0 Introduction It has long been a matter of concern to teachers in higher education why certain students get stuck at particular points in the curriculum whilst others grasp concepts with comparative ease What might account for this variation in stud ID: 30395
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Threshold concepts andRay Land (Coventry University), Glynis Cousin (Warwick University), Jan H F Meyer(Durham University) & Peter Davies (Staffordshire University) 1.0Introductionget stuckat particular points in the curriculum whilst others grasp concepts withcomparative ease. What might account for this variation in student performance and,more importantly, what might teachers do in relation to the design and teaching of theircourses that might help students overcome such barriers to their learning? As studentsissues are becoming of increasing importance across all disciplines. Afurther and relatedtroublesometo students. What makes particular areas of knowledge more troublesomeWithin all subject areas there seem to be particular concepts that can be considered assomething. Athreshold concept represents a transformed way of understanding, orinterpreting, or viewing something without which the learner cannot progress. As ainternal view of subject matter, subject landscape, or even world view, and the studenta paper presented at an earlier ISLconference that they are irreversible(unlikely to be forgotten, orunlearned only through considerable effort), and hidden interrelatedness of something). They also entail a shift in learner subjectivity and Part II:Course and programme design 53 * Please note that this chapter constitutes the third in a series on this topic. The two earlier pieces are listed in 2.0Threshold conceptsmeaning and derivation of the term threshold concept. The idea of a threshold concepthas been developed by Meyer and Land (2003) in the context of the ETLproject.Threshold concepts are defined as concepts that bind a subject together, beingfundamental to ways of thinking and practising in that discipline. They have attractedparticular interest from economics communities in the UK (Davies, 2003) and Australia(Shanahan and Meyer, 2003). Once a student has internalised a threshold concept theyare more able to integrate different aspects of a subject in their analysis of problems.Students who have not yet internalised a threshold concept have little option but towho are studying a subject (such as economics) as part of their degree. Students who donot think of themselves as learners of economicsare likely to face particular difficultiesto a novice. This problem arises because the acquisition of such concepts (eg opportunitythinkand practice.3.0Troublesome knowledgetroublesomeof which is that such transformation entails a letting go of earlier, comfortable positionsand encountering less familiar and sometimes disconcerting new territory. ThresholdAnd why I think depreciation is a threshold concept, is that because what it drawsin to an understanding of depreciation is a particular way of viewing businesscommonsense or intuitive framework it isnt a particularly natural process andactually the more you look at it the more contrived it gets, because it isnt just astraightforward alternative framework. Actually, within the framework, there arelots of compromises. And it is based, in part, on the intuitive framework. In fact themore I think about it now, I am changing my mind about the students Improving Student Learning: Diversity and Inclusivity 54 The transformation mentioned earlier can also entail a shift in the learners identity. Theresult may be that students remain stuck in an in-betweenstate in which they oscillatebetween earlier, less sophisticated understandings, and the fuller appreciation of aconcept that their tutors require from them. This in-between state we have termed a statelearned which we have characterised as a form of mimicry. Amore serious outcome isways of helping students to overcome such epistemological obstacles(Brousseau 1983).We would seek to create supportive liminal environments to help students through suchdifficulty what might be characterised as a kind of conceptual peristalsis that theyconsciousness(Giddens, 1984) though its emergent but unexamined understandings areoften shared within a specific community of practice (Wenger, 1998). In other instancesNow if you think about the word cost, really all it means is, it is a value, anacquisition value. So instead of using the word costyou could say this acquisitionvalue, and it would mean the same thing wouldnt it? But the words valueandcostare quite troublesome, literally, in accounting (and in economics), becausecostcan mean very different things depending on who the user is, and for whatpurpose you are calculating the cost. So, you know, in accounting you might havethree or four very different understandings of what costmeans. 