Learning About Learning

II. How We Learn: An Introduction and 4 Basic Observations

II. How We Learn: An Introduction and 4 Basic Observations

The key elements of learning involve perception, thinking, and memory. Some learning comes simply from perception and seems automatic—you see something, your mind somehow marks it as worth remembering, and it gets stored in long term memory where it stays for a lifetime. Other learning is anything but automatic. You take in an idea, a bit of description, a reading, a lecture, you may even understand it, but then within a few days or weeks it just seems to have disappeared.

So how we learn is not very predictable, and that’s a reason why the study of learning has become big business. Most of us, whether students or not, would like to be able to learn more and to remember what we learn longer and more clearly. And as teachers we’d like our students to do the same. But figuring out how best to promote learning is actually quite difficult. Still, a few things are clear, and I set them out here as four basic observations about what we do when we learn:

1. New things we perceive by reading, seeing, or hearing all first go into what cognitive scientists term the “working memory,” a kind of memory different from our “long-term memory.”

Working memory (WM) (sometimes called “Short Term Memory” [STM]) is the place where we begin and then carry out the work of conscious understanding. It is a kind of scratch pad in the brain, except that its contents are of relatively short duration—often only a few seconds. Ideally, the things we decide have value we then transfer to our long-term memory, where they reside until we need them to accomplish one sort of task or another. So perhaps we take in an explanation of “marginal profit” in an Econ class, we store it in mind, and then we recall it when we need it, either for a test or for a real-life purpose at some time later in life.

Unfortunately, learning is rarely “ideal.” There are two major problems that make learning more difficult. First is that the human brain is not actually built for the kind of thinking that school learning requires. It’s built to react to stimuli, to make decisions without reflection, often at very high speed. Cognitive scientists like to think of the human mind from an evolutionary point of view—noting that a long time ago humans (who have no claws or huge teeth or great physical strength relative to many other animals) had to have the capacity to react quickly to threats or opportunities without first having to think about them. If you see a tiger approaching at a run, you’d better be able—in no more than a second or two—to recognize the threat, inventory your options, and then act swiftly and effectively. If you have to stop and think, you’ll be dead—not a good evolutionary outcome. To be sure, few of us any longer have to deal with tigers, but the brain we human beings have evolved is in many ways still set up to work as if we did.

That said, it is also true and central to our life in a complex society that we can learn/be taught a lot of things, even if the rate at which we load this into our memories are relatively slow compared to how fast other parts of our brain work. For contrast, take a quick look out the window and notice how quickly your mind interprets what your eyes see—in less than a second you can see and respond to a huge array of visual stimuli, and do so with astonishing levels of accuracy. Would that we could master and retain calculations connected with the quadratic equation with anything like the same rapidity and accuracy!

So what? For one thing, most of the work our brains do is unconscious—and therefore mysterious. Sure, we are aware of paying attention to things, but although we can try, we actually have little conscious control over our brains’ decisions to remember something, nor can we decide how long to remember it. Fortunately, we can at least influence our brains on this score, even if we cannot control them. Figuring out how to help our brains remember more, and retain what we learn longer, has long been one of the challenges of being a good student.

For a second thing, the limitations of human thought mean that the best way to maximize memory and retention is to build at least a basic understanding of how human brains work. Educational psychologists have actually learned much about how to maximize our learning, and over the next few weeks you will have a chance to learn about some of the concepts they have developed to describe—and control—the phenomena they have observed.

In what follows I’ll outline some of the basics of the cognitive science of learning, and then I’ll supply a glossary (a word for a small and specialized dictionary) of key terms—many of which we’ll encounter in our course readings.

Illustrating the Limits of Working Memory

Look at the row of numbers below for 3-5 seconds, then close your eyes and try to repeat them aloud.

4930215675

Few of us can do this trick--10 numbers is more than most of us can hold in our working memory. But even if you managed to get those 10 into your working memory, they haven't stayed there. To test that claim, without looking back at the sequence, close your eyes again and try to repeat the number string again.

Almost no one can do this, because your brain has not actually uploaded that string of numbers to your long-term memory, and because your working memory is very short-lived, simply paying attention to making sense of the next sentence will have forced your mind to clear your working memory, and, along with it, any ability to repeat the numeric string.

