EDITORS’ PREFACEstudents bring to a <strong>threshold</strong> concept in the preliminal state, for, as with priorcontent knowledge, students may vary greatly in the amount of prior tacitknowledge they have of particular <strong>threshold</strong> <strong>concepts</strong>. The authors then tread newground in researching whether an association exists between <strong>threshold</strong> conceptunderst<strong>and</strong>ing <strong>and</strong> attrition from a course of study. The focus of their study isan examination of the association between students’ observed grasp of certain<strong>threshold</strong> <strong>concepts</strong> in economics at the start of a semester <strong>and</strong> their likelihood ofleaving an introductory microeconomics course in that same semester. An interestingsecondary consideration of their study is the hypothesis that an important ontologicalshift is also required on the part of students – a shift in which one comes to viewoneself as a bona-fide student learner – as ‘a necessary preliminary stage ofthinking that must be attained by students before discipline <strong>threshold</strong> <strong>concepts</strong>become relevant’. In terms of attrition they speculate that it is the students who failto make this shift that are the most likely to leave the course early. Moreover, theysuggest that ‘the impact of preliminal knowledge of economic <strong>threshold</strong> <strong>concepts</strong> isonly relevant once this transformation is made’. The findings of the enquiry leadthe authors to believe that, though the factors associated with student attrition aremany, an important conceptual portal that many students must negotiate as a markof commitment to their studies is that of ‘self-identification as a university student’.An interesting secondary finding is that, once a student has committed to study(roughly completion of the first semester of teaching), then variation in students’grasp of discipline-based <strong>threshold</strong> <strong>concepts</strong> may be associated with an individuals’preparedness to sit the exam. Self-identification as a university learner is a cleardeterminant of student retention in these findings, although, as the authors indicate,‘the distribution of previously acquired <strong>threshold</strong> <strong>concepts</strong> does appear to besystematically related to other differences that place students at risk of failing’.Ference Marton, a leading proponent of variation theory, recently commentedthat:The one single thing that would improve the quality of teaching <strong>and</strong> <strong>learning</strong>in higher education would be if academics in different disciplines took timeto meet together <strong>and</strong> discuss what they should be teaching in their subject,<strong>and</strong> how they should be teaching it. This is something that Variation Theoryhas not done, <strong>and</strong> I think the Threshold Concepts approach encouragespeople to do this. In my opinion there is absolute complementarity betweenThreshold Concepts <strong>and</strong> Variation Theory. (Marton 2009).In a significant example of academic specialists engaging in exactly such a conversation,<strong>and</strong> also reaching conclusions on the possible complementarity betweenThreshold Concepts <strong>and</strong> Variation Theory, Michael Flanagan, Philip Taylor <strong>and</strong>Jan Meyer (Chapter 14) examine the ways in which ‘transmission lines’, a <strong>threshold</strong>concept in electrical engineering may come into view quite differently dependingon whether the concept is introduced from a perspective of large-scale systems(power engineering) or small-scale systems (instrumentation <strong>and</strong> electronics) <strong>and</strong>whether students are envisaging power transmission along overhead power lines oralong coaxial cables. In experimental tests in the former, students struggled withxxiii
LAND ET ALthe notion of reactive power. As a complex idea of what is in effect ‘powerlesspower’, requiring the use of (imaginary) complex number, students found this bothcounter-intuitive <strong>and</strong> ‘mentally awkward’. With small-scale systems studentsstruggled similarly with the idea of characteristic impedance. Students in bothengineering contexts were left frustrated, perplexed <strong>and</strong> confused, <strong>and</strong>, as we haveseen elsewhere in <strong>threshold</strong> analyses, resorted to ‘mimicry’ as a coping strategy.For some students, the authors point out, it became clear that ‘elaborating thesimpler concept of current flow down a wire into a mathematical treatment of theassociated electromagnetic field was troublesome <strong>and</strong> counter-intuitive especiallyas the concept of the electric or magnetic field itself is troublesome’. Indeed, toexacerbate the problem, the authors comment that ‘fields’ may operate as <strong>threshold</strong><strong>concepts</strong> in their own right. One source of the conceptual difficulty was that thestudents found it difficult ‘to envisage