The first clue to the secret of deep tutoring came, almost by accident, in a 1998 experiment. Schwartz and Bransford were working on what became “A Time for Telling,” the ground-breaking paper we encountered when discussing explanations. The researchers did something curious. Instead of having students listen to a lecture and then attempt to solve some associated problems, they switched the order. They had students attempt problems, such as measuring the density of clowns packed in a bus, without having been introduced to the concept of density. Students listened to the lecture only after working the problems.

On the face of it, this seems like a recipe for frustration. How can you solve problems before you have been given the tools to do so? Indeed, the problem-first students did poorly at solving the problems before hearing the lecture. But after the lecture, they performed as well as lecture-first students on surface-learning questions and much better on deep-learning questions. Schwartz and Bransford had discovered a way to induce deep learning.

Why might this topsy-turvy approach work? Schwartz and Bransford suggest that putting the problem first gives students a chance to develop the prior knowledge they need to get the most out of the lecture. For example, when students analyzed pictures of clowns in different numbers on buses of different sizes—lots of clowns on a small bus versus a few clowns on a large bus—and tried to think of ways to summarize the differences, they may have begun to develop a proto-concept: call it the “crammed-ness” of clowns on a bus. “Crammed-ness” then provides a seed for the formal notion of density presented in the lecture. Attempting to solve the problems first made them better prepared to learn. This is akin to the idea we encountered when considering explanations: later is better.

Manu Kapur, a learning scientist based at eth, a public university in the heart of Zurich, Switzerland, took this idea and ran with it. He systematically showed across dozens of studies that the cognitive free-for-all induced by problem-first instruction is actually beneficial for learning. His name for this phenomenon was productive failure, though widespread usage has morphed the term into the slightly less abrasive productive struggle.

Kapur even showed that the lecture-first approach may be damaging. When asked to invent ways of summarizing the variation in a basketball player’s point scores over 20 games, students quickly came up with five or six. When asked to do the same thing after having been told the “official” answer—standard deviation—students couldn’t come up with any; they just kept repeating the solution they’d been given. “Students may infer from instruction by a knowledgeable adult,” says Kapur, “that all the relevant knowledge and procedures that they need to learn have already been taught.” Problem-first students have no such apprehension.

According to Kapur, problem-first instruction works not just because it seeds a framework of proto-concepts such as “crammed-ness” but also because it improves motivation. If you struggle with a problem for a few minutes without much success, you are considerably more interested in hearing the solution than if you are just presented with it cold. In one study, Kapur compared watching other students struggle with struggling yourself and found, perhaps unsurprisingly, that there is nothing like your own failure to incentivize you to hear the canonical solution. The enhanced motivation may enable instructors to push beyond surface learning into more cognitively demanding deep learning.

One of the most counter-intuitive findings in the science of learning featured in a 1992 paper by Robert Bjork and Richard Schmidt, professors at the University of California, Los Angeles. The paper systematically establishes that our intuitions about what it looks like when a student is learning successfully, or what it feels like when we are learning successfully, are way off.

Imagine, for example, that you are learning French vocabulary. You decide to cram all your practice into one afternoon, and when you do, it feels like you have made great progress. Your friend decides instead to space practice over several days. That feels like much slower progress, and she is frustrated by how much she keeps forgetting. But if you both take the same test a week later, you may be surprised to discover that she has retained far more than you.

Or perhaps, to study a textbook chapter, you decide to re-read it. Your friend instead turns to the test at the end of the chapter and takes it. Your approach gives you a growing feeling of familiarity. Hers is painful. It is also much more effective.

Or take the order of learning: interleaving three topics—ABCABCABC—is more work than blocking— AAABBBCCC—but it reliably results in more learning.

The problem, Bjork points out, is that near-term performance feels good, but performance is not the same as learning. The sense that learning is hard may even be a good shortcut indicator of when it is actually happening⁷. Of course, no tutor likes to watch a student struggling, becoming more and more confused and frustrated. It is almost impossible to stop yourself jumping in and relieving the frustration by giving the answer, or at least a big hint. This entirely human impulse is, though, robbing the student of the very cognitive exertion that leaves learning as its residue. The harder you work, the more you will retain.

As a result, tutoring sometimes becomes a game of how much cognitive work you can get a student to do before they become demotivated. If the content is genuinely interesting to the student, or can be made so by relating it to their interests in an authentic way, or if they are motivated by some longer-term goal, the tutor’s job is easier. In other situations, the tutor may need to interleave tougher content with breaks or game-like interludes.

