No One Wants to Talk About Practice
An example from some Colorado-provided professional development
There’s a way of talking about math education in the United States that I’m not a big fan of. But I don’t want to write a post that says, “here’s a vibe I don’t like, trust me it’s influential,” that seems kindof lame.
Then I took a course sponsored by the Colorado Department of Education and it is a perfect encapsulation of this thing I dislike, so now I’m going to write about it.1
The course is titled “Powerful Practice: Evidence-Informed Math Teaching.” It’s the kind of course lots of teachers, including me, take to meet professional development requirements or move up on the salary scale. The course goal:
After successfully completing this course you will employ evidence-informed instructional routines in your classroom that support accelerated learning in mathematics for all students, especially those furthest from opportunity (multilingual learners, students with disabilities, students of color, and students experiencing poverty).
I’m a fan of evidence. I would like to accelerate learning. Sign me up.
There's a lot I agree with in the course. It has solid sections on multilingual learners, connecting multiple representations, and alternatives to keyword strategies for word problems. Good stuff! Like any PD I have some disagreements, but overall it's thoughtful and research-informed.
A Sleight of Hand
Here’s the part I don’t like. It honestly feels sneaky, like a sleight of hand. It’s not about any of the content in the course. It’s about what’s missing.
In the whole course, which is worth 25 hours of professional development, there is close to nothing about practice.
Here is the closest I could find to a statement that practice plays an important role in math learning:
While students likely need practice, the emphasis here is not drill and kill or timed repetition of math facts. Instead, we want to help students see patterns and identify pen-and-paper and mental strategies to perform calculations accurately and efficiently.
There’s a passing acknowledgment that practice is maybe necessary, and then equivocation. Don’t “drill and kill” (a phrase which is not defined anywhere in the course). Help students see patterns. Identify strategies.
Look, drill and kill is a real phenomenon. When students are asked to practice too much too soon, or when practice is excessively repetitive, that’s bad. And yes, I am in favor of having students see patterns and identify different strategies to solve problems.
But I am also unequivocally in favor of practice in math class. After learning something new, students should solve some similar problems to move that learning into long-term memory. Beyond my personal opinion, this course claimed to be “evidence-informed.” It is not possible for an honest person to read the evidence on math learning and not come to the conclusion that practice plays a critical role. If I were in charge, I would include multiple modules on structuring effective practice. Worked examples, fading supports, retrieval, interleaving, spacing? Among 14 modules, close to nothing. The attitude here seems to be that practice is something that’s grudgingly accepted as necessary, but not to be talked about.2
Practice is hard to get right. We should be talking about it! Why is practice important? Where does it happen in the learning sequence? What are some common pitfalls? There’s so much to talk about!
The Vibe
This is a vibe I get from lots of other places in the math world. I was on a curriculum adoption committee a few years ago. None of the curricula emphasized their approach to practice. They all had supports for multilingual learners, multiple representations, and routines for word problems. Good stuff! Keep all of that. But it was obvious that practice was an afterthought. Practice wasn’t mentioned in the marketing materials. The practice problems got too hard too quickly, or skipped important problem types, or were lazily written with too much repetition.
Similarly, if you attend a conference run by the National Council of Teachers of Mathematics, you’ll get the same message. Sessions on every hip and cool approach to math learning you can imagine...except practice, which will come up here and there but not in featured sessions, avoided by the vast majority of presenters.
If practice was being done well in typical math classrooms this would be fine. But it’s not! Go talk to teachers. They’ll tell you that the curriculum doesn’t provide enough practice. That they struggle to find good practice resources. That they can’t agree with their colleagues about how much practice is necessary, or even basic questions like whether most practice should happen in class or for homework, or digital vs paper and pencil.
One more thing that drives me crazy. The quote from above is in a section on balancing procedural fluency and conceptual understanding. And I get it, I think procedural fluency and conceptual understanding both play an important role in math learning. But they’ve become these two pillars of math education in a way that I think is counterproductive. In some circles you can’t talk about practice without talking about procedural fluency, then debating whether fluency means fast and accurate or also flexible, and the role of timing, and which standards call for fluency, and whether conceptual understanding has to come first.
Look, some of you are overthinking this. Practice is important because practice is how humans learn things, and math is no different. Don’t let all the fancy theory distract from the idea that, after learning something new, a bit of practice and repetition is exactly what humans need to retain what they have learned.
You can read more about the course here. While the course was funded by the Colorado Department of Education, the content itself was designed and delivered by TNTP. I don’t know much about TNTP but subjectively it is very similar to the type of PD delivered by the established math organizations in the US. The course was free, but required a login — I think Colorado was paying TNTP for every signup.
One more example in the course is another section on procedural fluency that talks about students coming up with their own strategies, discussing math problems, connecting representations, and then finally the idea that maybe they should practice — but they should practice “why a procedure works and when to use that procedure.”
Sure, all of that is fine, but students should also just practice. Solve some problems. Don’t be afraid of a little repetition. See how students do. If they need more practice, give them more practice.
I couldn't agree more. There probably was a time when mindless "drill and kill" was stifling children's thinking, but in many classrooms the pendulum seems to have swung too far the other way.
One thing I'd add is that conceptual understanding is often recursive. Students revisit an idea later, from a new perspective, and that's when the deeper understanding emerges. But that later insight is only possible if the earlier skill has become automatic enough that it no longer consumes their attention. In that sense, practice isn't just about retention or fluency—it frees up cognitive resources for future learning.
We sometimes talk as though understanding must precede practice. In reality, understanding and practice often take turns leading each other.
I’ve always wondered if these PD/curriculum providers ever taught how to shoot a jump-shot, hit a backhand in tennis, or play a pentatonic scale. They are avoiding what gamers call “the grind”: practicing in math is the grind, for students who must do it and teachers to assess it.
In class I aim for 8-12 examples per period, and 12 per day as homework for 5 days/week. This amount does not guarantee understanding, which is why I must interleave and space throughout the entire year.
My students who consistently and faithfully complete our practice by the end of the year, surprise, learn the most math.