Abstraction

If I had read How to Bake Pi before my first college math course, I probably would have gotten a lot more out of it. Eugenia Cheng, a mathematician, gifted writer, and experimental baker, somehow makes the connection between abstract mathematics and real life. In the prologue, Cheng lists common myths about math. One that she encounters a lot: “You’re a mathematician? You must be really clever.” Here’s her written response.

“Much as I like the idea that I am very clever, this very popular myth shows that people think math is hard. The little-understood truth is that the aim of math is to make things easier. Herein lies the problem – if you need to make things easier, it gives the impression that they were hard in the first place. Math is hard, but it makes hard things easier. In fact, since math is a hard thing, it also makes math easier.”

I wish I had thought about math along those lines back in college. Having had a bunch of calculus under my belt pre-college, I was credited with two semesters of calculus and therefore placed into Real Analysis. The first half of the semester was spent on Proof and Number Theory. I had no idea what was going on. I did not understand the point of proof and the seemingly strange arguments being made for things that seemed “trivial”. Except they are not. But I only came to appreciate this later in life. Needless to say I did not take another college math course for credit. (I did sit in on Linear Algebra because I was told it was useful for a Chemistry major, although not required.)

An early chapter in How to Bake Pi is the topic of Abstraction. Cheng describes abstraction as a blueprint. By ignoring some details, one can focus on the key ingredients to bake one’s pi. How does one do that? By looking at the similarities between different things. It also acts to de-clutter one’s thought process. Cheng says it can feel uncomfortable because one is “stepping away from reality for a bit” but it pays dividends when it comes to solving real-world problems as the complexity is added back bit by bit.

Cheng gives many examples of abstraction, connecting the real world to mathematics. My favorite is Road Signs. She writes: Road signs are a form of abstraction. They don’t precisely depict what is going on in the road but represent some idealized form of it.” She shows a couple of road-signs, and you can figure out what they are even if you have not encountered them often.

While actual bridges and mooses/meese might not look like their stylized images, “the benefits of this system are clear. It’s much quicker to take in a symbol than read some words while you are driving. Also it’s much easier to understand.” However, if you were to encounter a more abstract sign such as the “No Entry” (shown below), would you know what it was if you hadn’t learned it beforehand? If you do know it, however recognition is simple and immediate. Also, you’ll tend to encounter these a lot, particularly in a city center with many one-way streets. The principle here: Abstracting that which is common allows you to take in other things that require some degree of complexity and cognition. Driving in a news city can be complicated.

All this reminds me about the use of symbols in chemistry. I am going to quote Cheng but substitute “math” with “chemistry” and her explanation still works well. “Once you know what they mean, the symbols are quicker to take in, and you can reserve your chemical brainpower for the more complicated parts of the chemistry you’re supposed to be focusing on. It also makes the chemistry easier to understand across different languages – it’s surprisingly easy to read a chemistry book in a language you don’t know.” Actually that last phrase isn’t as true for chemistry as it is for math, but it’s somewhat true. As an undergraduate, I had to look up a German paper for an organic synthesis procedure. I was actually able to figure out a chunk of it, and filled in the gaps on names with the help of a German-speaking friend.

In the same chapter on Abstraction, Cheng makes a very interesting point about teaching. It’s all meta. She introduces this first by suggesting the building of a machine to do something rather than doing it by yourself, especially if it is a tedious process that will need to repeated frequently. But “in order to build [such] a machine to do something… you have to understand that thing at a different level. It’s like giving someone directions. When you walk somewhere you know well, you don’t really think about exactly what streets you’re walking on… you [go] instinctively. But when you’re telling someone else how to get there, you have to analyze more carefully how you do it, in order to explain it.” That’s why all teaching is meta. I’m trying to help my students work through a process in their minds, but I can’t think for them. Somehow I have to translate the process through designing appropriate activities and exercises, to get them to see and think chemically the way that I do as an expert in the field. This is not easy. Even more so as students may have a wide range of different misconceptions they have picked up along the way before showing up in my class. It keeps my job interesting and keeps me creative!

I’m only a quarter way through the book, and I’m looking forward to more insights! Meanwhile I end this post with an excerpt from the chapter on Generalization. If this sort of writing tickles your fancy, I highly recommend How to Bake Pi. And get yourself a pi plate!

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Here are [some] “why” questions with various levels of answer. You can ask yourself whether you find each answer inadequate, satisfying, or over the top, to see what sort of level of abstraction you like.”

Question: Why does anyone use a three-legged stool?

a) Because a three-legged stool is more stable than a four-legged stool.

b) Because if you try and put four legs down on the floor, one of them might stick up a bit more than the others, leaving a gap between it and the floor, which means the stool could wobble.

c) Because given any three points in 3-dimensional space, there is a plane that goes through them all. Whereas given any four points, there might not be a plane that goes through them all.

