Key to learning in pecific ubject area of engineering education an example from electrical engineering Anna-Karin Cartenen,, and Jonte Bernhard, School of Engineering, Jönköping Univerity, S- Jönköping, Sweden. E-mail: caak@ing.hj.e National Graduate School in Science and Technology Education, Linköping Univerity, Campu Norrköping, S-6 74 Norrköping, Sweden. Engineering education reearch group, ITN, Linköping Univerity, Campu Norrköping, S-6 74 Norrköping, Sweden Abtract Mot previou educational reearch on univerity teaching and learning ha looked for generic principle, which could then be ued to inform practice [6]. Reearch in engineering education ha for example dealt with the alignment of aement to the curriculum or progreive teaching/learning environment. Through reearch in pecific ubject area it ha been hown that there are pecific way of thinking and practicing (WTP) in each ubject area (ibid). In cience education the focu ha been on tudent view of ingle concept. One of the common objective in cience and engineering education i to learn relationhip. In our reearch we have been invetigating what we call complex concept, i. e. concept that make up a holitic ytem of ingle interrelated concept. A in many dicipline we find threhold concept [9], concept which are tranformative, irreverible, integrative and troubleome[]. Thee concept are often recognized by teacher in a field, but we alo ugget that it i poible by reearch to find key concept, but not in the ene that the term i often ued in ome educational context, a interchangeable with core concept, and meaning imply that the concept are an important part of the precribed yllabu. Here we ue the term a a more precie metaphor to mean that the concept in quetion act like a key to unlock the portal of undertanding. We ue variation-theory [8] in order to find key concept, critical apect that can act like a key to unlock the portal of undertanding. In our paper we will decribe how we have deigned labwork in an electrical circuit coure, taking the idea behind threhold concept and key concept into our pecific topic Tranient Repone a one example of how reearch into pecific ubject area i made poible through qualitative reearch. Keyword: threhold concept, variation theory, capability-driven curriculum, electrical engineering education. INTRODUCTION Reearch in engineering education i a growing field, epecially ince the number of tudent going into the area in many countrie i decreaing. Some area which have been the focu are aligning aement to curriculum, new teaching method, generic kill and program development. All of thee area have been, and till are, of great importance. But, the learning i alway a learning of omething[8], and to witch from content-driven curriculum deign, to a deign where content i not dicued at all i to go from one ditch to the other. Bowden[] ugget capability-driven curriculum deign, where content and capabilitie are not eparated, different piece of content not taught a iolated iland, but where relation between the different piece of knowledge i in focu. To adopt thi view, you need to determine the programme goal firt (the intended capability outcome), then the coure goal, then the neceary learning experience and, only then, the teaching plan [](p. 4). In variation theory there i a ditinction between the intended object of learning, the enacted object of learning and the lived object of learning [][], i.e. between what i planned, and what i actually opened up to the tudent, and what they really learn. Thu by tudying what the tudent do during lab-work it i poible to ee how the intended and the lived object of learning correpond, i.e. whether the goal et up are poible to
meet, or change need to be made. A well what the tudent ee a what they do not notice are reult to ue in the development of new intruction. In many field of higher education it i poible to recognie threhold concept [9][], concept that are tranformative, irreverible, integrative and troubleome. Thee concept are of pecial importance, ince a deep undertanding of them i neceary for learning other concept. Example invetigated are e.g. recurive function in computer engineering[], and opportunity cot in economic [7][7]. All of thee are difficult to learn, and if not learned in a deep way, they hinder the tudent from learning following topic. In our reearch we have found tranient repone to be a threhold concept, but we have alo found the critical apect, apect neceary to vary ytematically, through variation theory. We have therefore uggeted a ditinction between threhold concept and key concept [], not in the ene that the term i often ued in ome educational context, a interchangeable with core concept, and meaning imply that the concept are an important part of the precribed yllabu. We ue the term a a more precie metaphor to mean that the concept in quetion act like a key to unlock the portal of undertanding, the portal which open up for learning of other concept. We have developed a model, the model of learning a complex concept, which we have ued in three different way, firtly to identify what i troubleome for the tudent, econdly to find out what need to be changed in order to open up for learning, thirdly to identify the change in tudent' action in relation to our model []. In the paper we will decribe how we have developed the model, and how we ugget it may be ued in other area of engineering education reearch.. METHOD DATA COLLECTION We have videorecorded the labwork carried out in a firt year univerity coure in electrical