Thinking and Learning

Terms defined: chunking, cognitive load, cognitive transition, competent practitioner, diagnostic power, expert, expert blind spot, extraneous load, formative assessment, germane load, hypercorrection_effect, intrinsic load, long-term memory, mental model, novice, short-term memory, working memory.

We know as much about teaching and learning as we do about public health. The problem is, while university professors are experts in their own fields, many of them don't know what we know. Most people in the tech industry don't either, which means many of us learn more slowly and less reliably than we could. This chapter will give you a short overview of a few key facts that can help fix that.

Different Kinds of Learners

Research starting in the 1980s showed that most neurotypical adults undergo a series of fairly predictable cognitive transitions on their way from being a novice to being an expert in any domain Benner2000. (We say "most" and "neurotypical" because as with anything involving people, there will be outliers.)

For our purposes, we will say that people are novices, competent practitioners, or experts. Some characteristics that most novices share include doing things by rote (i.e., following a series of steps without understanding why they work), asking questions that don't make sense ("What color is the database?") and not being able to tell what is and isn't relevant—for example, using their own filenames or variable names when searching for help online because they don't yet have a clear distinction between what belongs to the library and application and what is specific to their code.

What ties these things together is that novices don't have a mental model of the problem. A mental model is a simplified representation of something that's good enough for present needs. One example is the ball-and-spring models used to represent molecules in chemistry classes: real atoms aren't marbles and atomic bonds aren't springs, but this model is good enough to explain why burning methane produces carbon dioxide and water and a host of other things.

What about experts? They can typically solve problems at a glance, and are usually much better at debugging than competent practitioners because they are better able to reason backward from effects to causes. They also tend to be less good as teachers because of expert blind spot: they know their subject so well that they've forgotten how hard it is for newcomers.

To explain where these differences come from, imagine that the knowledge in your brain is stored as a graph in which ideas are nodes and the connections between them are arcs. (Your brain doesn't actually work this way, but it's a useful metaphor.) A novice's mental model is disconnected: some key facts are missing, and other pieces don't join up (). In contrast, a competent practitioner's mental model is fully connected: given fact A, he can reason his way through B and C to solution D. He might take a wrong turn to Y and Z along the way and have to backtrack, but he'll get there eventually.

What makes an expert different isn't that she has more facts (though she usually does). What makes the difference is that she has many more connections, so the distance between any two ideas in her head is usually much less. In fact, in many cases the problem and its solution will be directly connected so that she can go from one to the other in a single step. This is what we mean by expert intuition: rather than reasoning their way through problems, they recognize them in the same way that most people recognize human faces. Being able to do this explains why they can solve problems at a glance, but also why they have trouble explaining their thinking: they can't tell someone else how they did it any more than we can explain how we recognize faces.

Mental models
The differences between novice, competent, and expert mental models.

Learning styles aren't a thing

You may have heard of "learning styles", i.e., that some people learn better visually, while others do so more quickly or more accurately by listening, reading, or otherwise using language. It's bullshit: while lots of companies make and sell materials based on this myth, no one has ever shown that tuning what or how we teach to match people's preferences has any impact on outcomes DeBruyckere2015. Like Myers-Briggs personality types (), learning styles belong with healing crystals and astrology.

This model of learning leaves almost everything discussed in Kirschner2018 and other recent work, but is good enough to start with. Novices, competent practitioners, and experts are at different stages of cognitive development, so they need different kinds of teaching Kalyuga2003. Novices need to be told what to learn next: since they don't have yet a mental model of the problem, they don't know what to ask for. As Kirschner2006 and many others have shown, discovery-based learning in which people are told "go figure out how to solve this problem" is less effective for novices than guided learning because they don't know what to ask next.

Once someone is a competent practitioner, though, being told step-by-step what to tackle next is both unnecessary and frustrating. Competent practitioners should be mentored instead of lectured: they should tackle problems on their own, but have someone at hand to get them unstuck if it takes them more than a few minutes to figure out what to do next.

Finally, the most effective way to "teach" experts is to have them reflect or introspect on their own practice Schon1984. This usually happens in three stages:

  1. You do some work and get feedback on it. For example, someone in grade school might write an essay about what they did with their summer holiday and get feedback from the teacher on their spelling, grammar, and structure.

