Extended metaphor, Dept.

We frequently hear about how in math education we should engage students in “productive struggle”. While there is some value in having students synthesize prior knowledge from worked examples and scaffolded problems, this is generally not what is meant by “productive struggle”. Generally it means having students solve problems that are usually one-off types that do not generalize. What prior knowledge students may have to draw upon is in most cases very small and lacking in sufficient practice for students to be able to apply it efficiently. And if prior knowledge is absent, students are expected to obtain it via “just in time” learning, which would arrive without sufficient practice and mastery.