engineering. The firt year () there were two-hour problemolving eion and two-hour lab-eion. The econd year () there were 9 four-hour integrated eion. In both coure there were two-hour lecture. Our focu ha been the lab concerning tranient, the next to the lat lab, and by mot tudent conidered very difficult to undertand, but alo the lab where we aw the larget difference between the old and the revied coure. Thi part of the curriculum wa in the former coure appointed * hour for problemolving and *4 hour for labwork, and in the new coure *4 hour integrated eion, thu the ame amount of time wa appointed for thi ubject both year. The change in the problem to olve during the eion were very mall but ytematic [4] (ee alo the appendix for the example). The intruction for the labwork integrated theoretical iue (mathematical), imulation, and meaurement, aiming at pointing out ome link that were not made by the tudent in the old coure.. RESULTS DEVELOPMENT OF A MODEL OF LEARNING A COMPLEX CONCEPT Tiberghien and co-worker (e.g. [], [4] and [])categorize knowledge into two domain: the object/event world and the theory/model world. Thi dichotomy ha proved very effective when analyzing and developing lab-intruction. She point out that it i important in education to make explicit the link between the theory/model world and the object/event world. When learning complex concept there are a well more than one concept in the theory/model world, a there are more than one in the object/event world. Very often thee concept are taught in eparate coure, e.g. differential equation in math coure, but even when they are mentioned in the ame coure, the tudent may not make link, i.e. find relation between them, and the reult i knowledge a iolated iland. Building on Tiberghien work we tried to identify which concept that belonged to the object/event world, and identified the real circuit and the meaured graph. We alo identified the differential equation, the tranfer function, the time domain function and the calculated graph a concept in the theory/model world. The arrow are what the teacher would conider intended link to make. Often the teaching follow the circle, i.e. from the real circuit the differential equation i derived, then tranformation by mean of the Laplace Tranform i carried out, from the tranfer function the time domain function i derived by mean of the invere tranform, and then a graph i ometime derived. In the lab, the tudent meaure the graph, and are aked to compare the calculated and the meaured graph. They are alo aked to try to find out which mathematical expreion that will give the ame calculated graph a the one they have meaured. Thi i done by mean of a real time meaurement program where it i poible to get graph from meaurement a well a doing curve fit.
T/M T/M Real Circuit Differential equation T/M T/M Meaured graph Tranfer function O/E O/E O/E Calculated graph Time domain function Figure. Our model Model of learning a complex concept and the model tranlated into the example in the Tranient Lab In the coure, the link that tudent actually made were very few, and all followed the circumference of the circle. Since the mot difficult relation to undertand are thoe where the boundary between the two world cro, few opportunitie to link the world are opened up. The change in the lab-intruction that were made were: Simulation of ytematically varied example (ee appendix) of tranfer function were uggeted the link between calculated graph and tranfer function wa explored The tudent were explicitly aked to figure out the tranfer function from the meaured data (which in the lab-environment are preented a a graph) the link between the meaured graph and the tranfer function In the revied intruction were ued and the converation wa totally different. Of coure tudent till ak quetion, but the quetion are more informed, epecially toward the end of the lab. An example of how the link can be explored through the tudent converation focue on Te and Benny, tudent. Te ha been doing all the calculation, and Benny ha worked on the imulation. After about 4 minute they are uppoed to wire up the circuit, and they read: Te: "Wire up the circuit" (read from intruction) (turn her head toward B) It eem taken for granted what circuit he talk about Benny: Yea, we'd better read thi again The gap in undertanding may be illutrated by the circle which how the relationhip that the tudent now had been working on: Figure. a) Benny' lived object of learning in thi firt part of the lab eion b) Te' lived object of learning in thi firt part of the lab eion
In thi part of the eion, Te and Benny encountered different object of learning. At thi point, neither of them i thinking about the real circuit, becaue in order to do o they have to make link back: Benny from the graph and Te from the mathematic. One often recurring quetion during the firt coure i "I thi good enough for the report", a quetion which how that the tudent do not know what to expect, and we can ee from the tudent' dicuion that thi i due to the lack of link made between different object of learning. In the new coure thi quetion i not raied at one ingle time, and we can refer that to the way the tudent do etablih link between theory and the real circuit in the new revied coure. In the firt coure, many tudent do not know how to attack the problem at all. They ak for help e.g. what formula to ue for the curve fit. A exemplified in the appendix, there can only be two type of olution; a damped inuoidal function or a function of the um of two negative exponential function. The teacher want the tudent to find thee equation by calculation and tate: Jut calculate the pole to the expreion and find the function to ue. The tudent notice thi expreion, although they do not undertand it, which i indicated by two action; firtly they repeat the quote from the teacher: Jut calculate the pole to the expreion and find the function to ue, at everal time during the ret of the lab, and they how a heitation to tart doing any calculation. Thi heitation i in the new coure totally gone; a oon a the tudent have tried a few imulation ome of them tart to do calculation, by ue of note from lecture. 