Where a tutor–tutee arrangement is expected to persist for several weeks or months, it makes sense for the tutor to invest time in the relationship itself: building trust, taking an interest in the tutee’s interests, helping them navigate ups and downs, and so on. There do not appear to have been long-term studies of tutor–tutee relationships to guide us here, but just knowing that solid learning demands hard work is enough to tell us that tutors need to find ways to increase student stamina for it. Plus, it is of course more pleasant for both parties to spend time with someone they like. And, perhaps most importantly, a tutee who trusts their tutor is more likely to take leaps into the unknown and risk falling, which is exactly what reveals how to make a better leap next time.

Bjork and Schmidt’s finding that performance is not a good indicator of learning was focused on surface knowledge. Is the same true of deep learning? Sidney D’Mello, an expert on confusion at the University of Colorado, thinks it is. “One important form of deep learning,” says D’Mello, “occurs when there is a discrepancy in the information stream and the discrepancy is identified and corrected.” If there is no discrepancy, “there is no learning, at least from a perspective of conceptual change.”

When researchers tracked tutee emotional states during tutoring, the most common emotion displayed was confusion. “Confusion reigns supreme during deep learning activities,” says D’Mello, reporting on studies in which students worked on complex scientific concepts. And confusion was the only emotion that significantly predicted learning. Not even tutee engagement could match it.

D’Mello concludes that there is value in running lessons that “intentionally perplex learners.” Of course, confusion has to be resolved for it to lead to learning. The trick is to help the student uncover the resolution for themselves, not to serve it up to them. According to D’Mello, “confusion resolution requires the individual to stop, think, engage in careful deliberation, problem solve, and revise their existing mental models.” These are all examples of what Bjork calls desirable difficulties.

There are a wide range of ways to induce confusion. D’Mello lists “obstacles to goals, interruptions of organized action sequences, impasses, contradictions, anomalous events, dissonance, unexpected feedback, exposure of misconceptions, and general deviations from norms and expectations.” In short, bumps in the road. Kurt Van Lehn calls them impasses that “motivate a student to take an active role in constructing a better understanding.” He points out that impasses aren’t only about getting stuck but include whenever a student “does an action correctly but expresses uncertainty about it.”

That last point is fascinating: asking a student “Are you sure?” might create a learning moment, even if their answer was correct. Contrast that with the common practice of moving on quickly once a correct answer is arrived at. The great expert in math for little kids, Herb Ginsburg, has a wonderful technique for getting students to think harder: after every answer they give, right or wrong, simply ask them “How did you know that?” Here, then, is a way for any tutor to reliably induce deep learning. The research of Bjork, Kapur, Van Lehn, and others has given us a formula—one that will be familiar to every Hollywood screenplay writer.

The secret to deep learning, like the secret to a good story, is (1) a conflict or impasse that leads to (2) a resolution. And in learning, as in a good story, you do not want to rush either of them. The impasse has to feel like a genuine impasse, which it won’t if it is not properly established or if, from an abundance of eagerness, it is resolved too quickly. The resolution, when it comes, has to come from the actions of the main character. In learning, the main character is the student, not the teacher.

This is what makes the job of the tutor a rich and rewarding one. Crafting a problem to bring the student to an impasse, letting them dig in just deep enough, and then nudging them toward a resolution take skill and often art. When done well, it will feel to the student as if the tutor did nothing at all—except perhaps add some formalism, such as correct terminology, after the fact.

Here is an example of this impasse–resolution technique call—it deep tutoring—in action. A student is asked to read the first part of the task shown on the previous page (created by Malcolm Swan, a virtuoso designer of math problems at the University of Nottingham).

The student has established that segment ab represents the initial part of the journey, starting from Providence, ri.

T: Okay, what’s happening from b to c? S: It shows a short distance traveled. T: Okay. It looks like the line from b to c is flat. What do you think that means? S: I think it means the road flattened out a bit; then, they went up another hill. T: I see what you’re thinking, but if b to c is flat, that means there is no distance being traveled. S: Ah, okay, that makes sense.

The student is reading the line segment bc as an illustration, not a graph. This is a common misread of graphs, especially distance–time or velocity–time graphs. In fact, it was precisely this misread that Swan was trying to uncover when he created the task. The tutor makes a very standard tutor move: they give feedback along with the correct interpretation of bc. What is the likely effect of choosing that move?

It’s possible that it leads to surface learning: the student might remember “flat means no distance traveled.” But it’s doubtful that they have understood why (even if they think they have). And any deeper learning is unlikely to have happened here. What could the tutor have done instead?

You may want to look away from this page and come up with your own answer to that question based on the idea of impasse/resolution before reading on.