But while the working memory is limited in its ability to retain information, it is still important because it is the doorway through which most of your school learning enters your brain. You take in a fact, you process it, and if you think it has value you silently tell your brain to remember it. The work the working memory does, then, is processing and evaluating and, if appropriate, sending new learning along to long term memory. (You can actually test the actual limits of your working memory at: http://cognitivefun.net/test/4 )

As the name implies, the working memory requires "work"—and that is something our brains want either to minimize or to be rewarded for doing. One way to reduce work is to put things in long term memory. Once you’ve done that, you can recall things easily and with almost no work at all. We are also very efficient in terms of our sense perceptions. Thus we process any visual or other perceptual input without even noticing we do it, and that is because so much of what we actually see or hear or taste or feel from day to day in the world we have done in very similar ways before. We see something, and recognize it, and decide how to react to it in milliseconds. Our native language knowledge is like that, too. We hear a phrase, and we instantly recognize the words and assemble and speak a response. And in speaking, our brains are able to control our speech muscles in our tongue, mouth, lips and throat at what are amazing speeds—up to 30 muscle movements a second!

That kind of thinking has been called “ fast thinking” to distinguish it from other much slower processing, or “ slow thinking”—the kind of processing we do in working memory when we are taking in new knowledge. Fast thinking can be fast because it is mainly a form of recall. We hear a question (“what shape is the earth?”), we instantly come up with an answer (“round”). Because it is an answer that is in our long term memory, we do almost no thinking to complete the exchange.

With the slow thinking of working memory, however, the brain has to process what we see or hear or read, and then call up information of various sorts from our “long term memory” to see whether we know how to connect this new problem to what we already know, and if so, bring that knowledge to bear to solve the problem. Consider what happens when you do simple multiplication.

Suppose you are asked in a math class to multiply 2 by 2. Though the first time as a small child you tried to do this you probably took a while to figure it out, perhaps (like my 4 year old granddaughter!) by counting on your fingers, most of us are drilled in simple multiplication so early and so often that by the time we are in third or fourth grade our working memory can retrieve the right answer in an instant. That is very fast thinking indeed.

But now suppose in that same class you are asked to multiply 36 by 21. Few of us have memorized the answer to that problem, and so your brain will have to use its working memory first to ask your long term memory to supply what it knows about multiplying, and then, depending on what you’ve stored there from your elementary school days, you will have to recall that 1 x 36 is 36, and that 2 x 36 is 72, and you’ll remember, too, to add a zero for the tens column, and you’ll then add 36 to 720 to come up with 756 as an answer. Many of us could do that problem in our heads, though almost none of us will be able to do it instantaneously. So our working memory can enable us to do that much work, even if it does so relatively slowly.

But now imagine that you are asked to multiply 3519 x 46779. Very few of us would be able to do this problem in our heads even if we were given an hour to do so, and the reason for this that there are now so many numbers involved that we will run out of room in our working memory. The basic math in the problem hasn’t changed—it is still multiplication, and the rules of multiplication are the same here as they were for the preceding two problems. What is different is that we have more numbers to keep track of, and that’s enough to ensure that we can’t do the problem without the help of writing things down and invoking from long term memory all the subroutines we learned long ago about multiplication. (It’s worth note that one of the principal means of supporting our working memory is with pencil and paper—whether when doing complex mathematical problem solving or when working through challenging classroom assignments in English or history or sociology classes. Writing things down is not just a way to communicate; it is also a powerful way to help working memory expand its reach.)

This multiplication process is a classic example of “slow thinking,” as opposed to those lightning quick solutions we have for so many other inputs and problems. What is important to know here, however, is simply that even when we already know how to do something, we may be limited in our abilities to solve problems because our working memory's capacity is also limited.

2. Although our brain's working memory is limited, our minds have ways to expand its capacity.

The most common way we can expand our working memory is by building up in advance a store of knowledge that can be recalled from long term memory when needed. The mind does this by memorizing, obviously, and in many cases it can make what it stores more efficient by learning it so well it becomes “routinized” or “automatized”—by which we mean turned into an automatic routine with no slow thinking required at all.

