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Concept Development and Meaningful Learning Among Electrical

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1. lt follows the path flows of least directionally ina p hich Be Ss C Circuit vee gt divisible Second Lab Observation Voltage wattage stays the affects same ina brightness parallel of N P changes S linearly LED ee f ina affects paralel brightness power Current of smallest Pa r reduces dissipates smallest he t S ogm resistor negative Fig 5 Concept maps created from JF s interviews and observations JF showed a great deal of practical knowledge of circuitry in both interviews showing an increased ability to make connections between concepts by the end of the term This has got something to do with a term that I don t remember Um Voltage divider I think Something to do with that I don t know It s just I just know it I don t know why that s the problem Subject TA Out of all of the subjects only TA included as much talk about voltage and resistance as he did about current in the initial interview see Fig 6 Like MJ he struggled to understand what voltage was Well I guess voltage is it s kind of potential energy It s always measured at a reference But I guess I don t have a really clear concept of okay this wait voltage is supposed to be like if you compare it with water like a hose the pressure However he could describe what voltage did generally in mathematical terms In comparing two bulbs in series to a single bulb connected to a batter
2. A Springer J Sci Educ Technol determines what knowledge is meaningful in the problem solving context The findings described in this paper are derived from a larger study on reasoning and concept development in electrical engineering students engaged in problem based learning Bledsoe 2007 This paper reports concept for mation by selected subjects with weak and strong prior knowledge The goals of this portion of the study were 1 to document analyze and trace changes in students concepts of current voltage resistance for students with low prior knowledge and students with high prior knowledge as students are engaged in a project based engineering laboratory 2 to observe and document the development of mean ingful learning and changes in the body of meaningful learning throughout an electrical engineering course Theoretical Framework Student understanding of electrical phenomena was examined within a phenomenological perspective in order to best describe 1 the students experiences of electrical phenomena and 2 the relationship between each student and the content knowledge across time In this study phenomenology is defined using Lincoln s 1990 description of phenomenology as an inquiry paradigm where both researcher and respondent are co participants in the inquiry process In addition Moustakas 1994 view of phenomenology as a research method framework and Roths s 2005 studies using cognitive
3. s the Same current A Springer TA was adept at developing explanations using the relationships between resistance voltage and current recognizing the interrelatedness of all three concepts TA s post survey score was 24 out of 24 Making Knowledge Meaningful Solving Lab Problems One would expect conceptual change over a 10 week course Pertinent to the questions of this study however is how students use their prior knowledge and the knowledge they gained from instruction as they approach problems The Whitehead Bransford model Fig 1 suggests that the body of meaningful learning the learning that students use spontaneously as they problem solve increases as students increase their knowledge base and increase their experience with problem solving In this study concept maps assembled from student comments during lab actions taken during lab written homework responses and later discussions during interviews describe a body of knowl edge that students found meaningful solving problems in J Sci Educ Technol lab Separate concept maps were constructed for separate events in order to determine what knowledge emerged as meaningful during each event The lab tasks were complex requiring that students remember and apply multiple abstract concepts as well as appropriate procedural knowledge and apply them simul taneously and accurately to the problem at hand The cognitive load was at times overwhelming Working in pai
4. We re trying to see let s see we re trying to find out show the nature of the diode So that we can know what a diode does and how it works MJ and her partner wired a circuit that included an LED and a potentiometer which acted as an adjustable resistor This allowed them to change the resistance in the circuit without removing and replacing resistors They were to wire an ammeter into the circuit and use another multim eter to measure voltage across the LED What students had to discover was that the LED acted as a switch When MJ and her partner wired the circuit the LED did not light a significant event that they failed to notice As they mea sured voltage and current MJ showed increasing uneasi ness that something wasn t right but her numbers showed a linear relationship between voltage and current that her prior understanding predicted In fact they should have found that current remained at O until voltage was high enough at which point current should have increased exponentially The linear relationship satisfied MJ and she went on to the next activity until one of the teaching assistants saw the graph and asked them to re do the cir cuit On doing so they discovered that the LED was defective and may have been wired into the protoboard incorrectly MJ s understanding of polarity and direction ality of current came up in the conversation Still it wouldn t make sense that we had both nega tive and positiv
5. as it loses which make up a polarity have Voltage _ is additive resistors eee across Sm circuit elements caused by determined by reversed gives measurin i related by g ae ah in excess Ohm s Law g overheats to related by to dissipation of Caren heat which make up a knowledge remained similar from the beginning of the term to the end while new connections were added between concepts giving me too much voltage This statement suggest an idea that voltage flows like current but MJ also described voltage as being like pressure MJ also used the term load in her descriptions of circuit phenomena to describe what was happening around resistors and bulbs She had initially thought that the first of two bulbs in series should A Springer be as bright as a single bulb in its own circuit She was surprised to see that both bulbs in series dimmed equally and in trying to explain the discrepancy she stated It s because it has a bigger load on it And it s drawing more MSJ s final interview also shown in Fig 4 demonstrates an integrated understanding of both voltage and current Interestingly MJ s concept of current became slightly more material as she did not describe current as energy but instead described current being used up by circuit ele ments At the same time she recognized that current was conserved in the circuit and she struggled to reconcile a
6. the chemical that s inside it He also expressed a belief that a battery was where elec trons were stored and emerged from the positive end A Springer Initial Interview reaction light by has is like with takes path W of least material x hole back oo Resistance is used up by comes from circuit is elements __ are used a a electrons C Circuit gt which is divsibte which make up a come from First Lab Observation EED _ A J Sci Educ Technol Final Interview energy conversion creates f A is caused by isa source of isa or measure of Battery electrons takes path Resistance of least r holds back lt is Current 7 a is e ergy is additive in used up by shared by Eoi gt Circuit J which is divisible Second Lab Observation resistors circuit resistors if incomplete elements j Bulb has no NO l flows installed backward is additive in a Hows ina directionally ina M is equal create negative series of across lights is parallel 7 measured A N Voltage Voltage Current across is additive in a series of heat nn N is a creates i Current source of is is IS f measured measured Resistance negligible gt wires Battery across installed through in backward is positive oe ae ean be create durin is disspation dissi aie of of ea localiza ace p is en source of around power ci
7. view of current as something both used up and con served as well as the idea that current flows one direction while the actual electrons flow in an opposite direction a concept that had been taught in lecture Voltage she understood as a force that drives current and its source was the battery on the circuit board While MJ was dissatisfied with her explanations about current and voltage she was adept at using Ohm s Law and similar mathematical for mulas used in class to discuss the relationships between current voltage and resistance This result is similar to other work on college student understanding that contrasts conceptual understanding with mathematical modeling of physical phenomena Melendy 2008 When she employed Ohm s Law in trying to explain circuit phenomena MJ was better satisfied with her explanation For example when asked to describe the dimming of a bulb placed between two resistors regardless of which resistor was changed MJ explained It s changing the current because the current through all three of them has to be the same because they re all in series but the current let s see since V IR if you increase the resistance then the current has to go down And if you decrease the resistance the current has to go up So we increased the resistance and the current went down so now there s a dimmer light bulb While MJ s conceptual understanding of current and voltage were not stro
8. By contrast MJ tended to ponder the problem first alone or in discussion with a neighboring student and attempt to apply conceptual knowledge in order to predict how a given circuit would behave before she assembled it If her predictions were not supported she turned to the teaching assistant or another student and again sought to understand the problem conceptually The first observation of AM took place within days of the initial interview when the class was working on a set of theoretical exercises involving protoboards and a variety of circuit elements including resistors motors and diodes to understand how they functioned All of these circuit elements would be used as students designed and assem bled their bump bots later in the term The activities that AM worked on in the first observation were highly struc tured so as to develop necessary procedural skills and conceptual understanding During the observation AM and a lab partner wired resistors in parallel and series then measured voltage across and current through the resistors and noted the dissipation of heat energy from the resistors A concept map based on AM s talk and actions during the activity Fig 4 shows a focus more on procedural knowledge and practical applications of concepts than on the concepts themselves and reveals changes in his understanding since the initial interview Fig 4 AM had altered his concept of batteries to include them as a sour