4. CONCLUSIONS AND IMPLICATIONS FOR FURTHER RESEARCH In thi part we will dicu the relevance of the model, and how it may be ued in other ubject area to inform coure development, particularly lab-intruction. 4. Quetioning the model The tranition from the real circuit to the differential equation, and on to the tranfer function, through the invere tranform to the time domain function and on to the calculated graph, can be conidered obviou or elf-evident, but we have never een anyone decribing the object of learning in uch a way before. Therefore we conclude that the circular paradigm i not elf-evident, but i perceived in that way becaue the link between the iland are taken for granted, and are therefore not made explicit during teaching. There i alway a poibility that the iland in the circle hould be labeled differently, and that there hould be other iland in the circle. However, we claim that thee are the iland we can notice when litening to the tudent dicuion. One quetion often tated, i whether the calculated and meaured graph hould be one or two iland. A tated aim in the lab i to: compare the meaured and the calculated graph, or later on: ue the curve fit function in the program, enter the math expreion, and vary the parameter until you get a curve that look a your meaured graph. Thu alo the teacher view the graph a different categorie. Another quetion might be whether the real circuit and the circuit diagram ought to be two different iland, but in the lab we never ee the tudent making any ditinction between the two. When they have quetion about the circuit, e.g. in the quetion above: What circuit?, they only ak thi becaue they don t remember that they have een a circuit diagram, and not that they would have problem interpreting what to wire up when the ee the diagram. A quetion that may be dicued and invetigated further would be what kind of relation that the link may repreent. The link we have uggeted are pragmatically derived from the tudent converation, but they are of different type. The one between the real circuit and the differential equation i phyical modelling, the next two are mathematical derivation, firt uing the Laplace tranform and then the invere tranform. Next link i to draw a curve from the mathematical expreion, and going in the oppoite direction, derive the expreion from the given curve (which i new to many tudent). The link between the calculated and the meaured graph i an interpretation, the tudent kill in recogniing different part of a graph temming from different function uch a exponential and inuoidal function in combination. The lat link i the one between the real circuit and the meaured graph, which comprie kill uch a the ue of the computer a a data collection medium, a well a the knowledge about where to connect the meaurement intrument. Alo a dicuion on whole-part relationhip would be ueful, e.g. when conidering tranient repone a one ingle iland, where other iland could be frequency repone, tate equation, etc. in a coure in control theory. Or, in a le advanced coure to ee that the iland preented here are divided into ub-circle.
4. Unlocking the portal of undertanding The ytematically varied example (appendix) help the tudent to identify poible olution to the mathematical problem they have to olve in order to carry out the lab-tak. The mot obviou outcome i that the tudent work with the problem more independently, their dicuion are totally different they know what to do. Here our model helped to find what wa critical for learning, namely which link between the world to open up for. Epecially to make the link between the graph and tranfer function dicernable through variation, helped the tudent to identify the typical curve. But by identifying thee type, the tudent alo received an indication of what to expect from calculation, a well calculation of the tranfer function a the time domain function, which they were to ue for the curve fit. Thu their initial heitation to do calculation gradually diminihed. According to the threhold concept -theory it i neceary to vary alo the liminality, Variation in how the portal, that i the liminal pace itelf, i entered, occupied, negotiated and made ene of, paed through or not liminal variation []. To open up the learning pace by variation of the critical apect, we alo open up the liminal variation, o that the tudent may feel that the tak i not an impoible one, but they feel encouraged to attack the problem they had. 4. Further ue of the model We are now trancribing data from another part of the coure, where we alo expect to be able to ue our model, namely AC-circuit. However, we alo ugget that thi model can be ued in evaluating other lab-coure epecially when the lab are dealing with modelling of real world phenomena, i.e. enterprie modelling in information technology or computer aided deign of mechanical tructure, which will be our next project.
