I was in a class this week where students were reviewing addition of fractions They had recently learned multiplication of fractions and several students confused those solutions by adding across numerators and denominators (like you would for multiplication) instead of finding the common denominator and adding the numerators.
This common error underscores a learning principle outlined in Make it Stick, the Science of Successful Learning by Brown, Roediger III, and McDaniel. They note that many learning environments are designed to produce the familiarity trap.
Beware of the familiarity trap: the feeling that you know something and no longer need to practice it.
The students who knew how to add fractions months ago are now tripped up by that very skill because they have now been taught to multiply fractions and they are confusing the two solutions.
Many teachers tell me that students need to stay focused on one thing until they master it. The familiarity trap tells us this is not the case. When we stay with one thing until mastery (a luxury not afforded often in the real world) we will gain a false sense of knowing when we receive a similar problem that requires a different solution.
The solution is interleaving, which is practicing two or more subjects interchangeably so that they not only see the underlying differences between the problems, but will be able to discriminate between the problems and solutions when they face them outside of the sanitized and carefully organized classroom setting.
Let's go back to that fraction conundrum. Teachers and learners would be better off practicing addition and subtraction of fractions side by side (which is exactly what was happening in those classrooms I saw this week) so they can see the different solutions that are required and be able to choose the proper path.
This learning structure slows down and seems to frustrate the learner --- and the teacher --- however, it turns out, that it has one overarching, hidden quality - it produces deeper learning.