9. by the motor and would drop when the motor ran He also applied a highly material view of current when he expressed the idea that the circuit could not work because current from the wall plug and current from the battery would collide like two streams of water Here the teaching assistant stated that differences in voltage would determine which direction current would flow that the wall plug had a higher voltage and that current would flow from the higher to the lower voltage JF was satisfied and proceeded with the exercise In a second observation JF was working on the same diode problem that gave MJ difficulties Like MJ JF ini tially expected that as the potentiometer was turned the current should increase linearly with the voltage His partner referring to instruction from lecture noted that the transistor in the circuit acted as a switch allowing no current through until the voltage reached a given level JF then observed the circuit again and noting the LED pre dicted that changes in resistance and voltage produced by turning the potentiometer should change the brightness of the LED Here JF drew on prior knowledge of how incandescent bulbs behaved expecting the LED to behave in the same manner His partner reminded him that the LED was a diode that was either on or off and did not change in brightness To test this idea JF spent several minutes turning the potentiometer and observing the LED until he was satisfied that thi
10. continued to refer to Ohm s Law and other relational models learned in lecture as he approached lab activities and the final bump bot problem The two students with low prior knowledge demon strated a similar dichotomy AM demonstrated a trial and error learning approach somewhat similar to JF s but lacked a similar knowledge base at the start of the term There was less purpose to his actions less of what Dewey 1938 called productive inquiry JF had the knowledge and an overall sense of purpose that brought otherwise A Springer haphazard activity into organized information linked to current knowledge JF s failure to solve the bump bot problem was something he attributed to his lack of knowledge of mathematics and logic required to carry out the programming rather than a lack of knowledge of basic electrical concepts In contrast AM had more mathemati cal background but had difficulty making predictions regarding the circuits on the initial survey because of low prior knowledge regarding the behavior of electrical cir cuits As AM s knowledge increased over the term his ability to predict the outcomes of circuits increased lead ing to increased success on the same problems on the post survey AM s predictions were based on prior observations and examples he had observed the difference between circuits wired in series and those wired in parallel during the lab activities and applied the prior observations
11. current Transcripts were coded using TAMS Analyzer 3 3 qualitative data analysis software Weinstein 2005 Ini tially the data were coded to categorize student statements regarding the concepts of energy electricity current voltage and resistance After the categories were estab lished from multiple passes through the data and student statements were sorted the researcher consulted prior lit erature on student concepts in electricity to compare the boundaries of phenomenological categories obtained in the current study with earlier descriptions of student concepts with most notably Shipstone 1984 1985 Osborne and Freyberg 1985 and Osborne 1981 Triangulation with prior research showed that the categories uncovered in this J Sci Educ Technol study around the concepts of energy electricity current and voltage aligned well to descriptions of electrical con cepts found in prior studies A full description of this portion of the analysis and the conceptual categories can be found in Bledsoe 2007 Analysis then tracked the responses of individual sub jects to concentrate on following the changes in their conceptions and the interplay between material learned in lecture and material actually used in lab to uncover what emerged as meaningful learning during problem based instruction Subject statements from each interview and from the observations were used to construct concept maps to document the relationships between c
12. harder on under standing a particular concept The final survey suggested that both AM and MJ achieved similar gains in content knowledge around the basic concepts of current voltage and resistance AM scored 6 on the initial survey and 15 on the final survey out of a possible 24 MJ scored 8 on the initial and 16 on the final survey Content knowledge gains therefore may not account for the difference in problem solving success and meaningful learning between these two students Students with High Prior Knowledge JF and TA Two subjects JF and TA entered the course with high prior knowledge and high prior experience with electrical systems The expectation based on prior research Ander son 1987 was that these two subjects would demonstrate higher problem solving ability in the lab as they had greater knowledge to draw upon However as with AM and MJ these two subjects experienced different levels of success in lab suggesting that other factors than content knowledge influenced their outcomes JF described himself as a hands on learner His preference was to apply a trial and error approach based on his prior experience For JF experience and observation preceded concept formation While this led him to under stand the target concept by the end of an exercise it often led him astray at the beginning Insufficient conceptual knowledge or incorrect application of conceptual knowl edge frequently led JF to choose inappropri
13. phenomenology shaped the perspectives of data collection and analysis Moustakas framework is grounded in Husserl s 1913 work on transcendental phenomenology which focused on intentionality the orientation of the learner s mind toward the object The researcher s role is to set aside biases and prejudices or at least to recognize them at the outset then describe the subject matter as much as possible on its own terms This position termed epoch strives for a descrip tion of the phenomenon as seen by the respondent clear of the researcher s own perspectives of correct or incor rect conceptions Phenomenography as a research method grew from the phenomenological framework Phenomenography attempts to capture the learner s perceptions of natural phenomena and the variations in perspectives within a group of learners Liu et al 2002 Within this perspective student concep tions are viewed not as fixed mental models but as a fluid relationship between the learner and the subject Marton and Booth 1997 Out of a study of a group of learners the researcher attempts to sort student conceptions into mutu ally exclusive descriptive categories often hierarchical that may later drive curriculum development Ebenezer and J Sci Educ Technol Fraser 2001 Within this study student perspectives on electrical phenomena were analyzed through phenomeno graphic methods to develop categories of knowledge which pro
14. the number of correct answers circled Written responses were later analyzed along with interview data to develop a description of stu dent conceptual understanding The entire survey appears in Bledsoe 2007 A sample question is shown in Fig 2 From a pool of students who volunteered for the remainder of the study twelve were selected those scoring in the lowest quartile and the highest quartile of the range of class scores The purpose of this deliberate selection was to identify students entering the course with high prior knowledge and low prior knowledge compared with the larger body of students Out of this pool seven students completed the study Two subjects with high prior knowledge and two with low prior knowledge are described in detail in this paper These students were selected for description as exemplars of high and low problem solving success within their prior knowledge class The implications of an apparent discon nect between prior knowledge and problem solving will be discussed Data Collection All subjects were interviewed within the first 2 weeks of the term During the interview subjects were shown their initial survey and asked if they still agreed with the pre dictions they had made and were asked to explain their ideas They were then given a board with batteries in holders bulbs in sockets and a bundle of wires with alli gator clips at the ends and were asked to construct each of the circuits in the s
15. which make up a circuit canbe ____ Voltage is gt pressure elements divided by remains equal drives h regardless of ave going direction of backwards may polarity damage i has go melts with a rise in Pi fuse Third Lab Observation Battery loses charge polarity as it loses have Voltage _ is additive resistors es across circuit elements caused by determined by reversed gives related by o Bl a in excess Ohm s Law g overheats to related by Resistance Ohm s Law gt Current to dissipation of heat Fig 4 Concept maps created from MJ s interviews and lab obser vations While MJ s initial understanding was low and the connec tions between concepts were few the overall framework of her as voltage was printed on the battery and she believed that voltage affected the brightness of bulbs in series stating it seems like the voltage would be determining the brightness of it and it seems like if the only way they would not be the same brightness if there were something in the light bulb regulating it to say you know you re Final Interview determines brightness Voltage is gt constant of T is source of affects P may circuit be Battery elements used e a which make up a may be takes path restricts conserved x sh of least Si Se lt across a which is divisible Second Lab Observation Battery loses charge
