Self-Regulated Learning

Thinking about why some of my students choose sub-optimal learning strategies encouraged me to re-read a review article in the Annual Review of Psychology. The title and abstract give you a good idea what the article is about.

The article begins by discussing how memory works. For example, we do not store memories akin to a video recording. Nor do we retrieve them akin to mentally pressing the Play button. Instead memories are formed in connection to things we already know. Our storage capacity is not like a USB thumb drive. Long-term memory doesn’t seem to have a maximum limit; but it takes active work to move things to long-term memory. Retrieving information can modify how it is encoded, and often strengthens the memory and its ease of accessibility. That’s why testing yourself is an effective way to learn. While I verbally tell my students this, and it’s also on the “how to study” portion of my syllabus, many students hardly use this strategy. (Maybe I need to shorten it to these five quick points.)

How to monitor one’s own learning effectively is also discussed. The authors summarize research demonstrating that “(a) learners can easily be misled as to whether learning has been achieved, typically resulting in overconfidence, and (b) what people tend to believe about activities that are and are not effective for learning is often at odds with reality.” Learners often unconsciously emphasize their present performance, and do not make appropriate connections to past and future performance. ‘Fluency’, or how easy something feels, also influences (pun intended) assessment of one’s own learning even though such cues can be misleading. For example, interleaving or spacing practice feels harder than mass or blocked practice. Although the former is more effective than the latter, students often mass their learning in a single block because it feels easier. Sometimes difficulty is desirable.

Students under-predict the effectiveness of multiple study trials over a period of time, even though this provides superior performance than cramming. On the flip side, students over-predict how much they think they will be able to remember from when they first encounter new material. I don’t think any of my students would disagree with these statements – they makes sense – but why don’t students act on it? The authors think this is due to presentism. If it’s not affecting your present experience right now, it tends to get ignored.

In a section on “attitudes and assumptions that can impair self-regulated learning”, three important things are discussed. First, students should not be afraid to make errors during the learning process. This can be challenging because making mistakes may affect one’s self-esteem. As I tell my students often: Make the error now so you won’t do it on the exam. When I pose a question, I always try to wait a moment so each student has a chance to individually think or scribble something down before I call on someone to attempt an answer. (This advice is also in my syllabus.) If a student just hears the answer right after the question, this ‘fluency’ can be self-deceptive: Of course it’s obvious when someone tells you the answer. Erring, however, is important for learning.

Second, the authors note “an over-appreciation in our society of the role played by innate differences among individuals in determining what can be learned and how much can be learned… coupled with an under-appreciation of the power of training, practice and experience.” And third, students assume that learning should be easy. It isn’t. In fact, it shouldn’t be. Geary’s framework of biologically primary versus secondary information is crucial here.

I’m pleased to say that after my pep talk, more of my P-Chem students have been starting to work on their problem sets earlier and coming to office hours. I’ve continued to emphasize the importance of finishing the problem set before looking at the solutions and annotating, but I still think some students are not following these instructions to their detriment. That false sense of fluency without the struggle might feel easier, but the needed learning (which is hard) hasn’t taken place. The next exam is coming up in a week so we’ll see.

Upside Down Periodic Table

Different point of view? Recently the journal Nature Chemistry published a short article by Poliakoff et al. suggesting flipping the Periodic Table upside down. For the sticklers of symmetry operations, technically you are rotating 180 degrees about a horizontal axis.

The authors suggest several reasons to do this. If you’re used to a typical x–y two-dimensional graph, the origin starts at the lower left. Numerical values therefore increase both rightward and upward. The way electrons are ‘filled’ using the aufbau principle suggests a building up from lower to higher energy ‘orbitals’. And if you happen to be a kid, and there’s a periodic table in your classroom hung up on the wall, the elements you’re most likely to encounter would be closer to eye-level rather than way up there closer to the ceiling. Also, “looking at a problem from a new viewpoint often gives rise to new ideas, so this orientation of the table will undoubtedly give us all a new perspective.”

