The First Rule of Thoughtful Learning

The first rule of thoughtful learning as I see it is that, short of abuse, pretty much any pedagical technique is sometimes appropriate. The point is to be aware of costs and benefits so that we can mindfully make tradeoffs and design coherent learning experiences.

When I critique a practice, it is rarely if ever my intent to say that no one should ever use that practice. Sometimes, I may use it myself. I may think the technique is oversold or has downsides that are rarely considered, but there is almost certainly still be a place for it somewhere, in some particular situation. If thoughtful learning means anything, it is shifting the emphasis from action to thought, and this applies to teachers just as much as to students.

Make Learning Objectives Honest

Lately, learning outcomes/goals/objectives have become all the rage in higher ed. (As this post is written in English rather than ed-speak, I will use these terms interchangeably.) These typically have the form, "After this lesson (or unit or class), you should be able to do X".  But does learning work that way?

As a practitioner of Brazilian jiu jitsu, I get twice-weekly immersion in the experience of being a student. During a typical lesson, the instructor explains and demonstrates a new technique and then has us try it out. Very often, the initial result is complete confusion. How do I get from the starting position to the intermediate one? Where do I grab? And which limb should I be using, anyway? (This is not just a result of my disability -- many physiotypical students go through the same thing.)

Even after the initial confusion abates and I can execute the move, I don't really know the technique. I may forget it by the next session. I may be able to do it on a cooperating partner, but what about one who's resisting? How do I set up the technique and when is a good time to use it? What small details make the difference between success and failure? Learning these things takes years. At what point can I be said to know the technique?

Academic learning is just as messy and multi-layered as physical. Coming to understand anything nontrivial takes time. Learning objectives that say, "After this lesson/activity/whatever, you should be able to do X" lie to students about the nature of learning. At most, a single learning experience or even a short sequence of learning experiences can make you slightly better at a skill or deepen your understanding of a concept. They should not promise to do more.

 Education consultant and blogger David Didau writes:

All too often our learning intentions are lesson menus; here is what you should know, or be able to do by the end of today’s lesson. Students are unlikely to do more than merely mimic the understanding or expertise we want them to master.

If instead we were to share our intention for students to struggle with threshold concepts, then we could tell them that it might take them weeks to wrap their heads around such troublesome knowledge. We could remind them that in this lesson they are making progress towards a goal and that there is no expectation for them to ‘get it’ in the next hour or even the next week...

Learning does not follow a neat, linear trajectory, it’s liminal. Students not only need to spend time in that confusing, frustrating in-between space, they need to know how important it is to stay there for as long as need be. If learning intentions rush or limit this experience then they might be doing more harm than good.

If you agree with this critique but still like the idea of explicit learning goals (or are required to write them), what else could you do? One possibility is to use thought-focused rather than action-focused language. I like the following possible goals for lessons or short sequences:

1. Introduce a concept or skill
2. Deepen your understanding of a concept or practice a skill
3. Connect a concept or skill to others
4. Extend a concept or skill to new contexts

If the purpose of writing goals is to structure a course and show students what they will be learning, consider using organizing questions. There can be a few overarching questions for a course -- one class I taught used "How do systems behave?",  "How can we use math to model biological systems?" and "How can we use models to predict behavior?". Each question can have subquestions and sub-subquestions that you can introduce at the start of a lesson. The virtue of this approach is that few things pique curiosity like a question.

There's nothing wrong with explicitly stating the purpose of a lesson. But let's do it in ways that don't mislead student about learning.

What is Thoughtful Learning? Take 1

The short answer: That's what I'm trying to figure out. Thinking out loud on this topic is why I started this blog (which would have been called "Thoughtful Learning" had that not already been the name of an educational publisher) .

The longer answer: The term "thoughtful learning" as I use it deliberately carries a twofold meaning: learning experiences that allow students to think and thoughtfully designed teaching. The two go together, as it takes a good deal of imagination and reflection to create such learning experiences. Thoughtful learning develops from coherent relationships between the teacher, the students, the subject matter and the environment in which learning takes place.

The ingredients of thoughtful learning are human connection, coherence, good questions, time and space to reflect, and a fit between the subject, the circumstances and the method.

I believe that to make thoughtful learning happen, we need a synthesis between (not just a mix of) traditional and active methods of teaching with attention to the context in which learning takes place.

The bullet points: Teaching for thoughtful learning is

• Teaching information in a coherent way, not as a series of disjointed facts to be memorized by rote, while recognizing the importance of knowing key facts.
• Recognizing that the deepest thought often takes place in silence and solitude, while appreciating the contribution of a lively discussion.
• Understanding how much guidance beginners need, while seeing Leonard Cohen's line, "There's a crack in everything; that's how the light gets in" as highly applicable to teaching.
• Valuing activity as a way of promoting thought, not an end in itself. 
• As teachers, aiming for the fluency to choose an appropriate technique for the situation rather than mechanically sticking to one approach.
• ???

What Are Grades For?

At almost all educational institutions, students get grades when they finish a course. Grades are primarily supposed to evaluate how well a student has learned the course material. They should tell other people (future instructors, potential employers, graduate and professional school admissions committees, etc.) roughly how well the student learned what they were supposed to learn in a given course. (This is one of the multiple reasons why grading on a curve is an abomination.)

As hard as it may be to assign a single letter or number to learning, most people would agree that a student who learns the material better than another student should not get a worse grade. Grades should be monotonic with respect to knowledge.

Modified from http://ars.els-cdn.com/content/image/1-s2.0-S0951832013000525-gr1.jpg

So far, the situation is simple. Grades evaluate performance. High grades are desirable because they improve your options later in life, so students typically try to get the highest ones possible, which means learning the material -- or at least the material that will be assessed. As long as instructors create reasonable assessments and students do not resort to cheating, their incentives are aligned and things more or less work out.

