College Arms Race: WMD Version

Weapons of Math Destruction lifts the veil on the darker side of Big Data. In ten chapters of vignettes, the author Cathy O’Neil appropriates the acronym WMD bringing it very close to home to anyone touched by the new economy – a globalized technocentric world order. O’Neil has had a varied career. With a Ph.D. in Mathematics from Harvard, she started out as an academic at Barnard. But then the siren song of investment banking and hedge funds called out to her, and she joined D.E. Shaw as a quant. (Having a computational background, I was once tempted to apply to D.E. Shaw earlier in my academic career, but I think I’m much happier teaching college students.) Disillusioned by the financial crisis, she “was especially disappointed in the part that mathematics had played [and] was forced to confront the ugly truth: people had deliberately wielded formulas to impress rather than clarify.” Leaving the hedge fund, she has worked on illuminating WMDs, and also started the Lede Program in Data Journalism in Columbia.

The chapters include (1) a peek at predictive crime models that can create pernicious feedback loops, (2) personality “tests” on job applicants that lead to new automated forms of discrimination, (3) corporate efficiency schedulers that disenfranchise employees, (4) using credit reports as proxies for all manner of future predicted risk behavior, (5) large-scale social media manipulation, and more. If any of these topics interest you, I highly recommend reading her book in full. The two topics I will highlight in today’s post are Chapter 3 (“Arms Race”) and Chapter 4 (“Propaganda Machine”).

As a faculty member in a private liberal arts college in the U.S., I have grown increasingly concerned with the unsustainable arms race that has accelerated in earnest over the last 5-10 years. Holding down tuition is increasingly difficult as institutions fight for the small swath of students that will increase their prominence so as to keep themselves afloat. Administrative staff must be hired to support the ever-increasing facilities and amenities in an effort to be a full-service college. Increasing mental health concerns among students are putting strains on universities struggling to provide adequate support. The current strategy of discounting to draw more desirable students is financially unsustainable, and yet the arms race continues.

O’Neil begins this story in 1983 with U.S. News and World Report’s first set of college rankings. It says something that in 2017, the “rankings” have expanded to cover more types of institutions and programs, while its original news-magazine roots have died with the times. Top Ten lists have always been popular, but Big Data, with its whiff of being scientifically based, has turned these lists into a gargantuan beast of its own. The siren call of Big Data is strong, perhaps overwhelmingly so. With more data, we should be able to make better decisions. It is a strategy that runs well when making a pitch to administrators for more money; I’ve used it myself multiple times. The larger and more complex a system becomes, the more it needs to feed on Big Data to optimize efficiency. We humans might say to ourselves that we are the overlords of the system, but more and more are becoming enslaved. How exactly? Thanks to the correlation between increasing complexity and obtuseness, things are becoming less and less clear. That’s why O’Neil’s book is important in highlighting these WMDs.

Everything starts with a model. Ideally, and this is most true in the “hard” sciences, the feedback loop in developing a model is much more rigorous. You test the model with experiments, generate more data, and then refine the model using the new data. Rinse. Repeat. The models that work best have narrow and clearly defined outcomes. But many complex problems are “squishier” (O’Neil’s term), and the journalists tasked with ranking colleges were trying to measure something as nebulous as “education excellence”. O’Neil writes: “They had no direct way to quantify how a four-year process affected one single student, much less tens of millions of them.”

So what do most people do in this case? You pick a proxy. Now hopefully you choose a proxy that correlates well with what you’re trying to measure, and you provide appropriate feedback into your model. In the college rankings game the proxies that “seemed to correlate with success”: SAT scores, student-teacher ratios, acceptance rates, retention rates, alumni giving, and peer evaluations. With fame or infamy come problems. O’Neil explains: “As the ranking grew into a national standard, a vicious feedback loop materialized. The trouble was that the rankings were self-reinforcing. If a college fared badly in U.S. News, its reputation would suffer, and conditions would deteriorate. Top students would avoid it, as would top professors. Alumni would howl and cut back on conditions. The ranking would tumble further. The ranking, in short, was destiny.” In recent years we’ve heard a number of stories exposing institutions that attempted to game the system. What a sad state of affairs.