Reference: [] Bernhard, J., Cartenen, A.-K., & González Sampayo, M. (). Connecting the theory/model world to the real/event world - The example integrated lab- and problemolving eion in electric circuit theory. Paper preented at the ESERA conference, Barcelona. [] Booth, S. Engineering education and the pedagogy of awarene in C.Baille et.al (ed.) Effective learning and teaching in engineering. NY: RouthledgeFalmer [] Bowden, J.A., (4) Capabilitie-driven curriculum deign, in C.Baille et.al (ed.) Effective learning and teaching in engineering. NY: RouthledgeFalmer [4] Cartenen, A-K, Bernhard, J. (4) Laplace tranform - too difficult to teach learn and apply, or jut matter of how to do it. Paper preented at EARLI ig#9 Conference Gothenburg 4 [] Cartenen, A-K, Bernhard, J. (8) Threhold Concept and Key to the Portal of Undertanding: Some Example from Electrical Engineering in Ray Land et al.(ed.)threhold concept within the dicipline Senen Publiher, Rotterdam [6] Entwitle, N. et.al () ETL-project - Subject area report for electronic engineering, acceed at http://www.ed.ac.uk/etl/publication 7-4- [7] Davie, P. (6). Threhold concept: how can we recognie them? In J. H. F. Meyer & R. Land (Ed.), Overcoming Barrier to Student Undertanding: Threhold concept and troubleome knowledge (pp. 7-84). London: Routledge. [8] Marton, F., & Tui, A. B. M. (Ed.). (4). Claroom Dicoure and the Space of Learning. Mahwaw: Lawrence Erlbaum. [9] Meyer, J. H. F., & Land, R. (6). Overcoming barrier to tudent undertanding: Threhold concept and troubleome knowledge. London: Routledge. [] Meyer, J. H. F., Land, R., & Davie, P. (8). Threhold concept and troubleome knowledge (4): iue of variation and variability. In R. Land & J. H. F. Meyer & J. Smith (Ed.), Threhold Concept within the Dicipline. Rotterdam: Sene. [] Perkin, D. (999). The many face of contructivim. Educational Leaderhip, 7(), 6-. [] Runeon, U., & Marton, F. (). The Object of Learning and the Space Variation. In F. Marton & P. Morri (Ed.), What Matter? Dicovering critical condition of claroom learning (pp. 9-8). Göteborg: Acta Univeritati Gothoburgeni. [] Tiberghien, A. (). Deigning Teaching Situation in the Secondary School. In R. Millar & J. Leach & J. Oborne (Ed.), Improving Science Education: The Contribution of Reearch. Buckingham: Open Univerity Pre. [4] Tiberghien, A., Veillard, L., Buty, C., & Le Maréchal, J.-F. (998). Analyi of labwork heet ued at the upper econdary chool and the firt year of univerity. Working Paper, Labwork in Science Education Project. Lyon: Univerité Lyon. [] Vince, J., & Tiberghien, A. (). Modelling in Teaching and Learning Elementary Phyic. In P. Brna (Ed.), The Role of Communication in Learning to Model (pp. 49-68). Mahwah: Lawrence Erlbaum.
Appendix: Example of ytematically varied Laplace-function to analye, mathematically and graphically G ( ) + G ( ) + + G ( ) + +..4 Step Repone Step Repone Step Repone 4. 9. 4 8. 7.8 6.6. 4.4... 4 6 7 8 9 Time (ec) G ( ) + 4 6 7 8 9 G ( ) Time (ec) + + 4 6 7 8 9 G ( ) Time (ec) + +..8 Step Repone 6 Step Repone Step Repone.7.6. 4..4..... 4 6 7 8 9 Time (ec) 4 6 7 8 9 Time (ec) 4 6 7 8 9 Time (ec) Important characteritic: ) Solution to the characteritic polynomial, i.e. the pole to the tranfer function give different hape to the curve: ± + j j ±, ±. +.7..7.7 give under-critically give critically give overcritically damped behavior damped behavior damped behavior ) Note the different tart behavior that depend on the difference in degree of power in the nominator and denominator polynomial ) The Steady-State value depend on the tranfer-function' limit-value when approache zero.