The Hemodote Potion

I am now in the home stretch of my semester with just three more weeks of classes before Finals week. Today, in my non-majors chemistry class we discussed the details of the final project: Designing a Magical Potion. To prepare the students for the project, I had written a Prologue to the project seven weeks ago, and I make occasional references to potions in class sessions. One class was dedicated to talking about drug design, after the students had learned about protein structure and intermolecular forces.

A couple of weeks ago I wrote a full example of what a Final Project would look like. Thus, I invented the Hemodote Potion. Along with this sample, I provided detailed parameters for the project, and in class today we discussed and agreed upon the final due date, and the mechanics of what, when and how to provide me information on their projects. I had included a question on the previous problem set asking the students to list two potions they might invent with a one-paragraph of justification for each.

In class we divided into small groups and batted around some initial ideas of the science and chemistry that needs to be considered, before having a whole-class discussion. Cure for cancer and levitation potions are inherently challenging, but we came up with some ideas for camouflaging, memory-enhancement, skin anti-aging, and more. The best suggestion from a student, which I would never have thought of myself, was a potion that magically and non-toxically dissolves the skin or peel of vegetables and fruits. Just pour the potion on the desired object and moments later you are ready to eat (or cook) the food item!

Here are the required components for the project (per my instructions to the students):

Think of your project as adding an entry to a Potions textbook. Your entry must contain:

1. Name of your potion and the names of the authors contributing to the entry.

2. Background information on why this is a useful potion. Key features of the active chemical substances and how they might interact should be described here.

3. Design Considerations: A detailed section that describes each of the important substances that will be included in the recipe. This is where you justify the proposed chemical interactions you hope to achieve, and how this might interact with the larger scale organism or object to which the potion is applied.

4. Amount Considerations: This is where you show calculations estimating how much of each active substance will be needed.

5. A Detailed Recipe as you might see in a cookbook.

6. A list of potential side-effects or cautions for your potion. This is not just a generic list but is tied to the effects of the specific potion you have proposed.

7. References

There are also certain requirements such as some number of chemical equations and structures, minimum number of active ingredients, and calculations involving masses, moles and molarity. No specialized reagents can be used directly. They must either be synthesized or extracted from a magical creature or plant. Two different font colors must be used to highlight the “creative” parts of the project and the “science-y” parts.

Hemodote is a powerful easy-to-use liquid antidote against hemoglobin poisons such as cyanide and carbon monoxide. I had sketched out my initial ideas in a previous blog post, but here is the more detailed version of the “Design Considerations” section in the full example provided to the students. I have made minor edits removing the figures, and I did not renumber the references since this text is about one page of a four-page document. I have a detailed recipe with calculations and amounts, but since I’m taking on the mantle of an alchemist, I will keep my recipe a secret for now. (My students have seen the full recipe.) Except I can’t resist telling you that I have good reason to believe that mincing and boiling the liver of the Blue Behemoth will provide one of the active ingredients. Enjoy!

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To counteract hemoglobin poisoning, there are two general approaches: (A) Introduce substances that bind cyanide or carbon monoxide more strongly compared to hemoglobin. (B) Provide an infusion of oxygen to reduce or prevent cell death due to the poison.

Two kits used to treat cyanide toxicity are Cyanokit and Nithiodote.⁶ The active agent in Cyanokit is hydroxocobalamin, a molecule closely related to hemoglobin and Vitamin B12.⁷ Hydroxocobalamin actively binds cyanide more strongly than hemoglobin, and thus can scavenge the cyanide away freeing the hemoglobin to bind to oxygen. The active center in hydroxocobalamin is a cobalt ion instead of an iron cation in hemoglobin. Cyanide displaces the hydroxide and binds strongly to the copper center. A natural source of hydroxocobalamin comes from eggs, dairy, and meat.

Nithiodote contains sodium thiosulfate (Na₂S₂O₃) as an active ingredient. This compound can be prepared from mixing sulfur with concentrated lye (or sodium hydroxide, NaOH).⁸ In the presence of Na₂S₂O₃, a natural enzyme in our bodies, rhodanese, converts cyanide into thiocyanate (SCN^-).⁹ While both kits require intravenous transmission in the Muggle world, acquiring the equivalent of hydroxocobalamin from the appropriate magical creature should suffice for an oral potion.

The treatment for carbon monoxide poisoning is to obtain an oxygen infusion.¹⁰ This will also help in cases of cyanide poisoning. Finding a hyperbaric oxygen chamber or an oxygen tank to breathe from can be challenging when the cells in your body are being rapidly depleted of oxygen. One way to quickly deliver oxygen is by using hydrogen peroxide (H₂O₂). It rapidly decomposes into H₂ and O₂ because of the weak O–O single bond in H₂O₂. However H₂O₂ cannot be consumed directly because it is a very strong oxidizing agent and will damage the cells in our body.