It gets worse. O’Neil explains that to establish initial credibility, the early lists needed to have the known “elites” on top. What made them special? High SAT scores, great graduation rates, excellent retention, strong giving from rich alumni, and name-recognition among peers. Sound familiar? Glaringly, cost of attendance was not included in the formula of the model. Perniciously, this led to gaming the system without needing to keep tuition down. In O’Neil’s words, “in fact, if they raised prices, they’d have more resources for addressing the areas where they were being measured.” Tuition has skyrocketed in the last twenty years – a correlation, at least, if not one of the causes.

As the arms race increases the gap between the haves and have-nots, the next WMD comes into play: the propaganda machine of for-profit higher education advertising. Big data has sharpened this model with deadliness in targeting the most needy with the taglines most likely to succeed in prying cash they don’t have from their wallets. Uncle Sam steps in with federal loans to make up the difference, up to a whopping ninety percent! O’Neil writes: “Anywhere you find the combination of great need and ignorance, you’ll likely see predatory ads… they zero in on the most desperate among us at enormous scale.” That last phrase is what defines a WMD, the enormous scale. Tuition is set to maximize borrowing at the limits of federal loans. But, that’s not so important if you’re selling the dream of upward mobility. Society’s veneration of the entrepreneur, coupled with well-chosen anecdotal stories, provide what may sound like the only hope of those in difficult circumstances. No risk, no payoff.

The details of this sad story are told in Lower Ed: The Troubling Rise of For-Profit Colleges in the New Economy by Tressie McMillan Cottom. Before she became a sociologist and professor, Cottom worked as a recruiter and enrollment specialist in the for-profit world. She eschews the simple tropes used to explain what is happening at the other end of the spectrum, far away from the noses of the “elites”. Her analysis is penetrating, and I strongly recommend her book if you want to know how and why Lower Ed began its thriving ascent. As they add a slew of graduate programs and post-baccalaureate certifications to their programs, their nimbleness is outpacing traditional public and private institutions of higher education. There is no simple way to assign blame, because this complex issue is part of a much larger ecosystem

Here’s a quote from the Epilogue that summarizes one of the main issues. “In the absence of social policy, public subsidies to Lower Ed become a negative social insurance program. A negative social insurance program is a market-based response to collective social conditions. Negative social insurance, unlike actual social insurance programs (e.g. Social Security), doesn’t actually make us more secure. It only makes our collective insecurity profitable.” Given the limited information I’ve seen in the current (U.S.) Administration’s higher education stance, the gap between the haves and have-nots will widen further. For-profits aren’t going to bridge this gap but instead will “perpetuate long-standing inequalities”. I’m not doing justice to Cottom’s careful argument; I recommend reading her book in full.

O’Neil closes her book by reminding us that Big Data is here to stay. “Predictive models are, increasingly, the tools we will be relying on to run our institutions, deploy our resources, and manage our lives. [But] these models are constructed not just from data but from the choices we make about which data to pay attention to – and which to leave out. Those choices are not just about logistics, profits, and efficiency. They are fundamentally moral. If we back away from them and treat mathematical models as a neutral and inevitable force, like the weather or the tides, we abdicate our responsibility. And the result, as we’ve seen, is WMDs that treat us like machine parts in the workplace, that blackball employees and feast on inequities… Math deserves much better than WMDs and democracy does too.”

Potions Project: How It Went

Time flies. It was six months ago when I seriously considered the idea of a potions-themed class. A month later I even came up with a name: Magical Potions and How to Design Them. In the end, my non-science-majors chemistry class completed a final project on this theme, but the tie-in was weaker than originally anticipated. Some class time was spent discussing potions, references were made to potions early in the semester, and we covered a fair bit of organic chemistry so that students would recognize interesting molecules they might consider for their potions. I estimate that a third of my class was spent on topics that were relevant to the theme, and the rest was what you’d see in a standard introductory chemistry class (with less math and more pictures).

The outline of the final project can be found here. The majority of students formed pairs to work on their projects, although there were a few trios and a few soloists. Students who started their work early and sent me drafts for the most part had strong entries. Groups that waited to the last minute did less well, although there were still strong entries in cases where I had not seen a draft. (Sending me a draft was optional.) Amazingly I did not have any requests for extensions, and student work was turned in on time! (Final entries were due Monday morning at 8am.)