  2. You give feedback on other people's work and get feedback on your feedback. This is what most literature courses are about: instead of writing new material, people learn how to critique and analyze things.

  3. Once you know how to critique things, you can start to critique your own work as you produce it. This is the tightest feedback loop there can be, and people who reach this stage start to see continuous improvement in their work as a result.

Formative Assessment

Suppose you are teaching a child how to do addition and you give them this multiple-choice question:

What is 37 + 45?

  • 82
  • 72
  • 712
  • 73

If they pick the first answer, it shows they know how to add multi-digit numbers. If they pick the second, it signals that they don't know how to carry: they add 7 and 5 to get 12, throw away the 1, and then add 3 and 4 to get 7. (Alternatively, they might write down 12 and then write the 7 on top of the 1.)

If they pick 712 it also signals that they don't understand how to carry, but it's a different kind of error: instead of throwing away the 1 or overwriting it, they're treating the problem as two parallel single-digit problems. As for 73, it's a sign that they've learned that they're supposed to add the 1 from 12, but they're adding it back into the ones column instead of carrying it over to the tens column.

Each of these wrong answers has diagnostic power. Like a good unit test, this multiple choice question doesn't just tell us that something is wrong: it points us at the source of the problem. Using questions like these in class in order to diagnose misunderstandings so that they can be corrected is called formative assessment because it forms (or shapes) the learning as it is taking place.

A good formative assessment question takes 30–60 seconds to do (so that it doesn't disrupt the flow of the lesson) and has an unambiguous right answer (so that it scales—if the answers are paragraphs long, it won't be practical to use in a class of 20 students, much less 200). The most important thing, though, is that it tells the instructor what to say next. Different learners can misunderstand things in different ways; a good formative assessment tells the instructor what misconceptions these particular learners have and therefore what needs to be corrected.

Recordings can't respond

If an instructor uses a formative assessment in class and then says whatever they planned to say next instead of responding to the learner's actual misunderstandings, they're not a good teacher. Unfortunately, that is what almost all recorded videos do: they always say the same next thing regardless of what the viewer did or didn't understand. Good video games provide many paths around or through each obstacle; recorded courses could in theory do that too, but in practice the cost is prohibitive.

Formative assessments have many other benefits. One is that in order to come up with good ones, the instructor has to build a mental model of all the ways in which the learner's mental model might be wrong. Doing this helps them write a better lesson, in the same way that if you think about how your program might fail you'll write code that prevents or handles those potential failures.

Another benefit is that formative assessments tell the learners what they do and don't actually understand. It's common for someone to come out of a lesson believing that they've grasped the key ideas, only to discover when they to do homework that they didn't understand after all. Formative assessment on its own won't fill in the gaps in their knowledge, but at least they'll know what they do and don't actually understand.

Finally, formative assessments can be used pre-emptively. I once had a professor start a math class by putting up a multiple choice question. It was pretty easy—I think everyone in the class got it—so he said, "All right, here's twenty minutes of your life I don't need to waste," and set aside a section of his slides. He then did it again, and again, enough of us got it right that he said, "Here's another twenty minutes of your life I don't have to waste," and set aside the second chunk of slides. It wasn't until his third question that enough of us were wrong that he started lecturing. He did that with every topic in the course, and it was great: it meant he wasn't wasting time telling us things we already knew, which meant he had more time for helping us understand the things we didn't.

Cognitive Load

Cognitive architecture
The cognitive architecture of the human mind (simplified).

shows a very (very) simple model of the cognitive architecture of the human brain. On the left is long-term memory (LTM), which is where you store things like the spelling of your name and how that awful clown scared you when you were ten years old. It is very large—you can keep adding to it as long as you live—but you don't have direct conscious access to it.

Instead, evolution has given you a second subsystem called short-term memory (STM) or working memory. (More sophisticated models distinguish between these two concepts, but this simple model is good enough for our needs.) You are constantly fetching things from LTM into STM to use them, then re-encoding them and writing them back to LTM. This is one of the differences between your brain and a computer: reading data from a hard drive doesn't alter it, but every time you access something in LTM, you may write it back in a different or augmented form. We call this "learning".

