Crossing the Thresholds

On the TLAD course we’re looking at threshold concepts. This is the idea that as students learn, they come to point where they need to transition from one ‘understanding’ to another. It’s that ‘click point’ – where students ‘get it’.

Kairos moments.

There seem to some similarities between the ‘threshold’ and the ‘kairos ‘ moments. Kairos is an idea from classical, rhetorical Greek which is defined in Wikipedia (referencing EC White) as: “a passing instant when an opening appears which must be driven through with force if success is to be achieved.” I’ve written about kairos before (when reflecting on Freire’s Pedagogy of the Oppressed [1]).

Key ideas of Threshold Concepts

There appears to be two main ideas behind the threshold concept: liminality and the threshold. The term ‘liminality’ is borrowed from the idea of ‘rites of passage’, and conveys the idea that someone remains in an uncomfortable position (or state): perhaps the information a student has memorised just bounces around their brains, making no sense, and leaving them confused. The threshold is that point at which the student crosses into a new understanding: all the memorised facts, and rota-learned schemes (“..do this, then this, followed by that…) fall into place and become an integrated, mental ‘schema’. (A schema being something that organises information and defines the cognitive relationships between the different bits.)

In this article [2], the author unpacks some of the history of threshold concepts and highlights five characteristicst:

  1. Integrative: I’ve mentioned that above.
  2. Transformative: I’m comfortable with that idea as a ‘kairo’s moment’.
  3. Irreversible: the idea is that there’s no going back. As I reflect on the irreversibility I’m not too comfortable with that (see below).
  4. Troublesome: this refers to the liminality I think, but again gives me some cause for concern (see below).
  5. Bounded: I struggled to understand this idea. The best explanation I could find (and there wasn’t much because they all seemed to repeat Cousins (2006) [3]), was by Elliott et al (quote below) highlighting the defined ‘working roles’ in which transformation was occurring.

” … I reflected and analysed my stance in relation to my role as a clinician and that as a researcher…. it is evident that I was transforming and becoming a researching practitioner, rather than just a clinician. Life would never be the same again…”[4]

Irreversibility and Troublesome

As I reflect on these two aspects for the conditions of Threshold Concepts, I have some concerns. It may be the language used, but even then, I think we need to be careful in the words we use (which lead different listeners and readers to different ideas). In the quote above, the author highlights that ‘life would never be the same again’, but (if I’m allowed to keep the same analogy) if clinicians are irreversibly changed to researchers, that’s not always going to be good if someone then decides they want to go back and be a clinician! In my own thinking as a research scientist I can get ‘disorientated’ in my ‘analytical and methodological enquiry’ mode of thinking, when external circumstances require me to be ‘something else’: for example a father, husband, friend, artist, musician. In my personal journey, I needed to leave research to re-orient myself. So, I think that we (as teachers) need to ensure that we get the students into the right post-threshold space(!) and that they (the students) are clear about how life may be different afterwards. As they say – “With great power comes great responsibility”!

Being ‘troublesome’ might be an issue as well: one person’s ‘liminality’ might be another’s torment. My personal opinion is that the idea of ‘rites of passage’ can’t be allowed to be carried too far into the Threshold Concept as it applies to teaching: what I mean by that we need to guard against the idea that students may be deliberately left in a liminal space as some sort of (well intended) ‘rite of passage’ to the professional community.

Threshold concepts in chemistry teaching

I couldn’t find a lot of literature about Threshold Concepts in chemistry, but I did like the paper by Talanquer [5], who highlights five possible threshold crossover schema;

  1. From an “Additive Property” to an “Emergent Property” Schema: students can misunderstand that the properties of a compound are not simply the averages values of the atoms, but that as atoms come together they form something with new emergent properties.
  2. From a “Centralized Causal Process” to an “Emergent Process” Schema: student may see a process as a simple causal process acting ‘en masse’ rather than a complex, and semi-random action of individual molecules. For example, a student may understand that the water in a kettle boils because it’s heated, whereas at a molecular level it’s energy transfer, speeding up individual molecules, who follow a random path to higher energy to the point that they diffuse into the gas phase.
  3. From a “Homogeneous Population” to a “Varied Population” Schema: this is related to the idea of boiling water above, but focuses a bit more on the idea that there are variations in the individual molecules in a system, and that those variations play a key role in making sense of a system’s behaviour.
  4. From a “Intrinsic Chemical Property” to a “Extrinsic Chemical Property” Schema: a student sees that an acid always donate protons regardless of what chemical system the acid is in, rather than recognising that the properties exhibited by a compound are dependent on it’s chemical environment.
  5. From a “Variation” to a “Conservation” Schema: students are used to thinking about different events in terms of ‘what changed’, whereas in chemistry an equally important question is ‘what stayed the same’. It’s natural to look at a chemical reaction and ask ‘which part of a molecule changed?’ But equally important is the questions ‘which part stayed the same?’

I couldn’t find any reports of more specific issues relating to pharmaceutics.