Here’s what I thought worked well: (1) Covering organic chemistry earlier meant that we talked about relevant molecules sooner. (2) Writing up a full sample of what I was expecting led to better overall quality of the work turned in by the students. There were just a few C+ entries, and the vast majority turned in A or B work. The project was worth 20% of the course grade. There is still a final exam worth 30%. (3) Having students suggest potions as part of a mid-semester homework assignment generated entries for class discussion. (4) Devoting a class to fully discussing the parameters of the project helped students generate lead ideas. Basically, I compiled the list of prior student suggestions. Then students discussed (in groups) a subset of these. It got them thinking about what they would need to consider for different potions. In some cases it also helped students form groups. More than half of the final entries came from the student-generated list although not all of them were discussed in class during that one session. (5) Giving students a deadline by which I would read drafts and return comments. This helped prod some groups to start early with better end results.

Here’s what I thought did not work as well: (1) While I made reference to Potions in several early classes, the theme did not feature strongly in the first two-thirds of the semester. This led to some last-minute scrambling by both me and the students. (2) Having a late start meant that I pushed the original due date of the project into the second half of Finals week, which is also when the students needed to be studying for the final exam. (3) I was not sufficiently clear in explaining students how to leverage the “creative” part of their potion to mesh with known chemistry. I thought it was obvious from the full sample I provided, but I only realized how puzzled they were as I read drafts and answered student questions in my office. And this was right after the last day of formal classes. (4) My original plan was to have students contribute to a Wiki, i.e., we would all write a collaborative “potions textbook”. But not providing the students any prior Wiki exercises meant that they were not comfortable with using the Wiki embedded in the LMS. Students ended up e-mailing in pdfs and so the groups generally worked in isolation from one another.

Would I do something like this again? Yes, but I think the theme needed to be more strongly embedded in the class and I needed to do a better job meshing class content with the final project. I should also restructure the class so students start thinking about the project earlier. Last semester in my General Chemistry class, the students creatively designed a new element and discussed its uses and how it would interact with known elements in our Periodic Table. But in that case, I had scaffolding exercises throughout the semester getting students to think in “alien” ways as they came up with their “alien” element. I should have done this much more strongly this semester. I don’t have a good excuse and I’m not sure why I didn’t do this. Maybe in my mind this project seemed more straightforward.

Highlights: The top entry was a potion that peels away the skin of consumable fruits so that you don’t have to! One of the students shared with me some cool chemistry, which was related, but ultimately not used as part of this project. The entries that got me reading the most for my own interest (and looking up references) were two camouflage potions. Both proposed extractions from magical octopi as part of the recipe, but they took different approaches and concentrated on different molecules in the overall recipe. Several groups made explicit references to Harry Potter books or movies, but other magical or sci-fi worlds also showed up. These were fun to read! I hope the students enjoyed writing them and exercising some creativity.

In closing I leave you with an image from Gryffinroar. This recipe for curing boils does not provide chemical justification, unlike the ones designed my students!

Student Heuristics in Learning Chemistry

In my most recent post, I mentioned a monograph I’ve been reading: Concepts of Matter in Science Education. One of the articles that made me really stop and think was by Vicente Talanquer, titled: “How do students reason about chemical substances and reactions?” How do they indeed? It turns out that they often rely on heuristics – some of which mislead them. What are heuristics? Here’s how Talanquer describes it from p340 of the monograph minus the many references. (If you’re interested I encourage you to read the article in full.)

“Heuristic reasoning in judgment and decision-making has been analyzed from a variety of research perspectives. Despite differences in conceptualization and approach, existing frameworks highlight the capacity of the human mind to make decisions with very little time and information, using implicit and preconscious reasoning mechanisms. These types of reasoning strategies have been characterized as fast and frugal because they employ a minimum amount of time and information to generate a choice or decision and [are] adaptive or ecologically rational because they fit to the structure of the in which they are used. Heuristic processing can be expected to dominate over more analytical ways of thinking when a person has less knowledge, capacity or motivation to do well in a task. Although heuristics usually provide satisfactory answers, they do not always lead to the correct solution and seem to be responsible for many systematic biases and errors in human reasoning.”

Let’s look carefully at that second last sentence and apply it to students. When a student has less knowledge or capacity, there is a reliance on applying heuristics rather than more a careful analysis. That’s certainly true in my experience. The less knowledgeable and less capable students do provide heuristic type answers on an exam. Some of these have the “correct” buzzwords but are used incorrectly, and I can tell that the student doesn’t have a clear understanding of the concept being applied. Others are just plain wrong. On the other hand, the students who have a stronger grasp on the underlying concept are able to justify their arguments rationally and logically.

