Category: Teaching

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Study skills

I’ve been listening to an audiobook called “Make It Stick” by Peter C. Brown et al. In the past, I’ve come across to references to this work on educational methodologies and underlying psychological principles in my work as a university professor. I even recorded a video note to my students on the so-called curve of forgetting (see below). This time, I stumbled upon a review of this book in the “Perpetual Chess” podcast and decided to listen to the entire thing. It certainly doesn’t disappoint in terms of the academic soundness of the presented ideas and a good mix of psychological principles and practical takeaways. As I listen to it, I am constantly tempted to ask my daughter to listen to some parts that relate to study skills in the hopes that she would be able to use these techniques for herself. I actually did so the other day and, in the spirit of what is argued in the book, even asked her to summarize what she learned in her own words. I probably used up quite a bit of my parenting credit with her, as she obliged. I am not sure if that was in any way productive, but for what it’s worth, here is my own summary of that part (advice for students) that we listened to together:

  1. Embrace the fact that effective learning is challenging. Self-quizzing as the main study technique is very effective.
  2. Practice, i.e. retrieving the learned information from memory, is most effective if it is spaced in time and interleaved. Spacing means that instead of long continuous practice sessions that immediately follow the introduction of the new material, we should allow some between the sessions in order to some amount of forgetting to take place. The effort of trying to recall the information makes it stick better. Interleaving means that several topics/subjects/skills are better studied together, rather than in blocks of similar examples/problems. This approach models real-life situations, where identification of the types of problems is necessary. Spacing and interleaving are so called “desirable difficulties“, and they subjectively do not feel as effective as massed practice. One needs to “trust the system”, though, to benefit from it.
  3. Elaboration is an effective technique for reflecting on the learned material. It means formulating the concepts in your own words and using analogies with already-familiar concepts (e.g., warming your hands on a cup of coffee as an example of thermal conduction).

One thing I noticed as a result of this exercise is that my “spaced repetition” video needs a footnote that it is not re-reading of the material that is beneficial, but self-quizzing of it.

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Critical thinking

Yesterday, our daughter invited my wife and me to visit her after-school robotics club. I was quite impressed by how her teacher handled the problems that the students encountered while working on their codes and mechanical designs. When they reported a problem, he would ask a variation of this question: “What element do you think needs to be changed?” I think this question is incredibly powerful, because it simultaneously encourages the students to do two things: to critically analyze the current state of the project and to identify the next specific step in the solution.

For example, my daughter was writing a code for her Lego EV3-based robot to undergo a mission consisting of driving to a specific spot on the table while avoiding the specified boundaries, performing a 720-degree turn while keeping one wheel inside the target spot and returning back to the starting area. She had trouble with returning back to the base, but with the above prompt from the teacher was able to identify the problematic lite in her code – the robot was turning a bit too much during one of the turns on the way back – and to fix it. Another student was having an issue with the design of his robot – it was getting stuck on its way to the target spot. The same question helped him to realize that the wheels were catching on the base, and the solution was quickly found.

I would certainly like to borrow this question for my own use – in the interactions with my students in the courses I teach and in the lab, with my daughter (helping her to solve the problem at hand without offering a ready-made solution) and directed to myself as a means of teasing out a constructive way forward in whatever I do without being overly critical for the apparent failure of the current state of affairs (the question asks to think about one specific aspect to be changed, not the worthiness of the entire project).

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Desirable difficulties

While listening to an audiobook called “Range” by David Epstein, I’ve come across the concept related to learning called desirable difficulties. These are features of the learning process that, as the name implies, create difficulties for the student but improve the long-term learning outcome.  There is compelling evidence that increasing the difficulty of tasks is beneficial in the long-term, even though it slows down the initial progress.

This is counter-intuitive, and it creates a conundrum, both for the student and for the teacher: one needs to trust the process to continue viewing the difficulties as desirable even in the face of decreased performance, e.g. relatively poor test results. There is some consensus, though, on how desirable difficulties can be created by the teacher or by the students themselves (the key assumption here is that everyone agrees that the difficulties are, in fact, desirable).

One tactic is retrieval practice, which is, basically, testing. Again, it’s been shown that spending some learning time on testing, including self-testing, is beneficial. It sounds like a truism, but exerting effort in retrieving the information that needs to be learned helps with the learning. Flashcards is a typical example of a retrieval practice tool, and progressively increasing the size of the stack of flashcards is a desirable difficulty.

Not surprisingly, feedback is important for learning, i.e. the student needs to receive correct information about their performance. Surprisingly, though, delaying the feedback, or the test itself, is a desirable difficulty. This idea clashes somewhat with the huge body of research that shows that immediate feedback is beneficial for building skills, being a key characteristic of so-called “kind learning domains,” e.g., classical music, golf, chess, etc. I think there is no logical problem here, though. Kind learning domains facilitate reliable immediate progress, while “wicked domains”, where feedback is delayed, are conducive to better long-term learning. I should note, that delayed feedback can be intentionally used in a kind domain, and that wicked domains are sometimes characterized by misleading feedback, which is definitely not conducive to learning and what makes these fields “wicked” in the first place.