4.0Threshold To complicate matters further, in some instances students may grasp concepts but thestudent finds difficulty in appreciating what Perkins (2005) has termed the underlying. Like the characters in Buñuels (1962) film, , who cannot leave the house in which they have attended a dinner,but are unable to account for their immobility, the students similarly are unaccountablyunable to move on. An example would be where students of electrical engineering canIn computer programming, similarly, students may grasp the concepts of class, objects, Part II:Course and programme design 55 underlying game, of the interaction of all these elements in a process of ever-increasingcomplexity. Such instances present teachers with particularly difficult challenges in classSavin-Badens work (2005) on the notion of disjunctionin problem-based learningDisjunctionrefers to the idea of becoming stuckin learning and I have suggestedelsewhere (Savin-Baden, 2000) that disjunction can be both enabling and disablingplace that students might reach after they have encountered a threshold conceptthat they have not managed to breach. Many staff and students have describedvarious strategies to try to deal with it. These include retreating from the difficultydirectly in an attempt to relieve their discomfort (Savin-Baden 2005: in press)If the portal appears bricked upthen clearly the threshold of new transformativeunderstanding is not visible to the student. Savin-Baden argues that, although disjunctionoccurs in many forms and in diverse ways in different disciplines, it seems to beShe suggests that this may be because PBLprogrammes prompt students to critique andbeing troublesome earlier than students in more traditional programmes. However, sheit might also be that problem-based learning encourages students to shift awayfrom linear and fact finding problem-solving. Instead they move towards forms ofproblem management that demand the use of procedural and personal knowledgeas students are asked to engage with strategy or moral dilemma problems. Thus itmight be that disjunction is not only a form of troublesome knowledge but also aspaceor positionreached through the realisation that the knowledge istroublesome. Disjunction might therefore be seen as a troublesome learning spacethat emerges when forms of active learning (such as problem-based learning) areused that prompt students to engage with procedural and personal knowledge5.0Considerations for course design andfor learning and teaching. At a general level we would argue that programmes should bea)the sequence of content; Improving Student Learning: Diversity and Inclusivity 56 b)the processes through which learners are made ready for, approach, recognise, andinternalise threshold concepts. We would argue that this process of the studentsc)the ways in which learners and teachers recognise when threshold concepts havebeen internalised in effect what would constitute appropriate assessment for the5.1 Jewels in the curriculumthe students learning experience. In this sense they may be viewed as the jewels in thecurriculuminasmuch as they can serve to identify crucial points in the framework ofcomplex insights into aspects of the subjects they are studying. They may also serve alikely to encounter troublesome knowledge and experience conceptual difficulty thestuck placesto which Ellsworth refers (1997:71).5.2 The importance of engagementin which it was presented (Colby et al, 2003: 263). We would wish to appropriate theseemphases and, with Wenger, think about constructing a automotive design. We will wish our students not only to understand how historians Part II:Course and programme design 57 spoken of the kinds of engagement or praxis where the effort is to provoke somethingelse into happening something other than the return of the same(1998: 492). As coursedesigners what provocationsmight we be seeking through these forms of engagement to5.3 Listening for understandingHowever, teaching for understanding of threshold concepts needs to be preceded byvariationin the ways in which students approach, or come to terms with, a thresholdconcept, we cant second guess where students are coming from or what theiruncertainties are. It is difficult for teachers, experienced and expert within the discipline,backwards across thresholds and understand the conceptual difficulty or obstacles that astudent is currently experiencing. This requires cultivating a third ear that listens not forstudents knowledge, her not knowing, her forgetting, her circles of stuck places andresistances(Ellsworth1997:71). 