I Built a Math Fact Practice App

I also learned a few things about teaching math along the way

I made a math fact practice app. It’s called Pulse, you can see it here. If you're a teacher it might be a good fit for your students but it also might not. The point of this post is to share two things I learned about teaching math by making the web app.

Thing one: How do you respond when a student forgets something?

Let's say a student forgets that a negative times a negative is a positive, or 4x8=32, or the sum of the angles of a triangle. I'm not talking about when these topics are first introduced. Students have already learned something and they've forgotten it. What do you do?

Option one is to remind them and move on. "Don't forget, a negative times a negative is a positive."

Option two is to remind them of the conceptual foundation or a strategy. "Remember when we cut out the corners of a triangle?" or "What is 2 x 8? How could that help?"

Option three is to remind them and then have them practice it. "The angles of a triangle add to 180 degrees. Here's a triangle, what is the third angle?"

Option four is to remind them, have them practice it, then have them practice something else, then have them practice it again. "Remember, 4 x 8 is 32. What's 4 x 8? Ok what's 2 x 10? What's 4 x 8? What's 5 x 3? What's 8 x 1? What's 4 x 8? What’s 8 x 4?"

Option four is my choice for math facts. The best way to secure something in long term memory is to retrieve it from memory. If students don't know something I need to remind them of the thing, have them rehearse it, then have them think about something else, then retrieve the thing to solidify it in memory. Repeating something you were just told is different from pulling it out of memory, even if that memory is from a few moments ago. Ideally that continues another time or two — do something else, then retrieve the thing again. That retrieval makes a big difference in making the learning stick.

For lots of topics I would also use option two. For multiplying negative numbers I would give students a quick reminder to help them connect that example to what they already know. For math facts I don't think those types of explanations are always helpful. Students can know lots of strategies and still struggle to remember math facts. There are a few hundred facts to remember, which makes math facts different from other mathematical topics where there's less to commit to long-term memory.

That’s the sequence: Student struggles to remember 5 x 7. Remind them that 5 x 7 is 35. What's 5 x 7? Ok what's 3 x 5? What's 5 x 7? Then a few more problems and 5 x 7 again.

Thing two: Is it important to answer math facts quickly?

The other thing that makes remembering math facts different from remembering other stuff in math is that there are lots of strategies students can use besides remembering — skip-counting, finger tricks, relating to another fact, and more. It’s good to have strategies, but over-relying on strategies can be an obstacle to retrieval practice and moving facts into long-term memory. Humans can only think about a few things at a time. If you have to think about a math fact it’s harder to think about other concepts and solve more complex problems.

This is where timed tests come from. If students take five seconds to answer a math fact question they're probably not retrieving it from memory. So, the logic goes, time students to get them to recall their math facts quickly.

This can work for some students. Some students say to themselves, "oh, I need to know these more quickly," and that motivates them to try to retrieve facts, move away from strategies, and commit them to memory. Others get stressed out by the time. Even if they aren't stressed, timing students doesn't necessarily cause them to get faster.

Here's how I think about it. Time is an indicator that students haven't committed something to memory, but timing students doesn't by itself cause them to remember things more quickly. I want to use time as a way to figure out which facts students need to commit to long-term memory, and then give them a chance for retrieval practice with those facts.

The App

Those are the key ideas I used to build my app. Students open it and they get a series of random math facts. The app rotates through different fact families — for instance x2s and x5s for multiplication, or +1s and doubles for addition. If the student answers correctly and reasonably quickly, it moves to the next fact family. If the student either gets it wrong or answers slowly, the app enters "practice mode." Practice mode means that problems alternate: a fact from the family the student didn't seem to know, then one they hopefully do know. For instance, if a student is practicing their x4s, they might get a series like this:

• 4×5

• 10×3

• 8×4

• 6×1

• 4×8

• 8×10

• 6×4

• 5×2

• 5×4

If a student gets a question wrong or answers slowly in practice mode, that same question is repeated two questions later. If the student takes five seconds to answer 4x5 in the example above, they’ll see 4x5 again instead of 8x4 two questions later.

Here’s what it looks like:

The link is here. I recommend checking it out, and putting yourself in the shoes of both a student who struggles to remember math facts and a student who is more confident. The app is designed to give simpler, more focused practice to students who need it, and more varied practice to students who have a strong grasp on their facts.

A few more notes:

• The app gives students 45 questions a day, then they’re done. It’s designed to feel focused and manageable each day.

• There are no visuals or representations. These can be helpful in some situations, but they can also encourage strategies that avoid memorization.

• The app doesn’t try to label facts as “mastered” or anything like that. Learning math facts doesn’t always happen in a nice linear way.

• There’s no login, just open the website and practice.

• There’s an about page on the site with more details about how it works.

I need to give credit to a few different sources of inspiration:

• Michael Pershan's blog posts summarizing the research on multiplication facts and describing the flash card routine he uses with his students. I teach 7th grade and I’m reluctant to put together a physical flash card routine because of the time investment necessary, hence trying to build a digital version.

• Multiplication by Heart uses a simple and straightforward design that helped me think about how to design Pulse.

• MathFactLab inspired some of my thinking about time and how to respond to students who take a long time to answer a question.

The Point

The point of this post isn't "this fact practice app is perfect and magical and if you use it every kid will learn their math facts and math class will be happy and perfect." For me, for my goals and my context, this app is a little better than the other options I've found. Maybe it will work for you too. I doubt it will catch on with very many other teachers, the difference between this approach and other approaches is small and subtle. I’m passionate about getting those small things right but other approaches also work.

The biggest things I learned while building this thing are about how to structure practice to help things stick, and how to think about speed. I use those principles for all sorts of other things besides math facts. I want my students to remember that pi is equal to 3.14, and a hexagon has six sides, and a negative times a negative is a positive, and 3/4 is equal to 0.75. I use the principles I described above to structure practice for those things too. I think online practice makes sense for math facts because there are so many of them, it's hard to put together enough practice without a computer doing some of the work. For other stuff, one of my everyday teaching moves is to give students mini whiteboards and give them a couple questions, then try to help them with whatever questions students get wrong. I use those same principles to structure practice that helps all those little pieces of knowledge stick. Math is more than remembering multiplication facts and decimal to fraction conversions. But those things are part of math. An important part of math teaching is helping students get those little things committed to memory so we can move on to the bigger and better stuff.

I wrote a few weeks ago about how there are no shortcuts in teaching. That applies here. This was a fun project to work on over the last few months. If I did a decent job my students will improve their math fact skills a bit. That’s cool but it’s not going to change the world or transform my classroom. I learned a lot, I hope it’s helpful to a few other people, but there is more to math than math facts and now I’m on to my next project.