Modelling and learning a complex concept - an exploration in light of some examples from electric circuit theory (original) (raw)
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Investigating engineering students' learning – learning as the ‚learning of a complex concept
In both engineering and physics education, a common objective is that students should learn to use theories and models in order to understand the relation between theories and models, and objects and events, and to develop holistic, conceptual knowledge. During lab-work, students are expected to use, or learn to use, symbolic and physical tools (such as concepts, theories, models, representations, inscriptions, mathematics, instruments and devices) in order both to understand the phenomena being studied, and to develop the skills and abilities to use the tools themselves. We have earlier argued that this learning should be seen as the learning of a complex concept, i.e. a "concept" that makes up a holistic system of "single" interrelated "concepts" (i.e. a whole made up of interrelated parts). On the contrary, however, in education research it is common to investigate "misconceptions" of "single concepts". In this paper we will show ...
webstaff.itn.liu.se
For a long time, most research relating to science and engineering education has examined "misconceptions" about "single concepts", despite the fact that one common objective in many subjects is "to learn relationships". In this paper we introduce the notion of "a complex concept", i.e. the idea of describing knowledge as a complex, a holistic unit, consisting of interdependent and interrelated "single concepts". We describe how this conception could be used to identify both problems associated with learning as well potentials for learning. We will also relate the notion of a complex concept to the notion of threshold and key concepts.
The fundamental cycle of concept construction underlying various theoretical frameworks
ZDM, 2005
In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning.
Higher Education, 2005
The present study builds on earlier work by Meyer and Land (2003) which introduced the generative notion of threshold concepts within (and across) disciplines, in the sense of transforming the internal view of subject matter or part thereof. In this earlier work such concepts were further linked to forms of knowledge that are 'troublesome', after the work of Perkins (1999). It was argued that these twinned sets of ideas may define critical moments of irreversible conceptual transformation in the educational experiences of learners, and their teachers. The present study aims (a) to examine the extent to which such phenomena can be located within personal understandings of discipline-specific epistemological discourses, (b) to develop more extensively notions of liminality within learning that were raised in the first paper, and (c) to propose a conceptual framework within which teachers may advance their own reflective practice.
Threshold Concepts and Transformational Learning Rotterdam
Journal of Transformative Education, 2010
This series maps the emergent field of educational futures. It will commission books on the futures of education in relation to the question of globalisation and knowledge economy. It seeks authors who can demonstrate their understanding of discourses of the knowledge and learning economies. It aspires to build a consistent approach to educational futures in terms of traditional methods, including scenario planning and foresight, as well as imaginative narratives, and it will examine examples of futures research in education, pedagogical experiments, new utopian ix RAY LAND, JAN H.F. MEYER AND CAROLINE BAILLIE EDITORS' PREFACE Threshold Concepts and Transformational Learning LAND ET AL x students experience difficulty. The transformation may be sudden or it may be protracted over a considerable period of time, with the transition to understanding often involving 'troublesome knowledge'. Depending on discipline and context, knowledge might be troublesome because it is ritualised, inert, conceptually difficult, alien or tacit, because it requires adopting an unfamiliar discourse, or perhaps because the learner remains 'defended' and does not wish to change or let go of their customary way of seeing things. Difficulty in understanding threshold concepts may leave the learner in a state of 'liminality', a suspended state of partial understanding, or 'stuck place', in which understanding approximates to a kind of 'mimicry' or lack of authenticity. Insights gained by learners as they cross thresholds can be exhilarating but might also be unsettling, requiring an uncomfortable shift in identity, or, paradoxically, a sense of loss. A further complication might be the operation of an 'underlying game' which requires the learner to comprehend the often tacit games of enquiry or ways of thinking and practising inherent within specific disciplinary discourses. In this sense we might wish to talk of 'threshold practices' or 'threshold experiences' that are necessary in the learner's development. This is our third book on the topic of threshold concepts. The first, Overcoming Barriers to Student Understanding: Threshold Concepts and Troublesome Knowledge (Meyer and Land, 2006), drew together the early seminal writings and some first disciplinary applications of this approach. It offered, in an exploratory fashion, a tentative conceptual framework and a lens through which to view the pedagogy of higher education anew. After a lively international symposium on this topic in Glasgow, Scotland in the autumn of 2006, a second volume was published. Threshold Concepts within the Disciplines (Land, Meyer and Smith, 2008) built and expanded on the first in significant ways. It provided more empirical data concerning the experience of threshold concepts and troublesome knowledge, particularly from the students' perspective. It also extended the range of disciplinary contexts in which thresholds had been studied. This encouraged further work to be undertaken, culminating in a second successful international conference in Kingston Ontario organised by Caroline Baillie in the summer of 2008, from which this third volume has taken shape. With Threshold Concepts and Transformational Learning the empirical evidence for threshold concepts has been substantially increased, drawn from what is now a large number of disciplinary contexts and from the higher education sectors of many countries. The central section of this new volume adds to that evidence base, ranging across subjects that include,
Recognizing the Limits of Threshold Concept Theory
(Re)Considering What We Know: Learning Thresholds in Writing, Composition, Rhetoric, and Literacy, 2020
In "Threshold Concepts and Troublesome Knowledge," Jan Meyer and Ray Land (2006) explain that "interviews and wider discussions with practitioners in a range of disciplines and institutions" (6) led them to identify the characteristics associated with threshold concepts that have become familiar to researchers who have adopted or adapted this framework for thinking about learning and teaching. That is, threshold concepts are transformative, probably irreversible, integrative, potentially troublesome, and bounded. It's this latter idea that is significant for this chapter. Specifically, as Meyer and Land explain, threshold concepts are "possibly often (though not necessarily always) bounded in that any conceptual space will have terminal frontiers, bordering with thresholds into new conceptual areas. It might be that such boundedness in certain instances serves to constitute the demarcation between disciplinary areas, to define academic territories" (6). They follow this with two illustrations: one from a faculty member in cultural studies and one from veterinary sciences, both of whom explain the consequences for students of seeing through or seeing with threshold concepts from other disciplines, or of invoking ways of thinking and practicing (Hounsell and Anderson 2009) associated with operationalization of threshold concepts inconsistent with the threshold concepts of the discipline. The idea that threshold concepts serve as portals into disciplinary participation has become an important one for teachers, learners, and researchers working with the idea.
Threshold concepts and troublesome knowledge
Planet, 2006
The present study builds on earlier work by which introduced the generative notion of threshold concepts within (and across) disciplines, in the sense of transforming the internal view of subject matter or part thereof. In this earlier work such concepts were further linked to forms of knowledge that are 'troublesome', after the work of Perkins (1999). It was argued that these twinned sets of ideas may define critical moments of irreversible conceptual transformation in the educational experiences of learners, and their teachers. The present study aims (a) to examine the extent to which such phenomena can be located within personal understandings of discipline-specific epistemological discourses, (b) to develop more extensively notions of liminality within learning that were raised in the first paper, and (c) to propose a conceptual framework within which teachers may advance their own reflective practice.