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2. Threshold Concepts

Threshold concepts have been proposed as a way of characterising the progression of students at the discipline level. Meyer and Land (2003, 2006) suggest that within each subject there are certain ideas that present themselves to students as portals that can open up a new way of thinking within a particular domain. They propose that threshold concepts integrate, transform and set boundaries to the discipline and probably are irreversible and troublesome for the learner.

The approach is thus concerned with conceptual change and whether students have reached a certain level of understanding that may be interpreted as ‘thinking like an economist’. Getting to this position does not simply require a one-off change, but the integration of previously acquired (but maybe not fully understood) concepts and is likely to take time. On the basis of evidence gathered from students and lecturers in economics, the project suggested that a three-way categorisation of conceptual change may be useful in economics. This is summarised in Table 1 and explored in the rest of this section.

Table 1 Definition and exemplification of three types of conceptual change

Type of conceptual change
Type of transformation and integration
Examples in economics
1. Basic
Newly met concepts some of which transform understanding of everyday experience through integration of personal experience with ideas from discipline.
Distinctions between price/cost; income/wealth (stocks/flows); nominal/real values; investment/saving. Real money balances, natural rate of unemployment.
2. Discipline threshold concepts
Understanding of other subject discipline ideas (including other threshold concepts) integrated and transformed through acquisition of theoretical perspective.
Marginality, opportunity cost, incentives (in particular the role and limitations of the price mechanism), cumulative causation (as for instance in the multiplier).
3. Modelling concepts
An understanding of the subject’s modelling procedures that enable the construction of discipline specific narratives and arguments (ways of practising).
Comparative statics (equilibrium, ceteris paribus), time (short-term, long-term, expectations), elasticity.

Adapted from Davies and Mangan (2007)

Students have to acquire the specialist language which is associated with the discipline mode of thinking. This involves several types of development:

  • They importantly have to rework prior (naïve or ‘common-sense’) understanding that may come from their general life or from their previous studies in economics. Students have to differentiate between price and costs, money and income, real and nominal values, and between savings and investment. They may need to develop their understanding from A level and appreciate how different the concept of aggregate demand is from the concept of demand for a particular good. Prior concepts may also be coalesced into a single concept. For example, the task of explaining a change in wages may come to be seen as similar to the task of explaining a change in prices since wage is the price of labour.
  • Also, a concept that is defined in terms of properties may be transformed into a concept defined in terms of relationships. A conception of price as a property of a product may be transformed into a conception of price as the outcome of a relationship between demand and supply.

The notion of ‘troublesomeness’ is involved in such development since students come with pre-conceived ideas on what is meant by, for example, terms such as ‘money’ (usually considered as income) and ‘investment’ (not distinguished from saving) which they then need to revise given the more precise use of the concept in the discipline. However, we have labelled all such changes in understanding as ‘basic’ in Table 1, row 1 as they do not involve substantial integration of thought.

Basic concepts provide ways of categorising phenomena in ways that are necessary for the deployment of threshold concepts. However, students cannot fully appreciate why these categorisations are necessary at this stage and this creates a problem for learners. The lack of a framework for their understanding may initially mean that the learning is ‘shallow’ with students trying to remember formal definitions and outcomes. Students may appear to understand a basic concept when they use the appropriate terms. But this can be deceptive as they probably do not understand these words in the same way as an expert. But this initial, shallow understanding is a necessary first step on the road towards a richer understanding. It is only once a transforming threshold concept has been subsequently incorporated into a learner’s thinking that the full significance of a basic concept can really be grasped; they will have to revisit these concepts as they acquire the integrating framework to achieve a more sophisticated understanding.

Top Tip

Students frequently only half understand concepts that have been covered before. So get them to revisit and develop their understanding of an idea in a new context.

As teachers of economics we typically imagine that learning our subject is relatively ‘untroublesome’ when students are prepared to work at it. In fact, many students get stuck, even with ‘basic’ ideas. Whenever research has attempted to uncover what economics students really understand (as opposed to what they can produce in a more or less verbatim fashion) the findings have been frankly shocking. Within the Embedding Threshold Concepts project we recorded students’ group discussion on applied topics in class that were related to the more formal teaching over the previous weeks (at Level 1 in three institutions). An example is given in the case study in section 5 of this chapter. These revealed considerable misunderstanding of basic concepts as well as in many cases a basic lack of understanding that economists usually start the analysis by considering which model to use. Teaching that fails to appreciate the limited nature of students’ understanding is bound to fail. Providing detailed guidance and cues in examination questions can disguise the problem but it comes at the cost of undermining public confidence in the value of what we do.

Conceptual change may also operate at a more profound level through the acquisition of organising schemas that can be associated with the development of disciplinary thought. These developments in academic thought have not occurred simply through supplanting naïve, common-sense notions by more powerful explanatory frameworks. New developments within subjects change the way that members of academic communities think about other ideas that have been developed within the discipline. An example in economics could be the marginalist revolution. Initial learning of some ‘basic’ concepts such as marginal cost and marginal revenue may be as isolated objects in the learner’s thinking, but acquiring such frameworks helps the learner to revisit these concepts, employing a deep approach to learning that integrates basic concepts into these organising schema. In these cases the new conception is transformative insofar as it integrates and reworks other disciplinary ideas that the learner has previously acquired and we refer to this as a ‘discipline’ threshold concept in Table 1. New phenomena that the learner encounters are then interpreted within that framework.