any associated physical reality in thecalculations of the properties of a travelling electromagnetic wave (the signaltravelling along the line) using complex arithmetic’. In terms of a ‘spiral curriculum’(Bruner, 1960), <strong>and</strong> an analysis of how earlier preparation in the simplified equationsof high school physics might have adversely affected subsequent coping with a morecomplex university curriculum, the authors conclude that such earlier <strong>learning</strong>presented three potential barriers to <strong>learning</strong>. Firstly, the concrete had preceded theabstract; secondly, the detailed had preceded the general; <strong>and</strong> thirdly, perceptionwas now preceding cognition. The authors’ view was that each of these <strong>concepts</strong> ofreactive power <strong>and</strong> characteristic impedance were in fact acting as portals to usherstudents into a far more complex liminal space involving underst<strong>and</strong>ing of electromagnetictheory. A number of issues follow from this. One practical problem isthat students are not in a position realistically to experiment with large-scale powersystems. Though recent computer simulation packages open up interesting <strong>and</strong>potentially helpful possibilities in this regard there is the danger of studentsperforming calculations in a ‘ritualistic’ fashion without underst<strong>and</strong>ing (Perkins,1999). Moreover, in relation to possible complementarity between <strong>threshold</strong><strong>concepts</strong> <strong>and</strong> variation theory the authors observe that:If a troublesome concept is flagged by students <strong>and</strong>/or staff that is, in reality,a portal to a much more complex liminal space there is a risk that a variationalapproach constructed around this troublesome concept alone may noteffectively aide the students in mastering their difficulties.In terms of the kinds of knowledge that engineering students should encounterduring an engineering degree, the study of <strong>learning</strong> <strong>threshold</strong>s in relation toelectromagnetic theory raises more far-reaching issues of where applied physicsmight end <strong>and</strong> electronic engineering begin, <strong>and</strong> whether engineering graduates aredefined by their skills or their particular industry.In Chapter 15 we encounter another ‘disciplinary conversation’ taking place.Lynda Thomas, with her colleagues Jonas Boustedt, Anna Eckerdal, RobertMcCartney, Jan Erik Moström, Kate S<strong>and</strong>ers <strong>and</strong> Carol Z<strong>and</strong>er, report on thefindings of a multi-national, multi-institutional project that has now been underway for four years <strong>and</strong> which is seeking an empirical identification of <strong>threshold</strong>xxiv
- Page 1 and 2: EDUCATIONAL FUTURES: RETHINKING THE
- Page 3 and 4: EDUCATIONAL FUTURESRETHINKING THEOR
- Page 5 and 6: A C.I.P. record for this book is av
- Page 7 and 8: TABLE OF CONTENTS10. Threshold Conc
- Page 9 and 10: Pax Intrantibus Salus Exeuntibus. L
- Page 11 and 12: LAND ET ALstudents experience diffi
- Page 13 and 14: LAND ET ALModePreliminalLiminalPost
- Page 15 and 16: LAND ET AL(Barker, 1991, p.184). Th
- Page 17 and 18: LAND ET ALvariations arising from t
- Page 19 and 20: LAND ET ALform of a model of concep
- Page 21 and 22: LAND ET ALQuestions of intersection
- Page 26 and 27: EDITORS’ PREFACEconcepts in the f
- Page 28 and 29: EDITORS’ PREFACEIn the final illu
- Page 30 and 31: EDITORS’ PREFACEhence becomes a n
- Page 32 and 33: EDITORS’ PREFACElearning. This th
- Page 34 and 35: EDITORS’ PREFACEa lens or ‘way
- Page 36 and 37: EDITORS’ PREFACEHence learning is
- Page 38 and 39: EDITORS’ PREFACEthe Communitas, w
- Page 40 and 41: EDITORS’ PREFACEBuilding on these
- Page 42 and 43: EDITORS’ PREFACECousin, G. (2009)
- Page 44 and 45: DAVID PERKINSFOREWORDEntrance…and
- Page 46: FOREWORDMeyer, J.H.F., Land, R. & D
- Page 50 and 51: JULIE A. TIMMERMANS1. CHANGING OUR
- Page 52 and 53: CHANGING OUR MINDSKegan’s (1982)
- Page 54 and 55: CHANGING OUR MINDSKegan describes e
- Page 56 and 57: CHANGING OUR MINDSIn fact, Kegan an
- Page 58 and 59: CHANGING OUR MINDSat the epistemolo
- Page 60 and 61: CHANGING OUR MINDSMight a learner r
- Page 62 and 63: CHANGING OUR MINDSreveals an additi
- Page 64 and 65: CHANGING OUR MINDSBendixen, L. D.,
- Page 66: CHANGING OUR MINDSSibbett, C., & Th
- Page 69 and 70: SCHWARTZMANScholarship in liminalit
- Page 71 and 72: SCHWARTZMANTC: the entityThe term T
- Page 73 and 74:
SCHWARTZMANA resource for teaching
- Page 75 and 76:
SCHWARTZMANunprecedented to attract
- Page 77 and 78:
SCHWARTZMANspectrum of scholarship
- Page 79 and 80:
SCHWARTZMANrupture and phenomenolog
- Page 81 and 82:
SCHWARTZMANfield(s) of one’s cons
- Page 83 and 84:
SCHWARTZMAN36DATA: PARTICULARS GIVI
- Page 85 and 86:
SCHWARTZMANchallenge than interpret
- Page 87 and 88:
SCHWARTZMANStrategies for Teaching:
- Page 89 and 90:
SCHWARTZMANThey are redefined here
- Page 91:
SCHWARTZMANLoder, J. (1981). The tr