Recent scientific work on delivering oxygen to cells in our body is to enclose calcium peroxide (CaO₂) in a polycaprolactone polymer casing.¹¹ Calcium peroxide can be synthesized by heating slaked lime (calcium hydroxide) with hydrogen peroxide.¹²

Ca(OH)₂  +  H₂O₂  -->  CaO₂  +  2 H₂O

Caprolactones are cyclic esters and can be found naturally in flower aromas and insect pheromones.¹³ Using caprolactone as a monomer to form polycaprolactone requires catalysts that are specialty chemicals not found in nature but synthesized by chemists.¹⁴ However, extracting caprolactones from an appropriate magical insect or plant should also provide the catalysts needed to form an appropriate polycaprolactone that will encase the CaO₂ for delivery into the bloodstream.

[6] http://emedicine.medscape.com/article/814287-treatment (Cyanide Toxicity Treatment & Management)

[7] https://en.wikipedia.org/wiki/Hydroxocobalamin

[8] https://www.youtube.com/watch?v=J_IboipV5A8 (Preparation of Sodium Thiosulfate)

[9] https://chemm.nlm.nih.gov/countermeasure_sodium-thiosulfate.htm (Reference to “Effects of thiosulfate on cyanide pharmokinetics in dogs”)

[10] http://www.mayoclinic.org/diseases-conditions/carbon-monoxide/basics/treatment/con-20025444 (Carbon Monoxide Poisoning Treatment)

[11] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3708668/ (Oxygen Releasing Biomaterials for Tissue Engineering)

[12] https://en.wikipedia.org/wiki/Calcium_peroxide

[13] https://en.wikipedia.org/wiki/Caprolactone

[14] http://pubs.rsc.org/en/Content/ArticleLanding/2009/CS/b820162p (Synthesis of polycaprolactone: A review)

Thinking in Pictures

The magazine Nautilus has a series on Consciousness this month. I was drawn to an article titled The Kekule Problem by Cormac McCarthy. The late Friedrich August Kekule was a famous organic chemist, while Cormac McCarthy is not a chemist of any sort, as far as I know. Kekule is known for his elucidations of chemical structure. He was also a pioneer in building the field known as theoretical chemistry (I’m closely related as a computational chemist). But he is best known for elucidating the structure of benzene, in a Eureka moment, by dreaming of a snake eating its own tail. At least that’s how the story goes.

Where did Language come from? That’s the root question McCarthy is attempting to answer. He has an intriguing and speculative hypothesis, rooted in how the unconscious “thinks”, not in words but in pictures. This he calls the Kekule Problem. McCarthy begins with a question: “Why the snake? That is, why is the unconscious so loathe to speak with us? Why the images, metaphors, pictures?”

We think that we think in words, but McCarthy suggests that the “actual process of thinking… is an unconscious affair.” Language is a very useful tool in posing problems and explaining them, asking questions and answering them, but it is a sign-posting tool – one that we use as a breadcrumb to mark our trail. McCarthy discusses evolutionary ideas of language, making comparisons to other biological evolutionary processes. But he still feels that nagging questions remain, perhaps even ones that cannot quite be put into words.

Could dreams be the gateway into the process? McCarthy writes: “Of the known characteristics of the unconscious its persistence is among the most notable. Everyone is familiar with repetitive dreams. Here the unconscious may well be imagined to have more than one voice: He’s not getting it, is he? No. He’s pretty thick. What do you want to do? I don’t know. Do you want to try using his mother? His mother is dead. What difference does that make?” This is, of course, a caricature personifying the unconscious speaking in a language and using words. But McCarthy is a writer, and that’s how he communicates this idea to us. Although if we were in Star Trek world, perhaps a Vulcan mind-meld may achieve the wordless communication.

As to the evolution of language: “[Language] would begin with the names of things. After that would come descriptions of these things and descriptions of what they do. The growth of languages into their present shape and form—their syntax and grammar—has a universality that suggests a common rule. The rule is that languages have followed their own requirements. The rule is that they are charged with describing the world. There is nothing else to describe.”

I’d like to ask John McWhorter what he thinks about this. Three weeks ago I read The Language Hoax, which, in my opinion, thoroughly and successfully debunks the popular and speculative versions of the Sapir-Whorf hypothesis. An example of such Whorfian thinking is that if a language has different words for the color blue, speakers of that language physically perceive blues differently. Thanks to The Arrival movie, sci-fi has run with this idea and created a masterful narrative of dreams, aliens, and the blending of the conscious and unconscious in a time-travel story. It’s very clever and very effective. McWhorter discusses why such ideas are so popular despite evidence against them, and his book was written before the movie was released. He has an even greater uphill task now.

McCarthy discusses the idea that the unconscious “thinks” or narrates in pictures. Pictures have the advantage of simplicity-in-complexity. A picture is rich in structure and content, and can potentially be recalled in their entirety much more easily than an essay of a thousand words. “The log of knowledge or information contained in the brain of the average citizen is enormous. But the form in which it resides is largely unknown. You may have read a thousand books and be able to discuss any one of them without remembering a word of the text.” The unconscious also resembles a parable, a tool for teaching and learning; it requires the conscious to chew and churn over to learn its secrets. Is this why oracles and prophets receive their knowledge in dreams?