Pursuing the example of marginality, initially most students approach marginal utility, marginal cost, revenue, etc. as separate concepts to define and calculate (remembering them by rote learning). However, being able to carry out these functions is not the same thing as understanding the importance of marginality in economic thinking. This raises the problem that a deep understanding of any of these ideas often requires a student to create links with a broader conceptualisation of the topic, which has to be built from the very ideas that the student has yet to understand. The importance of the concept of marginality comes in recognising its central role in decision making and some students may first come to understand this when using it in the theory of the firm, but revisiting the concept in welfare economics may deepen their understanding and transform their previous understanding of the theory of the firm.

However, there is another important aspect that we need to consider. Discipline thresholds (row 2 of Table 1) are associated with ways of practising the subject: the discipline specific procedures that are used in analysis and the construction of arguments – in economics our use of models. For example, economists make considerable use of ‘comparative statics’. This procedure involves the use of comparison of equilibrium positions, using the notion of ‘ceteris paribus’ in their reasoning. We use this idea in lieu of being able to conduct closed experiments so it is employed as a ‘what if’ assumption in deductive reasoning. A student who does not understand this device appropriately will have great difficulty in constructing narratives that appear appropriate to an economist and they will be reduced to the ‘shallow’ learning of specific outcomes. At level 1, which was the primary focus of our project, models are often represented graphically and understanding the modelling procedures is necessary to understanding rather than reproducing the diagrams. Many of our students may come to us having found ‘learning the diagrams’ an approach that gave them good marks at A level, but with the increasing number and complexity of diagrams they meet in their undergraduate experience this ‘surface learning’ strategy will fail them. In the threshold concepts approach they need to understand the conceptual basis of the techniques behind the diagrams in order to progress. Learning how to select, amend and test economic models is a central part of undergraduate education in economics and we will refer to this as ‘modelling’ conceptual change (row 3 of Table 1). The modelling concepts are ‘enablers’ without which a students cannot achieve a more complete understanding of the discipline concepts and so again are integrative and transformative and may be considered as threshold concepts.

Top Tip

Make the modelling process explicit in lectures and seminars. In introductory economics courses students need to understand that our diagrams are tools to make sense of a problem and not things to try and simply memorise.

We therefore have a framework in which students will have to revisit concepts in order to develop a deep understanding. The links in this process are illustrated in Figure 1. Although we want students to progress from basic concepts to threshold concepts, this is shown as a long grey arrow in the diagram as largely this is not achieved directly. Students need the modelling concepts as ‘enablers’ in the process and so the link is from basic concepts to modelling concepts to threshold discipline concepts. In addition there are feedback loops, shown as dashed lines from the modelling concepts and threshold discipline concepts back to basic concepts, representing the deeper understanding of these concepts as learning progresses.

Figure 1: Learning and integration between concepts

There is, however, one final complication in learning; in economics the threshold concepts themselves form a web of understanding. Newly acquired threshold concepts may deepen understanding of previously acquired threshold concepts; for instance, understanding marginality (through applications, for instance, in the theory of the firm) may deepen the understanding of opportunity cost – a learning spillover (Guest and Vecchio, 2003). In analysing particular applications, both in their course and outside, students are likely to require a range of discipline, modelling as well as basic concepts. Figure 2 illustrates this using the threshold concept of opportunity cost. Students usually meet opportunity cost in the first few weeks of their undergraduate course and usually have little difficulty in applying this to simple, single country or personal examples. However, they often fail to understand the implications of opportunity cost in more complex situations. The diagram illustrates two ways in which opportunity cost is an important element in theories that are met by first-year students, the competitive equilibrium of the firm and comparative advantage. In these theories opportunity cost is used along with a range of other concepts (that is different in the two cases) in deriving the outcome and the diagram illustrates some of the ideas that are necessary. Most of these are basic concepts, although some may be other threshold concepts – for instance the competitive equilibrium of the firm example includes the threshold concept of marginality.

Considering the comparative advantage example given in Figure 2 in more detail, students need to understand that the analysis proceeds on the basis of full employment of resources and that more consumption is interpreted as a gain in welfare in order to consider the application of opportunity cost in this context. Recordings of student discussion of the gains from trade carried out within the Embedding Threshold Concepts project found that these were dominated by discussion of jobs. Although in mainstream economics we may want students to pursue such aspects in a critical analysis, starting with jobs was preventing student comprehension of the theory. Understanding differences in factor endowments and technology may help students in considering why the differences in opportunity costs arise; while crucially students need to consider the relative costs of production (measured of course in opportunity cost terms).

Students need to recognise the value of other concepts and how they interact with opportunity cost given the particular issue under consideration. Rather than seeing each new context as simply something different to be learnt, students need to be encouraged to reflect on how this new situation can develop their thinking in an integrated fashion, rather than treating each new context as a separate entity.

Figure 2 Opportunity cost and the integration of concepts in two applications