Mixing different kinds of problems improves math learning

Most mathematics assignments consist of a group of problems requiring the same strategy. For example, a lesson on the quadratic formula is typically followed by a block of problems requiring students to use that formula, which means that students know the appropriate strategy before they read each problem. 

In an alternative approach, different kinds of problems appear in an interleaved order, which requires students to choose the strategy on the basis of the problem itself. 

In the classroom-based experiment reported here, grade 7 students (n = 140) received blocked or interleaved practice over a nine-week period, followed two weeks later by an unannounced test. 

The mean test scores were greater for material learned by interleaved practice rather than by blocked practice (72 % vs. 38 %, d = 1.05). This interleaving effect was observed even though the different kinds of problems were superficially dissimilar from each other, whereas previous interleaved mathematics studies had required students to learn nearly identical kinds of problems. 

Interleaving improves mathematics learning not only by improving discrimination between different kinds of problems, but also by strengthening the association between each kind of problem and its corresponding strategy.