16. J Sci Educ Technol DOI 10 1007 s10956 01 1 9303 6 Concept Development and Meaningful Learning Among Electrical Engineering Students Engaged in a Problem Based Laboratory Experience Karen E Bledsoe Lawrence Flick Springer Science Business Media LLC 2011 Abstract This phenomenographic study documented changes in student held electrical concepts the develop ment of meaningful learning among students with both low and high prior knowledge within a problem based learning PBL undergraduate electrical engineering course This paper reports on four subjects two with high prior knowledge and two with low prior knowledge Subjects were interviewed at the beginning and end of the course to document their understanding of basic electrical concepts During the term they were videotaped while solving problems in lab Concept maps were generated to represent how subjects verbally connected concepts during problem solving Significant to PBL research each subject s body of meaningful learning changed with each new problem according to how the subject idiosyncratically interpreted the activity Prior knowledge among the four subjects was a predictor of final knowledge but not of problem solving success Differences in success seemed related more to mathematical ability and habits of mind The study con cluded that depending on context meaningful learning and habits of mind may contribute significantly to problem solving success The
17. across them is the same MJ So are you trying to come up with the number that goes here indicating a blank on the lab worksheet Partner Um yeah MJ Just do V equals IR and get voltage which equals I times R the resistance In building circuits for the exercises MJ carefully observed the resistors to make sure they were installed in the right direction concerned with the polarity of parts In the course of the activity she and her partner discovered that resistors gave off heat and by touching the resistors they had physical evidence of the energy conversion Talk between the partners was around data gathering as they measured voltage and current and about calculating the dissipated power MJ indicated that she knew that too much current through a circuit element could cause the element to overheat recalling warnings in lecture about smoking the resistors in the circuits As they worked MJ used the multimeter to directly measure the resistance of resistors she was using She also used the colored bands to determine the resistance curious to see if the resistance she measured was the same as the resistance that was indicated by the color coding On discovering that she obtained a 1 4 ohm resistance on a ohm resistor she asked the teaching assistant why that would be and they engaged in a conversation about the resis tance of the wires in the meter the meter itself and the precision of the resistors as sources of error T
18. alysis The researcher engaged subjects in conversation from time to time to elicit their ideas about the purpose of the lab to capture student student talk during the labs and to capture explanations of what they observed as they completed the lab exercises Each subject was observed a minimum of three times during lab Course lectures were also observed Packets of class notes made available on the class website were collected for analysis to identify the instructor s target concepts and to determine if students used the target concepts examples and model circuits as they addressed the problems in lab At the end of the term the survey was administered to the class again The seven subjects were interviewed regarding their post survey answers using the same inter view methods as the initial survey Analytical Method Transcriptions of video records observation notes and responses on the survey forms for each of the seven sub jects were analyzed to infer categories of knowledge held by the subjects Rather than categorizing statements as scientific or alternative analysis attempted to capture the subjects viewpoints using the phenomenographic methodology described in Ebenezer and Fraser 2001 The phenomenographic method holds that a natural phenomena is conceptualized in a finite number of ways and can be described as mutually exclusive categories Marton and Booth 1997 Ebenezer and Fraser 2001 For example
19. article presents a testable model of learning in PBL for further research Keywords Electrical engineering Undergraduate Student concepts Reasoning Problem based learning K E Bledsoe DX Division of Natural Science and Mathematics Western Oregon University Monmouth OR 97361 USA e mail bledsoek wou edu bledsoek gmail com L Flick Department of Science and Mathematics Education Oregon State University Corvallis OR 97331 USA e mail flickl science oregonstate edu Published online 28 April 2011 Introduction Problem based learning PBL is an active learning strat egy for promoting concept development and addressing alternative conceptions Widely applied in medicine law and business PBL has been shown to develop active learning strategies and hypothesis driven reasoning abili ties across content areas PBL places students in a social learning context fostering conceptual change as students reveal explain and defend their ideas within a group Petrosino 1998 Sherin et al 2004 However research on contextualized learning suggests that there are always cognitive consequences some of which may be problem atic Son and Goldstone 2009 As students apply newly acquired knowledge they may not apply it appropriately For example in studies on medical students those students engaged in PBL developed more elaborate explanations than their peers in traditional medical courses but their explanations tend
20. ate procedures TA by contrast used conceptual strategies similar to MJ s He generally read the problem and studied the diagrams or schematics first until he could understand the problem in terms of mathematical relationship Once conceptualized TA then selected strategies from his procedural knowledge relying only on trial and error to tweak a completed circuit until it performed to his satisfaction While JF s knowledge measured at the high end of the survey scale 15 out of 24 JF stated that his ability to predict the outcomes of simple circuits came more from his physical experience with wiring and circuitry during building construction than from an understanding of the underlying phenomena However in spite of his perfor mance on the initial survey and in the initial interview JF came into the lab with several prior conceptions that J Sci Educ Technol influenced his thinking about the concepts of voltage current and resistance The first observation of JF took place during a lab in which students were carrying out introductory activities on the relationships between current voltage and resistance Their first problem was to discover which of several methods was the most accurate means of measuring cur rent JF after looking over the schematics concluded that the activity was about measuring voltage to the motor wired into the circuit with and without resistance and expected the motor to slow down when a resisto
21. ce of power a term he used interchangeably with cur rent and as a voltage source In the course of conversa tions about why there was no voltage reading on a circuit they had built AM said to his partner that the circuit might be incomplete suggesting a belief that voltage is present only in complete circuits where current is flowing This is a consistent application of his belief in the initial interview that voltage is something similar to current Reinforcing this was the discovery that it was important to install cer tain circuit elements in the right direction or the partners would obtain a negative reading for voltage AM also discovered that installing a diode backwards caused it to heat to the point of smoking further reinforcing the idea that the term polarity referred to the direction in which elements were meant to be installed in reference to con ventional current flow When measuring voltage across and current through resistors in series and in parallel AM predicted based on knowledge obtained from lecture that one large resistor should dissipate as much heat as several small resistors in series and easily solved the lab problems involving addi tivity of resistance in a series circuit However while AM was able to measure voltage across a resistor he then tried to measure current in the same fashion that is connecting the terminals of the meter across the resister while set on a current scale risk
22. controller effectively cut off current He reminded his partner of concepts they had discussed in the prior observation that where voltage measured 0 there would be no current and that voltage must be measured across a resistor He also stated that any resistor in the circuit would affect the entire circuit not just those components downstream of the resistor and that current takes the path of least resistance By the end of the term TA had successfully completed his bump bot project creating a robot that would successfully negotiate a maze He also completed optional challenge problems in addition to the required lab activities Both TA and JF began the term with prior experience and with high prior knowledge though TA had greater A Springer J Sci Educ Technol prior knowledge than JF At the end of the term both TA and JF showed similar understanding of current voltage and resistance and were able to successfully solve the circuitry problems on the survey Yet while TA was sat isfied with his progress and performance JF ended the term dissatisfied and questioning his career path A number of factors contributed to the different outcomes between these two subjects JF believed his mathematical ability was not up to the level he needed to succeed in the course while TA was in second year calculus This difference could as JF believed have contributed to their differing success with digital logic Habits of mind
23. demonstrated during lab also differed between the two subjects When working with a partner TA took a mentoring role and guided his partner during the exercises JF on the other hand received guidance and mentoring from another partner and relied heavily on concrete examples from lecture as models when trying to create circuitry to carry out a particular function Meaningful learning also appears to have been a factor TA seemed more facile at applying his understanding of Ohm s law and basic electrical concepts to lab problems and the final bump bot problem while JF struggled to understand the intent of many problems JF s preferred mode of learn ing hands on experience leading to conceptual under standing did not align well with the expectation that he create his own problem solving procedures based on con ceptual knowledge While both subjects had adequate con ceptual knowledge their meaningful knowledge that body of knowledge that each subject recognized as relevant to a problem differed considerably Discussion The results of analysis indicate that there were different kinds of knowledge in use during problem solving The detailed examination of initial knowledge experiential background and approaches to problem solving revealed that high academic understanding was valuable for perfor mance on the bump bots problems However higher knowledge also came in the form of procedural knowledge gained through experience t
