## Saturday, November 23, 2013

### Multiplication Tables

Third grade is the year when children are typically asked to master basic multiplication facts. I haven't let myself think too hard about this because I'm not sure what conclusion I would come up with. I know that by the end of the school year, my students will be expected to have reached mastery in this skill, and that's the end of it. No way around this one, really. Besides, some things just have to be memorized, right? Simple multiplication must be one of them. Yes, we've talked at length about what multiplication means, and my students are all aware that 4x5 means taking four groups of five items. But when it comes to working through problems, it's good to have the facts memorized so that one doesn't have to spend a great length of time finding the answer. At least that's what I tell myself.

I, for one, never finished memorizing my times tables as a child. When I multiply, I struggle when I get to points such as 7x8 or 6x9. And of course, I'd like to spare my students from that struggle.

So we studied our multiplication tables.

I began with the assumption that my students, who were blessed with a wonderful teacher last year, were already proficient with 2x (which was correct). So our proper start began with 3x. I stood at the white board and asked the students to count slowly by threes. (I amended this for all later sessions to, "Give me the multiples of [x].") I wrote them down as the students counted, stopping at 30. Then I circled the multiples into groups of three, leaving 30 by itself, to give more easily remembered chunks. We said them aloud with a little rhythm, "Three, six, nine. Twelve, fifteen, eighteen. Twenty one, twenty four, twenty seven. Thirty!" We did this little chant three times, then repeated the process every day of the week. On Friday, while they were working on another assignment, I called them individually to my desk to recite. If they stumbled, I asked them to go back to their seats and practice a little more, then called them back at the end of the rotation.

I didn't take grades on it. I didn't put their names on the board. I just kept track of it in a little notepad and gave only the reward of a small praise. Hopefully it kept the intrinsic motivation going.

The next week, once the multiples of four were on the board on Monday, the students commented on an easily follow-able pattern. On Tuesday, they kept going past forty. By Thursday, they recited multiples of four up to 100. On Friday, when I called one boy up, he kept going past forty. I remained quiet, merely listening. Other students came up to ask questions about an assignment, but I signaled for them to wait. Around 120, some groaned with boredom. Closer to 500, an excited crowd had gathered around him. By 800, nearly the entire class had gathered, and at 1000, the crowd burst into applause. The boy grinned and went sheepishly back to sit down.

It wasn't repeated, however, because whatever excitement they found in the game somehow became lost after the first initial run.

At any rate, we DID manage to make it through our 9x tables. They wondered if I would have them continue on through 10x, 11x, 12x,... where would we end? I didn't see the need to go on, though, because while it might have been an interesting venture, I wanted to spend more time making sure that they were all completely confident with 3x through 9x.

The next week, we started our timed tests. I found this useful website that generates multiplication problems, however many of them you want and with whatever maximum and minimum numbers you want. We started with 30 problems, minimum of 0, maximum of 9, then graduated to minimum of 3. I gave them one minute to complete as many problems as they could. Again, I took no grades, just kept track of progress in a notebook.

When they began asking for more time on the clock, I became a little concerned. After a week and a half of no progress, I decided that we needed to have a conversation about what was happening. They told me that the timer was putting too much stress on them and they could hardly focus on the problems for the want to finish on time. So we stopped the timed tests.

"But what should we do?" I asked them. "You all need to master these facts before you go to fourth grade so that you don't struggle."

We decided to give flash cards a try. So I guess we'll see how that goes in a few weeks.