Here's the problem: STM is very small. Miller1956 famously estimated that it could hold 7±2 things at one time; more modern estimates put the number closer to 4±1 Didau2016. This means that STM is a bottleneck for learning: if too many new ideas are presented too quickly, the new arrivals will knock older ones out of STM before you have a chance to encode them and store them in LTM, so learning won't take place.

This realization and others have produced the theory of cognitive load, which (among other things) divides the things you have to do while learning into three categories. The intrinsic load is the thinking that is required by the learning task itself. The germane (or relevant) load is the other thinking that the problem requires, but which isn't the focus of the lesson, while the extraneous load is everything you're being asked to do that is irrelevant.

For example, suppose you are learning the grammar of Frisian. If I ask you to translate, "How is her knee today?" then the intrinsic load is the rules of grammar, but there is also the germane load of recalling vocabulary (which is necessary, but isn't the main focus of the lesson). If, on the other hand, I give you the words as shown in and ask you to rearrange them, I have eliminated the germane load, but have added some extraneous load by using a mix of fonts. You will solve the problem more quickly and more accurately if the words are all in the same font, no matter what that font is, than you will if your brain is wondering whether the difference is significant.

Translating a sentence
Reducing germane load while increasing extraneous load.

Cognitive load theory explains why tools like Scratch work so well: they reduce germane load by getting rid of the commas, curly braces, and other distractions so that learners can focus on mastering concepts like assignment and loops. It also explains why working with code written in a mix of styles is so painful: each minor difference adds extraneous load.

In order to handle larger sets of information, our minds create chunks that only take up one slot in STM. For example, most of us remember words as single items rather than as sequences of letters. Similarly, the pattern made by five spots on cards or dice is remembered as a whole rather than as five separate pieces of information.

Experts have more and larger chunks than non-experts, i.e., experts "see" larger patterns and have more patterns to match things against. This allows them to reason at a higher level and to search for information more quickly and more accurately. However, chunking can also mislead us if we mis-identify things: newcomers really can sometimes see things that experts have looked at and missed.

Given how important chunking is to thinking, it is tempting to try to teach design patterns directly to learners as early as possible. These patterns help competent practitioners think and talk to each other in many domains, but pattern catalogs are too dry and too abstract for novices to make sense of on their own. However, giving names to a small number of patterns does seem to help, primarily by giving the learners a richer vocabulary to think and communicate with Sajaniemi2006.

Learning Strategies

All of this leads to six strategies that have been proven to help people learn faster and better Weinstein2018. While researchers still disagree on why they work, everyone now agrees that they do.

Spaced practice.
Ten hours of study spread out over five days is more effective than two five-hour days, and far better than one ten-hour day. You should therefore create a study schedule that spreads study activities over time: block off at least half an hour to study each topic each day rather than trying to cram everything in the night before an exam Kang2016.

You should also review material after each class, but not immediately after—take at least a half-hour break. Doing this also helps you catch any gaps or mistakes in previous sets of notes while there's still time to correct them or ask questions.

Retrieval practice.
The limiting factor for long-term memory is not retention (what is stored) but recall (what can be accessed). Recall of specific information improves with practice, so outcomes in real situations can be improved by taking practice tests or summarizing the details of a topic from memory and then checking what was and wasn't remembered.

Recall is better when practice uses activities similar to those used in testing. For example, writing personal journal entries helps with multiple-choice quizzes, but less than doing practice quizzes. One way to exercise retrieval skills is to solve problems twice. The first time, do it entirely from memory without notes or discussion with peers. After grading your own work against a rubric supplied by the teacher, solve the problem again using whatever resources you want. The difference between the two shows you how well you were able to retrieve and apply knowledge.

Another method is to create flash cards. Physical cards have a question or other prompt on one side and the answer on the other, and many flash card apps are available for phones. If you are studying as part of a group, swapping flash cards with a partner helps you discover important ideas that you may have missed or misunderstood.

Interleaving.
One way you can space your practice is to interleave study of different topics: instead of mastering one subject, then a second and third, shuffle study sessions. Even better, switch up the order: A-B-C-B-A-C is better than A-B-C-A-B-C, which in turn is better than A-A-B-B-C-C Rohrer2015. This works because interleaving fosters creation of more links between different topics, which in turn improves recall. Interleaving study will initially feel harder than focusing on one topic at a time, but that's a sign that it's working. If you are using flash cards or practice tests to gauge your progress, you should see improvement after only a couple of days.
Elaboration.
Explaining things to yourself as you go through them helps you understand and remember them. One way to do this is to follow up each answer on a practice quiz with an explanation of why that answer is correct, or conversely with an explanation of why some other plausible answer isn't. Another is to tell yourself how a new idea is similar to or different from one you have seen previously.

