What Does Effective Practice Look Like?
It's more than drill and repetition
I think practice is important but I keep hearing people say "yea, sometimes students just need to practice a skill over and over until it's in their bones" or something like that. I disagree!
Learning is deceptive. Doing something over and over again makes you feel like you've learned it well but doesn't help it stick for the long term. Repetition isn't all bad, but "practice means doing a skill over and over again" isn't a very good model. It's also easy to get sucked into repetitive practice because so many tools seem interested in repetition. It's easy to print out a Kuta Software worksheet or assign a bunch of problems from a textbook or put students on IXL. Those tools reinforce the idea that practice is all about repetition.
I think math teaching lacks a clear vision of what effective practice looks like. We see practice as the vegetables of math education. It’s necessary but we all just look the other way and avoid talking about it. There's talk in cognitive science circles about the importance of spacing and interleaving and retrieval but that stuff often feels like it's written by researchers miles away from real classrooms. Here is my attempt to articulate more specifically what effective practice looks like.
Effective practice:
Requires thinking. Students learn what they think about. If practice is only repetition students aren't doing much thinking.
Transitions from massed to spaced practice. Early on, practice repeats the same skill. Later, practice is spaced at increasing intervals.
Transitions from massed to interleaved practice. Early on, practice is chunked by skill. Later, different skills are mixed together.
Transitions from predictable to varied practice. Early on, practice involves predictable, consistent question types. Later, practice asks questions in a variety of ways using a variety of contexts.
Transitions from guided to independent practice. Early on, practice is guided by the teacher or other scaffolds like worked examples or completion problems. Later, practice is completed independently and without scaffolding.
Strives for a high success rate, and uses the success rate to guide the transitions above. This is the most important piece, and the one that people often miss. If I’m doing lots of spacing and interleaving but students are getting most questions wrong that's not very effective practice. If students are getting every question right it's time to make the transitions described above.
Provides feedback. Feedback happens on a few levels — feedback on individual problems, feedback on common misconceptions, whole-class reteaches when most students are having trouble with something, and individual support for students who need more help.
Involves retrieval of anything students should remember. If I want students to remember the formula for circumference of a circle I shouldn't provide a reference sheet or ask them to use their notes to look up the formula every time. They should be retrieving it from memory. If I don't care whether students remember it then notes or a reference sheet are fine.
Considers every student. It's easy to focus on the class-wide success rate. If 90% of students are getting questions right I might want to move on to the next thing and forget about the last 10%. Practice is a great time to provide extra support to students who are confused and get them on track.
Meeting all of those goals is the ideal but it's pretty hard to do in a real classroom. Most resources aren't designed to provide that type of practice. I structure practice with a patchwork of different tools — problems from my curriculum, handouts I make myself, DeltaMath (an online practice tool), mini whiteboards, and random other stuff I find. It's never perfect. There’s also plenty of other stuff that can be helpful, but these are the parts that I find essential.
If I were to give one piece of advice about structuring practice it would be: use lots of small chunks of practice with opportunities to adjust in between. Mini whiteboards are my favorite tool for this. Sometimes I give problems one at a time, have students solve, then have them hold up their boards so I can see how students did and adjust. If they're doing well I interleave different skills and ask questions in different ways. If they're having a hard time I reteach or provide more repetition. I also sometimes give a chunk of 4-8 problems and use that time to check in with students who are struggling. Mini whiteboards are a great way to make sure students are ready for tougher problems and to smooth the transition between different resources I'm using. Small chunks of practice are more engaging and give me more chances to adjust when I need to.
The final misconception I see around practice is that practice is just about the basics. I don’t see it that way at all. Practice starts with simpler problems, sure. But the goal is for students to successfully solve interleaved, varied, challenging problems, drawing on everything they know. Part of designing practice effectively means creating an on-ramp to give more students access to that level of challenge. I love giving students hard problems to solve on whatever concepts we’re learning about. That’s part of practice. Everything else is designed to get students to a place where working on hard problems is productive and not just frustrating.