Other chemists were polled for their thoughts. Some liked it. Others preferred the original. For example, if you think of a data table rather than a graph, then information typically starts at the top left. As a follow-up the upside down table was then shown to non-chemists with identifying markers stripped out and eye-movement was tracked to generate heat maps of where participants spent the most time looking. I’m not sure how useful this was but the asymmetry could be interesting from a perception point of view. 6 of the 24 observers recognized the outline of a periodic table. When asked which was preferred, the conventional model won, although the upside down version was rated as more symmetrical. It sort of looks like the silhouette of a desk.

I prefer the conventional periodic table. Possibly that’s because of sheer exposure and familiarity, but I do have one argument for it. Chemistry is about making and breaking chemical bonds, i.e., moving electrons around. How electrons move around is related to how strongly they are bound to their nuclei. So it’s a question of energy. The element with the lowest ionization energy is in the bottom left corner (francium) and the one with the highest ionization energy is in the top right corner (helium). In fact, I think of the periodic table in terms of diagonal lines rather than orthogonal ones. But the elements have their idiosyncracies. The periodic table is kinky!

Coming up with the periodic table in its current form is partly due to historical contingency. There were plenty of clever ideas in the 19^th century before Mendeleev’s won out. One was a cool spiral by Hinrichs. But organizing all that data was no easy feat. I’d previously designed an Alien Periodic Table activity to give students a glimpse of the challenges faced by the early scientists. What was interesting is that students inevitably started with the least massive element in the top left corner. I suppose it comes from habit! They’re used to a particular construct of the Periodic Table, and I suppose it would take extra cognitive work to imagine starting at the bottom left. I suspect we won’t see a large-scale change towards the upside down periodic table.

Structure

This morning I’ve been pondering two senses of the word structure. As a chemist, my first instinct is to think about molecular structure – how atoms are connected to each other within a molecule. A dictum of chemists is ‘structure determines function’, i.e., when you know the structure of a molecule you can start to predict how it will behave or react with different molecules. In this sense, structure refers to the physicality of the molecules.

However, there is another sense in which structure is used. Structure can refer to how things are ordered. At first glance this sounds similar to the “how atoms are arranged” definition above, but now I’m thinking about organizational structure. If you’re joining a new company, you should care about the ‘org chart’. It helps you figure out who you need to talk to when you need to get certain things done. Structure in this sense is not the physicality of any object, but the functional relationship between these objects.

I’m interested in how complex systems arise from seemingly ‘simpler’ systems. However, it isn’t clear how one measures complexity. What makes something simple versus complex? If I say “that’s a complex molecule”, I might be thinking of structure in the first sense. If I say, “that’s a complex mixture”, I might be thinking of structure in the second sense. Is there a third sense? Can these be quantified on a similar or related scale? If there is a scale, it’s unlikely to be linear. Different order parameters will come into play at different length and time scales.

If complexity resides somewhere between order and chaos, why is it observed? Or is it observed only because we the observers are coarse-graining through an anthropocentric lens? The world we live in, possibly the pocket of the universe we live in, is strange. It seems to have started in a low entropy state, but then we get to see all sorts of interesting things happen as the entropy increases. For some reason, en route to overall higher entropy, mini-pockets of low entropy structures (in both senses) show up. How do these structures persist? They could either change very slowly (first sense of structure). Or they could replicate quickly in a cycle of destruction and creation (second sense of structure).

I recently read a physicist’s dictum that “order can only arise from more order”. When we see mini-pockets of seemingly low entropy order arise, it is because fundamentally there is higher order behind it. Symmetry breaking is the rule as events progress through time. A perfect sphere seems simple because it possesses an infinite symmetry – our minds somehow grasp this abstraction. Lower symmetry polyhedral on the other hand have finite symmetry operations. Why do we instinctively think the lower symmetry cube is simpler than an octahedron or a dodecahedron? It could just as well be the other way around. Methane (CH₄) is more symmetric than Water (H₂O) and therefore more sphere-like. And what happens when thousands of such molecules interact with each other? Structure is more complicated than it seems.

