When Intuition Gets In the Way of Effective Instruction
Say you’re a math teacher, standing in front of the class posing a word problem to your students. The word problems goes like this: “There are 42 cows in a field, and five go back to the farm. How many cows are left in the field?” The students understand that the answer requires them to subtract five from 42 to get 37.
But say you ask the question this way: “There are 5 cows on the farm, and after the farmer rings the cowbell there are 42. How many cows were out in the field and not on the farm?” Students will be tempted to answer by figuring out how to go from 5 to 42 and therefore fail to solve it efficiently.
Researchers at the University of Geneva say the difference lies in something called “intuitive knowledge”: While the first version of the question makes intuitive sense to students because they already know from experience that subtracting means “taking something away,” the second version complicates understanding because they might not yet know that subtracting also means simply “finding the difference.”
Here’s how they explain it:
“When intuitive knowledge—what we experience on a day-to-day basis in everyday life—coincides with an educational concept, we are within the scope of this intuitive knowledge (‘subtracting means taking something away’). However, when intuitions are not mobilized—having to grasp, for instance, that subtracting means ‘finding the difference’—the task is considered difficult, and seemingly requires the use of specific educational strategies.”
The problem is, many teachers don’t use specific educational strategies in the latter case; instead, they assume the task is consistent with intuitive knowledge and therefore don’t bother with more complex instructional methods.
“Teachers sometimes struggle to understand the difficulties encountered by pupils when attempting to solve apparently intuitive problems that are in fact very difficult,” the researchers write. The findings of their study, published in the journal Educational Studies in Mathematics, suggest that “teachers only use their pedagogical skills when a problem seems to mobilize counter-intuitive strategies.”
For the study, the scientists compared 36 primary school teachers with 36 individuals from other professions, asking them to perform four different tasks. For each task, participants had to solve math problems that either did or did not involve intuitive knowledge, then report which problem was easier to solve and why.
The results showed that when a problem did not involve intuitive knowledge, the non-teachers could not explain why it was harder to solve than when the question did involve it. What’s more, the teachers themselves—whom the researchers thought would call on pedagogical background for assistance—couldn’t explain it either.
“This proves that the educational skills of the teachers are overshadowed by their intuition in some contexts,” the researchers suggest. “This prevents them from assessing the difficulties that a mathematical problem may cause to young pupils, regardless of how much professional experience the teacher may have.”
They argue teachers should be trained to avoid “the pitfalls of intuition” so that “the seemingly obvious does not get in the way of understanding the difficulties faced by students.”