I’ve been thinking a lot about pictures lately. They are indispensable, in my opinion to grasping the unseen world of chemistry at the molecular level. The representations are artificial in the sense that they represent models we can see and touch to get a “feel” for how chemistry works. Videos add a dynamic layer of representation – crucial for chemistry unless you’re at zero kelvin. Even then, the atoms still “move”. It seems fitting that pictures and representations help us handle the cognitive load as we learn the “language” of chemistry. Imagine trying to learn chemistry in a purely narrative text. I’m not sure I could.

But the image of the molecule is not the thing-in-itself. It simply provides a facet, a signpost, a breadcrumb on the trail. Kekule’s idea of the ring isn’t exactly what the pi-electrons are doing in benzene. We don’t really no what the electrons are doing, but we no they are delocalized, and we can measure a ring current. In General Chemistry, we teach students how to draw Lewis structures of molecules including their resonance structures. It is difficult to describe exactly what a set of “good” resonance structures represents – the true structure is not exactly the average of the set, even though I tell the students to sort-of-think in this way, at least when we discuss properties such as bond lengths, formal charges, and dipoles.

Perhaps magical spell-casting power is mediated through pictures. I’ve speculated about this, at least in terms of chemistry. The words themselves are perhaps simply an anchoring channel. They do not need to be verbalized, but maybe a word acts as a signpost in the organization of mental-thought power. Maybe thinking in pictures should be a key curricular piece in a Hogwarts education. I recommend “Arts for the Magical Arts”! My personal challenge (likely to remain unfulfilled): Can I draw a picture to represent the thousand words in this essay?

University Admissions: Arcane Edition

Over Christmas break, I read The Name of the Wind by Patrick Rothfuss, reviewed by my sister in a blog post last month. I enjoyed the book, especially the parts that delve into how magic works. Rothfuss has a more scientific approach to magic, which follows more consistent rules compared to the world of Harry Potter.

Given the recent long Easter weekend, I was able to binge-read the second book in the series, The Wise Man’s Fear. It was long – close to a thousand pages. In much of the sequel, the main protagonist Kvothe, takes some time off from his university studies to visit faraway lands and pick up new skills. This story arc is common in fantasy literature, but I personally found it less interesting. Academic that I am, I prefer the university-related parts of the story because they are often strewn with tidbits about how magic works.

Instead of reviewing the book in today’s post, I will just concentrate on one aspect of Kvothe’s world: university admissions. The process there is very different from the universities of our world. Are there lessons we can learn? Students at Kvothe’s university are training to be arcanists. The word arcane carries the connotation of mysterious, secret, and knowledge known by only a small select group. This is fitting for a school of magic. The alchemists of old, living in an era where magic and science blended, pursued arcane knowledge and were secretive about their “discoveries”. So technically, if I was a true arcanist, I should not share any part of the university admissions process. But I’m not, so here goes.

First, Admissions is not a single event. It takes place at the beginning of every school term. The main point of Admissions is to determine your school fees (often referred to as “tuition” here in the U.S.). The decision of how much a student has to pay is supposedly dependent on the performance of an oral exam held during the Admissions period that lasts several weeks. I say “supposedly” because while prior knowledge and talent is a factor, personal rivalries, politics, and idiosyncracy also enter into the process.

Here’s how it works. First the student draws an “admissions tile” by random lottery indicating the day and time of his/her oral exam. If the student feels that (s)he needs more time to prepare for the exam, there is a bustling marketplace to trade admissions tiles for money and/or other favors. At the oral exam, the nine Masters of the university (equivalent to Professors) take turns to ask you any question(s) they desire. Ideally, they take into account your level of learning. Some do. But if you have offended a Master in some way, you are likely to be asked ridiculously difficult or impossible questions. On the other hand, a Master trying to help you out might lob some standard or relatively easy questions. A Master may even choose not to ask you any questions. After all questions have been asked, the Masters determine the school fees for that term. If you can pay it by the end of the admissions period, you continue. If not, you can take a leave of absence or even drop out. There is no negotiation by the student. It’s unclear if there is an appeal process.

In a perfect world, with wise Masters who cared about student-learning, and who didn’t stoop to politics, bitter rivalry, personal favors, or irrational idiosyncracies, one would expect that school fees would be set fairly taking into account ability to learn magic and ability to pay. My reading suggests that the decisions are not totally meritocratic and that financial need is taken into account. And the story wouldn’t be as interesting without the politics and rivalry. No mention is made of how much needs to be collected from admission fees to keep the university running. Perhaps a truly talented arcanist can turn base metals to gold, so there is no need. Or perhaps no one has successfully made a true philosopher’s stone.