So, as is clear from the problem outlined above, when you were a child learning arithmetic you had to memorize the multiplication table, and what that really did was enable your mind to turn 1 + 1 = 2, and 14 + 14 = 28 into instantly recallable and useable routines. For most of us these became essentially automatized or routinized, and thereby available in an instant to speed us through what might otherwise overwhelm our working memory’s capacity.

Other ways of expanding the working memory's capacity include "chunking" information (what one does with a telephone number—breaking it into small chunks: 206, 555, 1234, for example—making it possible to remember 10 numbers which, unchunked, one could easily forget), and "schemas" or "frames" (pre-existing patterns or groupings of thought into which the working memory can parse new material, thereby assimilating new material to pre-existing structures. New information that can be attached to a pre-existing schema is more easily remembered.) This is actually the solution to the problem described above of remembering a string of random numbers:

4930215675

As a set of ten numbers, few of us can remember that string. But if we turn it into shorter chunks, the problem of memory becomes simple: 493-021-5675. Most of us have memorized a dozen or more of such sequences—each a phone number. Properly chunked, no problem at all.

4. Among the ways to increase learning is to make people more aware of both what they do when they learn well, and what they do when they don’t learn well.

That process is called “metacognition” and involves using written or oral self-reflection skills to become more fully aware of one’s mental processes, whether focused on the questions of how we learn learning or on how learning has been blocked or on the question of the writing strategies we take and whether or not we could have made different choices. Whether in learning or in writing, metacognition can be a powerful way to give students more control of their working abilities—sometimes referred to as higher “self-efficacy”—the ability to take control for oneself of the problems a teacher assigns one to solve.

What is appended below is thus a list of well-recognized learning phenomena, and I supply them to you as a kind of primer. Some of these terms arise in Kohl's "I Won't Learn from You." Others are used in other course readings. They will also arise in other readings in the course and will be central to the research students will be doing for the learning/writing conference.

A Final Caution:

Routinized Error and Cognitive Bias: The Role of Critical Thinking:

The brain’s ability to routinize, because it enables complex thinking and problem-solving, is essential to human intellectual life. Unfortunately, we not only have information and procedures that we have so committed to memory that we can perform them automatically and therefore without reflection, we also over our lifetimes have accumulated information and procedures that are misleading, even dead wrong, which we also have committed to memory and perform without reflection.

Like all other routinized knowledge, the things we “know” that are in fact wrong are unconscious for the most part, and quite obviously their effects deeply limit how, and how well, we think. Some of these things are facts, but others are values or attitudes. Many of these things we call “prejudices”—“pre-judged understandings or beliefs formed without full reflection but still unconsciously influential on how we behave.” Many of these unconscious ways of thinking feel completely normal—meaning that it is actually very hard to avoid them even when you have come to understand that they are not reliable and you are trying to pay attention to them. They systematically limit our abilities to process information, and as such are called “cognitive biases” because they automatically suggest answers/significances to us which distort or even override our ability to think clearly.

So cognitive bias and prejudices are sneaky, and when someone tells us about them we may use those very biases to deny that we are biased! Perhaps the best known is called the “confirmation bias”—the tendency we all have to interpret what we see in ways that “confirm” what we already know. It is, in fact, a form of “not-learning” that is almost always unconscious. (For more on confirmation bias go to https://en.wikipedia.org/wiki/Confirmation_bias.)

Many believe that the best solution to the problem of the partial, distorted or false knowledge we all acquire is to cultivate a capacity for “critical thinking”—a metacognitive reflex that continually reflects on what we say and do in an effort to double-check our thinking. Strong critical thinkers cultivate an ability to question or push back against new ideas in order to test them against both what they know and what they don’t know. Critical thinking is one form of resistance to learning, an automatic skepticism that tries always to keep in mind how easy it is to accept new information, and yet how often new information can mislead.

What is appended below is thus a list of well-recognized learning phenomena, and I supply them to you as a kind of primer. Some of these terms arise in Kohl's "I Won't Learn from You." Others are discussed in other course readings. All will be central to the research students will be doing for the learning/writing conference.

II. A Glossary of Common Learning Terms

Long-term Memory: The place in your mind that learning goes to live. Some of what goes there will last a lifetime; other things have varying half-lives. One goal of learning theory is to increase the duration and completeness with which we retain learning.

