Heuristic Shield

In the previous post I discussed the example of a bonfire to counter students’ misapplying electrostatics when explaining why cations are smaller than their neutral atoms. Why did students misapply electrostatics in the first place? Because all of us often fall back on heuristics to explain phenomena.

There’s however a problem with the bonfire example, so let me repeat the relevant portion of the quote (not mine): A possible analogy to teach the nuclear attraction for an electron is to say that it is similar to the heat one receives from a bonfire—this is dependent on how big the bonfire is, the distance one is away from the bonfire, and whether one is blocked (screened/shielded) from the bonfire, but is independent of how many people are present at the same distance away from the bonfire.

The problem I’ve been pondering is how students interpret the words blocked or screened or shielded. I certainly use the phrase electron-shielding when discussing this topic in G-Chem, and the textbooks use it too. But now I’m suspicious as to how students conceptualize this idea. When used as a heuristic, it’s hard to imagine that the word shield doesn’t invoke the picture of a shield. Bet you visualized one too!

This line of thought is fleshed out carefully by Taber (Chem. Educ. Res. Pract. 2003, 4, 149-169). In our effort to provide pictorial chemical shorthand for students, we come up with terminology such as electron-shielding. What we mean by this, and I will quote Taber’s precise language, is “give rise to a repulsive interaction that partially cancels the nuclear attraction”. But then Taber continues with a key observation, “… although once the shorthand is accepted the notion of shielding may become reified and used without conscious awareness of its derivation.”

Here’s the problem. While I may have been careful in the way I introduced this explanation (I’d like to think so, but pondering the issue gives me pause), it’s likely that my students reify the shield by imagining a literal shield when they trot it out as an explanation, i.e., electrons closer to the nucleus literally block electrons further away from ‘experiencing’ the positive nuclear charge. If anything, the bonfire explanation will strengthen such a notion – the folks closer to the fire literally block me from experiencing as much heat! An analogy to counter one problematic heuristic reinforces another problematic one.

One might argue that if a heuristic helps students ‘explain’ the correct observations, what harm is there? After all, they’re getting the chemistry right even if the underlying physics is wrong or misleading. But then what kind of an explanation is the literal shield that defies physics? A magical one? That’s what I will ponder next.

Knowledge in Pieces

One part of my job is “helping students understand that they leave each class with Swiss cheese knowledge – it looks solid but it is full of holes.” That’s #4 of Hoyle’s Top Ten, an insightful list that I regularly revisit.

I was reminded of the Swiss cheese analogy today while reading “A Friendly Introduction to Knowledge in Pieces: Modeling Types of Knowledge and Their Roles in Learning” by Andrea DiSessa. I was cued into this article having read a different article related to Ionization Energy – more on that in a moment – and that’s how going down the rabbit hole works.

The article is aimed at math educators but it also provides some interesting examples in physics; since the Knowledge in Pieces (KiP) framework began in physics education. KiP attempts to bridge the gap between theorizing about how conceptual change and the actual practice of learners as they work their way through a problem. KiP assumes that learning is a complex and messy process, taking place over multiple scales and timeframes. It’s also one of the few frameworks that considers the value of what others might consider folk-science intuitive thinking, because such ‘primary’ approaches are unlikely to be easily discarded and for good reason. Instead of just labeling such an approach a ‘misconception’, why not leverage it to good use by providing more examples and varying contexts?

Several things that jumped out at me: KiP assumes that naïve knowledge is both conceptually rich and productive. This doesn’t mean it gets things right all the time – there are many examples of intuition leading one astray especially when encountering non-intuitive ideas in science. There are plenty of examples in physics and chemistry, which has led to increased use of concept inventories in introductory classes at the college level. The richness of this naïve knowledge means that it is interconnected with many other intuitive experiences, hence context matters. DiSessa emphasizes the point that as students experience conceptual change as they learn, there are also contextual changes. This is why we often think a student has learned the right concept when they demonstrate it in one context, and then be flabbergasted when they fail to apply similar reasoning in another context moments later.

One of the broad intuitions that students (and even instructors) have is some notion of balance. Things sorta balance out, somehow. Here’s an example that shows up in general chemistry: Students can easily tell me that a cation is smaller in size than its neutral atom. When asked to explain why, they will reason thus – when an electron is removed from an atom, the number of protons remains the same but the number of electrons has decreased by one. Hence the positive charge of the nucleus is now spread out over fewer electrons so it can attract them more strongly, pulling them closer to the nucleus, and thus reducing the size of the cation.

