A month ago I wrote a post called Just the Facts where I talked about the way my daughter has been practicing her multiplication facts with me at home. In case you don’t want to check out that post, here’s a quick recap of the way she’s practicing her facts:
- She answers as many multiplication flash cards as she can in one minute. She does two trials of one minute each.
- She counts the cards after each trial.
- I monitor and provide feedback as needed.
- After two trials, she graphs her higher score.
Here’s how she was doing after five sessions back in late August:
And here’s how she’s been doing after 16 total sessions between August and now:
I feel like I’m supposed to do some statistical analysis of this and talk about the median or mode or something, but I don’t really care to be so formal. These are our informal takeaways:
- She has good days and better days. We don’t focus too much on her results for any given day.
- She appreciates getting two trials each time because if she blows it on one trial she knows she can make up for it on the other trial.
- She and I were both excited when she set a new record of 23 correct in one minute.
I’m so proud to see her flexibly use appropriate strategies for finding various products. She can double like no one’s business when she sees a factor of 2, 4, or 8, but she can just as quickly build up or down from a 5 or 10s fact when she sees a factor of 6 or 9.
I wrote earlier about how she struggles with mentally doubling numbers like 18 and 36. I offered to let her use a whiteboard to help her with that doubling when she needs it, and that has been a huge help. I’m especially proud that it hasn’t turned into a crutch for every problem. She really only uses it when she knows the number crunching in her head is too much for her to handle.
For a few sessions, I was doing some flash card practice with her around those challenging doubles, but I decided to move away from it. After I wrote my previous post, Michael Pershan shared this excellent post called What People Get Wrong About Memorizing Math Facts. He said something in the post that I needed reminding of:
“…the best practice for remembering something is practicing remembering it.”
This led me to change tactics. I created a set of flash cards of facts that my daughter is able to solve using a strategy, but I want to give her an opportunity to practice remembering the products.
When we practice these facts, it is untimed, though I only give her about 5 seconds per card, otherwise I can see her start using a strategy to derive the answer. I usually run through these cards once or twice before her two trials for that session. I told her the goal here is to practice remembering the products. I don’t want her to try and use a strategy. I just want her to see if her brain can pull up the answer from memory. I told her it’s fine if it can’t, but the act of trying to remember is a good thing to practice. I also made clear that during her two one-minute trials I still want her to try to remember these products, but if she doesn’t it’s totally okay to use a strategy at that point.
We’ve been using these cards for a while now, and I’m noticing that slowly she is starting to remember some of the products, though not all of them. What I’m really excited to see is that if she doesn’t quite remember the product I’ll ask, “What tens do you think the product is in?” and she is getting pretty good about knowing which ones are in the 50s or 60s even if she doesn’t remember if the exact product is 54 or 56.
So that’s where we are now. We only do this facts practice 1-2 times per week now that school has started. Here’s what I like about it:
- It’s quick to do.
- When we first started, she felt pretty down on the days when she only got 10-14 correct. But because we’ve continued doing it and graphing her results, she sees that those days are blips in an overall pattern of success.
- She loves that there are two trials each time we do it. That feeling of getting a second chance is powerful.
- I’ve been able to watch her work and provide support and modifications that specifically help her be successful and feel confident.
- We’re able to work on dual goals of memorization and strategy use.
My next step is going to be introducing division flash cards into the mix. We’ve done some work relating multiplication and division already, and we’ve specifically talked about how thinking of a related multiplication fact can help her solve a division fact. I expect some bumps as that gets started, but I feel confident she’s on a good path.