Threshold concepts from a students perspective

I interviewed students from one of our courses about topics that were – from their point of view – threshold issues. The two that we discussed were ‘Quality by Design’ and ‘Maths and Stats’. One was a threshold subject because it was brand new, and the other because it was too old.

Quality by Design more an operational philosophy than it is a science fact: a principle to work by, rather than a physical/chemical principle. It’s a relatively recent introduction into the field of pharmaceutical production, and focus on ‘tools’ that can be used to drive scientists and engineers to a deeper understanding of the processes that they are involved with. As with any production process, pharmaceutical drug manufacture has many inputs (chemicals, temperature etc) and variables (equipment type, size etc) and each of these will have a big or small impact on the final product. (To make it more complicated there can be ‘confounding factors’ where variable A has no effect when variable B is small, but a massive effect when variable B is big!) Some of the tools we teach are conceptual (like the fishbone diagram) and other are mathematical. On reflection I think that, in teaching QbD we are trying to move students move from simple reactions on a small scale, to a multi-dimensional process on a huge scale. One student commented that after revisiting QbD several times, it eventually fell into place (which is pretty much according to the Threshold idea!)

Maths and Stats is a subject that is covered in the school curriculum, but it’s not always revisited (to any great extent) in graduate studies. Even in science subjects the amount of maths a student does might be quite low. I’m sure most topics will talk about maths, since it’s a fundamental way of understanding most sciences, but it might stop at ‘math’s shows up variable X gives us response Y: don’t bother with the maths but remember the X-Y correlation.’ One of the issues in moving from undergrad to postgrad is the rigour with which we expect students to question the fundamental underlying suppositions of established correlations (even if it does involve maths!). Many Universities now have dedicate maths support centres. I see maths skills like a language skill: if you don’t use it you lose it.

The discussion also showed that my assumption that ‘chemistry maths’, was just maths, was incorrect: from a student perspective it’s a particular form of maths because it deals with specific practical problems like dilutions and unit conversions. Assistance through the normal maths support channels might not always be available for this specialised form of maths.

Imagining Threshold Concepts as a manufacturing process

To begin with I struggled to comprehend ‘Threshold Concepts’, but after a while I found a mental image that helped me: crystallisation! Over a year ago, I and a masters student were watching a continuous crystallisation experiment. The researcher had a solution flowing continuously through a series of long tubes (called OBR’s), at one point they added (what is called) an anti-solvent, and crystals started to form. The idea of the experiment was to control the different test parameters (flow rates, oscillation rates, concentrations etc) to produce crystals of a certain type, size and consistency, but the OBR started to block. This image helps me picture the ideas of threshold concepts and liminality, by thinking of solvent and solution additions: everything is in place, but something just get ‘stuck’ and the smooth flow of the solid understanding is blocked.

For me it’s the ‘analytics’. In the crystallisation example above, it’s easy to see where the flow is blocked. As I reflected on ‘threshold concepts’ I was left with the question of how do I detect when students are left in liminality and are not transitioning? I have an image in my head of the clear, glass OBR being painted an opaque black. As I read a blog post from one of my co-TLAD delegates (Mohammed Asfar), I saw that he’d used the idea of surveying students who struggled with particular ideas on the course. To exploit that route, I’d need to open up a dialogue with the class of honest feedback: scrape off some of that paint! In Rhem’s article [2] he mentions the idea of a ‘third ear’ directed toward the students, which listens out from those who are in a liminal space. I frame this ‘third ear’ this in terms of ‘detectability’.

My Praxis

For me the key is detectability, and opening up those lines of communication with students so that I/we can identify threshold concepts. Ultimately, I’d like to try and get some solid analytics to be able to support the ‘Obstacles to Learning‘ approach.

I am (as always) concerned that I can’t find published data about the effectiveness of the Threshold Concept approach. I can see that it’s a sensibly argued (laid out in a way that is logical, sequential and explainable), has some anecdotal experiences behind it (it has moved beyond a ‘thought experiment’) and popular (so the pedagogical community has found it useful), and adopting it is a better idea than using nothing, or some other idea that comes without these three attributes. But, it would still be nice to have some data.

————–

[1] Pedagogy of the Oppressed (book) by Paulo Freire (published in English in 1970). Wikipedia link here.

[2] Before and after students “get it”: threshold concepts, James Rhem, National Teaching and Learning Forum, #66: available at https://teachingcommons.stanford.edu/teaching-talk/and-after-students-get-it-threshold-concepts. (Incidentally I was very interested in Land’s comments on peer-review in this article, but that’s another blog post!)

[3] Cousin, G. (2006) ‘An introduction to threshold concepts’. Planet 17, 4-5.

[4] S Elliott et al, From Practitioner to Researcher: A Threshold Concept – A personal reflection on my own ‘tug of war’, International Journal of Practice-based Learning in Health and Social Care Vol. 4 No 1 July 20165, pages 78-87

[5] Vicente Talanquer, Threshold Concepts in Chemistry: The Critical Role of Implicit Schemas, J. Chem. Educ., 2015, 92 (1), pp 3–9

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