The Order of Time

My students enjoy my occasional digressions into speculative science. These are often prompted by a student question, thus encouraging them to ask interesting relevant questions. Sometimes I pose the question instead, and every spring semester when we discuss thermodynamics I bring up the issue of entropy and time’s arrow.

Time is a strange and funny thing. We don’t really know what it is. But unlike all the other laws of physics, where symmetry plays an important role and there is no difference between forwards and backwards, time is different. Or maybe I should say heat is different. Heat is the ‘thermo’ of thermodynamics. It’s stranger than you think. Exploring this strangeness is Carlo Rovelli’s The Order of Time. Rovelli is a wonderful writer with engaging prose. I’ve quoted one of his earlier books in a previous post on – you might have guessed – thermodynamics!

Heat spontaneously moves in one direction. Never the other way around. A quantity was invented by Rudolf Clausius to describe this behavior: Entropy, from the Greek word for transformation. Rovelli has only one simple equation in his book. It represents the second law of thermodynamics. He writes: “It is the only equation of fundamental physics that knows any difference between past and future. The only one that speaks of the flowing of time. Behind this unusual equation, an entire world lies hidden. Revealing it will fall to an unfortunate and engaging Austrian, the grandson of a watchmaker, a tragic and romantic figure, Ludwig Boltzmann.”

In my class, I illustrate the counting of different configurations (microstates) with coin-tossing examples. We calculate probabilities, certainly at the G-Chem level, and in P-Chem we derive the Boltzmann distribution in all its glory. (My students would say “gory”.) Why does the Second Law ‘work’? As the sample size increases the Boltzmann distribution becomes overwhelmingly the most probable. It’s the one that maximizes that strange quantity called entropy. The experience of observing low entropy situations changing to high entropy situations gives us that feeling of the unidirectional ‘flow’ of time.

But time doesn’t really flow. A crucial point that Rovelli makes, and one that I try to emphasize in my classes is that entropy-counting is not just a matter of probability, but also one of perception. It depends on how you lump the microstates together and count them. You are counting what you cannot see. Weird, huh? Rovelli puts it this way: “Boltzmann has shown that entropy exists because we describe the world in a blurred fashion… The difference between past and future is deeply linked to this blurring…” If I was the size of an atom (molecular-me!), there might be no distinction between the future and the past. You would not be able to tell if you were moving forwards or backwards. My students find this idea crazy!

Rovelli goes on: “This is the disconcerting conclusion that emerges… the difference between the past and the future refers only to our own blurred vision of the world… is it really possible that a perception so vivid, basic, existential – my perception of the passage of time – depends on the fact that I cannot apprehend the world in all of its minute detail?” There’s a word for this activity of blurring things. Computational scientists use it all the time. It’s called ‘coarse-graining’. It’s uncanny when and where coarse-graining shows up. For example, it is used to describe complex systems and might even be involved in the origin of life (and complexity). And if we could get over our perception limitations, perhaps we could time-travel?

The ancients make their appearance in Rovelli’s book. It's a topic I encountered as an undergraduate when I wrote an essay in a philosophy class on Augustine’s description of Time in Book XI of The Confessions. Rovelli discusses these ideas and more. The strongest parts of the book are when Rovelli distils complicated concepts in physics to thinks a non-physicist can follow. I now have some idea why quantum loop gravity is interesting. He has a knack for communicating why physics is both interesting and strange. The weakest parts of the book are at the end when he ventures into speculative areas far afield. One should take these with a grain of salt or whimsy, depending on your disposition. But all in all, it’s an engaging little book and I will be pointing my students to it!