But sometimes students who seem to be able in a class discussion or in my office to make coherent, logical, rational arguments in answering a conceptual question fail to do this on an exam. (When a student asks a question, I usually don’t answer them directly, but rather provide them the tools to formulate their argument through prompts.) I think this is where time pressure can lead a student to fall back on a heuristic. I have timed exams in the majority of my classes (although I have experimented with other open-ended forms) because I think a time constraint does provide some measure of how well the student actually knows the material. It’s not a perfect measure by any means, and there are disadvantages to having timed exams. (Open-ended exams however have a different set of disadvantages.) For that matter, using exams in both teaching and assessment has its pros and cons. I think the pros outweigh the cons in a number of chemistry courses especially in the first year of college

Talanquer’s article makes reference to studies in first and second year college chemistry (usually General Chemistry and Organic Chemistry) whereby a large proportion of students “rely on heuristic strategies, rather than analytical thinking based on atomic-molecular models of matter... Heuristic reasoning allowed participants in our studies to reduce cognitive effort by minimizing the number of cues that needed to evaluate to make a decision.” This has echoes of cognitive load theory, and I think the cognitive load is particularly high in chemistry because of the back-and-forth between atomic-particle level explanation and macroscopic observations mediated by a symbolic language and a dizzying array of models. This problem in chemistry is often referred to as the Johnstone Triangle.

A few heuristics are highlighted in the article. Recognition is used when an object is recognized and exhibits the known property. The example provided is that students often select NaCl as being more water-soluble than NaBr simply because the first is more recognizable. One-reason decision-making is the tactic of searching for a single differentiating cue to answer a question. The example used is that the student might assume that BaO has a higher melting point than MgO because Ba is “heavier” than Mg, and simply stop there without any further analysis.

As an expert, I also use heuristics of a sort when thinking about chemistry, but my knowledge base is much wider and deeper than the student’s. Thus my recognition heuristic isn’t limited to just a few representative cases, nor would I quickly stop at a single differentiating cue or use a one-reason approach. The question is how to help my students move towards a deeper analysis. Clearly widening and deepening the knowledge base is important – and that is why content is important in the study of chemistry. But the process of reasoning through multiple factors can also be modeled in the classroom.

This semester I was starkly reminded of the differences between students who had knowledge and capability in chemistry and those who did not. I am teaching the Honors second semester General Chemistry course, i.e., the students are all strong students interested in being science majors who’ve had first semester chemistry the previous semester. Some of them also have very strong mathematical skills and are enrolled in physics and biology courses. On the other hand, the students in my non-science-majors course, while they may be knowledgeable and capable in many other areas, are typically not knowledgeable in thinking chemically. The wrong use of heuristics was apparent time and again, and I needed to do a much better job at helping the students build the necessary foundations to reason in chemistry. This summer one of my goals is to think about how to better build that foundation.

Concept Inventories

In an Education in Chemistry feature article last year, Ross Galloway and Simon Lancaster discuss the challenge of measuring learning gains in students. First, they mention standard measures and their associated difficulties. For example, higher final exam scores might indicate more learning, but these may be highly dependent on student background in the subject. This has certainly been my experience in the first semester introductory science level courses.

Assessment officials continue to ask for measures of student learning. The public questions what a college education actually provides. For better or for worse, measurement tools are here to stay. As educators, we should push for better measuring tools rather than allow some administrator to (mis)use a worse tool and draw spurious conclusions. Galloway and Lancaster suggest Concept Inventories. The most well known example is the Force Concept Inventory (FCI) in physics. The questions are insightful, well-validated, and the FCI is widely used. The authors list five concept inventories available in chemistry. I downloaded all the references and read through the articles. I’m not sure all of them have gone through the same validation rigor as the FCI.

One of the challenges in regularly using a concept inventory is the danger in starting to “teach to” the questions in the inventory. Strictly from an education point of view, this is not a bad thing; because if the questions are well-designed, then as a teacher I would want my students to grasp key concepts. This however decreases the use of the inventory as a measurement tool. There is an adage known as Goodhart’s Law: “When a measure becomes a target, it ceases to be a good measure.” This is not just true of concept inventories, national high-stakes exams in many countries exemplify this, in my opinion.