Now, if you read the explanation too quickly, you might nod your head in agreement. While I’d like to think I haven’t consciously used this explanation, it makes me wonder how careful I am when I’m helping students formulate the argument. Most of the argument works except the part where the student invokes the principle of balance – with one less electron, things need to balance out so the nucleus attracts the remaining electrons more strongly. (What actually happens is that the electron-electron repulsion is reduced.) I was reminded of this example reading a paper on student misconceptions related to Ionization Energy by Daniel Tan and co-workers (Intl. J. Sci. Educ. 2008, 30, 263-283). To counter the misleading intuition, the paper actually provides an excellent counter-example: the bonfire! I’ll quote the paper.

To challenge the common notion that the nucleus gives out an amount of force or attraction to be shared by the electrons, teachers need to emphasise the basic Coulombic principles. A possible analogy to teach the nuclear attraction for an electron is to say that it is similar to the heat one receives from a bonfire—this is dependent on how big the bonfire is, the distance one is away from the bonfire, and whether one is blocked (screened/shielded) from the bonfire, but is independent of how many people are present at the same distance away from the bonfire. This analogy may prevent students from thinking that electrons share the attraction from the nucleus. However, it does not take into account the equal and mutual attraction of the nucleus and the electron, as well as the repulsion between electrons, so these have to be highlighted.

I think I need to start using this example in class to help counter the misconception that I’m sure many of my students would fall back on. A graphic illustrating said bonfire would probably help too! I’ve started showing the picture of a large thumb (with a crown) to remind the students that the octet rule is a rule-of-thumb! Otherwise, they invoke it as the explanation for all manner of things. They have knowledge in pieces, like Swiss cheese, but today I’m reminded of how much of my knowledge is also in pieces especially as I’m learning new things during my sabbatical.

Sixth Digit

I’m shocked it took me over four months to come across this article. My usual news sites somehow didn’t alert me! The article is open-access so you can read it for yourself.

While uncommon, I have in my lifetime met at least two people with six-fingered hands. But in both those cases, the extra fingers were non-functionary appendages that were much smaller than the normal fingers. And just a couple of months ago, I was having a conversation with my 11-year-old nephew where I described this phenomenon. Clearly, I hadn’t been reading the latest science, and was just relying on my rather limited anecdotal experience. Humph! What non-scientific behavior on my part.

Turns out there are people who have functional and independent sixth fingers. When I first saw the picture above (in the paper), my automated system blared the message “photoshop”! Even now when I look at it, part of me still thinks it looks like a photomanipulation, but I doubt this article would have made it to Nature Communications if it was faked. The extra finger in this case is a supernumerary. That’s a fancy way of saying “in excess of the normal number”. But it sounds super!

The subject was trained to single-handedly manipulate the controls of a video game which would have taken a regular five-digit-handed fellow the use of both hands. Now that’s a truly single-handed feat. Okay, okay, I know that I’m just looking for punny excuses. But how often do you encounter something seemingly alien. It makes me think that TV or movie CGI folks can collaborate with scientists to better understand how six-fingered aliens exhibit surpassing hand-manipulative skills. Would related everyday objects look different in a world of sixth digit aliens? What about seven digits? Come to think of it, whenever I’ve watched sci-fi, you might have weird-looking aliens with different appendages, but they all seem to still operate in an environment built for homo sapiens, even when they’re not on or invading planet Earth. I see some room for a new vision of creativity here – moviemakers, take note!

Can’t say that we chemists do any better. When imagining the microscopic world, I think of blobs bumping into other blobs. Sometimes new blobs are made. Sometimes blobs rearrange themselves. Maybe I can come up with something visually more exciting – I’m sure the students would appreciate it. The last time I remember doing something remotely exciting along these lines was end of Spring semester when describing polydentate molecules such as EDTA. Cation scavengers! Maybe I need to figure out how to bring molecular machines into my classroom discussion. Call it nano-something. And no, I don’t know where this blog post is going.

What The Photon?

Zany is how I would describe Hitchhiker’s Guide to the Galaxy. I read the first installment a long time ago, but recently found the “trilogy of five” at the library. I think this is also known as the Omnibus version. The cover features what I think is the large head of Marvin the Android Paranoid and there’s also a “Don’t Panic” button.