Working Memory: The place in your mind where conscious “thinking” takes place. It is limited in its capacity, though its limitations can be minimized by various mental strategies, like routinization (or what some call automaticization), schemas, and chunking. (Working Memory is more or less co-extant with what we think of as our consciousness.)

The “Three Things Rule”: This is a way of talking about the limits of working memory’s cognitive capacity. I don’t know if “three” is the right number for how many new things one’s working memory can think about at once (it might be four or even six), but the important thing is that the capacity of working memory is quite limited, and, therefore, when learners come to material that is new to them, they will often reach that capacity very quickly. That can cause frustration, resistance, even anger.

But for those who have learned that difficulty and frustration are merely stages in the learning of complex things, that feeling of difficulty can be understood as a signal that they just need to slow down, get one, two or three things clear, make some connections to what they already know, and ask questions. That will speed routinization (the movement of some of this new thinking into long term memory), and greatly help reduce their sense of difficulty. (The ability not to be discouraged by the negative feelings that difficulty engenders is called “resilience” [see below].)

Routinization, Automaticization: These are equivalent terms for the speeding up of mental processes enabled by the brain’s having committed information to long term memory. Processes that have not been routinized are processes that still require involvement of the working memory—the slow thinking mind that we use to process things as we learn them. Our brains convert things we know very well into automated routines which can be run with little to no involvement of the conscious mind—or working memory.

Every one of us has felt the difficulty that comes from the limits of working memory. and we have felt as well the way that routinization of basic processes helps overcome those limits. When you learn to drive a car, for example, it’s difficult at first to manage all the steps required to put the car in motion, and it’s just as difficult (as my brother learned the hard way) to find the brake pedal. But after a few weeks or months of experience, new drivers not only run a car’s controls without much conscious thinking about them at all, but also know to check the rearview mirrors regularly, to check side mirrors when changing lanes, and so on. At the outset of this learning process, however, every single one of these acts had to pass through and be directed by working memory. That made us poor drivers for a time, but for most of us, in relatively short order each of the acts of driving became so routinized that we could do them effortlessly. (This process is explained in more detail above in section II.1.)

Cognitive load: The degree to which the cognitive capacity of your Working Memory is full. Our brains work easily with a few concepts or numbers at once, but when we work with more than three to five entities the “load” begins to get heavy. Sometimes the heavy load can be exacerbated by having other things also “on your mind.” The need to spend mental energy to tend to those issues can increase cognitive load and reduce your ability to process thought efficiently.

Prior knowledge/preconceptions: Everyone has learned things before they enter a classroom, so each also brings prior knowledge or preconceptions—ways of knowing, “facts,” strategies, commonplaces—with them. Some of this prior knowledge is essential to learning—indeed, learning becomes much easier when we already know something about whatever it is we are studying. It gives us something to connect new knowledge to, and thereby enables us to remember more easily what we are learning. (It’s the sticky side of what I think of as a mental Velcro© strip to which the tiny hooks of new learning can successfully attach.)

But prior knowledge is not always an advantage: it may also create difficulties when it involves misconceptions, irrelevancies, or even outright error. Moreover, this second kind of prior knowledge may not just be partial or wrong. It may also be (and in fact often is) so strongly held that even with great effort it cannot easily be dislodged.

Unlearning: This is the process one must undergo in dealing with prior knowledge that is wrong or misleading. Unlearning is often neither straightforward nor easy, though teachers often assume it is. Teachers may just say, “That’s the wrong way to think about it,” and then move on. But that’s not always enough. Classic example? In the field of composition it is the five paragraph theme. Students the world over learn the five-paragraph essay and use it for SAT, TOEFL, ACT and similar tests. For many it becomes a helpful and pragmatic way of coping with the challenge of developing and organizing a successful formulaic essay. As a result, many students think of the 5-paragraph form as the source of strength and confidence, and many do not give it up just because a new English teacher says they should. Metacognitive reflection about prior knowledge can help students locate and replace it, but without help some students will never unlearn the matter in question.