24. e even if it were backwards I can see it could be wrong Um let s see Is it back wards though because I was going by the polarity on the voltage er voltmeter so that might be back wards Is it checks diagram in book Okay here because the current is flowing that direction And the current flows from positive to negative right Once the circuit was wired correctly and the LED lit MJ and her partner took measurements again Once again MJ s expectation that current and voltage are linearly related drove her expectations of the outcome At one point MJ asked her partner Do you have any voltage Her partner indicated that he did MJ asked Well then how come I have zero current The teaching assistant who was watching indicated the potentiometer and noted that it was turned to the highest resistance so you re losing the whole voltage MJ responded It makes sense A Springer then that it has zero current drawing this time on her understanding of the relationship between current and resistance that she extracted from Ohm s Law From there MJ was able to predict the switch like nature of the diode and predicted that the outcome for the graph would be exponential not linear To explain their first results MJ drew on her knowledge of shorted circuits hypothesizing that the first circuit that they had built must have had a short in it somewhere Later in lab she applied this concep
25. e solved and talked more about mathematical relationships than about what he believed A Springer Initial Interview is is potential Voltage J like Pressure i when increased resistor increases causes brightness of conversion hEN of IS DN f has A Bulb is the when increased Ta flow of flowing creates light in a decreases Current energy lt electricity electrons brightness of restricts lt takes the path of least is divisible flows in a directionally in a divisible whichis creut Y First Lab Observation ae Voltage divided by resistance l l equals is equal in is measured parallel aa eee across dissipate divided into when resistors voltage dissipated Ean equals creates dissipate is measured through a heat must connect T to ground to Resistance complete Curent ae is constant through a is additive in g Pa series will not flow a series in a broken Cae J Sci Educ Technol Final Interview Voltage when increased increases brightness of if O produces no if O produces no C Bulb Nin series have the same constant lt is when increased converted decreases to light in affects brightness of eneray lt of when increased has ES decreases the flow of is essentially is divisible can flow 0 across a affects ina more than behavior of one direction entire divisible wens C arut Second Lab Ob
26. e voltage should be equal across resistors wired in parallel which TA remembered from lecture He also made multiple references to the relation ships in Ohm s Law as he explained how to determine power dissipated in the circuit TA s statements also included the practical aspects of assembling circuitry He reminded his partner several times that voltage must be measured across resistors while current is measured through He noted that if the circuit wasn t completed by connecting the resistors to the ground on the protoboard that current would not flow stating If you don t complete to ground you re going to have an open circuit While a linear model of circuits was rare among the responses on the initial survey it was not uncommon for students in lab to have initial difficulty in creating a complete circuit on the protoboard without some assistance In the next observation which occurred 2 weeks later TA and his partner had completed the required lab prob lems and were engaged in an optional challenge project to create an audio amplifier As in the prior observation TA s partner had difficulty creating complete circuits prompting TA to remind his partner that the circuit must connect to the ground in order for current to flow The circuit they were attempting to build included digital logic gates that controlled whether current reached the motor or not TA noted that the high resistance in the circuit through the motor
27. ed to be more error prone Patel et al 1986 1990 1991 Much of cognitive research on PBL has shown that students draw on their prior knowledge when solving problems A strong knowledge base correlates well to success in problem solving Anderson 1987 College stu dents working in courses outside of their majors as well as secondary and elementary students may be at a cognitive disadvantage when confronted with a science based or technology based problem because of their sparse knowl edge base Learners of all ages possess alternative mental con structs around natural phenomena Wandersee et al 1994 At the college level even students majoring in the sciences may hold alternative conceptions regarding phenomena within their field of study for example Ebenezer and Fraser 2001 Liu et al 2002 Westbrook and Rogers 1996 A Springer Lawson et al 1993 Students reasoning within a PBL context may rely on misconceptions and reach erroneous conclusions thus rendering the more meaningful problem based context less effective for learning A Model of Task Based Learning Critical to the understanding of student knowledge con struction in PBL is an examination of meaningful learning learning that students recall and apply spontaneously to a given problem Whitehead 1929 Bransford et al 1993 The knowledge that students recall on a post test and the knowledge that they actually use in problem solving may be very different Mode
28. eer instruction a user s manual Prentice Hall Upper Saddle River NJ McDermott LC van Zee EH 1985 Identifying and addressing student difficulties with electric circuits In Walters RD Rhoneck C eds Aspects of understanding electricity proceed ings of an international workshop Institut f r der Naturwissens chaften and der Universitat Kiel Ludwigsburg Melendy RF 2008 Collegiate student s epistemologies and concep tual understanding of the role of models in precalculus math ematics a focus on the exponential and logarithmic functions Doctoral dissertation Oregon State University 2008 Scholars archive http hdl handle net 1957 8656 Moustakas C 1994 Phenomenological research methods Sage Publishing Thousand Oaks CA Oregon State University College of Engineering 2007 TekBots resources website Retrieved April 6 2010 from http eecs oregonstate edu education products index php Osborne R 1981 Children s ideas about electrical current N Z Sci Teach 29 1 12 19 A Springer J Sci Educ Technol Osborne R Freyberg P 1985 Learning in science the implications of children s science Heinemann Aukland London Patel VL Groen GJ Frederiksen CH 1986 Differences between students and physicians in memory for clinical cases Med Educ 20 3 9 Patel VL Groen GJ Arocha JF 1990 Medical expertise as a function of task difficulty Mem Cogn 18 4 394 406 Patel VL Groen GJ Norman GR 1991 Effects of c
29. embling the Tek Bots Subsequent assignments used the robotic platform to address problems in circuitry The first problems were short structured problems that were usually solved within the lab period Later problems were more open ended and required time out of class to solve By the end of the term the students were to successfully solve an open ended engineering problem in which they were to make their wheeled robot into a bump bot that would on encoun tering an obstacle back up and change direction As an extra credit problem students could add photoreceptors to their TekBots and create a robot that would follow a flashlight beam Subject Selection The subjects were purposefully selected from first year engineering students enrolled in the winter quarter course On the first day of the class a two tier survey developed by the researcher was administered to the entire class as a sorting tool The pretest consisted of seven questions on DC circuits derived from Mazur 1997 McDermott and van Zee 1985 and Shipstone 1984 The first question asked students to draw a simple circuit made up of a bat tery a bulb and one or more wires The next six questions showed a circuit and asked students to make predictions about the behavior of the circuit Students were given a choice of answers to circle then asked to provide a written explanation of their answers For sorting purposes the surveys were initially scored for
30. ended to rely on the teaching assistants and fellow students for guidance TA high prior knowledge and MJ low prior knowledge tended to view the problems as examples of a larger con cept or model and applied that concept or model to solving the problems Their problem solving success rate was higher and while MJ and her partners tended to rely equally on one another TA took a mentoring role toward the student he partnered with The results cannot be explained by prior knowledge of electrical concepts alone Other factors appeared to influ ence the outcomes one of which was habits of mind Mathematical achievement may have been a contributing factor JF at least perceived his lower mathematical ability as a barrier to success Self efficacy i e one s sense of what can be done with the knowledge in hand was not considered in this study however given that some subjects took a mentoring role while others were habitually recipi ents of mentoring suggests that self efficacy is a factor worth examining in the future Figure 7 is a proposed model outlined originally in Bledsoe 2007 to capture the complexities of learning in a problem based context In this model meaningful use of knowledge is both an input into a complex problem space and a product that is applied to other similar problems Inert knowledge may be activated and becomes meaningful during the task Likewise portions of the body of knowl edge that emerge from the pr
31. hat was not as easily translated into problem solutions Similarly lower initial knowledge supported early success when coupled with productive habits of mind such as seeking abstractions or gener alizations resulted in successful problem solving This discussion will outline a synthesis of knowledge use in problem based learning that suggests students with lower initial knowledge going into a problem based setting can apply and build on that knowledge through strategic support in relevant reasoning skills These skills include approach ing a problem systematically reflectively examining one s J Sci Educ Technol own sense of the overall purpose for solving the problem and looking for generalizations and abstractions leading to knowledge transfer It was clear by the end of the 10 week term that all four students conceptual knowledge had changed as most moved toward the target concepts presented in lecture More pertinent to the study however was how subjects were using their knowledge when working on solving problems in lab and how the lab activity in turn contrib uted to conceptual change The body of meaningful knowledge each subject demonstrated while working was derived from knowledge obtained from lecture and from prior labs interacting at times with prior conceptions and with each other What is significant is that while the total body of acquired knowledge grew and changed the meaningful learning that is to say the