The original Hitchhiker is the first part (#1) of five. The following four parts, in order, are:

·      #2 The Restaurant at the End of the World

·      #3 Life, the Universe, and Everything

·      #4 So Long, and Thanks for All the Fish

·      #5 Mostly Harmless

I’m about two-thirds through the book, and #1 is the best by far. #2 is still quite good. #3 couldn’t hold my attention and I gave up partway; I thought it was poor, #4 seems mediocre so far, but I’ve only just started. Hard to say. And we’ll see if #5 is mostly harmless or if I simply give up.

What makes Hitchhiker (#1) work? It’s a nutty, crazy, roller-coaster of a story, throwing one thing after another at you, the reader. The premise begins with a seemingly ordinary Englishman, one Arthur Dent, suddenly finding out that his home is about to be bulldozed to make way for a highway bypass. Very improbably, the same fate is about to befall Planet Earth. But it so happens that Arthur Dent has a friend named Ford Prefect, a strange friend with a rather improbable sounding name. Ford (not his real name) turns out to be from Betelgeuse and helps write entries for a Universal bestseller named The Hitchhiker’s Guide to the Galaxy. Ford will help Arthur hitchhike his way through zany adventures with far-fetched elements thrown together in what seems like a ridiculous mix.

Again, what makes the story work? The key feature, in my opinion, is that the story hinges on improbability. A spaceship will appear partway through, equipped with an Improbability Drive that smashes previous technology for travel exceeding the speed of light. How much better to explore the far-flung galaxy! But using the improbability drive requires improbable events, and maybe vice-versa, and maybe there’s an improbably explanation to how it all really works in the story. Sure, there are ridiculous parts; but there are also very clever parts in the story. Improbable, perhaps, but clever. And that’s what gives #1 it’s charm!

One clever invention is the Babel fish. You can even order T-shirts with the design shown below (from teepublic.com). The Babel fish is a universal translator; perhaps it should be called the Anti-Babel because it reverses the breakdown in communication from people speaking different languages while trying to construct the Tower of Babel (see The Bible, Genesis chapter 11). I vaguely remember using babel-1.0 in a Unix environment to ensure language interoperability between C and Fortran; that was some twenty years ago. In today’s world with Google Translate and the latest apps, your cellphone performs almost the same functions as the Babel fish. Our tech is not perfectly streamlined but at least you don’t have to put a fish-like organism into your ear.

Eeeeks! Put a fish in your ear? According to Hitchhiker: “The Babel fish is small, yellow, leech-like, and probably the oddest thing in the Universe. It feeds on brainwave energy received not from its own carrier, but from those around it. It absorbs all unconscious mental frequencies from this brainwave energy to nourish itself with. It then excretes into the mind of its carrier a telepathic matrix formed by combining the conscious thought frequencies with nerve signals picked up from the speech centres of the brain which has supplied them. The practical upshot of all this is that if you stick a Babel fish in your ear you can instantly understand anything said to you in any form of language. The speech patterns you actually hear decode the brainwave matrix which has been fed into your mind by your Babel fish.”

Many folks who haven’t read Hitchhiker, have experienced being annoyed by references to the Meaning of Life. What is the meaning of life? Apparently the answer is 42, at least according to a super-duper computer which took millions of years to crank through its calculations. This doesn’t resolve anything because apparently the question was ill-posed. Thus another gizmo was created to figure out what the question should be. Asking the right questions seems to be universally important.

And like any stereotypical sci-fi today, time-travel must be involved. It allows one to enjoy the spectacle that is #2, the Restaurant at the End of the Universe. When you first read the title, you’re thinking space instead of time. You’re thinking of going to the edge of the universe, to some far-flung outpost, to enjoy some rare (and hopefully amazing) food. But the End here is about time. The restaurant in question is an extravaganza experience that allows diners to view the end of the universe – the Big Crunch’s closure to the Big Bang’s opener – fireworks and all. You’ll need to time-travel forward to have a sumptuous meal and drinks while you watch the spectacle. Then time-travel your way back. Expensive Excursion completed!

Your legitimate response to all this zany improbability might be “Egad!” if you were an Englishman like Arthur Dent. Or perhaps “Riddikulus! It’s all just an illusion.” Less charitably, you might quote initials such as “W.T.F.” but in universal hitchhiker faster-than-light-speed travel, you would appropriately respond “What The Photon?” Yes, even those who have seen almost everything in the galaxy can still be surprised. But Don’t Panic. New light is shed. Photons show up. What the Photon? Indeed.

