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.