The idea of tying admissions each term to satisfactory progress isn’t a bad idea. But it’s not novel. Most universities have some rule where a student finishing a term below some GPA cutoff goes on academic probation. A failure to get grades back up may result in the student being asked to leave. I like the idea of oral exams that include my fellow examiners for a more holistic approach, but this could only work if the number of students was relatively small. A small rich exclusive college could potentially do this. Tying school fees to performance is trickier, but not unheard of. Merit-based scholarships do a similar thing. Need-based scholarships help to offset the costs for capable students with only modest financial support otherwise.

Having an oligarchy of “experts” decide on the fees? I don’t know what qualifies the Masters to do this – they could certainly test for academic competency in their subject area, but how does one weigh this against the financial need of the student and the economic needs of running the university? This looks crazy today, but one to two hundred years ago when many small colleges were first started, there were a small number of faculty-administrators who taught the classes but also ran the institution. The increasing size and complexity of tertiary institutions has forced a division of labor, perhaps for reasons of efficiency. Perhaps there isn’t really anything arcane about admissions to the Arcane University. It mirrors what we might have done in a different era although it looks strange today.

Revisiting Johnstone's Triangle

In an earlier post discussing the heavy cognitive load imposed in learning chemistry, I described the ways in which practicing “expert” chemists fluidly move among the macroscopic phenomena, microscopic atomistic models, and chemical symbols. On the other hand, the “novice” student attempting to wrap his or her brain around all this three-legged stool of chemistry is a monumentally difficult task. This “iron triangle” problem was articulated by Alex Johnstone many years ago in a series of articles. Chemical educators often refer to it as Johnstone’s Triangle.

Participating in events with a science education expert in March led me to revisit Johnstone’s triangle. In today’s post I will highlight two papers, one is a reflection by Johnstone with a provocative title: “Teaching of Chemistry – Logical or Psychological?” that kicked off a new journal (Chem. Educ. Res. Pract. 2001, 1, 9-15). The other by Keith Taber revisits the Johnstone Triangle with some new insights that usefully refine the model (Chem. Educ. Res. Pract. 2013, 14, 156-158).

First, let’s look at Johnstone’s article. It’s hard to beat the opening line of the introduction: “I should like to begin by recording a number of depressing facts about chemical education in the last forty years…” I won’t do justice paraphrasing, so here’s a snapshot of his “unpleasant observations”.

Point #1 is interesting. Were students almost everywhere opting out of chemistry back in the 1990s? Possibly, although my particular department has the opposite problem – we have too many interested students. In chatting with my colleagues from other parts of the country who are mostly at small liberal arts colleges, we are seeing stable numbers or growth.

Point #3 is depressing. Have chemistry educators “solved almost none of the problems in chemistry teaching”? I admit that students still have misconceptions with the mole, chemical bonding, and more – but I’d like to think I’m getting better at teaching these concepts and I’m seeing fewer problems. But maybe I’m deluding myself with anecdotal selective memory.

Point #6 is similarly depressing. “For normal daily living most people believe that they need no knowledge of chemistry, and maybe they are right.” In my Chemistry and Society class, I am constantly making reference to where chemistry shows up in the everyday lives of my students, but maybe I’m not really making any impact in changing that belief. Perhaps the students just humor me because I’m the instructor who “controls” their grade. Maybe subconsciously I know this, and perhaps I’m trying to sell the importance of knowing chemistry to a fictional magical community!

I have personally experienced Point #7 multiple times. “I was never any good at chemistry” and “I never understood [fill in the blank with some chemistry-related word]” come up all the time. I’d like to say I was never good at English Literature or Business Accounting or whatever else the other person might be good at, but I’m not sure what purpose this serves. In fact I’ve done this on several occasions, only for the conversation to drag into why chemistry is clearly more difficult than [insert other subject here]. But maybe my new acquaintance is on to something. Maybe chemistry really is more difficult conceptually than all these other subject areas. Maybe Johnstone’s Triangle is a cognitive killer.

Johnstone’s reflection is about how to harmonize the internal logic used by chemistry experts with insights from psychology into how novices learn, hence the title of his article. Much of what he discusses is material that I have previously read from the cognitive science literature – there’s information processing, perception, working memory, long-term memory, cognitive load, and how to make things stick. He then presents the chemistry issues illuminated by his famous triangle and its implications in teaching: the cognitive overload of working memory when all three aspects are used simultaneously at an introductory level. The learner has trouble finding a good way to properly embed this into long-term memory, at least in a way that makes conceptual chemical sense. Often the attempt results in the building of a framework riddled with misconceptions.

Johnstone makes some drastic curricular suggestions. Getting away from using hybrid orbitals to rationalize structure is one I wholeheartedly agree with, at least at the introductory level. He also suggest introducing the mole first only as an extensive property, and to make sure students really understand it, before moving to intensive properties such as concentration in solution (or molarity). Johnstone suggests starting at the macroscopic level with metals and not salts. This is one I hadn’t quite considered, but it has merit and I’m going to think about this a bit more when I rework my Fall semester General Chemistry I class sometime over the summer. (Read his article if you’re interested in his argument.)