The most deeply held prior knowledge is that concerning self-concepts and ethical behavior. People often have emotional and personality stakes in the things they have learned and the way they know them, and if teachers want to help them revise their thinking, they will be most successful by helping them surface and reassess those internal commitments. (The difficulty of unlearning prior knowledge is the subject of a 1987 video called “A Private Universe.” http://learner.org/resources/series28.html )

Metacognition: Metacognition is thinking (often via writing) in explicit ways about how one learns and thinks; it is one of the most valuable learning strategies any student can develop. Its main challenge is that by nature we are in most ways quite unaware of what we know or of how we learned it. Indeed, because so much of our learning is essentially unconscious, students new to self-reflective writing about learning often think that such writing is pointless.

In fact, however, metacognitive awareness fostered by reflection can help students in a number of ways. One, described in the preceding entry, is by making efforts to unlearn prior but misinformed learning more effective (see above); another is by helping students build better self-assessment skills. Very few students enter the university with strong self-assessment skills, and the results of that are often confusion and diffidence when faced with new and more demanding grading standards. Developing a conscious understanding of one’s learning strengths allows one to direct attention to weaknesses even as it promotes self-confidence in the skills one already has.

Metacognitive reflections can also build resilience in the face of difficulty because it enables students to analyze better what in their efforts to learn something is causing confusion, and thus what needs more work and/or help.
Finally, by making students more consciously aware not just of the particular elements of their learning but also of their connections to other things they know, strong metacognitive habits can greatly help students develop their ability to transfer learning from one context to another.

Self-assessment: Self-assessment is the ability to assess one’s own performances accurately. Students very often bring weak self-assessment skills to any given class. Jerry Graff (in Clueless in Academe: How Schooling Obscures the Life of the Mind [2004]) argues that academic experience is often highly mystified and mystifying for students, and nowhere more so than in how they are graded. Many students never develop a good sense of what they do well and what they do not do well, and in the absence of a genuine understanding of their abilities they can become diffident and anxious, or (an even less helpful outcome) resistant to and alienated from the entire learning process. When, by contrast, teachers build and share realistic criteria with students, much of this mystery can be removed, since students then have the means to assess for themselves how they have or have not succeeded.

Motivation: extrinsic, intrinsic; autonomy, competency, and connectedness. Motivations in learning are the thoughts, hopes, pressures or needs that make one want to learn. How students can be motivated has long been a major interest in learning theory because, quite simply, many students in many classrooms seem uninterested in learning. We may be learners by nature, but our motives for learning “on demand” and in school settings have proved very difficult to develop and maintain.

The most frequent analysis of motive talks of “intrinsic” vs. “extrinsic” factors. In this way of thinking people act either for their own internal (“intrinsic”) reasons, or for rewards of one kind or another (“extrinsic”—or external to the self) reasons. Many feel the strongest possible motives for anyone to do anything are intrinsic—motives build into one’s understanding of self and value. Others may acknowledge that that is true, but note that it’s very difficult to explain to students convincingly why multiplication, for example, is worth all of the mental exertion required to master it. So they may offer an extrinsic reward—cookies, or toys for youngsters, high grades for older students—instead.

Much of the motivation conversation has concerned which extrinsic factors work best. Will workers (or students!) be motivated better by cash or by a promotion? Those are positive rewards, but extrinsic motivations can also be negative: if you won’t do your homework perhaps you are made to stay after school, or be grounded for the weekend. Grades are a frequent form of extrinsic reward, and the range from A to F is also a range from positive motivation to negative motivation.

Other work focuses on “intrinsic” factors. Self Determination Theory, or SDT, sees us as being moved most powerfully by three basic inner needs: the needs for autonomy, competency, and connectedness. Autonomy is the sense one can have of control over one’s own life and action; competency is the sense that one has power to do things of value, and connectedness is a sense one can have that one’s actions are serving or helping to build some kind of valued social meaningfulness. These are indeed powerful motives, but how does one connect them to the seemingly miscellaneous tasks of memorize new vocabulary or studying a list of state capitols?

Self-Efficacy/Autonomy: This is a student’s inner level of confidence and capability when facing a learning task. Unsurprisingly, this varies a lot from student to student, but its effect on learning is significant. High levels of self-efficacy usually mean higher levels of engagement and achievement because students with strong self-efficacy don’t let short term difficulty put them off learning. When students think that they will be able to do something successfully, they often also have more willingness to problem-solve and to succeed than when they do not think they’ll be able to do it well. Contrariwise, when students have a low sense of self-efficacy, they may show less willingness to engage in a task at all.

