Cognitive Science Meets Pre-Algebra

Monday, September 9th, 2013

If you need to practice multiple skills, you’ll do better and your practice will go more smoothly if you give each skill it’s own block of time — but you’ll improve more if you interleave skills into the same training session.

Finally this bit of cognitive science meets pre-algebra in a Tampa experiment sponsored by the Institute of Education Sciences in the Department of Education:

The students were split into two groups. Half got interleaved assignments on the first two problem types — linear equations and word problems — and regular, blocked assignments on the second two types. The other half got the reverse: blocked homework for linear equations and word problems, and interleaved for graphs and slopes. The students scored near zero on these kinds of problems at the beginning of the study.

For the teachers involved in the study, the mixed assignments seemed, essentially, like review work. “Sometimes we do what we call ‘bell work,’ which is where we give them a little review before each class,” said Brendan Paul, another Liberty math teacher who helped run the study. “The difference here is that the review is built into the homework, every day.”

Though the interleaved homework took longer at first, most of the students adjusted. “I usually need a lot of time to study for tests,” said Marigny Duga, who was a student in Mr. Paul’s class, “but doing this mixed homework, I felt like, when the test was coming I needed less time than usual, because everything was still pretty fresh in my head.”

Over nine weeks, each student in the study got 10 assignments with 12 problems each. Same students, same problems. But each student got half a semester of mixed homework, and half a semester of blocked.

Two weeks after the last homework assignment, the researchers gave a surprise cumulative test.

The results were striking. Students scored 72 percent, on average, on the interleaved material. They scored 38 percent on the homework-as-usual problems. This is a large difference, but it’s not unheard of in laboratory studies of interleaved practice, experts said.

Similar Mind, Brain and Education methods include spaced repetition and retrieval practice.


  1. Ross says:

    “You’ll do better and your practice will go more smoothly if you give each skill it’s own block of time — but you’ll improve more if you interleave skills.”

    So, “doing better” is not “improving more”?

    I understand the overall “interleave is good” pitch; I do not understand the prefatory summary.

  2. Isegoria says:

    Right, doing better during your practice session does not mean improving more from session to session. Getting into the groove improves your immediate performance while reducing the amount of learning.

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