Talking to yourself may seem like an odd way to study, but Bielaczyc1995 found that people trained in self-explanation outperformed those who hadn't been trained. Similarly, Chi1989 found that some learners simply halt when they hit a step they don't understand when trying to solve problems. Others pause and generate an explanation of what's going on, and the latter group learns faster. An exercise to build this skill is to go through an example program line by line with a class, having a different person explain each line in turn and say why it is there and what it accomplishes.

Note-taking is a form of real-time elaboration: it forces you to organize and reflect on material as it's coming in, which in turn increases the likelihood that you will transfer it to long-term memory. Many studies have shown that taking notes while learning improves retention Aiken1975,Bohay2011.

Concrete examples.
One particularly useful form of elaboration is the use of concrete examples. Whenever you have a statement of a general principle, try to provide one or more examples of its use, or conversely take each particular problem and list the general principles it embodies. Rawson2014 found that interleaving examples and definitions like this made it more likely that learners would remember the latter correctly.

One structured way to do this is the ADEPT method: give an analogy, draw a diagram, present an example, describe the idea in plain language, and then give the technical details. Again, if you are studying with a partner or in a group, you can swap and check work: see if you agree that other people's examples actually embody the principle being discussed or which principles are used in an example that they haven't listed.

Dual coding.
Different subsystems in our brains handle and store linguistic and visual information, so if complementary information is presented through both channels, they can reinforce one another. However, learning is less effective when the same information is presented simultaneously in two different channels, because then the brain has to expend effort to check the channels against each other Mayer2009.

One way to take advantage of dual coding is to draw or label timelines, maps, family trees, or whatever else seems appropriate to the material. (I am personally fond of pictures showing which functions call which others in a program.) Drawing a diagram without labels and then coming back later to label it is excellent retrieval practice.

One powerful finding in learning research is the hypercorrection effect Metcalfe2016. Most people don't like to be told they're wrong, so it would be reasonable to assume that the more confident someone is in the answer they've given on a test, the harder it is to change their mind if they were actually wrong. It turns out that the opposite is true: the more confident someone is that they were right, the more likely they are not to repeat the error if they are corrected.

Motivation

One of the strongest predictors of whether or not a neurotypical adult will learn something or not is whether they are intrinsically motivated to learn it, i.e., whether they're learning it to satisfy their own goals. If someone is extrinsically motivated—for example, if they're taking a course because it's a degree requirement but they have no real interest in the topic—the learning probably won't stick Wlodkowski2017. While motivation is deeply personal, these three factors influence most people:

Self-efficacy.
Also called self-determination, this is the degree to which you feel you are in control of your own life. People don't enjoy being treated like robots; anything the teacher does to put control back in their hands will increase engagement, and with it, learning. This is one of the reasons formative assessment works: if the teacher changes course to respond to students' answers, it shows students that they have some control over their lives.
Utility.
Students will learn more if they think the material is useful, but it has to be useful to them. One reason to create learner personas like the ones in is to remind instructors of the second rule of teaching: "You are not your learners." (The first is, "Be kind.")
Community.
Most people prefer to learn things that they can share with other people who are also learning it. (I can only dream of inspiring the same enthusiasm for programming as I see in baseball forums and fan discussions of Avatar: The Last Airbender.)

What about demotivation? Again, it turns out that the same few things turn most people off:

Unpredictability.
If what you do seems to have no effect on the outcome, you soon learn to stop trying. This is called learned helplessness, and anyone who has ever wrestled with an intermittent bug or a poorly-written grading rubric is familiar with it.
Unfairness.
If people believe that a game is rigged, they will all try less hard: the people who are favored will know they can slack off, while everyone else will see less point in trying Wilkinson2011.
Indifference.
Most of us have had a teacher who didn't care whether we learned or not, and that kind of apathy is infectious.

These factors, both positive and negative, affect teams and team projects. You may not be able to control all of them, but whatever you can do will be repaid many times over.