32. heoretical foundations and data on problem solving and transfer In Penner LA Batsche GM Knoff HW Nelson DL eds The challenge in mathematics and science education psychology s response American Psy chological Association Washington DC Cook SDN Brown JS 1999 Bridging epistemologies the generative dance between organizational knowledge and organizational knowing Organ Sci 10 4 381 400 Dewey J 1938 Experience and education Collier Books New York A Springer Ebenezer JV Fraser DM 2001 First year chemical engineering students conceptions of energy in solution processes phenom enographic categories for common knowledge construction Sci Educ 85 509 535 Husserl E 1913 Ideas general introduction to pure phenomenology Translated 1958 by W R Gibson George Aleln and Unwin London Lawson AE Baker WP DiDonato L Verdi MP 1993 The role of hypothetico deductive reasoning and physical analogues of molecular interactions in conceptual change J Res Sci Teach 30 9 1073 1085 Lincoln Y 1990 Toward a categorical imperative for qualitative research In Eisner EW Peshkin A eds Qualitative inquiry in education the continuing debate Teachers College Press New York London Liu X Ebenezer J Fraser DM 2002 Structural characteristics of university engineering students conceptions of energy J Res Sci Teach 39 5 423 441 Marton F Booth S 1997 Learning and awareness Erlbaum Mahwah NJ Mazur E 1997 P
33. his kind of curiosity that led her beyond simply following lab instructions was characteristic of MJ in all observations To satisfy her curiosity MJ relied on her own observa tions as well as knowledge she obtained by asking the teaching assistant and other students for their ideas Like AM MJ s talk was more situational than theoret ical She talked less about what voltage and current were than what they were doing at the moment Her under standing of the relationship between voltage current and resistance was expressed mathematically using Ohm s Law which she used successfully to find answers to the questions posed in the lab Nevertheless expectations created by her underlying conceptual understanding influ enced her actions during lab For example her idea that current flowed directionally influenced her to check the direction in which she installed resistors in the circuits At the third observation Fig 4 MJ s concepts around voltage had increased As in the prior observation she demonstrated expectations that voltage should drive cur rent and that if she got a negative reading for voltage she should get a negative reading for current as well The expectation however led MJ and her partner into an error during one of the activities The first section of the lab had students compare two types of semiconductors diodes and bipolar junction transistors MJ expressed the purpose of the first part of the activity as
34. in this study subjects were interviewed to uncover their concepts of current voltage and resistance Two of seven A Springer subjects interviewed stated they could not describe what voltage was in the initial interview The remaining subjects in the initial interview and all subjects in the final interview expressed some concept of voltage and their concepts fell into one of four hierarchical categories While the beliefs of individual subjects did not necessarily move stepwise through all categories in the hierarchy the hierarchical order emerged from the overall direction of conceptual change across all subjects from na ve no concept of voltage to the target concept as taught in lecture Lowest on the hierarchy was the belief that voltage and current were similar in nature expressed in statements that described voltage as moving or flowing Instruction during lecture explicitly contradicted that belief yet some students continued to equate voltage and current with a second belief in which they described voltage as a measure of current A third belief also following instruction and reflecting models involving pool balls moving through a tube was an expression of voltage as pressure or push At the top of the hierarchy of beliefs about voltage was the belief that voltage was a form of potential energy This was the target concept taught in lecture Students using this belief discussed voltage as a causative factor in creating
35. ing a blown fuse A teaching assistant told him that the multimeter must be wired in series into the circuit and intervened to help AM wire the circuit correctly While AM stated the knowledge in the initial interview that current takes the path of least resistance even after instruction from the teaching assistant he had difficulty applying this knowledge to the correct use of a multimeter The instrument measured current when its probes were placed across a resistor creating a short in the circuit that is creating a path of least resistance AM appeared to view the multimeter as a measuring tool that was separate from the circuit and therefore not involved in the circuit s functions While AM did not express this explicitly other subjects in the study and other surrounding students expressed surprise on first learning that the mul timeter became part of the circuit when in use A second observation took place 3 weeks later AM and his partner were working separately on a 2 week exercise A Springer in which they were to apply prior lessons on digital logic to create a control board for the motor of their robot If suc cessful students should have a board that would cause the robot to move forward and backwards When moving forward a green indicator LED should turn on If moving backward a red indicator LED should light up Students had model schematics to work from that suggested part of the solution and were guided by written instr
36. ions meaning fully but was not readily able to connect that knowing to explicit statements about electric circuits While JF s hands on approach helped him form concepts in lab as when he adjusted the potentiometer and observed the behavior of the LED he did not appear to abstract the knowledge into an overall explanatory model Each new problem he appeared to treat as unique and it took some coaching from teaching assistants or other students before JF recognized a series of small problems as all relating to a particular concept JF s ability to successfully perform certain procedures his knowing cannot be directly translated into explicit knowledge According to Cook and Brown 1999 this will require a dynamic interaction with the learning opportunities of this situation TA s knowledge on the other hand was expressed from the beginning of the course in terms of relational models such as Ohm s Law which he operationalized and applied to various problems on the surveys and in labs TA was able to successfully predict the outcomes of circuits on the survey by taking a model based approach applying what he knew of Ohm s Law to each of the problems and taking into account the interactions between voltage current and resistance to predict outcomes TA appeared to view the individual problems on the survey as examples of a single unifying set of principles described in Ohm s Law Throughout the lab activities TA
37. ips between voltage current and resistance were sufficient to make accurate predictions regarding the circuits on the initial survey and during the interview During his first observation TA worked quietly and alone to assemble his robotic platform which yielded too little science talk to construct a useful concept map However at the second observation TA worked with a neighbor who needed help with the activities which yiel ded considerable conversation about the activities and the underlying concepts TA s talk reflected both his grasp of the lab exercises and his underlying concepts During an activity that involved measuring power dissipation in resistors TA A Springer measured voltage and current in order to calculate power dissipated then used the results obtained to frame his understanding of the circuits in his explanations to his partner For example TA and his partner ran current through a single large resistor and found that resistor became very hot then arranged several resistors in series that equaled the total resistance of the large resistor Even before applying current to the circuit TA predicted this was the overloaded resistor I bet by using the same amount of resistance but spreading it over five resistors that the power dissipated by each one will be within the range TA and his partner then applied current and dis cussed the results noting that the dissipation of power produces heat and that th
38. iterature about prior knowledge and problem based learning suggests that sub jects with low prior knowledge would achieve less over the course of the term than those with high prior knowledge results were more complex than expected These four subjects exemplify the range of results obtained A full description of the results for all subjects can be found in the original study Bledsoe 2007 Subject AM low prior knowledge was male age 19 He had studied electricity in a college level physics course and had built his own computer giving him some prior practical experience with electrical circuits He was enrolled in the first year of a 2 year calculus sequence AM scored 6 out of 24 on the initial survey Subject MJ low prior knowledge was female age 23 MJ recalled no prior courses where she had learned elec trical concepts and due to advising errors had not taken the fall introductory electrical engineering course She believed she had an aptitude for math and had been advised to consider engineering as a career She was enrolled in the second year of a 2 year calculus sequence MJ scored 8 out of 24 on the initial survey Subject JF high prior knowledge was male age 24 JF could recall no prior coursework that included electrical concepts but he had worked in construction where he had learned about wiring and had wired lights in his own home giving him practical experience with electrical cir cuits He was enrolled in an i
