Desirable Difficulties

Should a teacher always be clear and streamlined in a classroom presentation? While this is my aim, I wonder if I should occasionally be murkier and a little disorganized.

Why would anyone purposefully do such a thing? I’m not talking here about being a last-minute disorganized teacher as one’s natural state of affairs, or the trope of the mumbling bumbling professor that no one can understand. Rather I’m pondering whether the smoothness of my pre-digested carefully arranged material gives some students a false sense of security. They think they understand the material because it seems so comprehensible – but actually they don’t. Reality kicks in when attempting to do the homework problems, or worse, when taking the exam (if they didn’t struggle through the homework themselves).

A common student refrain: “Everything seemed so clear in class, but I don’t know why I can’t solve these problems.” Yes, I do carefully go through worked examples in class and strategies for problem-solving. Sometimes there are worksheets for the problem-solving to actually take place in class. There are homework problems to help solidify the material.

A common question from me: “Did you read the textbook and look through the worked examples there?” Often the answer is a sheepish no. With further probing a student will admit that “the lecture is easier to understand than the textbook” so why bother with the struggle? It seems inefficient to the student to look at both textbook and lecture notes. My students think that it’s worth attending class. (I get very good attendance even though that’s not part of their course grade.) This makes sense, to some extent. Chemistry is challenging. There’s lots to learn and I emphasize what I think is most important in class. And my exams do assess what I think is most important in class.

But the nagging question remains of how to get students to grapple and struggle more with the material, rather than giving in to strategies that ‘look’ easy, some of which are known to be rather ineffective. There’s also the occasional study that touts the introduction of a desirable difficulty that improves learning in the classroom. You’ve likely heard of the study that taking notes the old-fashioned way with pen(cil) and paper is better than using a laptop or other electronic device. Or more obscurely, there’s the study that harder-to-read font can encourage more eyeball time and therefore more understanding and reading comprehension. Or you might overhear a student proclaiming (about another class, not yours!) that “I had to do all the studying myself in Professor X’s class because he’s so confusing in class.”

There are in fact studies showing that introducing so-called ‘desirable’ difficulties can promote deeper learning – longer-term retention and (in the lingo) ‘transfer’. The difficulty is that it may slow down learning short-term. For example, interleaving practice shows evidence of longer-term learning compared to massed practice. But there’s a fine line. Making things too difficult or frustrating has a negative impact on learning. Taking an earlier example, you could make the font so blurry that the student, instead of reading more slowly and carefully, resorts to skimming and skipping. That’s going to be bad for learning!

In an open-access review paper published last week in Educational Psychology (DOI:10.3389/fpsyg.2018.01483) Paas and co-workers analyze how and when desirable difficulty turns into undesirable difficulty. (Abstract above.) The key theory used to analyze the issues is cognitive load theory. John Sweller, one of the principals in this area, is one of the co-authors. The three desirable difficulties that are discussed: testing, generation, and varied conditions of practice. Let’s take these in turn.

Testing. Students do not like this. Tests stress them. But they can be very effective for learning. The poster study for the testing effect shows that students who took quizzes before a final exam performed better than students who used the time reading the material more instead. (There are many other related studies that support the testing effect.) That’s why my General Chemistry classes have plenty of very low-stakes five-minute pop-quizzes. I also provide practice exams, but for the coming semester I’m going to try something new to help students test-and-reflect with take-home exams.

The generation effect is “the finding that generating one’s own answers rather than studying the answers of others may have long-term advantages for learning”. Most of these studies involve word generation or sentence completion although some contain math calculations. In my classes, I stress writing out the answers with intermediate steps included. It’s also why multiple-choice questions do not feature strongly in any of my classes. A multiple-choice question requires recognition (or luck), while a generation question forces the student to utilize what they have learned by drawing on resources in long-term memory. (Note, this doesn’t come from sheer memorization. While definitions and some procedural knowledge must be memorized, the rest can be constructed.)

By varying the conditions of practice, for example through interleaving (mentioned above), or providing different-looking problems that help the student practice the same concept, studies show signs of long-term retention. This is contrasted with repeating the same solution or procedure (massed practice) under the same conditions, which is effective for short-term remembering and regurgitating, but shows little lasting effect. (Note that this principle doesn’t apply to automating physical movements such as one might practice in sports, because in those cases one is aiming for autonomous memory rather than long-term memory.) I try to provide varying homework problems, because there’s only so much you can cover in class, but I’m not sure how effectively I’m doing this. I need to work on this more systematically.

In all three cases (testing, generation, varied conditions of practice), there are also studies that show the opposite effect, i.e., that learning is hindered (measured usually by retrieval or a final test of some sort). Cognitive load theory provides a framework to explain these cases. Our working memory is limited. Therefore if a novel task is presented, and there are too many new interactions among the elements of this task, learning is inhibited – what gets encoded in long-term memory is at best a jumble of incorrect notions. Folks in the learning sciences have quantified ‘element interactivity’ and they find that novices have difficulty with handling these interactivity, while experts are able to do with ease (up to a certain point). The authors illustrate how learning effectiveness decreases at the element interactivity increases, and this blunts the desirable difficulty into one that is less desirable.

Reading this article made me think about how to quantify element interactivity in chemistry. I know it’s high for novices from Johnstone’s Triangle. But I don’t know how high. Students starting college chemistry also have a very wide variety of prior knowledge. Some of them have had excellent high school chemistry courses that cover much of the material in first-year college chemistry. Others have problems with algebra and proportionality which seriously impedes learning base concepts such as the mole (quantity) and manipulating chemical formulae. In any case, I’m approaching the new semester with a sharp lookout for element interactivity in the material I’m teaching. I expect this to be significant in my Quantum Chemistry class, since the math is demanding, and the concepts are counter-intuitive and challenging.

There are occasions where I attempt to confuse the students, but I let them in on it. During class discussions, in trying to sharpen and clarify conceptual material, a student might provide a ‘textbook answer’. I respond by providing a spurious counter-explanation, often prefaced with “I will now try to confuse you by claiming…” and challenge the students to go a little deeper. I have also made deliberate common math or graph errors in class early in the semester to make sure students are paying attention and not just blindly copying what I write on the board. I alert them to this issue within a couple of minutes at most, and we discuss why I made the error. This strategy becomes very useful later in the semester when I inadvertently make a math error on the board. This inevitably happens in the math-laden physical chemistry courses. And I do veer off the beaten path occasionally in class, when our discussion uncovers something interesting. This is desirable and keeps us all on our toes!