P.S. For a different kind of zany, elements of time-travel included, there’s the Jasper Fforde Thursday Next series.

The Mysterious Benedict Society

No, it’s not a secret cult from a religious order. No Benedictine monks are involved. A Monk Building is involved on occasion. And there are mysteries to be solved.

The Mysterious Benedict Society, written by Trenton Lee Stewart, is a children’s trilogy featuring a tiny group of talented children thrown together in a seemingly mysterious way. A newspaper ad reads: “Are you a gifted child looking for special opportunities?” While many try, few are chosen.

The book begins with an orphan named Reynard, who has special talents, but does not fit in with the other children in his orphanage. The mysterious newspaper ad brings him, together with three others, into the orbit of the eccentric Mr. Benedict who needs their help for a mysterious special task that he thinks only they can accomplish. Reynard and his friends form the Mysterious Benedict Society, and combine their complementary talents to solve the mystery at hand.

While there are some similarities to the Harry Potter series, the Mysterious Benedict Society probably shares more in common with A Series of Unfortunate Events, both in tone and in whimsy. Like many other children’s “adventure novels” where a group of kids must band together, it’s about friendship and trust and looking out for your buddies. There are interesting puzzles to be solved, quirky characters, and hazards abound for the children. Help comes from unexpected quarters, and the adventures quickly pick up the pace keeping you the reader interested in what will happen next.

I’ve been purposefully vague in my descriptions so as not to reveal the plot. There are some interesting storylines involving mind and memory control. No scientific details are provided, although complex computer-attached devices are involved. I’ve previously speculated on ultrasonic brain control, and related to the Harry Potter spells, the workings of legilimency and memory charms. I find these topics interesting, not because I’m interested in mind-control, but because they intersect with teaching and learning. Our brains, our minds, how memory works, how we learn difficult concepts, how and why we forget things – these are all fascinating to me as an educator.

While I like the first book best because the characters are being first introduced, all three are good and of similar quality and pace. My niece introduced them to me a month ago, and I enjoyed reading all three back-to-back over the last several weeks. I’m surprised they haven’t been made into movies yet given the first book was released back in 2007, although an internet browse suggests a TV series is in the works. If you’re looking for fun and clean children’s fiction, I’m happy to recommend The Mysterious Benedict Society.

A Hogwarts Tenure Letter

Would Professor McGonagall get tenure at Hogwarts? If you’re familiar with the Harry Potter series and you’ve heard about the tenure travails of academia, there’s a hilarious excellent article in McSweeney’s this week: “Minerva McGonagall’s Letter to the Tenure Committee”.

Read the article! The rest of this blog post can wait.

Unlike McGonagall, I’m just a chemist with no ability to transfigure myself or any other object. I can transform one chemical substance into another in lab. But as a computational chemist, I don’t handle actual chemicals often, unless I’m teaching an introductory chemistry lab course. Even then, it’s mainly supervisory work to ensure students use good technique and aren’t endangering themselves.

Come to think of it, you don’t see Professor Snape handle potions ingredients either. In Potions class, he supervises the students, commenting sneeringly on the techniques of Gryffindor students. (I hope I’m not a sneering instructor.) In the books, Snape’s potion-making is usually in secret – wolfsbane for Lupin, something to slow down the poison in Dumbledore, and a series of potions (with a riddle) to protect the philosopher’s (sorcerer’s) stone. I don’t make any medications or antidotes for my colleagues; I don’t even brew beer as some of my fellow chemists might. Professor Slughorn, on the other hand, has at least on one occasion made potions for his class. I have performed a number of experimental demos in class, so maybe that counts.

Like McGonagall, I have served on many committees, although my service ramped up significantly post-tenure. I have functioned in some of the roles that McGonagall claims, although certainly not all, and not simultaneously. I haven’t had to battle Death Eaters or support a student rebellion, thankfully. But I have lived on campus as resident faculty, experiencing its highs and lows. I didn’t have to deal with magical creatures, but I did have to get involved when a few students attempted to hide an illegal pet in my residence hall. Thankfully, I did not have to get involved in disciplinary procedures.

Teaching is what I love, and I think it’s what I do best. McGonagall is a no-nonsense yet clearly devoted teacher looking to the betterment of her students. I think she successfully makes the case for her teaching portfolio. On the research front however, she hasn’t published any papers, being way too busy with other duties. Nowadays, as institutions battle for name-recognition, research productivity has become increasingly important; and in some institutions, it overshadows all other aspects. I think this is unfortunate.