The first thing we need is an impasse. The student is reading bc as a line that depicts a flat road. But that isn’t an impasse. They are not confused. They simply haven’t glimpsed the power of a graph like this yet. To create an impasse for them, we need them to see an alternative to their answer without telling them it. One way to do that is to ask a content-free question such as “How do you know that?” Sometimes, that’s enough for the student to realize there’s a problem. In this case, though, we could prompt the student to see a contradiction.

S: I think it means the road flattened out a bit; then, they went up another hill. T: Hmm, okay. Can you tell me from the graph how far they are traveling between points b and c? S: (Pause) Looks like a half. T: A half what? S: Er … half an hour? That can’t be right. Bingo. Now, we wait. T: (Silence) S: I’m not sure I get it.

We could now jump in with an explanation. But it’s worth checking that impulse and seeing if we can scaffold the student to the same conclusion, to do what they didn’t do earlier: read the graph. It could be that they just don’t know how to do that or that they do but they took a shortcut this time. The tutor may know which of those is true from earlier work with the student. But let’s assume not.

T: Well, the y-axis tells distance. S: Okay … So, from b to c … that’s zero distance. T: (Silence) S: So … they didn’t move. T: For how long didn’t they move? S: For half an hour. T: Right. So, what do you think is happening? S: They stopped. Maybe they went to the bathroom? T: Awesome! Who knew these charts could tell you about a bathroom visit? So, what does a flat line mean on this graph? S: It means you are stopped. T: Right. No distance traveled, but time passes. So, you must have stopped. Where do you think b and c are on the map? S: Well, if he’s stopped, b and c must be in the same place. But I’m not sure where …

What happened here is that the student began to produce the resolution to their own confusion. The tutor shifts to positive feedback to keep them moving. You can feel the new insight scratching like a pet at the door. The student opens it.

Do we have deep learning here? Not yet. The student doesn’t truly understand what the graph is telling them about this journey in a way that would allow them to read other graphs. That’s why the problem was designed with several more graph segments to make sense of. If the tutor had instead chosen a problem with just one line segment, we would lose the cumulative effect and the student’s growing sense of “Oh, now I can read these graphs!”

Making sense of a distance–time graph—a crucial skill if and when the student encounters calculus, since many of the examples will be about motion—is only part of what this problem is designed to tackle. Perhaps the more important challenge is translating among three different representations of the journey: the graph, the map, and a verbal description. Let’s rejoin the conversation a little later.

T: Okay, what’s happening from d to e? S: Well, the time is … an hour and a bit more. And they traveled … twenty-something miles. T: Great. Can you figure out how that relates to the map? S: You mean where they are? T: Right. S: Hmm … we don’t have enough information. T: Okay. Can you see anything different about the line on the graph from d to e? S: Ah … it’s bumpy. T: (Silence) S: Which doesn’t mean the road is bumpy. T: Nice. S: Bumpy … oh, maybe, when the line is flat, they are stopped, like in b to c. And the bumpy line is flat, or nearly flat, some of the time. So, maybe, they stop and start. T: You’re on to something. S: So, they’re in New York! T: How do you know that? S: Because they keep stopping and starting in traffic.

This is real progress. Ultimately, we are trying to get to something along these lines:

They drove at 60 mph from Providence on i-95 for one hour, then stopped for half an hour, and then carried on for another hour before reaching New York, and so on.

A lot has to come together to produce that description, and it is the coming-together—the connections— as we have seen, that characterize deep learning. Of course, that ability might not transfer—the student may stumble with the very next graph they see—but a new track has been etched in the learner’s brain, ready to be deepened.

**

The practice of tutoring is inherently asymmetrical. The tutor knows something the tutee does not. That fact itself creates pressure for the tutor to tell, an osmosis in which information wants to flow from tutor to tutee. But the membrane between them is semi-permeable: surface-learning molecules get across easily, but bigger deep-learning molecules do not. The fix is not to push harder but to put the tutee in a place where they are primed to learn and then to wait. Wait for them to assemble the deep-learning molecules for themself, on their side of the membrane. Deep tutoring is a matter of getting comfortable with silence and confusion.

This is the answer to the mystery of why all tutors seem to get similar results. Aside from a few rare practitioners, they are all pushing surface-learning molecules. Figuring out how to get bigger knowledge molecules through the membrane is what makes tutoring a demanding and rewarding enterprise. But at least it is possible for an artful tutor focused on no more than a handful of tutees at one time. If there is a way the same can be achieved in a classroom of one teacher and thirty students, I have no idea what it is. Tutoring may be the only reliably effective mechanism available to us.