Before I get to Taber’s paper, I’d like to quote another sobering zinger from Johnstone: “It may be that inorganic chemistry and the emphasis on acid/base titrations are historical artifacts of the time when chemistry was mostly analytical. One could be cynical and say that we keep stoichiometry in a prominent position because it is easy to set exam questions on it and easy for students to fail! A large number of practicing chemists never balance an equation or do a titration. We know this causes all kinds of trouble for students. Why do we persist with it and cause students such anguish?”

Taber revisits Johnstone’s Triangle but argues that the Symbolics corner is the triangle operates differently from the Macro and Sub-Micro. The problem with the triangle, Taber argues, is that these labels “lead to two areas of confusion: (1) confusion between two possible foci for the macroscopic: the phenomena studied in chemistry, and the conceptual frameworks developed in chemistry to formalise knowledge about those phenomena; (2) confusion over what is meant by a symbolic ‘level’ – how it fits in an ontology with ‘macroscopic’ and ‘submicroscopic’, and how it relates to notions of their being three different representational levels.”

The challenge to the student beginning to learn chemistry is that “the key macroscopic concepts only begin to make sense… in terms of the submicroscopic theoretical models… So in learning chemistry, students are indeed usually asked to coordinate learning about the subject at two very different levels: in terms of the observed phenomena reconceptualized at the macroscopic level, and in terms of the theoretical models of the structure of matter at the microscopic scale.” Taber has a very useful diagram (below) that illustrates this issue. The old Macro has two parts: events in the external world perceived as phenomena and macrosocpic level theoretical models. Both interact with the Submicro level in different ways.

Taber thinks, and I agree with him, that the Symbolics, while clearly useful and essential as a “language for communicating and representing chemical concepts”, are not on the same domain-level as the items in the diagram above. What the symbolic language does is facilitate between the macro and micro concepts through various forms of representation. Again, Taber provides a useful diagram (below).

Taber revisits the issues of information processing brought up by Johnstone with the following example. If you showed the following net chemical equation briefly to someone and then later asked for a recall, the results would vary immensely.

H₂SO_4(aq) + 2NaOH_(aq) --> Na₂SO_4(aq) + 2H₂O_(l)

This is a typical reaction you will see represented in an introductory chemistry class. In my first year of chemistry at the secondary school level, I had no idea what any of this meant. I would have a hard time recalling it if I had ten or maybe even thirty seconds to stare at it. Now, you can flash it to me for two seconds, and I can reproduce it perfectly. And this is not because I’ve used it many times as a teacher. You can pick a different acid-base reaction that I don’t commonly use and I can likely perform the same trick.

Reflecting on my own thought process, I would see an acid-base neutralization reaction to produce salt and water. My knowledge of salt solubility would allow me to figure out the states of matter. I can balance the reaction as I recall it. And I can figure out the chemical formulae of everything without explicitly memorizing what I see. In fact, all I need to know is the salt for any simple acid-base reaction (and if CO₂ gas is produced for carbonates and bicarbonates). Just seeing the “Na” and “SO₄” and recognizing the reaction type is sufficient for me to reassemble everything fluidly. My memory is hardly taxed by this activity.

Taber discusses the importance of scaffolding the material while paying close attention to the cognitive load we are demanding of our students. Effective teachers can help students build the necessary conceptual framework piece by piece by thinking carefully about how the chemistry curriculum is being “delivered” and reinforced. I won’t go into the details here but it’s an article well-worth reading, and one I should keep in mind as I continue to work on my teaching.

What Happens at Conference

“What happens at conference stays at conference.” That’s how I would paraphrase what Gordon Research Conference (GRC) organizers would say. The GRCs are small focused meetings typically with less than 200 participants. We eat meals together, purposefully, for more mingling and exchange of ideas. Presentations feature at least some cutting-edge results that are new and yet-to-be published, hence the call for confidentiality. On the first day, we’re told not to publicize the work presented at the conference. I’ve only been to a few GRCs, and none of them were in Vegas. In any case, I can’t tell you anything about them since what happens at conference, stays at conference.

This past week I was at a very different type of conference. The national American Chemical Society (ACS) conference is held twice a year and has ~15,000 attendees. The host locations are limited to places that have conference centers, usually in a downtown metropolitan area. The Spring 2017 meeting was in San Francisco. There was a national ACS national conference once in Vegas (I didn’t attend) but they were never invited back apparently because chemists aren’t good about spending money at the casinos and other tourist-hotel joints. Maybe chemists are an especially stingy group, because clearly Vegas didn’t make enough money off us.

The ACS does not have a confidentiality clause, so I can divulge what happens at this conference. The downtown conference center is actually not large enough to accommodate everyone so many of the conference sessions are spread out among the nearby hotels. Everything is within walking distance in San Francisco, and the weather was very pleasant. The main things at an ACS conference are: (1) oral presentations, (2) poster presentations, and (3) the Expo where vendors hawk their wares. But probably the most important part about these conferences is not the formal presentations, but the informal networking that goes on in hallways, hotel lobbies and local restaurants.