5.4 Reconstitution of selfrepositioning of self in relation to the subject. This means, from the viewpoint ofhas become ritualised, or inert, because it is conceptually difficult or alien, because it istacit and perhaps requires awareness of an underlying gameimperceptible to the studentas students acquire threshold concepts, and extend their use of language in relationto these concepts, there occurs also a shift in the learners subjectivity, arepositioning of the self What is being emphasised here is the inter-relatedness ofthe learners identity with thinking and language. Threshold concepts lead not onlyextended discourse (Meyer and Land 2005: in press).go the security of a previously held conceptual stance to enter less certain terrain. Againtransformations might take place and the need for the teacher to provide what Winnicott(1971) used to term a holding environmentor nurturing space. We prefer to call this asupportive liminal environment, feeling that Winnicotts term suggests a somewhat static,even inhibitive space, rather than the peristaltic process discussed earlier. Given, too, that Improving Student Learning: Diversity and Inclusivity 58 tolerate uncertainty.5.5Tolerating uncertaintyprogramme too conceptually difficult. She commented, however, that had she known, attransition would have been easier. The next time she faced such troublesome knowledge,she asserted, she would hang in therewith greater confidence because now she knewWhat distinguishes metacognitive feelings is their cognitive and affective nature.Metacognitive feelings take the form of feeling of knowing, of familiarity, ofdifficulty, of confidence, and of satisfaction, whereas metacognitive judgments orestimates can take the form of judgment of learning, of where, when, and how weacquire a piece of information, of time and effort spent on a task. Metacognitiveof the learning process and at thesame time provide an intrinsic context within which learning processes take place.This intrinsic context is to a large extent affective and determined by self processes,individual difference factors as well as task factors, including task difficulty, taskinstructions, and feedback used. The intrinsic context influences studentsstrategiesin problem solving, but also their emotions, causal attributions, and self-concept. Inthis way, metacognitive experiences affect both online task processing and futuremotivation towards learning. (Efklides 2005:in press)5.6 Recursiveness and excursivenesswill need to adopt a recursive approach to what has to be learned, attempting differenttakeson the conceptual material until the necessary integration and connectiondiscussed earlier begins to take place. The need for the learner to grasp thresholdlearning outcomesmodel where sentences like by the end of the course the learner will Part II:Course and programme design 59 be able toundermine, and perhaps do not even explicitly recognise the complexitiesof the transformation a learner undergoes. It is likely that any course requiring studentto some extent rattles the cageof a linear approach to curriculum design that assumesstandard and homogenised outcomes. Lather (1998:492) offers a counter-narrativerejecting the rhetorical position of the one who knowsin favour of a praxis of notbeing so sure. Apraxis of stuck placesmight tolerate discrepancies, repetitions,hesitations, and uncertainties, always beginning again(491). What it refuses is theprivileging of containment over excess, thought over affect, structure over speed, linearcausality over complexity, and intention over aggregate capacities(497). We wouldargue, similarly, for the notion of learning as direction. The eventual destination may be reached, or it may be revised. It may be a5.7 Pre-liminal variationAn abiding question for educators, and for course designers in particular, is why someearlier and others find difficulty in doing so. Does such variation explain how thecomes into view? And how does it come into viewfor individual students? We need toprogression (Meyer and Shanahan 2003). To this end a three-year funded study on6.0 below) to investigate systematically, amongst other phenomena, the issue of pre-5.8Unintended consequences of generic goodThere is emerging indicative evidence from research into threshold concepts (eg Meyerpedagogymay, on occasion, break down or prove dysfunctional in relation to theeconomics in a South Australian context. Improving Student Learning: Diversity and Inclusivity 60 one implication of the argument presented thus far is that first impressions matter.Efforts to make threshold concepts easierby simplifying their initial expressionand application may, in fact, set students onto a path of ritualisedknowledge thatactually creates a barrier that results in some students being prevented fromcrossing the thresholdof a concept (Meyer and Shanahan, 2003, p15)fuller, more sophisticated understanding which it was intended to lead on to, was foundto operate more frequently as a false proxy, leading students to settle for the naïveversion, and entering into a form of ritualised learning or mimicry. Such findings maydiscussed earlier. ineffective in a first year introductory accounting course which sought to help studentssignificant budgetary or financial experience in the studentsexperience which renderedthe approach ineffective. It would seem salutary, therefore, periodically to cast a coldreviewers eye over tried and tested good pedagogy.5.9 The underlying gameFinally, in the light of our earlier discussion of threshold advisable for course designers to query whether, in addition to the forms of engagementprogramme, there might remain what Perkins calls an underlying gameor thresholdand alternativeunderstandings of threshold concepts. Authorisedunderstandings