I hate using turn-by-turn directions. I often refuse to turn them on even in unfamiliar places. I look at a map and try to find major landmarks or make inferences based on what I know about an area. And I often get a little lost, but getting lost helps me learn where I am and I can find my way around more easily the next time.
I think this is a useful illustration of the difference between learning and performance. If I am interested in performance — getting where I’m going on time — I would want to use turn-by-turn directions. If I am interested in learning — being able to navigate around an area in the future — then looking at a map and thinking about where I’m headed is likely to be more helpful. As Dan Willingham writes, “memory is the residue of thought.” If I’m thinking “ok now I turn left here,” I learn less than if I’m thinking, “ok after I pass I-25 I need to keep an eye out for the exit, get off, and turn north.” That thinking might mean I trade a short-term drop in performance for durable learning I can use in the future.
Nicholas Soderstrom and Robert Bjork write about this in their review of research on learning versus performance:
…learners often mistakenly conflate short-term performance with long-term learning, ostensibly thinking, “If it’s helping me now, it will help me later.”
…instructors and students need to appreciate the distinction between learning and performance and understand that expediting acquisition performance today does not necessarily translate into the type of learning that will be evident tomorrow. On the contrary, conditions that slow or induce more errors during instruction often lead to better long-term learning outcomes, and thus instructors and students, however disinclined to do so, should consider abandoning the path of least resistance with respect to their teaching and study strategies.
I think of learning and performance when teaching topics like end behavior of polynomials and rational functions. End behavior is determined by a small number of principles — larger powers get larger much faster than smaller powers, even powers are always positive, and fractions behave in certain ways. But students often want quick, easy rules, like “If the degree is even and the leading coefficient is positive, the end behavior is positive in both directions.” The latter rule will improve performance in the short term, but misses an opportunity to connect the problem to the students’ prior knowledge in ways that can be applied in different contexts in the future.
Elizabeth and Robert Bjork call these “desirable difficulties,” difficulties that reduce performance but create thinking that improves learning. But here’s the catch. I sometimes get lost trying to navigate without directions, but I’m an adult with half-decent patience and self-regulation skills. And I still sometimes drive people I’m with crazy. Lots of students have a much more fragile relationship with math class. In a lab experiment, desirable difficulties sound like a great idea. But outside of psychological studies, students are largely motivated by their perceptions of success in school. Desirable difficulties might cause students to give up or convince themselves they’re destined not to understand a concept, erasing any benefits to learning. Students want to feel successful in school, and deliberately reducing performance undermines those perceptions and can prevent them from recognizing the valuable ideas they bring to class.
I think this is a great example of the complex relationship between research and practice. I have been dogmatic in the past pushing students to think in certain ways or struggle through problems, swinging the pendulum too far in one direction. But desirable difficulties don’t offer easy and straightforward solutions for the classroom, and neither do other areas of research.
Instead, I think it’s worth thinking about the tension between learning and performance, and the balancing act between desirable difficulties and unproductive struggle. And more broadly, whenever I encounter an idea that seems simple on the surface, it’s worth probing for the tensions and contradictions that come up whenever principles of teaching make contact with the practicalities of classrooms.