Another neat technique for introducing a desirable difficulty is interleaving. Here is an example from the “Range” book. Suppose that you are studying painting styles of van Gogh, Picasso, Monet and Kandinsky with the goal of being able to identify the author of a painting by their style during an upcoming visit to a museum. If you are using flashcards with reproductions of various paintings on one side and the painter’s name on the back to self-test your knowledge, it would be more difficult, but beneficial in the long-term, to make a deck of flashcards containing the works of all these painters, rather than studying them one-by-one.

When I was a graduate student, one of the professors in our department used to joke that one qualifies for a post-graduate degree not so much on the basis of acquired knowledge or on the level of contribution to the field, but on the certain amount of suffering one accumulates during the studies, e.g., suffer for two years – get a Master’s degree, suffer for four more years – get a PhD. It appears that there is some truth in this joke – the amount of struggling along the way correlates with slower initial progress, but also with deeper knowledge down the road.

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How to read books

Ready for battle. Stll life with chess pieces.

“I have never met a person I admired who did not read more books than I did.”
Kevin Kelly , “99 Additional Bits of Unsolicited Advice“

It seems easy to suggest that one needs to read books in order to become more knowledgeable and, generally, a well-rounded person. But these days, “reading” can mean many things, from turning the pages of physical paper volumes to listening to audiobooks to watching instructional videos online. Of course, movies and books have coexisted for years, but nowadays the boundaries between the media become blurred. The amount of content available is also remarkably huge. It actually makes it difficult to digest the information effectively. The over-abundance of material in almost any field makes the experience of learning similar to drinking from a fire hose.

Take chess, for example. As far as hobbies go, there is an incredible amount of literature available for those who want to learn the finer points of the game or to teach it to others. Reading chess books, particularly collections of annotated games of masters has been traditionally viewed as a necessary, and perhaps the most efficient, training method. Anders Ericsson, the author of “Peak”, who introduced the proverbial 10,000-hour rule, identified reading and playing through annotated games as the common and defining practice method of top chess masters. But similar to other fields, chess books come in a variety of forms. As far as analyzing positions, reading from a paper book and setting them up on a physical board sounds like a horrendous waste of time, when interactive versions of the same books can be read and played through on any electronic device. E-versions of chess books not only save time, but also, perhaps more importantly, allow us to read and practice almost everywhere, in small chunks of time throughout the day, since we constantly carry our smartphones anyway.

Yet the physical aspect of the game still has value. For my nine-years-old daughter, for example, it is the the wooden pieces themselves, setting up and moving them on the board, what provides motivation to play. To my daughter, chess is not an intellectual practice or a philosophical model of human life. It is simply a board game. Of course, once you start doing anything, it is much easier to continue. She also enjoys solving “mate in one” puzzles from László Polgár’s enormous collection called “Chess: 5334 Problems, Combinations and Games“. It is a physical paper book, which  in combination with a physical board and pieces provides  just the right  pace that prevents information overload for someone, who takes her her first steps.

Beyond hobbies or entertainment, e.g., in the area of academic learning, reading books have conventionally been the way to acquire new information. In my experience, recent forced transition to remote teaching resulted in an abundance of online material in the form of recorded lectures, examples, tutorials, course notes, etc. Like in chess, the  most effective type of practice is  the one you can sustain regularly. So if you are taking a university course and going through a textbook with a highlighter is not your thing, chances are there are video lectures that you can watch as a change of pace, if nothing else.

In the context of learning, an important thing is that reading needs to be active in order to be effective. This means taking notes. Ideally, you would paraphrase and summarize what you’ve read, but even copying passages verbatim is substantially better than doing nothing. This goes back to well-established concept in education that actively engaging with information is necessary for transforming it to knowledge. Interestingly, how exactly you do it doesn’t matter much, statistically speaking. So taking notes is an easy way of accomplishing that.

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Optimizing fun

A conversation I had with my nine-year-old daughter:

“What are you thinking about?” she asked.

“The videos I’ve been making for my class.”

“Do you have fun making them?”

“I do, but it takes a lot of time, so I am thinking about how to make them faster.”

“So you would have less fun?”

“… No, I would still have fun, just faster.”

“That doesn’t make sense!”

…

I think she has a point…

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On the value sketching

I realized a while ago that sketching is a good exercise for developing observation skills and, more generally, memory. It requires full concentration, because the subject is usually not standing still, and one needs to be able to consciously think about which features of the subject are essential and which are superficial. The deliberate thinking is important, because it is the mechanism that allows committing the visual information to long(er)-term memory. The short-term memory (the one in which information lives for a couple of seconds) is not sufficient for preserving the visual details until they can be captured on paper.

Lately, I’ve been recording video highlights to supplement lectures in my Advanced Fluid Mechanics course, and one of those is about the importance of being able to make conceptual sketches of flow features for understanding of the underlying physics. Incidentally, one of the forefathers of studies of fluid mechanics was Leonardo da Vinci, whose approach was based on (some would say it entirely consisted of) observation and sketching of the natural phenomena. We are not aiming at Leonardo’s level of artistry in my fluids course, but observation is an important skill for a scientist and an engineer, and sketching is way to develop it.

The book I am recommending in the video is “Boundary-Layer Theory” by Herrmann Schichting. It is one of the first technical books I bought as a grad student, because I knew that it would remain a classic.