Galloway and Lancaster mention the American Chemical Society (ACS) national examinations. A number of colleges use these as final exams at the end of a first-year college course in General Chemistry for science majors. I’ve been in discussions about the validity of such exams, and how the results can be adaptively interpreted at different schools for minor variances in the curriculum. (General Chemistry is quite standard across U.S. colleges although there is some variation on topics at the edges.) Has the use of standardized exams contributed to the rigidity of curricula in general and chemistry curricula specifically? Possibly. That’s one of the challenges dealing with legacy systems. Compared to the other sciences, chemistry has traditionally maintained the most hierarchical and rigid curriculum. It certainly allows for ease in transferability across institutions.

A number of the concept inventory questions in chemistry rely on interpreting atomistic-particle diagrams. I’ve been diving deep into this area after recently discovering Concepts of Matter in Science Education (Springer). This multi-author monograph contains many studies investigating how students think about atomistic and particle models – their conceptions and misconceptions. I’m increasingly convinced that models are crucial in the teaching of chemical concepts but they are susceptible to all sorts of problems when students misapply or misunderstand a model and its limits. I think that chemistry, more so than the other sciences, leans more heavily on such models and inherits the accompanying challenges in teaching and learning. Towards the end of the semester, I cut out some “new content” in my non-majors course and “reviewed” material from early in the semester using atomistic-particle models as a lens and emphasizing their usefulness and limitations. We’ll see if this “intervention” helped when I grade the final exams.

As to learning gains, I’m thinking of designing a model-based questionnaire for pre-test and post-test for my General Chemistry class next semester. Then I need to remember not to “teach to the test”.

Harrius Figulus

Guest blog post from my former student who majored in Literature, knows Latin, and much more well-versed in the Potterverse than I am. Enjoy!

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Harrius Figulus*

There are countless articles or lists online tracing the Latin or Pseudo-Latin origins of incantations in Harry Potter. The Harry Potter fandom’s Wiki boasts ‘an exhaustive, though not complete, list’ of such incantations. Much has also been said in different news sources about JK Rowling’s supposed degree in Classics - it really was a degree in “French with additional Greek and Roman Studies in the 1980s” - and why the Latin in the novels seems clunky. Even a famous classicist at Exeter who taught Rowling published an article detailing links between the Harry Potter series and texts Rowling would have read during her time at Exeter. For some reason, it really matters to readers that Rowling drew from the pre-Christian Greco-Roman world in writing the Harry Potter novels.

Now, I can’t remember when the idea of Latin as a language first occurred to me. Growing up in a fairly westernised Asian country, Latin (of a sort) would pop up in phrases like habeas corpus, streptococcus, or summa cum laude. These were just words -- as equally foreign as croissant, blitzkrieg or soprano, and because of regular usage, ultimately as normal. The connections between these phrases and Greco-Roman history never crossed my mind.

Only in my first semester of Latin in college did it become clear what the Greco-Roman world was and how much of it had found itself into the well-loved children’s series. Mazes, sagely old men, tyrants, the pursuit of eternal life and glory, mythical creatures, the tragic cycle, and, of course, Latin are staples of the classics. Granted that contemporary education in Europe places less emphasis on the classics than it used to, these tropes were given new life in the Harry Potter books.

To give an example, I was recently rewatching the Goblet of Fire, and when Harry sent up red sparks to signal to those outside the maze where Fleur had fallen, I was surprised by the incantation: “Periculum!” To the beginning Latinist, periculum means danger -- a fairly common word in Vergil, Cicero, or Livy. Now, to shoot up red sparks does not necessarily mean one is in danger. Presumably, one could send up sparks of different colours during a party, but it seems that in this case, Rowling directly links the act of shooting red sparks up to something like a flare. It suggests to us that in wizarding history, the spell developed specifically as a distress signal.

Moreover, it suggests that wizarding magic in Harry Potter is tied to language. The intention of the spell is clarified by the incantation. Certainly nonverbal magic exists in Harry Potter, as in the case of non-human magical creatures (e.g. house elves, centaurs), particular fields of magic (e.g. divination, flying), or young children. But for the most part, adults who wish to cast spells speak and use their wands. Only in the movies, particularly in duels, do instances of non-verbal spells increase. One could argue that this was for the sake of dramatic pace, but perhaps it was also to maintain the element of surprise in combat. Nevertheless, it seems that over-all, a wizard’s spell sans words is generally less potent or focused than it could ideally be.