Interestingly, students do not automatically have strong feelings of self-efficacy just because they have been successful as learners. Students with low self-efficacy may attribute success to luck or special conditions, not to their own problem-solving abilities. Metacognitive reflection as well as demystified classroom standards can help students develop a more just and positive understanding of their self-efficacy, and thereby strengthen self-efficacy beliefs.

Resistance: passive, active, conscious, unconscious: Resistance to learning is anything a learner does to put off or avoid learning something. Resistance is not just common among human beings, it is universal. None of us is always receptive to more and more learning. Moreover, some resistance needs to be cultivated as necessary to effective critical thinking. People are, after all, always trying to “teach” us things that are wrong or misleading. Being able to resist their theories is part of being a responsible critical thinker and citizen.

But while resistance is often conscious (like the resistances Herb Kohl describes in “I Won’t Learn from You,”), it can also be passive, unacknowledged—even unconscious. Students thus need to become able to recognize their resistances, and must be given constructive ways of voicing them. Resistance helps learning best when it is active (and conscious), not passive, and when a classroom environment supports students in voicing their resistance. Teachers can help students by “authorizing resistance”— inviting students to locate and describe what they are resisting. When resistance is authorized, a teachers can know better what and how a student might be resisting; then, having brought matters to the surface, overcoming, or at times agreeing, with resistance becomes more possible.

Not-learning: A form of resistance in which someone attempts to prevent learning from happening altogether. Among students it may be a conscious strategy—as Herb Kohl describes in recounting the anecdotes of Wilfredo or Rick in “I Won’t Learn from You.”

But not-learning is even more frequent in the world than Kohl suggests. Kohl’s focus is on conscious not-learning, a form of active resistance for either political or personal identity reasons. But the fact is that all of us not-learn regularly. One reason for this is that there are so many things to pay attention to that no one could ever attend to them all. As a consequence, our minds are constantly doing a kind of epistemic triage, deciding what we will attend to, and what we won’t.

But another reason is that many of the things the world offers us to learn run against what we already know or believe, and for most of these things we turn down anything that would disturb our normal ways of seeing the world. Al Gore talked of the facts of global warming as “inconvenient truths”—truths that would disturb how we think about the world and, more importantly, how we live our lives. His argument was that many of us are emotionally, economically or egocentrically unwilling to make the kinds of change such learning seems to demand, and thus we choose to not-learn either the science or its implications. “Temporary learning” (see next entry) is another common version of not-learning.

Temporary, or pro-forma, learning: A widespread phenomenon in academic learning where students learn things for a short period (sometimes only long enough to take an exam), but don’t actually learn them deeply and with retention. Inauthentic learning (see “Authentic Learning” below) is very often of this sort. When minds do not have strong motives for remembering something, the half-life of learning will often be correspondingly short. (One classic study suggests that retention of learning from many lecture classes—not high to begin with—is among most students cut by half or more within 6 months.)

Deep learning: Something like the opposite of temporary learning is deep learning. Education scholars use this phrase to mean learning that is highly motivated and fully (“deeply”) understood. Retention will be deepest and thus most robust when students have fully integrated the target learning into their own core understandings, and have been able to articulate it in their own language and in connection to other well-established understandings. Deep learning is also something like the holy grail of education, since such learning is not just retained longer but is also a better basis for extension and transfer to new contexts than is less fully integrated learning.

Authentic (vs. inauthentic) learning: Authenticity concerns a given student’s motivation for learning. Authentic learning is that which makes a kind of deep sense to a student—seems for whatever reason truly useful, or connected to a deeply felt life purpose. By contrast, the classic inauthentic motive for many an assignment and many students is a grade. Some of us were deeply motivated by grades, but many students are not. They may want good grades, and work hard for them, but they often do not retain that learning well. Inauthentic learning is frequently a kind of going through the motions, though many students will smile, look engaged, seem perfectly happy. And they may be engaged and happy, too. Paradoxically, students may even think they really do care about the material.

This is complicated by the mysterious nature of “motive.” Consider that while students really like to listen to music, often “know” it inside and out, they wouldn’t be able to articulate reasons why they are willing to “learn” it so well. Similarly, they may be happy in a given class, and even trying to learn, but they may nevertheless still have no authentic motive for remembering beyond the end of the course what their teachers are teaching. For students as well as their teachers, the challenge is to figure out what will motivate learning in an authentic way.

