was slow going. In December she’d been playing with Reflex Math for a couple of weeks when 4, 5, and 6 were introduced and she’d get 80+ right on first try. Of course, other factors can be at play. The higher number you go the easier it is since you’re reviewing old info (e.g. 2+4 = 4+2). And in the worksheets, I would switch numbers up so that the numbers we were working on were sometimes the first addend and sometimes the second addend so she was getting practice on the higher numbers while doing the lower numbers. But, given the starting score in the introduction of new numbers and how fast we’re able to progress between numbers, I think the app itself helped. We started doing multiplication the last week of December and I shall report whether I see similar effects and this is not a fluke.
Again, I know we’re not doing Montessori math here. I read a whole book on how we should teach math because of my research during the making of the fraction charts. I understand that having the child know how to think about math is equally if not more important. So knowing math facts is good. But understanding that there are multiple ways to add up to the same number or doing math discovery is important too. Given that I was exposed to both ways of learning math (East and West) and have heard the arguments both sides give when they try to move to the other side, I see values on both side and feel that you need both. I think Montessori makes you think about math and see math in the more discovery way and we will be using that still in our homeroom. For Astroboy we probably won’t touch this till he’s after 5 or has played with the strip boards and other Montessori memorization tools for awhile. But for Thumper, who is 7 and seems to dislike manipulatives, a combo of Reflex Math and worksheets seem to be doing the trick for now in memorization. I plan to add other ways for her to use what she’s memorized so that she sees how it’s applicable and doesn’t end up with a concept of math as purely moving numbers around abstractly.