But perhaps tenure requirements at Hogwarts should not be compared to our tertiary institutions. The Hogwarts seven-year model is based on a British system which would roughly translate to the U.S. version of middle school, high school and pre-university. Tenure at such a school is usually earned after being a teacher for a three to four-year probationary period. Assessment on tenure is based on teaching, not research. So perhaps McGonagall shouldn’t have to discuss her research productivity or lack thereof.

How is teaching evaluated at Hogwarts? Except for the short reign of Dolores Umbridge, where teachers were observed and evaluated, there isn’t any mention of how teaching effectiveness is assessed. McGonagall’s letter cites ‘active learning’, and many of the Hogwarts classes seem to have strong practical/lab components; one unfortunate exception is History of Magic.

Could I get tenure at Hogwarts? Being non-magical, I highly doubt it. Even though my students might liken computational chemistry to a magical box that spits out numbers allowing you to interpret (or mis-interpret) all sorts of chemistry. Not to mention, my skills in wet lab as a mixer of chemicals is highly questionable. Potions-master, definitely not. Although I did invent a potion once for one of my classes. I’d like to think I have theoretical ideas about magic and perhaps I could teach a Magical Theory course, or write a potions textbook, but no schools of magic have come knocking. Oh, well. I can stick to what I’m good at, and thankfully I already have tenure.

Elemental Pagoda

I recently returned from my first trip to Japan where I enjoyed being sated by new sights, smells and sounds. (Below is a shot of the pagoda at the Senso-ji temple in Asakusa.) One highlight was the Tokyo National Museum where I learned why pagodas have five levels – it’s elemental!

Elements feature in the first class of my introductory chemistry courses. We discuss the evolution of thought that led to modern atomic theory, highlighting the almost two millennia digression of Aristotle’s influence in championing the classical four elements: Earth, Water, Air, Fire. Occasionally I relate this to the Platonic Solids, in itself an interesting side tale. Sometimes my students read a section of De Rerum Natura by Lucretius expounding that everything is simply Atoms and Void. But mostly I try to impress upon the students why atomic theory is a strange idea: Why would you think that all matter is made up of tiny discrete things you cannot see or sense directly? Aristotle won then, but Lucretius has had the last laugh. Before even taking my course, all my students already believe in the existence of atoms and the void.

The Japanese pagoda is interesting by seemingly blending ideas from both Lucretius and Aristotle, although it’s unclear what, if any, influence Greek ideas had on early Japanese ideas. The museum placards did not delve into the details, simply mentioning that the five levels relate to the five elements earth, water, fire, air, and void. Further internet browsing led me to this interesting website, where I learned that the gorintou (five-ring pagoda) is associated with the five elements. I recommend reading the website for more details; here are just a couple of my thoughts based on the picture below.

The order is interesting. The base is Earth, perhaps not surprising. There seems something foundational, perhaps earthy, about earth. Water is next. Rivers and lakes have a bottom made of earth, so earth supports water. Interestingly, Fire comes next, rather than Wind. I’d speculate that if the Greeks had a hierarchical tower, that Fire would be on top and Air (the equivalent of Wind) would be below. Void is the highest level in the gorintou. It seems to have connotations of space, ether, or out-there-ness. Is Void elemental in the same way as the other four? That’s also unclear.

The shapes are also interesting. The Platonic cube of Greek philosophy is similar to the gorintou cube. Cubes pack well. Earthy, perhaps. Water is a sphere, it rolls and flows. The Greek equivalent icosahedron may act similarly. Fire is triangular or pyramid-shaped in the gorintou, which is akin to the tetrahedron in Greek thought. Pointy and poky. It burns! On the other hand, there seems no correspondence between the half-moon of Wind and the octahedron of Air. I think it’s cool that the Void is designated a jewel-shape, although I don’t understand its significance. I can’t say I understand the others either; I’ve simply speculated.

In the Tokyo museum, I saw a few requilaries, containers containing relics, in the shape of a five-level pagoda. The ancient artifacts section also had five-level stupas, common in various parts of Asia. (Here’s one of my pictures below from the museum.) I hadn’t noticed the gorintou shapes until after reading the website explaining them, at which point my temple and shrine sightseeing had ended. But now I know what to look for, the next time I visit historical sites in Asia.