Second Act

We just finished Week Ten so I’m two-thirds through the semester. As I was working on class prep, I had an epiphany. When it comes to revising and improving my class materials, trying new things, or infusing creative approaches, I’m much more inclined to do such things in the first half of the semester. In the second half, I seem content with minor changes and mainly upkeep more of the same. Why might this be?

When preparing my syllabus before the semester begins, my enthusiasm levels for my classes are at their highest. While I know the layout for the entire semester, I try not to determine all the details for every single class session. Every group of students is different and so adjustments will need to be made, and I want to be open to changes rather than rigidly following a fixed pre-determined plan. I do however plan the first four weeks or so in detail, and I make changes or flourishes I’m excited about. I have the luxury of time to think about these in detail because the busyness of the semester hasn’t started.

As I reflected on my classes this semester (and I’ve taught them many times over the years), I noticed that the first four weeks has the material which excited me the most, and I’ve constantly refined it so much so that I might call them a ‘work of art’. Material in the middle part of the semester sometimes gets a makeover, as when I revamped my approach to chemical bonding in first semester general chemistry. But sometimes it’s more routine. The last third of the semester seems to get short shrift in terms of modifications and improvements. Maybe I’m both busy and tired at that point. Two thirds into the semester is also when registration for the next semester takes place, so I’m meeting with lots of my students, signing forms, and performing other administrative tasks.

I owe it to my students to do a better job in the Second Act of the semester, although I’m not sure that will happen this semester. Maybe it’s because I’m going on sabbatical next academic year and the present semester is the end of a long stretch where my mind and body are looking forward to its renewal. I am excited about the classes I will be teaching after my sabbatical, and I have already thought of new things I would like to do. Maybe as I plan these things I should start at the back end of the semester and work my way to the front end. I should do this more often – envision the culmination and then work my way towards the setup.

I’m feeling particularly motivated to infuse a bit more creativity into my class prep, particularly since I just watched Ralph Breaks the Internet (on DVD). A clever story, creatively told, and chock-full of interesting tidbits alongside the main arc. Watching these movies makes me first wonder why I’m not in a more creative industry, but moments later I realize that it’s up to me to put in energy to do creative things in my industry. Higher education has room for flexibility and trying new things, even in a subject that is perceived as highly structured and hierarchical. Chemistry is creative! I should remember this and do a more creative job curating my class material so that the students catch that scent – the same scent I get when watching a creative movie!

Talking Up My Department

‘Tis the season for college visits, the last stretch of admissions frenzy.

This morning I had a visit from a prospective student and his parents. They were interested in learning more about our department and the biochemistry major. In my role as a faculty member, while I do meet prospective students, I don’t often communicate directly with their parents. (I did field more questions from parents back when I was department chair.)

I very much enjoyed the 45 minutes I spent chatting with the student and his parents, showing them the wonderful spaces in our building, answering their questions, and basically talking up my department. It’s easy to talk up my department because it’s a great place to be – certainly as a faculty member, but I’m very sure that our students would say the same thing! While I know this, I don’t often articulate it to parents of prospective students. I very much enjoyed the experience because it reminded me how blessed I am to be part of an excellent department.

We have a very nice science building which is kept up well, good facilities overall, and our department is chock-full of equipment. There was also plenty of activity. We peeked in the door-windows of lab classes in session, but also looked at some research labs where our students were busily working. I ran into a number of students I know (and I know most of our majors) while giving the tour and spent a moment chatting with each of them, and they also said hello or waved to the visitors. It just underscored the good relationships between faculty and students I had just been talking up a moment ago. While our number of majors has grown significantly, we still manage to engender the feel of a cozy tight-knit atmosphere in the department.

I should talk up my department more often. The enthusiasm carried with me the rest of the day especially when I was meeting with students in my office much of the afternoon. I was enthusiastic helping my academic advisees plan their Fall class schedule. I was excited when meeting with one of my research students going over some of the figures she had made from her data analysis. I was animated in answering questions on the P-Chem problem set (yes, more students are coming in!) and G-Chem online homework. I was chairing our department faculty meeting today (since my department chair was at a conference) and we discussed end-of-the-year student awards – it’s always a great reminder of the fantastic students we have, and to think about how far they’ve come in their four years of college.

