I’m currently reading Make It Stick: The Science of Successful Learning, by Peter Brown, Henry Roedinger, and Mark McDaniel. Make It Stick is a survey of cognitive science research on how humans learn, including many counterintuitive results that suggest teachers and students know less about learning than we think.
I’ll start with a quote, summarizing a piece of research:
It may not be intuitive that retrieval practice is a more powerful learning strategy than repeated review and rereading, yet most of us take for granted the importance of testing in sports. It’s what we call ‘practice-practice-practice.’ Well, here’s a study that may surprise you.
A group of eight-year-olds practiced tossing beanbags into buckets in gym class. Half of the kids tossed into a bucket three feet away. The other half mixed it up by tossing into buckets two feet and four feet away. After twelve weeks of this they were all tested on tossing into a three-foot bucket. The kids who did the best by far were those who’d practiced on two- and four-foot buckets but never on three-foot buckets. (emphasis original)
This has a few implications for me.
1. Practice is important. Let’s make sure this doesn’t become a diatribe against practice.
2. Let’s make sure we measure the right things. The article goes on to point out that
Even in studies where the participants have shown superior results from spaced learning, they don’t perceive the improvement; they believe they learned better on the material where the practice was massed.
Spacing out your practice feels less productive for the very reason that some forgetting has set in and you’ve got to work harder to recall the concepts.
If we measure right after the lesson with exit tickets, or right after a review day with a test just like the review, we aren’t assessing what students have retained. This information can be useful, but it can never be proof positive that students understand.
3. Math is more complex than throwing a beanbag into a bucket. There are more concepts to practice. There is also greater opportunity for students to flail in the dark without an idea what they’re doing. It’s important to balance considerations for the durability of memory with the reality that if students are constantly confused by mixed practice, they will get much less practice, more of it will be practiced wrong, and less learning will result.
4. Non-examples are critical. In any round of practice, no matter what, there should be deliberately chosen problems that are similar to the lesson, but where blindly following the lesson’s procedures is incorrect. This not only promotes thinking and learning, but gives invaluable information to the teacher. My first year, I was constantly surprised at how a student could look confident on a new topic, then blindly applied the same procedure to a totally unrelated problem.
How does this relate to homework? What are best practices for structuring homework?
How much of this is worth messaging to students?
Should practice ideally be mixed within related concepts, or among all of mathematics?