What you do at a conference to some extent is related to the stage in your career. As a young faculty member, I was very focused on the science. I went to as many talks as I could, walked the halls of the poster sessions, asked questions, and tried to learn as much as possible. I’d visit the Expo at least once to see if there was anything new and interesting. (As a computational chemist, the Expo tends to be less useful.) Nowadays, I spend my time differently. I still attend some talks and poster sessions, but a significant number of them are not in my research area – I’m simply interested in broader things that may or may not have any impact on advancing my career. Meeting up with friends, old and new, has become a much higher priority. Yes, we talk science, but we also just catch up on life. I don’t feel bad about missing some talks in lieu of meet-ups. I still give at least one talk every time I go to the ACS and my research students typically present posters.

One highlight of the conference: The faculty and students in my department who attend often try to have one dinner together as a group. I really enjoyed our dinner gathering in San Francisco. We have a great group of students! Being able to leisurely chat with them about life, family, food, and sometimes a bit of chemistry, is one of the most enjoyable things about being a faculty member! (I also enjoy consuming Asian pastries so having a good Chinatown nearby is a major plus! It’s a bit unhealthy but I did do a lot of walking and I refrained from overeating.) For the students I brought to San Francisco, this was their first national ACS conference, and I think they all enjoyed the new experience. The Expo is also a highlight for students looking to pick up chemistry swag. For me, it’s old hat and I’ve skipped the Expo the last five years.

The only drawback with going to a conference during the semester is the catching up on work responsibilities when you return. Colleagues covered my classes while I was gone (we have a great department culture in helping each other out), but I did have a lot of student work to read and grading to do. However, I managed to get a lot accomplished the last couple of days so I can enjoy a relaxing weekend. We’re in the middle of registration for next semester so I had lots of students coming by to talk about their schedule. My students and advisees also asked me about my trip so I was able to tell them a little about what happens at a chemistry conference. I spent a moment in my classes before my trip telling them about why scientists go to conferences. Hopefully, this gets some of them more excited about chemistry!

Changing Minds and Language

In the second half of March, I was part of a working group hosting a biologist who is also an expert in science education. Helping organize and attending multiple workshops and meetings made me think a lot about teaching and what I do in the classroom. It also prompted me to read a slew of chemical education papers. I’ll be sharing my thoughts on some of the readings in the coming weeks. Today I wanted to reflect on three things that stood out to me from the past two weeks.

The first has to do with crafting questions to change minds. I had recently thought more about how to ask questions as part of formative assessment, and started to apply some of these strategies in my classes. However, I feel that I’m still doing this haphazardly instead of systematically – although I expect to improve with time. At one of the workshops a couple of weeks ago, we discussed how to leverage asking questions into a “sticky” learning experience, particularly suited for important concepts we want to stick with the students.

I often ask questions at the beginning of class. These take two forms: Sometimes I have pop quizzes to assess whether students have understood material from the previous class or did the reading for the present class. Other times I use questions as a starting point to motivate thinking about the topic we will be covering. What I hadn’t considered was to carefully construct a single multiple-choice question pertaining to the topic that superficially resembled a quiz, but did not function as one. The question is used not primarily to assess student knowledge, but for students to assess their own thinking, and to see that as a result of learning something about the topic, that it is okay and perhaps even desirable to change one’s mind.

As part of her visit, our illustrious visiting professor and science education expert provided binders of material with data. While these were all in biology, they were mainly at the introductory level, and I was able to see many, many examples of different questions. Each of the questions showed the pre- and post-results of the student responses. They also included a narrative on why the faculty member chose the question (and the crucial multiple choice answers) and a reflection on whether they would reuse and/or modify the question. The questions and answer choices were crafted particularly to target misconceptions. Students have typically had some science in high school, and they remember or misremember a range of concepts that are also covered at the introductory college level.

When students see the pre-results, they see a diversity of opinion and this forces them to pay attention. Why did so many of my classmates choose a different answer from me? Some form of metacognition is triggered. The student looks more closely at his/her own answer in addition to the other offerings. From what I gathered about what actually goes on in class, the instructor makes clear to the students that being able to change one’s mind after learning new information is not just permissible but even encouraged. The actual lesson can then take various forms, but at some later time the same question is asked again. Inevitably the post-results are “better” than the pre-results from an assessment point of view, but more importantly the student retention of the “key concept” is increased significantly. (This can be tested in a variety of ways including crafting a different but related final exam question.)

The language of the instructor is important in all of this. It sets the framework for why we as a class are doing a particular activity. This brings me to the second thing that struck me. In discussions with our visiting expert and with my colleagues, and also watching how she ran the workshops, I became very aware of what words are being used to motivate a particular activity. I often use Think-Pair-Share in class. When I do, the class participates both visibly and audibly. But I do two things to ensure this happens. The question is not one that has an easy or obvious answer, and the students know that I will call on several of them individually. Nobody wants to look ignorant when called-on in class. Thus the motivation is fear. While effective, I’m not sure this is the best motivating factor. It occasionally works well in the early stages, but as an extrinsic motivator (and a negative one) I don’t think it is a good strategy for deep learning in the long run.

