The "science of math" is popular right now, at least in some corners of social media. I have mixed feelings. I think math teaching has a lot to learn from research, sure. But research doesn't have all the answers. I worry that the science of math movement is getting a little ahead of its skis. One theme I've seen a few times in recent weeks is nostalgia for mad minutes as a way to practice math facts. I don't like mad minutes very much, and I want to explain why and what I do instead.
First, what does the research say about math facts?
From my perspective, three big things:
Knowing math facts is important. Student knowledge of math facts predicts lots of other outcomes later on in math class.
Retrieval practice is the best way to commit math facts (or anything else) to long-term memory. This means retrieving the fact from memory, to see 6 x 8 and just know that it's 48, rather than skip-counting or using some other strategy to derive it.
There is no routine that is clearly the best for learning multiplication facts. Retrieval practice is a good broad guide, then there are some very specific practices that have been studied but it’s not clear which is best or how to adapt these for regular classrooms. You can read more here, here, and here. It’s worth noting that none of those studies look much like mad minutes.
What I don’t like about mad minutes
I did a Google Image search for “mad minute” and this is the first thing that came up:
Put yourself in the shoes of a student who doesn't know their facts very well.1 I teach a lot of students in middle school who have a decent grasp of simpler facts, stuff like 4x1 or 3x2 or 4x2. Maybe they have to think for a moment but they mostly know them. But for stuff like 9x8 or 6x6 or 8x6 they are skip-counting or something else, and not retrieving from memory.
So what does that student do with a mad minute like the one above? This student might skip those hard ones, only practicing facts they know. They might spend a while figuring out 9 x 8 (the first question!!), which means they will answer far fewer facts than the rest of the class. For facts they already know they are likely retrieving them from memory — the time pressure helps with that. But for the facts they don't know they aren't retrieving them from memory. If they don't know 9x8 from memory they will either skip it or find it using some other strategy. That's not a great way to learn 9x8. Maybe they think about it one more time when the class goes over the answers, which still isn't retrieval practice, and then they move on. Some students will be motivated to say to themselves "oh, I need to remember 9x8 next time" and maybe the teacher creates a positive culture of tracking progress and improving over time. But for students who struggle with math facts there are so many facts they don't know and they're getting less practice than everyone else. That isn't a great way to learn facts.
What should I do instead?
This student doesn’t know what 9x8 is. The solution is not to have them write down the answer on their page when the teacher goes over the activity, record their score, and maybe see that problem tomorrow. A better solution is to remind them of the answer, then ask them a different fact they know, then ask them 9x8, then ask them a few more facts they know, then ask them 9x8 again, then do the same thing with a few other facts, mix in some 8x9s, then come back to 9x8 one more time before the end.
I made my own fact practice website that I designed to address exactly these issues. Using my site, students:
Solve 45 questions each day, no matter how fast they are, ensuring that everyone gets enough practice.
Focus on one fact family. For students who have a hard time with math facts, they will typically get 3-4 reps each with a group of 5-7 related math facts, mixed in with some easier facts they likely know. Students who know more facts will get a broader range interleaved together.
Get extra practice on facts they either answer wrong or answer slowly, encouraging successful retrieval practice.
Don’t get overwhelmed by trying to learn too many facts at once.
Think about that student who is struggling on the mad minute. They don’t solve very many questions, there’s no focus, there’s no repetition of facts they don’t know, and they don’t retain much because there are so many they don’t know. My site is designed to be the opposite of a mad minute in all of those ways.
I understand the impulse to time kids. If you give kids too much time some will get stuck in a rut of using strategies and not retrieving facts from memory. But timing things mad minute-style causes other problems. I’m not even going to wade into the math anxiety thing. Timing a mad minute means the kids who most need the practice get less of it! A better strategy is to use time as an indicator of whether a student knows a fact. If they take a long time to figure out a fact, that means they need more repetition with that fact right away so they can practice retrieving it from memory.
I like my website but you don’t have to use it. I do this same routine using mini whiteboards all the time for all sorts of math topics. Math facts are tricky because there are so many; that’s why a digital solution can be a bit more efficient. Still, the goal is the same: be responsive to students by giving a bit of extra practice with facts they have a hard time with. It’s all about retrieval practice. If the student isn’t retrieving the fact from memory it’s less likely to stick. If a student isn’t retrieving a fact from memory, that’s an opportunity. Make sure they know the answer, then give them a chance to retrieve it a few moments later.
What’s the point?
My point is about mad minutes, but also about some of the rhetoric I hear from “science of math” types. Is the research clear that knowing math facts is important? Absolutely. Do I wish more teachers took learning math facts seriously? Yes. Has there been a decline in math fact practice in the last decade? I don’t have any data on this one but I’m sure it’s real. But those science of math folks should remember that teachers aren’t dumb. Part of the reason lots of teachers stopped using mad minutes is they used them for years and some students still didn’t learn their math facts. Yelling on Twitter about the “good old days” when mad minutes were everywhere just shows your ignorance. Let’s bring more research to regular math teachers. But lets be honest about what research can tell us and what it can’t. Let’s not use lazy logic like “research shows knowing math facts are important, everyone should go back to using mad minutes.”
I think mad minutes can be a perfectly good tool for students who already have a decent grasp of most facts, but if the practice doesn’t help the students who need help the most what’s the point?
English teacher here. I like the idea of kids knowing Math facts. Multiplication tables never killed us. It's so weird when kids can't do basic calculations in their heads. Even watching them with calculators, they struggle when they don't understand what a number is. But I could ramble here.
Now if only they could read analog clocks...
"Student knowledge of math facts predicts lots of other outcomes later on in math class."
I don't doubt that this is true. But I also suspect that many people draw the wrong conclusion from this observation -- that student knowledge of math fact **causes** later outcomes. On the face of it, that seems plausible; for instance, students cannot perform basic single-digit arithmetic will struggle when they encounter fractions. And I'm sure that many math teachers will have experienced this phenomenon in their own practice. But this is a classic example of confusing correlation with causation, and we should also consider the possibility that the causal connection isn't quite so strong.
Instead, I think a more plausible explanation is that there is an innate ability to do math, and that varies from person to person. Thus, an inability to grasp basic math facts is simply an early indicator that that person does not have a strong innate ability, and then later on this manifests as struggling with more advanced concepts. In this view, lack of skill with basic math facts doesn't **cause** difficulties in math later on; instead, students do not have strong innate abilities at math, and this then causes struggles with math at the early stages, which are observable when trying to learn basic math facts.
Both concepts can be simultaneously true! It can be the case that not learning basic math facts leads to problems later on, and it can also be the case that struggling with basic math facts is indicative of low innate ability. So they aren't mutually exclusive possibilities. But we should think carefully about the possibility that the causal connection isn't quite as strong as we might assume at first.