Some days, heck most days, I love this job!

Struggling Through P-Chem

I felt deflated after grading P-Chem exams this week. The class average was the lowest I’ve seen in many years. Some students aced the exam, as usual, and a number of students did better on this exam (#2) compared to their first exam. But most of them performed worse. My first thought: “Did I fail my students by not being stricter on the problem sets?”

One new thing I’m trying this year is to increase metacognition in my students assessing the state of their own knowledge. In my G-Chem classes I’m using take-home closed-book exams with accompanying annotations. In my P-Chem classes, the students annotate their problem sets. I thought this worked well in both my G-Chem and P-Chem classes last semester. I also thought it worked well in both classes earlier this semester. Until I graded P-Chem exam #2.

I’ve been teaching for a long time and I think my exams are well-calibrated from a summative assessment point of view. The average performance does not change very much over the years although when I have a smaller class size, the statistics occasionally skew one way or the other. Both my G-Chem and P-Chem classes were unusually small last semester. This semester they’re closer to the usual size. G-Chem seems to be going fine, but I’m worried about my P-Chem class this semester.

Besides the larger class size, there might be a number of other factors. For one, there’s a larger than usual crop of graduating seniors who waited to the last minute to take P-Chem. I’ve observed ‘senioritis’ over the years – P-Chem is sometimes not a high priority for these students, and I can accept that as an instructor. Another factor: A couple of years ago, we recently revamped the Biochemistry major so only one semester of P-Chem is required rather than two. (The Biochemistry majors now take two semesters of Biochem lecture rather than one.) Hence, when students show up in P-Chem 2, they’ve already experienced the shock of P-Chem 1. But exam #1 this semester showed the usual average performance compared to years past, so I’m not sure this is a factor. I might just happen to have an academically weaker crop of students. Or maybe a less motivated group. Or maybe folks who are just busier with other things. There’s a national biochemistry conference just beginning and student were preparing their research posters.

But the nagging thought I have is that by giving the students the solutions to the problem set as part of the annotation before they submit it, I have reduced their motivation to really struggle their way through the problems. Certainly, there are fewer students in my office hours this semester given the size of the class. That’s definitely a problem because P-Chem does not come easily to most. It requires the struggle. I’ve been banging on this theme throughout the semester. Every class I tell the students which problems they should work on before the next class, and make a point to connect material in class with what they will see on the problem set. I suspect that very few students have heeded my advice (given the reduced attendance in office hours). That being said, in previous years, the majority of students wait until the last minute to work on the problem sets before I had this annotation scheme anyway. I think the problem has to do with not struggling as much with the problem set regardless of timing. Starting late doesn’t help matters.

I considered changing the annotation rule and reverting back to the old system, but decided instead to remind my students both in class and in a detailed e-mail why it is important to keep up with the material and struggle through the problem sets. It’s easy to deceive yourself into thinking you know something when you really don’t, at least in a subject as difficult as P-Chem. I reminded the students of the learning recommendations on my course syllabus and why they were there. I tried to frame the issue in terms of making choices according to one’s priorities, and if doing better in P-Chem is a priority, one must put in the requisite work and struggle. That’s hard. No one likes the feeling of struggling. I tell the students what previous students have said about the importance of struggle.

As a teacher, I want my students to learn the material and be successful. I also want to treat them as adults and not force certain behaviors punitively through grades. I would like them to come in more to office hours so I can help them learn the material, but I’m not going to enforce it. In a sense, the students earn their grades. But by putting a bit more responsibility on the students to own their learning, they can make choices to avoid the struggle and thereby earn poorer grades. I feel like I’m in a dilemma. But at the moment, I’m sticking through my plan and not changing my class policies. We’ll see what happens on the next exam. Or hopefully even earlier, more students will struggle through the problem sets and come into office hours this coming week.