One wonders what it is about Rowling’s universe that magic is intertwined with language, particularly her type of pseudo-Latin. I myself am unsure, but I wonder if it has to do with a view of language that moves away from the Saussurean model of words as “signifiers” to an actual concept being “signified”. [5] Words, in Saussure’s view, are like containers for a concept, but in themselves don’t mean anything. However, in the world of Harry Potter, if words merely pointed to intentions or were simply ways of focusing intention, then it wouldn’t matter what incantation one used as long as one had the right intention while casting a spell. Having particular words attached to particular spells suggests rather that the words in themselves carry meaning. Moreover, since spells actually do things, then words also have the power in the Potterverse to effect tangible change -- something we wouldn’t expect from simple containers of concepts.

The question then is: “Why Latin?” Is it simply because of Rowling’s educational background? Perhaps. Exposure to Latin (especially through French, which Rowling once taught) would make it an easy source of words that are familiar to the average English-speaker because of the number of words English has inherited from Latin. I think the use of Latin also points to how Rowling treats magic in her texts. Magic is serious. It can control, it can hurt, and it can kill. It has gravitas in the same way that the contemporary reader often views Latin texts. However, there is also humour in Rowling’s magic with the many tricks and jokes the characters encounter that mimic her playful use of Latin. Much in the same way that a British schoolboy might write funny limericks with dog Latin, so does Rowling draw on the language for her spells.

Perhaps the use of Latin also tells us about an insight Rowling has into how contemporary readers view magic. Latin is uncommon and yet it is everywhere. We may not have learnt it in school, but we encounter it today because somehow it endures. In a sense, this is magic as Rowling presents it: unusual, but familiar, as if once upon a time, we Muggles could have had it too, if only we knew the right words.

*figulus, literally a potter

Trinity of Truth: Version Pi

In the final chapter on How to Bake Pi, mathematician Eugenia Cheng delves into her field of mathematics, Category Theory, having dropped hints and examples throughout the second half of the book. Early in the book (reviewed here), she asserted that the purpose of mathematics is to make hard things easier. But since “category theory is the mathematics of mathematics… [it] is there to make difficult mathematics easy.”

The final chapter purposes to discuss the role of category theory. Cheng thinks that mathematics can illuminate the search for truth. Her Trinity of Truth has three aspects: Belief, Understanding, Knowledge. She compares them to the three-dome-structure of St. Paul’s Cathedral. (I learned that the visible outer and inner domes are held together by the crucial but unseen middle dome.) Knowledge is akin to the outside dome – what the world sees. Belief is akin to the inside dome – what we feel inside ourselves. Understanding is what holds the two together. At least most of the time. In mathematical fashion, Cheng maps out a Venn diagram. There is an intersection of Knowledge and Belief that does not include Understanding. As examples, she writes: “I don’t really understand how gravity works, but I know and believe it works. I know and believe that the earth is round, but I don’t understand why.” But this doesn’t preclude understanding at a later time how gravity works or why the earth is round.

Cheng sees “mathematical activity in terms of moving around between these three kinds of truth.” In particular, knowledge comes from proof in mathematics. The aim is not so much to prove math theorems (which is an important activity) but more to “move things from the proved area to the believed area.” According to Cheng, “proof has a sociological role; illumination has a personal role. Proof is what convinces society; illumination is what convinces us. In a way, mathematics is like an emotion, which can’t ever be described precisely in words – it’s something that happens inside an individual.” But defining illumination is very tricky. How it leads to belief is somewhat mysterious. That’s where proof comes in. It enables me to move from my realm of belief to that of another.

The procedure is illustrated by the diagram above. Here’s how it works (quoting Cheng):

·      I start with a truth that I believe and that I wish to communicate to person X.

·      I find a reason for it to be true.

·      I turn that reason into a rigorous proof.

·      I send the proof to X.

·      X reads the proof and turns it into a convincing reason.

·      X then accepts the truth into his realm of believed truth.

Why this drawn-out procedure? Because “attempting to fly directly from belief to belief is inadvisable. We’ve all seen people try to transmit beliefs directly, by yelling.” What about just sending the reason? “The answer is that a reason is harder to communicate than a proof… The key characteristic of proof is not its infallibility, but its sturdiness in transit. Proof is the best medium for communicating [to avoid] danger of ambiguity, misunderstanding, or distortion.”

