The focus this week was on threshold concepts. They offer a refreshing view into the nature of the learning curve, but in my opinion, threshold concepts are less of a thing than a mis-construction of both educational content and concept sequencing. Yet, as often on this course, they are treated as being real, and discussions centre on how they are used.
On a personal note, my postings per week will be reduced in both length and quantity. I’ve been ‘asked’ to limit my involvement on the discussion board as there is the perception that my involvement inhibits the discussions of the others. That’s all I’ll say on that matter for now.
The existentialist problem of threshold concepts (TC) may be due in part to its definitional ambiguities (Rowbottom, 2007). Barradell and Peseta (2014) note that identifying a TC “is beset with conceptual challenges that remain unresolved” (p. 1). Land, himself, characterises the foundations of TC as “eclectic” (2011), leading philosophers to reject the ontological possibility of TC (Rowbottom, 2007). Meyer and his colleagues argue that the notion comprises five elements (2015). I argue that their definition is incomplete, missing the key component of derivation. This component aids individuals assimilation of new information inside existing mental schemata.
Radical constructivism sees individuals in a state of “isolation from reality” (von Glaserfeld, 1988, p. 2). That “we cannot transcend the horizon of our experiences” (Riegler, 2001, p. 1) compounds our isolation, and cognitive development requires expansion within our minds. It is this expansionist element that current views of TC lack. To understand why, here is a simplified example. When a child learns to add 3 + 4, the notion of the numeric 7 is not overtly present. The child needs to grasp the occluded existence of the 7. From this example, the notion of derivation is understood. The 7 is logically derivable from the given information. Meyer et al.’s (Meyer, Knight, Callaghan, & Baldock, 2015) use of integrative appears similar, but they limit this to the “hidden interrelatedness of something” (2006, p. 7), which does not include the notion of derivation.
One method of finding derivation is the constructivist framework of Kelly (1955) who describes the derivational properties of any construct by demonstrating their bipolarity (Raskin, 2002; Walker & Winter, 2007). One construct “cannot be understood except in relationship to” its opposite (Walker & Winter, 2007, p. 454). Marton and Pang (2006) identify how increase/ decrease interacts with supply/ demand. They explain that “learning to see”, i.e. grasp a threshold concept, is a function of differentiation, and “contrast” and “separation” are the first two conditions for perceptual learning (p. 199), building on Marton’s earlier recognition that learning cannot happen “without discernment and there is no discernment without variation” (Marton & Trigwell, 2000, p. 387). Contrasting implies opposites or at least significant differences. Using these differences, mastery of former TC can be helped through the presentation of carefully worked out derivations.
The economics notion of opportunity cost (OC) is used by Meyer and Land (2003; 2006) as an example of a TC. I will demonstrate how it can be used to show derivations. Within OC, there is the notion of resources. Resources are limited or unlimited. When resources are limited, derived notions from this bipolarity are scarcity (usually money) and therefore of choice of what can be bought. Finally, the action of buying one thing carries the understanding that the other was not bought. OC states that the cost of buying one thing includes the existence of the thing that was not bought.
Adding derivation to TC features aids students’ ability to reconstruct their schemata. However , TC theory cannot answer the problem of how individuals accommodate themselves to troublesome knowledge.
Barradell, S., & Peseta, T. (2014). Journal of Further and Higher Promise and challenge of identifying threshold concepts : a cautionary account of using transactional curriculum inquiry. Journal of Further and Higher Education, (July 2015). http://doi.org/10.1080/0309877X.2014.971105
Land, R. (2011). Threshold Concepts and Troublesome Knowledge. [Video]. Laureate.
Marton, F., & Pang, M. F. (2006). On Some Necessary Conditions of Learning. Journal of the Learning Sciences, 15(2), 37–41. http://doi.org/10.1207/s15327809jls1502
Marton, F., & Trigwell, K. (2000). Variatio Est Mater Studiorum. Higher Education Research & Development, 19(3), 381–395. http://doi.org/10.1080/07294360020021455
Meyer, J. H. F., Knight, D. B., Callaghan, D. P., & Baldock, T. E. (2015). Threshold concepts as a focus for metalearning activity: application of a research-developed mechanism in undergraduate engineering. Innovations in Education and Teaching International, (July), 1–13. http://doi.org/10.1080/14703297.2015.1017515
Meyer, J. H. F., & Land, R. (2006). Threshold concepts and troublesome knowledge: An introduction. In J. H. F. Meyer & R. Land (Eds.), Overcoming Barriers to Student Understanding: Threshold Concepts and Troublesome Knowledge (pp. 3–18). London: Routledge.
Meyer, J., & Land, R. (2003). Threshold concepts and troublesome knowledge: Linkages to ways of thinking and practising within the disciplines. Edinburgh: ELT Project.
Raskin, J. D. (2002). Constructivism in psychology: Personal construct psychology, radical constructivism, and social constructionism. American Communication Journal, 5(3). http://doi.org/10.1080/10720537.2014.850367
Riegler, A. (2001). Towards a Radical Constructivist Understanding of Science. Foundations of Science, 6(1-3), 1–30. http://doi.org/10.1023/A:1011305022115
Rowbottom, D. P. (2007). Demystifying threshold concepts. Journal of Philosophy of Education, 41(2), 263–270. http://doi.org/10.1111/j.1467-9752.2007.00554.x
Von Glaserfeld, E. (1988). Cognition, construction of knowledge, and teaching. National Science Foundation.
Walker, B. M., & Winter, D. a. (2007). The elaboration of personal construct psychology. Annual Review of Psychology, 58, 453–477. http://doi.org/10.1146/annurev.psych.58.110405.085535