Exams: Open or Closed Book

Once every five years or so a student in class asks if we can have open-book exams instead of the usual closed-book version. After I explain the types of questions I would ask on an open-book exam to test understanding of the class material, students decide they would much rather stick with the closed-book exam.

Perhaps I’m being unfair and I’m making the exam sound extra-hard for the students. However, it seems to me that if you can look at your notes or the textbook, you could certainly write down a conceptual explanation without understanding it or solve a problem with the help of a worked example not having internalized the actual required learning-to-solve mental models. Now, if the exam was timed it might not make too much of a difference. A student who didn’t know the material will spend time flipping pages or notes and would do poorly anyway. But I thing open-book timed exams don’t make sense. Open-book non-timed exams however make sense. I call these projects. And we do have them from time-to-time. In the jargon, I would place greater weight on higher order Bloom’s taxonomy questions in an open-book exam.

I do provide enough information on a closed-book exam so that students aren’t burdened with sheer memorization. Periodic Table, numerical constants and data values are always provided, along with equations that we have used in class but not extensively. Equations that are used extensively should be second nature to the students (i.e., they should be in long-term memory) because this facilitates learning of more complex material. I have experimented with allowing students to bring in a single index card with any information they choose to write, but I’ve found that on average it advantages the stronger students over the weaker students in my classes, so I’ve discontinued that approach.

In my general chemistry classes this year, I have a mixed approach. Students have three take-home midterm exams which are closed-book and timed. After the timed exam is over, they are allowed to consult their notes, textbooks, classmates, and annotate their exam in a different color. Regardless of how the students actually do, they receive full credit for the exam. The three exams are altogether worth 15-20% of the class grade (instead of 50%) but now the closed-book and timed final exam is worth half of the class grade (instead of a third). So far I think this strategy is working. In the jargon, I have made a sharper distinction between formative and summative assessment in the exam grades.

What prompted my thinking about these issues again is an article published last month (Rummer R, Schweppe J and Schwede A (2019) Front. Psychol. 10:463). The title of the article is “Open-Book Versus Closed-Book Tests in University Classes: A Field Experiment.” The abstract is shown below.

It’s a small study and the main conclusion can be found in the abstract – preparing for closed-book exams fosters long-term memory encoding. You can read the paper for yourself to draw your own conclusions as to how applicable this study might be to your particular situation and subject matter. One useful feature of the paper is that it provides extensive references for anyone interested in what other studies have been performed prior to this study, thus giving you a quick overview on what is known so far.

The authors carefully go through the limitations and interpretations of their study. Aspects of cognitive load theory show up in the article, and I find their arguments plausible. Here’s a snippet: “Thus, the finding that participants learning with a closed-book practice test outperformed those learning with an open-book practice test seems to support the theoretically highly relevant assumption that the testing effect is due to retrieval practice… Another indirect effect of the closed-book test concerns the preparation and repetition of the learning matter at home. Since the content of the learning materials was highly relevant to the students… [this] resulted in more extensive study at home in the closed-book group than in the open-book group.”

For many years I’ve made use of coupling ‘retrieval practice’ to the ‘testing effect’ by having many short 1-5 minute quizzes at the start of my general chemistry classes. These are low stakes enough so that students aren’t overly stressed, but provide enough motivation for students to keep up with the material and strengthen those learning connections they’ve been (hopefully) making. My quizzes are closed-book and feedback is immediate. It’s been helpful to me not just to apply a practice because it seems useful, but also to explore the theoretical underpinnings for its utility – this helps me explain to the students why I employ a particular practice as an instructor to help them learn. By and large I think my students this year ‘grok’* what I’m trying to do with the take-home exams and why it is important to actually do them closed-book and timed. And so I keep reading these articles even if they aren’t about chemistry specifically.

*Not a technical term unlike ‘retrieval practice’ and ‘testing effect’.