This made me think about the complexity of teaching chemistry. As an expert, I have a powerful interlocking conceptual map that allows me to travel fluidly throughout the realm of chemistry. But novice students do not have this, and the scaffolding has to be built layer by layer, tearing down old misconceptions while attempting to introduce more accurate concepts, all the while trying to avoid further confusion. Johnstone’s Triangle does not make it easy, and I’m constantly reminded when students ask questions, that the chasm is very wide between my chemistry “beliefs” and theirs. This is why it is a good thing to continuously probe student understanding and the more questions they ask, the better. (It gives insight into what they are thinking.) Chemistry however has no fool-proof Proof for transmitting knowledge. The dangers of ambiguity, misunderstanding and distortion are constantly present.

Cheng has a sobering view of why “many people grow up feeling great antipathy towards math, probably because [it was taught] as a set of facts you’re supposed to believe and a set of rules you have to follow… The important stage in between the belief and the rules has been omitted: the illuminating reasons… Schoolchildren try to follow the rules but are sometimes abruptly told that they have broken a rule. They didn’t do it deliberately… they really thought they had the right answer… being marked wrong feels like a punishment to them… Perhaps it was not explained to them in an illuminating way that could actually make sense to them. As a result, they don’t know when they will next be found to have broken a rule, and creep around in fear. Eventually they’ll simply want to escape to a more democratic place, a subject in which many different views are valid.”

That last phrase may partly explain why many students who start off enjoying math and science in the early years end up being fearful and hating it later, sometimes in college, sometimes before they even get to college. I suspect that some of my students feel that about chemistry in the way described by Cheng. I should look out for this, and continue to encourage my students to ask “Why?” questions. I’m not getting enough of those suggesting that I’m not using in-class time in the best possible way – for the asking and answering of questions through the lens of learning as a relationship. Questions can come from both teacher and student. Answers can come from both student and teacher. It’s a journey through knowledge together!

Bios Megafauna

This weekend I revisited Bios Megafauna, another one of Phil Eklund’s games (I previously reviewed Bios Genesis on this blog and here's a session report with pictures). I played 12 games back in 2012, and then it sat in my shelf for the next 4+ years. Megafauna is set during the exciting transition from the Mesozoic to the Cenozoic eras. It was a time when dinosaurs ruled, only to be replaced by mammals as cataclysmic events caused large swings in the environment. Supercontinent Pangaea broke up giving rise to the Atlantic Ocean. In all this turmoil, plants and animals continue to evolve and adapt. Less fit species are replaced by newcomers, while other older species adapt to fend off competitors edging into their ecological niche.

The game board depicts North America in the early Mesozoic. Empty squares represent potential habitats where biomes can take root. There are two types of biomes, marine and terrestrial, that can support suitably adapted herbivores. Carnivores can find a niche in biomes where they find suitable herbivorous prey. Above is a snapshot of my most recent game in progress. You can see a lycopod meadow in the lower right, suitable for Insectivores (indicated by the capital “I” on the tile). Players represent either a dinosauran or mammalian dynasty that could potentially lead to present day fauna. In the three-player game below, red is the archosaur that led to crocodiles and birds, green is the diapsid ancestor to lizards and snakes, and white a two-tusker synapsid (now extinct).

Since this is the time of the Megafauna, creatures can grow large. Unfortunately there aren’t big dinosaur pieces. Size is tracked on the board as shown in the upper half of the picture below. Red has two different smaller species, while the white two-tuskers are quite large in the two-ton range. The cards below have two functions. They can be “purchased” by players looking to expand their DNA pool or create new genotypic progeny. In the bottom left, the Seed-Cracking Bill adaptation can provide a herbivore access to (H)usker niches. The Sculling tail in the bottom right, provides (M)arine adaptations. These letters represent DNA adaptations present in a species allowing them to eat or move in appropriate biomes. The genotype card (bottom middle) allows spawning a new species type, in this case the ancestors to perching birds or rodents.

When a card is replaced, a new card is drawn from the deck to replace it. This triggers an event. In most cases, the card reads “Draw and place 2 new Era Tiles” which provides new biomes or introduces immigrant herbivores or carnivores. However, some cards trigger a Milankovich event, while others may trigger a cataclysmic event. The lower left card is “Volcanic acid rain”. It wiped out a number of overspecialized species if they had accumulated too many adaptations. It also caused an increase in the Greenhouse gas level. Below are the two archosaur species roaming the continent when these pictures were taken. On the left is a nocturnal amphibious serpentine creature that does courtship displays and has a switchblade claw. On the right is an amphibious armored spinosaur.