The third thing that stood out to me was how much jargon I was using in my non-majors chemistry class. The last two weeks of March coincided with my introducing organic chemistry. There is a lot of nomenclature that the students need to know as they learn about different functional groups. In a workshop two weeks ago, we did an activity on traxoline. If you’ve heard of traxoline, you know exactly what I’m talking about. (If you haven’t, a quick internet search will yield many ways this activity is used.) Subsequently in class, I found myself consciously modifying my language to make sure I didn’t throw too much jargon in a single sentence, and inserted extra “terminology checks” throughout the class to make sure students were on the same page. The traxoline activity was very timely for me.

Of the three things I highlighted, language and jargon is beginning to make an impact in my classes. These are easier changes to make, and being more aware of what I was saying was sufficient to prompt those changes. On the other hand, crafting excellent mind-changing multiple-choice questions is not so easy. While I inevitably started thinking about some examples, I expect it will take multiple drafts to really get some of these just right. I now have a new summer goal as I prepare for my classes next semester. I should identify some of those key concepts I want to stick with my students and then work on question-craft!

Spycraft

I just finished reading Code Warriors by Stephen Budiansky. The book covers the history of the NSA with a focus on secret intelligence during the Cold War. It was particularly interesting to be reading this in light of current U.S. political issues related to Wikileaks, wire-tapping accusations, and collecting data and metadata on persons and governments. However, that’s not what actually prompted me to borrow the book from the library. I got interested because I watched Season 1 of The Americans in early March. (I am on the waiting list for the Season 2 DVDs at my local library branch.)

I did not know much about the history of how NSA was formed. I was flabbergasted learning about the turf wars between NSA and CIA, the inefficiency of different government entities, and the ridiculousness (in hindsight) of some decisions made by high-ranking officials in the government and military during the Cold War. Budiansky sums this up well in the book’s epilogue: “… the crazy jury-rigged American intelligence structure, with its perpetual internal bureaucratic warfare, tangled lines of authority, and wasteful inefficiency and duplication… [and] that even in helping to attain the victory of containment over Soviet Communism, the intelligence agencies had often failed spectacularly at crucial moments, and had left in their wake an often sordid trail of transgressions against law, morality, decency and basic American values.”

There were many successes in the work from signal intelligence, but also significant failures such as the Gulf of Tonkin incident and the Tet Offensive in Vietnam, and the Chinese pushback in Korea. Budiansky critically analyzes these failures, confirming once again that as flawed human beings we repeat the mistakes of the past. The successes are not as showy, but just as significant. In his analysis, Budiansky finds that “the American cryptologists of the Cold War deserve as much credit as anyone for the fact that Americans, Russians and the rest of the world were never vaporized in a cloud of radioactive ash; without them it is hard to see that containment would have lasted long enough to matter.” Signal intelligence and NSA played a crucial role in averting the Suez and Cuban crises, amidst saber-rattling and political posturing through threats and counter-threats.

In an episode of The Americans, an incident escalating tensions is eventually averted thanks to double-checking and verifying information through “old-fashioned” spycraft. The series illustrates the complexity of decision-making when presented with incomplete raw data. Budiansky hammers this point home in his book when discussing intelligence, information and appropriate analysis. How should the raw data be interpreted? Who is in the position to interpret? The deep cover field agents in The Americans face the same dilemma as do their superiors stationed in the same foreign country, while communicating back-and-forth with headquarters.

It’s not just the Cold War tension and spycraft that’s interesting in The Americans. The deep cover field agents, having adapted to their new country experience the internal tension of fitting in while remaining apart. Truth and lies among family, friends and acquaintances threaten to tear lives apart. How does one live a lie in an attempt to remain true? It was also interesting to see U.S. life portrayed in the 1980s, the setting of the show, during the Reagan era of the Cold War. (I grew up in a different country and first set foot in the U.S. in the 1990s.) Another aspect I found really interesting was seeing the “old” clunky technology used by agents to spy on each other and gain intelligence information.

The gadgetry of spycraft today is orders of magnitude more advanced and more miniaturized than the equipment of the ‘80s. I’m impressed by the ingenuity of people in those days. Setting The Americans during this era was brilliant on the part of the creative team that put together this first season. Spies had to use their considerable skills and adaptability to get around numerous obstacles given the limited technology and information. Technology is also a topic in Code Warriors, and Budiansky details the impact of signal intelligence and cryptanalysis needs and how they pushed development of IBM and Cray computers. The history of the early code warriors, people and machines working together, from the Second World War through today, is one of the most interesting parts of the book. It also reminded me of the power of modulo arithmetic, and that I should crack open the boardgame Twilight Struggle soon!