However, the desirability of high grades introduces a complication. As instructors, we want students to do things that will benefit their learning. We want them to come to class, do their homework, participate in discussions, and possibly more. Ideally, the desire to learn and to get good grades should be enough to get students to do these things, but sometimes they're not. Sometimes the end of the quarter seems too far away or the student is sure that they know the material and don't need to do all of those chemistry problems. So why not directly include those things as part of the course grade? Students want good grades, so if 10% of the grade is based on completing their homework, they will probably complete their homework. Incentives do work, at least in the short term.

Many, perhaps most, instructors engage in this practice to some degree. Even I do, as I was the freshman chemistry student who found it hard to do ungraded homework. (I do have a second grading scheme that excludes such things.) But there are several problems with it.

First, using grades as incentives to do specific work doesn't distinguish between the student who spends too much time partying and the one who works 20 or more hours a week and supports family members. The latter student is already at a serious disadvantage; making them do a certain amount of work, often at very specific times, no matter how much they actually know is just kicking them while they're down. Furthermore, if one class grades in-class clicker questions or reading quizzes and another one taken by the same students doesn't, students will tend to spend less time on the second one, creating an incentive for its instructor to do the same thing and leading to grading arms races.

The second, less frequently discussed, disadvantage of grading things other than assessments is compromising the monotonicity discussed earlier. The larger the proportion of students' grades based on work, the greater the chances of a student with a better work ethic or organizational skills (or more time) outscoring a student who knows the material better.


This problem could be solved by the kind of multi-category grading my middle school and high school used. For each class, you got both an academic grade and grades in "cooperation" (basically behavior) and work habits. Only the academic grade counted toward your GPA, but the others were still on your report cards and transcript.

The third, deeper problem with using grades to manage the details of student activity is that it very likely undermines the maturation process supposed to occur in college. At some point during development, a person should go from being driven primarily by short-term rewards and punishments to being able to pursue a long-term goal even in the absence of short-term incentives. For many people, this happens in college, where they grow into adulthood by managing the abundance of unstructured time higher education traditionally provides. Often, we learn this lesson the hard way, but we do learn it. However, as colleges start managing the details of what students do and when they do it as much as any high school, this unstructured time is being taken away. If young people don't learn to create their own structure by the time they finish college, when will they learn it? (The heavy reliance of many higher education reformers on external motivators is a subject I will take up in a later post.)

Teaching frequently requires us to balance competing values against each other.  While the mission creep of grades both undermines their original purpose and creates other problems, it can be effective in promoting learning. Every teacher must decide for themselves what to do about this tradeoff, but we can only do so with a clear awareness of what is gained and lost in each decision.

A Modeler Thinks About Assessment

Originally published on Perceiving Wholes.

As a lecturer and DBER fellow, I hear a lot about assessment. Instructors are told that they must align what they teach with the questions that are going to be on their exams, that students shouldn't encounter a question type on an exam that they haven't previously learned how to answer.

I think this is profoundly wrong for one simple reason: assessment is a modeling problem.


Think of your knowledge of some topic -- evolution or cell metabolism or ordinary differential equations --  as a network of related concepts, facts and techniques in your mind. The beginner's network might be missing some important connections and contain extraneous, misleading ones. The expert's network is rich but well-organized.

In assessment that goes beyond simple factual questions like "what are mitochondria?", we are implicitly trying to find out whether a student's network is more like the one on the left or the one on the right. The more expert-like the network, the better the student understands our subject.

Of course, we can't observe this network directly. To a teacher, a student's mind is a black box. Therefore, we poke and prod the black box by asking the student questions and use the answers to build our own models of the student's knowledge network. Particularly valuable are those questions whose answers are easy to figure out if subject matter knowledge is complete and well-organized but difficult or impossible otherwise. If a student answers these types of questions correctly, they probably understand the subject well.

Unless, of course, the student has explicitly learned how to answer the question that you asked without figuring it out. Then the process is short-circuited and we are left without a way of assessing what a student actually understands. Ben Orlin writes about this in Math with Bad Drawings:

Need to prove these triangles are congruent? Do this. Need to prove that they’re similar? Do that. Need to prove X? Do Y and Z. I laid it all out for them, as clean and foolproof as a recipe book. With practice, they slowly learned to answer every sort of standard question that the textbook had to offer.

Months passed this way. But something wasn’t clicking. I kept seeing flashes and glimpses of severe misunderstandings—in their nonsensical phrasings, in their explanations (or lack thereof), in their bizarre one-time mistakes. Despite my best intentions, something was definitely wrong. But I didn’t know what.

And, more worryingly, I didn’t know how to find out.

I’d already coached them how to answer every question in the book. How, then, could I diagnose what was missing? How could I check for understanding? For every challenge I might give them, every task that might demand actual thinking, I’d equipped them with a shortcut, a mnemonic, a workaround. The questions were like bombs defused: instead of blasting my students’ thoughts open, they now fizzled harmlessly.

Orlin is describing his mistakes as a novice teacher. But this is the inevitable consequence of the "alignment" being pushed by proponents of scientific teaching. They would probably say that the student should initially figure out the procedure instead of being taught it, and this might indeed be better (or not), but it remains true that when the exam rolls around, all we will see is how well the students remember what they were taught. We will have lost our tools for modeling their minds and assessing their understanding.

Silence is an Answer

Realization: when students don't answer a question in class, they are in fact saying something. They're saying that they don't understand the material adequately or don't feel confident in their understanding (or your question was vague). If that's the case, a constructive response would be scaffolding with simpler questions, providing more explanation, or asking for a question rather than an answer. Cold-calling just papers over the cracks.

Your thoughts?