In this game, a number of volcanic eruptions led to an increase in the greenhouse level. Later in the game, the CO2 level went as high as 3200 ppm (although it is 1600ppm in the photo below). If it went any higher, a Hothouse Earth would have ended the game. On the other extreme, there could be a Snowball Earth which would also have ended the game prematurely. This game was eventually won by the archosaurs although there were a fair number of extinctions throughout the game.

Like other Eklund games involving evolution, the gameplay can be brutal. Survival can be difficult, and in most games I’ve played, no one species thrives for very long. As the biomes change, a species that is unsuitably adapted dies. But accumulating the appropriate DNA to eat the flora or fauna can lead to overspecialization. The changing environment wreaks havoc in this case. Human beings, in this sense, are an amazing species. In such a short period of time we have terraformed our own planet to suit our needs, not just to survive, but in some areas to thrive. Other organisms also contributed to the changing environment, but none have done so with the speed of humans. Eklund has a game for that; it’s called Origins: How We Became Human, and was actually published before Bios Megafauna or Bios Genesis. Unlike the two latter Bios games that take 2-3 hours, Origins is more of a 4-5 hour affair.

If you’re looking to pick up a game in the Eklund series, I would recommend Bios Megafauna. Remade as a more streamlined version of its ancestor American Megafauna, it is the easiest and shortest of the three. That’s not to say it is easy. Survival can be brutal. But you get to see if a snakelike archosaur can survive and thrive over millions of years. Would having a switchblade claw help? Would being amphibious and nocturnal help? Eklund games are part-game, part-simulation. If that’s what you’re looking for, and you enjoy delving into scientific minutiae, then you will enjoy Eklund’s games. If you are looking for something lighter that incorporates herbivores, carnivores, adaptations, and climate, but plays in 45-60 minutes, then I recommend Evolution: Climate from North Star Games.

A Crisper Story of CRISPR

The Curious Wavefunction is a science blog I follow. The author, Ash Jogalekar, is a talented writer who combines history, science and philosophy in his thoughtful contributions. This week he reviewed the book A Crack in Creation. Jennifer Doudna, one of the authors, is a co-discoverer of CRISPR technology. She might even win a Nobel prize in the near future. As an aside, Jogalekar often profiles famous scientists including many Nobel laureates – his personal take on these individuals and their accomplishments is very refreshing!

From Jogalekar’s review, A Crack in Creation sounds like a book I will enjoy reading. Except he has done such a marvelous detailed job reviewing it, that I actually feel like I’ve gotten all the major highlights of the book strung together in a coherent narrative. Oddly enough, this makes me unmotivated to go out and get the book. It’s like watching a superb movie trailer that highlights all the best parts. Most movie trailers don’t give you enough of a coherent story – they are a teaser to entice you to pay money to go watch the movie.

Since I’ve been thinking about inventing Potions based on science, the CRISPR-Cas9 system might be an excellent ingredient in a magical brew. By editing the genetic information to control transcription and downstream translation of appropriate proteins, a CRISPR-based potion could imbue a certain permanence to its effects. That’s a powerful brew. However I wonder if this would put the apothecaries and potion brewers out of business. A potion with temporary effects seems so much weaker, except that in many cases you probably only want the effects to be short-lived. It would get very annoying to be invisible all the time or looking permanently like someone else thanks to a Permanent Polyjuice Potion.

Then again, maybe there’s nothing truly permanent in a dynamic physical system. DNA mutates. Cells die and need to be replaced. Even rocks change over time, both physically on the outside and chemically on the inside. Isn’t dynamic change what constitutes life, rather than static permanence? Or should that be dynamic stability? That’s how Robert Pascal and Addy Pross would describe the bridge between chemistry and biology in the evolution of life. They argue that thermodynamically stable systems are a subset of a more general group of persistent systems. They describe the Persistence Principle as “change that takes place in the direction of increased stability/persistence”. I could attempt to summarize a crisper version of their article (“Stability and its manifestation in the chemical and biological worlds”, Chem. Commun. 2015, 51, 16160). But I don’t have Jogalekar’s skill or his persistence. Instead, I’ll stop here to keep today’s post crisp!