39. learning applied directly to each problem was highly contextual changing not just with a subject s entire body of knowledge but also with the problems themselves or more accurately what each student thought each problem was all about The primary question driving the study was Is success in problem solving due to the amount of knowledge a student has at the start of the problem or is it a factor of how the student uses the knowledge and how the student determines what knowledge is meaningful in the problem solving context Knowledge takes on multiple shades of meaning in this context Facts and examples that subjects could remember from lecture were not always recalled and applied where appropriate to laboratory problems White head s 1929 categories of inert and meaningful knowledge become critical in understanding the relation ship between conceptual knowledge and problem solving A comparison of conceptual change and of problem solving success in students with high prior knowledge and low prior knowledge shows that students in both groups experienced conceptual change as a result of both direct instruction and the lab experience A simple comparison of pre and post survey raw scores suggests that the students who entered with high prior knowledge had an advantage over those with low prior knowledge in terms of conceptual understanding AM scored 6 out of a possible 24 on the pre survey and 15 on the post sur
40. ls based on pre post test research designs fail to capture this important feature of learning within a PBL context what fraction of their knowledge that students actually apply when faced with a problem Understanding how students select from existing or newly introduced knowledge is essential for developing a com plete task based learning model The model should guide what to include in the problem or in direct instruction as well as what knowledge may be omitted if students can get by without it Sherin et al 2004 The relationship between inert and meaningful knowledge is shown in Fig 1 The model is a visual representation of Bransford s elaborations on Whitehead s descriptions of learning during problem solving The model is particularly important in understanding the differential success of students with weak or strong prior knowledge It invites the driving question behind this study Is success in problem solving due to the amount of knowledge a student has at the start of the problem as this model suggests or is it a factor of how the student Direct instruction Prior knowledge Student knowledge brought to the task Inert learning can be recalled when asked for but is not applied spontaneously Meaningful learning spontaneously applied to the tasks Fig 1 A model of learning based on Bransford et al s 1993 elaboration on Whitehead s 1929 model of task based learning
41. lso came into the class with low prior knowledge of electrical concepts but both her learning strategies and her outcomes were somewhat different from that of AM MJ s first observation took place the same day as the interview and her activities at that time consisted mostly of finishing the assembly of the robotic platform The second obser vation took place as MJ and a partner were working on the same activities that AM had worked on in his first obser vation including measuring voltage and current in a circuit that included an electric motor and working with resistors in series and parallel Most of the talk between the partners focused on procedures measurements and calculations During this observation MJ made references to Ohm s Law which had been learned in lecture and made sense of several of her observations by relating them to Ohm s Law At one point MJ and her partner also a subject in the larger study had measured internal ammeter resistance motor current and voltage across a 1 ohm resistor in the circuit and now had to fill in a blank labeled Calculated motor current using 1 ohm resistor J Sci Educ Technol Partner Got to figure out why we need the resistance of the voltmeter That we figure was 9 2 ohm resistor So thinks So resistors in series do you add them all 1 over 9 2 MJ Wait why are you adding all those together Partner Adding the resistance up MJ Okay Partner Because the voltage
42. ng enough to satisfy herself an understanding of mathematical relationships helped her successfully predict and explain circuit behaviors MJ s post survey score was 15 out of 24 Subject JF JF initially expressed a high degree of confidence in his understanding of circuits based on his prior experiences Having once wired a set of overhead lights in series he had discovered for himself that this would not give him the brightness that he wanted Like others in the study JF s conversation in the first interview focused largely on his concepts of current and he openly acknowledged that he A Springer J Sci Educ Technol did not understand what voltage was though he was familiar with the term JF s understanding of current was strongly material On his initial survey he expressed the belief that when a bulb was placed between two resistors if the resistance on the side where the current came from was increased the bulb s brightness would decrease but if the resistance on the other side were increased then the bulb should increase in brightness While he had changed his mind by the time of the second interview he explained that on the survey he had thought of current like a river and a resistor like a dam If current accumulates behind the second resistor the bulb should get more current If you if this is dammed up if you dam up before the light bulb it s going to get less if you dam after it s going to get mo
43. ng into an object AM did not have an effective strategy nor sufficient grasp of digital logic to design and construct circuits on his own During the final interview and several times during observations AM expressed a general frustration with the course He was aware that his understanding of electrical concepts was incomplete and ascribed his lack of success on the final project to his lack of understanding of digital logic He stated that given a schematic he could assemble the parts but found it difficult to understand the theo retical parts saying In lab I could make sense of where everything was supposed to go and I could trace where everything was flowing from and to on a board or what not I was able to set up the protoboards just fine but what was actually going on He described the practical hands on construction of circuits and the conceptual understanding of their function as pretty much two different worlds which he had been unable to reconcile While he recog nized his conceptual shortcomings at no time did he dis cuss any study strategies Observations and artifacts showed that he attended lab and did the required home work but did not attempt any optional problems nor did he attend any optional workshops that were offered AM ascribed his lack of understanding to external causes the difficulty of the class and his feeling that the instructor was not teaching well enough for him to understand MJ a
44. ntroductory algebra course JF scored 15 out of 24 on the initial survey Subject TA high prior knowledge was male age 29 TA had taken electronics courses in the US Navy about 10 years prior to the study and described himself as an electronics hobbyist He was enrolled in the second year of a 2 year calculus sequence TA scored 23 out of 24 on the initial survey Comparing Initial and Final Interviews All four students showed changes in knowledge during the course of the term as might be expected from instruction and practice with these concepts though not all students achieved the target concepts as defined by the professor in the written instructional documents for the course Concept maps based on student statements were used to diagram the ways in which concepts interrelated at the start and at the end of the term Subject AM In his initial interview AM described current as electron flow describing it in material terms as particles elec trons moving through wires Current was something that could be used up by bulbs and other circuit elements His material view is evident in statements about a light bulb lighting The bulb lights by a process of electrons moving through coming out of the positive end going in through there uh sparking with whatever element s in there and coming back through In clarifying what hap pens in the bulb AM stated The power s mixing with whatever s inside um the
45. o a photo vore arobot that would follow light While she understood the basic nature of the photoreceptors she struggled with developing a precise understanding of their response to specific light intensities as well as a way to incorporate them into the circuit After discussing the problem at length with one of the teaching assistants MJ sat down with her schematic again and worked out a series of equations as she traced the predicted actions in the circuit After some time she con cluded that she needed to test parts of the circuit in a more trial and error fashion to see how they would behave and use the outcome to inform her logic In the end MJ was successful at building a functioning bump bot Her schematic for the front bumper produced a working circuit that resulted in the behavior desired However she did not get the optional photovore to behave quite as she had hoped for While it detected light it did not consistently follow a light beam A Springer J Sci Educ Technol At the final interview MJ expressed a positive attitude toward further studies in electrical engineering Through out the term she attributed her knowledge gains to the extra work she had put in including taking circuits home to work on doing lab exercises over again and sometimes working optional problems When discussing concepts where she felt she lacked understanding she tended to ascribe this to internal causes that she needed to work
46. o say it s the A Springer change of um like electrons flowing Not flowing Just the like either the drop or the increase between one point and the other Contained in this is an idea of potential dif ferences which also was contained in his new view of batteries as a source of voltage rather than current Current itself he expressed as both energy and electron flow and his predictions regarding the outcomes of parallel and series circuits revealed that he expected current to be used up by circuit elements AM s post survey score was 15 out of 24 Subject MJ MJ s interview took place after she had been to several lectures She demonstrated tentative conceptions around current voltage and resistance A concept map of her ideas Fig 4 shows that like AM she focused on current in her explanations and less on voltage She described current explicitly as a form of energy and as electron flow and she believed that current could be used up by bulbs and other circuit elements She did not state the source of current in a circuit The battery she believed was a source of voltage J Sci Educ Technol Initial Interview _ Voltage is like pressure determines brightness of source of creates Bulb light by gt ener conversion gy Battery of A is circuit is used is the elements up by lt a x which make up a takes path restricts of least Sa a N which is divisible First Lab Observation Vv
