3. Implications: four principles for teaching and learning
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In this section we use some ideas from ‘variation theory’ (Pang and Marton, 2003, 2005) to develop some implications for teaching. The main pedagogic principle derived from variation theory is that the lecturer should draw the learner’s attention to simultaneous variation in the features of a phenomenon that are critical to the desired conception (i.e. the way of understanding something that the lecturer wants the student to achieve). This has led to the proposal of four principles for teaching (Davies and Mangan, 2008), which we reproduce here with discussion and examples:
(i) Highlight variation to ensure there is a sufficient foundation of basic concepts to make it possible to work towards acquisition of the threshold concepts
Students need to acquire certain basic concepts before they can move on to acquire the integration provided by the threshold concepts and although, as we considered above, they are unlikely to achieve a full, deep understanding of these at this stage, progress cannot be made without acquiring some initial knowledge. Highlighting variation in understanding of a conception and giving feedback on what dimensions are useful and what are not may provide a foundation for the deeper study. For example, Pang and Marton (2003) distinguish various conceptions of price held by students in terms of what is related to the inherent value of the commodity concerned, the demand conditions, the supply conditions, and the demand and supply conditions.
(ii) Expose the way in which scholars in the discipline use modelling threshold concepts by highlighting variation in the use of key procedures
This is concerned with developing an understanding of the way models are used in the discipline; why we set up models as we do. Given the complexity of the relationships in the economy, economists use economic models to understand the important interrelationships in the economy. Comparative static analysis is a procedural device developed by the discipline to portray these relationships. Students need to understand why we use such models, the importance of key aspects of such modelling and how this relates to the diagrammatic (or mathematical) representation. An important aspect of this is in understanding the nature of equilibrium in economic reasoning, in terms of it being a final resting point to which markets will move after a shock and also importantly in terms of the forces that resolve the disequilibrium in the model being considered. For instance, without an understanding of this, students may understand the multiplier as simply a never-ending process of interrelationships where an increase in income leads to increased consumption without recognising that in the model there is a limit, with the rise in withdrawals, where the new equilibrium point is reached.
(iii) Help students to integrate their understanding by re-working their understanding of previously acquired concepts in the light of threshold concepts
This helps students to think of their learning in terms of building a coherent structure. For instance, students may initially consider various ‘marginal’ concepts such as marginal cost, marginal revenue and marginal utility just as isolated ideas, but their understanding of the relevance of these may be enhanced as they acquire an understanding of welfare economics. In macroeconomics, the relevance of the distinction between money and income may only become clear when students start to understand the interaction between the goods and money markets in developing their understanding of the macroeconomy with models such as IS/LM.
We need to design activities that both highlight the role of threshold concepts and procedures and allow the revisiting of previously acquired concepts (both basic and previously ‘acquired’ threshold concepts, given our arguments about the web of concepts above). It is only when students do this that can they progress in their understanding and we need to encourage them to do this both in formal teaching situations and in their independent learning.
(iv) Help students to regard their understanding as provisional and to tolerate uncertainty
Students have to learn ‘incomplete’ conceptions in order to make more ‘complete’ conceptions accessible to them and be happy to move on. Since the acquisition of threshold concepts transforms understanding of previously acquired subject knowledge, students need to be ready to accept that at each stage in their learning their understanding is provisional. This problem becomes most intense when the acquisition of a new threshold concept transforms understanding of a previously acquired threshold concept: an inevitable outcome if threshold concepts work together in a web to define the way of thinking and practising in a subject.
Encourage students to understand that they need to re-work everything they have learnt before – and to see previous learning as necessary, partial and incomplete rather than wrong.