areAlternativeunderstandings of events and transactions are independent of authorisedconcept such as depreciationor profit. Alternativeunderstandings might on occasionbe substituted for, or provide an alternative to, the authorised versions. Often, whereto the authorised (and perhaps counter-intuitive ortroublesome) versions promulgated within the course. Thus a particularly important (orthreshold conceptionmay be required to recognise the difference Part II:Course and programme design 61 6.0Case study developing first yearundergraduatesacquisition of thresholdconcepts in economicsa given disciplinary context. Athree year national project, funded by the HEFCE FDTL5programme, is currently getting under way as a collaborative venture led by StaffordshireUniversity and involving the Universities of Coventry, Durham, and the West of England.understand these ideas in a deep-level transformative way. We aim to develop methods ofassessing variation in the acquisition of threshold concepts. These methods will helpstudents as well as lecturers to recognise levels of understanding. Studentsacquisition ofare therefore likely to initially approach their studies. The project will aim to developacquire these concepts. We anticipate that careful evaluation of the process and outcomeseconomics and in other subjects. The emphasis on teaching strategies that can respond toriskstudents. Shanahan and Meyer (2003) have shown how recognition of failure toacquire threshold concepts can form part of the process of identifying at riskstudentsand that remedial measures can improve retention. We hope similarly to be able todifferent named awards. Based on previous work on threshold concepts in economics(Davies, 2003; Shanahan and Meyer, 2003; Reimann and Jackson, 2003) the initial focuswill be upon studentsunderstanding of opportunity cost, price and value, equilibriumand gains from trade. These concepts feature frequently in standard first-year courses. OnSubject Centre in the UK we anticipate further threshold concepts in economics. The7.0ConclusionThe task for course developers and designers here is to identify, through constructivesubsequently to free up the blocked spaces by, for example, redesigning activities and Improving Student Learning: Diversity and Inclusivity 62 sequences, through scaffolding, through provision of support materials and technologiesnecessary shift in perspective that might permit further personal development. The wayin which chess players talk of developinga piece involves the removal of other piecesempowered to move. The significance of the framework provided by threshold conceptsstudents to negotiate such transitions more successfully.Bonamy, J, Charlier, B and Saunders, M (2001) Bridging Toolsfor change: evaluating aJournal of Computer Assisted LearningVol 17, no 3Recherches en didactique des mathematiques, Vol 4 no 2 pp165-198.Colby, A, Ehrlich, T, Beaumont, E and Stephens, J (2003) Educating Citizens: PreparingAmericas Undergraduates for Lives of Moral and Civic ResponsibilityThreshold Concepts, Troublesome Knowledge and Learning aboutConference of the European Association for Research on Learning andInstruction (EARLI), Padua, Italy, August 26-30.Davies P(2003) Threshold Concepts: How can we recognise them?the Biennial Conference of the European Association for Research into Learning andEfklides, A(2005) , in Meyer, J.H.F andOvercoming Barriers to Student Understanding: Threshold Concepts andTroublesome KnowledgeTeaching Positions: Difference Pedagogy and the Power of AddressTeachers College Press, New York.Lather, P(1998) Critical Pedagogy and Its Complicities: APraxis of Stuck Places,, Fall 1998, Volume 48, Number 4, 487-498.Lucas, U (2000) Worlds apart: studentsexperiences of learning introductory accounting.Critical Perspectives on Accounting, 11, 479-504.Meyer JHF and Land R (2003) Threshold Concepts and Troublesome Knowledge (1) Linkages to Ways of Thinking and Practisingin Improving Student Learning Ten YearsMeyer JHF and Land R (2005) Threshold Concepts and Troublesome Knowledge (2) Epistemological Considerations and a Conceptual Framework for Teaching and Learning Part II:Course and programme design 63 Meyer, JHF and Shanahan, M (2003) The Troublesome Nature of a Threshold Concept in, Paper presented to the 10th Conference of the European Association forResearch on Learning and Instruction (EARLI), Padua, Italy, August 26-30.Perkins, D (1999) The Many Faces of Constructivism, , VolumePerkins, D (2005) The underlying game: troublesome knowledge and thresholdconceptions, in Meyer, J.H.F and Land, R. (eds) Overcoming Barriers to StudentUnderstanding: Threshold Concepts and Troublesome KnowledgeThreshold Concepts in Economics: a Case StudyConference of the European Association for Research on Learningand Instruction (EARLI), Padua, Italy, August 26-30.based learning, in Meyer, JHF and Land, R (eds) Overcoming Barriers to StudentUnderstanding: Threshold Concepts and Troublesome KnowledgeFalmer.Wenger, E (1998) Winnicott, DH (1971) . New York: Basic Books. Improving Student Learning: Diversity and Inclusivity 64