47. oblem space may be inert in the context of successive problems but may be activated during that task While not a topic of the study some anecdotal evidence suggested that habits of mind may play a role in problem solving MJ s tenacity in attempting to solve problems which included reconstructing lab problems at home to further her understanding of the outcomes was a strategy J Sci Educ Technol Prior knowledge strong weak a Student knowledge brought to the task activation at start of task Inert learning can be recalled when asked for but is not e spontaneously activation applied duind applied to the t task spontaneously task asks Interpretation of the purpose of the task Problem solving skills Habits of mind Fig 7 Proposed model of learning in PBL that was instrumental in solving the final bump bot prob lem AM who did only the work that was required did not engage in reflection review and practice as did MJ did not succeed at the bump bot task Hence habits of mind are suggested here as part of the model but this is a feature in need of further research This model suggests that student learning is only one factor that influences success in PBL and is not necessarily the most predictive of problem solving success A deeper understanding of the factors that students bring to the complex problem space their problem solving approa che
48. oncepts that the subjects expressed during each observation The concepts expressed in the first interviews represented a body of knowledge that each subject carried into the lab experi ence Concept maps of the lab observations were more challenging to construct Asking subjects to think aloud during lab proved too intrusive Conversations with sub jects after they had successfully solved a problem did reveal approaches to reasoning as did conversations between subjects and their bench partners and with the teaching assistants Of particular interest was capturing the knowledge that subjects spontaneously applied during lab without coaching from the teaching assistants The researcher assumed that this knowledge held the most meaning for subjects After the concept maps were constructed the videos were again reviewed to test the consistency of the maps Copies of the graded lab exercises were collected from each subject and their responses compared with the concept maps as another test of consistency Where possible sub jects were asked to comment on representations of their prior concepts though member check was not possible on the final concept maps as analysis and concept map con struction continued after the study was over Results Description of results will focus on four of the subjects two who entered the course with low prior knowledge AM and MJ and two who entered with high prior knowledge JF and TA While much of the l
49. onventional and problem based medical curricula on problem solving Acad Med 66 7 380 389 Petrosino A 1998 At risk children s use of reflection and revision in hands on experimental activities Doctoral thesis submitted to the faculty of the Graduate School of Vanderbilt University Nashville TN 247 pp Roth WM 2005 Doing qualitative research praxis of method Sense Publishers Rotterdam and Taipei Sherin B Edelson D Brown M 2004 On the content of task structured science curricula In Flick LB Lederman NL eds Scientific inquiry and nature of science implications for teaching learning and teacher education Kluwer Academic Publishers Dordrecht The Netherlands Shipstone D 1984 A study of children s understanding of electricity in simple DC circuits Eur J Sci Educ 6 185 188 Shipstone D 1985 Electricity in simple circuits In Driver R Guesne E Tiberghien A eds Children s ideas in science Open University Press Miltone Keynes pp 33 51 Son JY Goldstone RL 2009 Contextualization in perspective Cogn Instr 27 51 89 Wandersee JH Mintzes J Novak J 1994 Research on alternative conceptions in science In Gabel D ed Handbook of research on science teaching and learning MacMillan New York Weinstein M 2005 TAMS analyzer version 3 3 computer software and manual Retrieved from http tamsys sourceforge net Westbrook SL Rogers LN 1996 Doing is believing do laboratory experiences promote concept
50. r was added The resistor however was equal to the internal resistance in the ammeter Like AM JF did not recognize that the ammeter became a part of the circuit when in use and saw it as something quite separate His alternate view of the activity s purpose left him puzzled when he was asked to calculate the motor current using Ohm s Law and the voltage from the batteries until his lab partner coached him JF But I don t know what the motor current is Partner Motor current Well you know the voltage You know the resistance You re good to go JF I don t know the voltage though Partner You don t JF That right there pointing to meter That s my batteries That s just Partner No it looks like it Yeah it s the voltage from the batteries Once coached JF recognized the activity as an Ohm s Law problem and successfully carried out the calculations However in the next activity JF expressed a new concept of voltage that led to another point of confusion In this problem students had to wire their robotic platform using suggestions from a schematic with a switch that in one position would allow the wall plug to charge the batteries and in another position would let the batteries discharge to run the motor In both cases the wheels of the robot would turn JF on discussing the problem with his partner and the teaching assistant believed that voltage from either the battery or wall plug would be used up
51. rcuit elements Fig 3 Concept maps created from AM s interviews and lab observations While current remained a central concept in both interviews AM s understanding of voltage and resistance increased in complexity As can be seen in the concept map in Fig 3 current figured largely in AM s discussion of circuits and other concepts were discussed in their relation to current When questioned about what he was measuring when he mea sured voltage AM first guessed that it might be the number of electrons at a given moment When asked to clarify he thought for a moment and stated Hmm the current would be the flow of electrons and R resistance is how many electrons are being held back er not how many it s just just a number I mean 4 7 ohms it s not going to hold back 4 7 electrons So yeah I guess it makes sense that voltage would be the number of electrons A concept map of the final interview also shown in Fig 3 shows that current was still the primary concept that AM used to discuss electrical phenomena AM s explana tion regarding light bulbs later changed to an energy con version theory in the final interview where he described electricity converting into heat and light However in the final interview AM maintained an essentially material view when he described resistance as something that holds back the flow of electrons and interpreted voltage as something to do with current I m going t
52. re water In the interview JF rejected this idea based on instruc tion in lecture and predicted that the resistor should have the same effect regardless of which side of the bulb it was located He also described bulbs themselves as resistors in a circuit and noted that the circuit in the problem that had a bulb between two resistors actually had three resistors in the circuit JF s only expressed understanding of voltage was based on hearing the term voltage divider in lecture He noted that bulbs wired in parallel split the voltage between them Implicit in this was the idea of voltage being something that flowed like current Figure 5 shows a concept map of JF s views in the initial interview In the final interview JF talked equally about current and voltage and discussed resistance in relation to both He described voltage as something like pressure that drives the flow of current Batteries he knew registered a certain amount of voltage across the terminals and the voltage in the battery pushed current through the circuit He strug gled however to explain why a resistor that reduced cur rent should register higher voltage across the two ends His view of current retained a material character as he dis cussed the highly directional nature of its flow through a circuit and described resistors as objects that impeded the flow of current An acceptance of voltage as something like pressure allowed JF to understand the func
53. rs or teams was encouraged and many students com bined their understanding with fellow students to solve the problems Subjects were as likely to encounter trouble by misremembering procedural knowledge such as wiring a multimeter to measure voltage versus current as they were by attempting to apply their alternative conceptions to the lab tasks The knowledge that students brought with them had a direct effect on their performance but prior knowl edge of electrical concepts was not the only influential factor Students with Low Prior Knowledge AM and MJ AM and MJ entered the course with low prior knowledge of basic electrical concepts and little experience with electronics The expectation based on prior research Anderson 1987 was that with a smaller knowledge base to draw upon they would have more difficulty solving problems than students with high prior knowledge How ever differences in habits of mind between these two subjects produced very different outcomes While AM did struggle with concepts as expected MJ s more intense study practices and methodical approach led to higher success in problem solving and greater conceptual change than AM During problem solving AM tended to rely on procedural knowledge where he could apply the procedures used in a prior exercise or a sample circuit in lecture to solve the problem before him When this strategy failed AM relied on the skills of neighboring students or on trial and error