Difficulty: As learners, we all have different responses to the difficulties we run into. Some of us look for it, seek it even; some of us hate it, can’t stand dealing with it. Most of us probably have a complicated relation to difficulty—embracing it on one occasion, shying away from it on another. Whatever one’s response, however, people tend to do best with difficulty when they have the metacognitive ability to recognize it, define it, and work to find a productive strategy for dealing with it.

Transfer: The act of taking something learned in one context and bringing it to bear in another, differently defined context. Recent work has stressed the notion of “dynamic transfer,” noting that we don’t usually transfer knowledge directly from one problem to another in a single moment of insight, but by working at something over time, trying first one thing and then another until a solution begins to emerge. One reason problem-based-learning (PBL) has become more widely used is its underlying claim that as one builds problem-solving skills one also builds the kinds of mental habits that promote transfer. In this way of thinking, the more success students have figuring out how to extend their knowledge to accomplish new tasks, the more extensive and resilient their transfer abilities become.

Bridging the School-Life gap: I’m convinced that students often keep the world of school learning at something of a distance from their life-learning. That doesn’t necessarily mean that they don’t like school, only that they see school learning as in at least some degree unreal or impractical. Students often do not themselves know how to bridge the gap from the subjects they care about in life generally to classroom subjects they care much less about. Teachers may actually encourage the maintaining of this gap when they don’t ensure that students bring their own enthusiasms and expert knowledges into a classroom. Teachers need to find ways to bridge that gap; students will benefit if they can learn (either on their own, but more frequently by being taught) to recognize the gap, and develop their own ways of bridging it, too.

Threshold Concepts: Those key concepts or ideas in any given discipline that define ways of thinking that differentiate that discipline from other disciplines by seeing (or re-seeing) a phenomenon in different, often even counterintuitive, ways. Thus in biology the concept of evolution is central to all that biologists do, yet natural selection, a big part of how evolution is claimed to work, conflicts with a general human tendency to see actions as goal directed. Thus for biologists fish (for example) did not evolve fins in order to swim in the sea, or in order to supply food to you and me, or for any other purpose. Rather, they evolved fins by a random process of genetic mutations, one of which happened to produce fin-like organs, and thereby provided an evolutionary advantage, and therefore over time became an essential feature. The point is that biological change is random, not purposeful, and if you don’t see what that means, you won’t “get” biology at all.

In economics one threshold concept is that of opportunity cost, differentiated from our normal, common sense use of “cost” as the price of something. Opportunity cost asks us to think of “cost” not in terms of price but in terms of what the acquisition of something would prevent our being able to do with the resources used for the acquisition. Price alone, or even how much money you have in your pocket, an economist might say, is not knowledge enough to evaluate whether or not you have made a good buy.

Threshold concepts are also often examples of what Meyer and Land (in “Threshold Concepts and Troublesome Knowledge”) call “troublesome concepts,” since they are often difficult to understand because they are counter-intuitive to anyone who does not understand the discipline in which they are used, or because they are particularly complex in their implications.

Failure. We all know what failure is, and it’s no surprise that we’d normally prefer success. We are less likely, however, to see many kinds of failure as healthy and necessary parts of learning. In the case of complex processes, it may even be that most learners will not be fully successful attempting them on a first or second go. For those who have developed a fear of failing, or a propensity to avoid situations in which they imagine failure as possible (failure aversion), they similarly will have developed a type of learning disability as well when faced with tasks that require persistence in the face of possible or actual failure. Until one learns to see many kinds of failure as normal costs of learning, and therefore something that may be of great value, one may resist the learning that would result from a process in which failure might be a temporary result. This is connected to the concept of “risk taking,” again something necessary to many kinds of learning. Those who cannot take risks on occasion will be less effective learners than those who can.

Resilience. “Resilience” is a term learning scholars use to describe people’s ability to keep working at a task in the face of difficulty and/or failure. Research shows both that different learners evince different degrees of resilience when facing a certain task, and that students’ capacity for resilience can be increased, primarily by metacognitive exercises and support as they encounter difficulty and its resultant frustrations in the course of learning difficult material.