54. s the lenses through which they interpret the purpose of the task and their habits of mind can further inform and improve PBL instruction To further inform and refine the model more work will be needed to understand the factors that appeared to influence subjects in this study including how student interpretation of a problem solving task influences the final product and the content learned how tacit conceptions of how to solve problems influence student performance in a Meaningful learning Complex problem space Direct instruction Interpretation of the purpose of the task Meaningful learning spontaneously applied to other tasks A activation during task Inert learning can be recalled when Pa activation at start of task asked for but is not applied to other tasks PBL context and finally whether a student s role in a mentor mentee student partnership influences or is influenced by a student s problem solving ability References Anderson JR 1987 Skill acquisition compilation of weak method problem solutions Psychol Rev 94 192 210 Bledsoe KE 2007 How do engineering students develop and reason with concepts of electricity within a project based course Doctoral dissertation Oregon State University 2007 Scholars Archive http hdl handle net 1957 5494 Bransford JD Goldman SR Hasselbring TS Pellegrino JW Williams SM Vye N 1993 The jasper series t
55. s was true and that he understood why This was consistently JF s preferred mode of learning which he demonstrated and expressed verbally on many occasions hands on activity observing the results then forming a concept JF s highly hands on try it and see approach to the lab activities resembled AM s strategy Like AM JF was dissatisfied at the end of the term with his understanding and his progress His knowledge of basic electrical con cepts had increased with a score on the final survey of 24 out of 24 but his bump bot had not succeeded JF expressed concerns that his level of mathematics achieve ment had interfered with his ability to understand the digital logic and programming necessary to make the robot operate Where other students in the study were in their first or second year of calculus JF was enrolled in college algebra While no calculus was used in the course JF felt that his lower level of mathematical understanding inter fered with his ability to solve problems particularly problems in digital logic He stated that he was re thinking his major and intended to take more mathematics before moving on in the engineering program TA entered the program with a past history of practical knowledge of circuitry from his Naval training His score on the pretest was near the ceiling 23 out of 24 While he struggled to recall vocabulary during the initial interview his understanding of the mathematical relationsh
56. servation is measured across when if 0 low produces produces resistors ng less Current Se Pa flows directionally in a entire x will not flow must be in a broken power lt completeto _ a allow flow of f 4 takes path of least Resistance n __ f high will stop affects behavior of Fig 6 Concept maps created from TA s interviews and lab observations TA showed extensive conceptual knowledge in both interviews as well as multiple connections between concepts voltage resistance and current were in terms of physics In his response to the problem of comparing two bulbs wired in parallel to a single bulb his written response in the second survey employed a more explicit use of Ohm s Law Given that the bulbs are made identically they will have equal internal resistance Given voltage V and resistance R the current through A will be V R The current through D will be V R also TA described the same problem during the final interview in similar terms Now that they re in parallel um you ve got well it s like two isolated circuits here You ve got one like the voltage is the same across both of these so you ve got the full your source voltage The resistance in each of these loops is just the one the light bulb s internal resistance so it s identical to this so V equals I times R and it s the same as this one it
57. subject drew from a larger body of knowledge only those facts examples or models that the student deemed appropriate in the context of the specific task Which knowledge was activated appeared to be influenced by a subject s interpretation of the task at the outset During the task knowledge that was contained in the body of previously inert learning could be activated if the A Springer J Sci Educ Technol student s idea of the purpose of the task changed or if the subject struggled with an unexpected outcome as when JF believed one lab was about measuring voltage to the motor with and without a resistor when the activity was about applying Ohm s law to determine the most accurate way to measure current Coaching from the TA and a fellow stu dent was required before JF was able to alter his views of the task and then reselect the knowledge that he believed was meaningful in that problem solving context Besides academic knowledge subjects brought other kinds of knowledge to the complex problem space that influenced the outcome of the task and further learning Within these four students appeared two very different problem solving approaches AM low prior knowledge and JF high prior knowledge appeared to look at each task as distinct and unconnected and attempted to solve the problems by recalling examples of similar problems Their problem solving success rate tended to be low compared with the other two subjects and they t
58. t to other circuits checking each one carefully for potential shorts that could bypass critical circuit elements MJ showed a tenacity in her work that worked in her favor as she struggled to understand concepts and complete lab activities Several times during observations she mentioned taking a circuit home and working on it outside of lab if she wasn t satisfied with the results or if she had not understood a concept in lab This was in contrast to AM who completed only the required exercises in class left early if he finished the minimum required work and did not work on problems outside of class MJ also formed a habit of drawing circuit schematics and using the schematics to predict outcomes before building circuits in contrast to AM s strategy of finding similar model circuits in lecture or lab notes and building those in a trial and error fashion MJ applied both of these habits to the bump bot problem While a fourth observation of MJ in lab as she worked on the bump bot yielded very little talk about her concepts she did talk about her problem solving approaches and she demonstrated both of these strategies as she worked on building the robot When she wasn t sure of the outcome of a schematic she stated that she would try it out and see what happened so her problem solving strategy involved both informed predictions and trial and error Particularly troubling to her was an optional challenge problem of making the bump bot int
59. tion of the bat tery but his belief that voltage was pressure that moved current failed to help him explain voltage as a potential difference across the ends of the resistor The knowledge that JF expressed confidently was based on his direct experience both prior to and during the lab itself He had no doubts that bulbs wired in series would be dimmer than bulbs wired in parallel as he had wired both types of circuits in lab and in his own home However when it came to explaining why JF was at a loss J Sci Educ Technol Initial Interview Voltage lt 4 __in parallel _____ splits material V has l dissipates qualities in parallel ofa splits a Pa is a reduces p follows Current J is gt electricity is gt power the path of least dissipates flows backs up directionally hich Be ne ie divisible First Lab Observation isa Voltage lt qd source Battery of Pa source aus is used of the up by po rom will conflict Resistance is like isa flows TER direction directionally Source affects ina of direction of y motor wall plug behind a ee ina resistor Final Interview if large has ist large a OF A Geis across Pa in excess burns out a is divided reduces brightness ofa Voltage drives when flow of is like increased shared between when reduced reduces impedes W the flow of reduces
60. to the tasks on the survey MJ who also scored low on the initial survey also had a low knowledge base to draw upon when making predictions However from the start of the course MJ tended to rely on abstracted relational models such as Ohm s Law to solve problems and was able to use these relationships between voltage current and resistance to reason her way through problems In addition MJ employed several habits of mind with success Like TA and JF she displayed productive inquiry with a distinct sense of purpose She showed a willingness early on to attempt optional problems and when puzzled displayed a tenacity that drove her to seek answers through continued study on her own or to consult with other students or the teaching assistant MJ also had higher mathematical knowledge than JF enrolled as she was in second year calculus at the time of the study Using digital logic in the bump bot problem was less of an issue for her than it was for JF Conclusions As the model in Fig suggests the students in this study demonstrated a difference between meaningful and inert learning To each problem they applied only that portion of their knowledge that they believed was applicable according to their interpretation of the task However contrary to what the model suggests the body of mean ingful learning among these four subjects did not neces sarily increase with each task but rather changed with each task as the
61. ual change Sch Sci Math 96 5 263 271 Whitehead AN 1929 The aims of education and other essays MacMillan New York
62. uctions through some preliminary exercises to measure voltage across transistors and other elements in the circuit By this observation AM s activity demonstrated his use of acquired knowledge that voltage is measured across circuit elements while current is measured through them Voltage he viewed as something that flows like current but with localized aspects as he asked the teaching assistant how to measure voltage through a transistor The teaching assistant indicated where to place the multimeter probes on one side of a transistor and the ground AM asked But wouldn t that just go through everything I just want to find the voltage around this AM made the LEDs on the board light up pointing out the success of a completed circuit to his partner indicating with gestures the flow of current through the board that caused the LEDs to light When it came time to measure current AM allowed his partner to do the measurements stating that his partner was more skilled Reliance on the skills of others was a frequent strategy that AM employed when he was unsure of his own success The two worked together to take and record readings from the multimeter Polarity of the transistors was important in the conversation as the two decided if the transistors were installed cor rectly AM stated at one point You need to switch em to which his partner replied that the results would be the same AM responded Not too sure abo
63. urvey They were then asked to explain what they observed The interviews were videotaped for later analysis The interviews were carried out as a dialogue between researcher and subject The subjects were assured that it was their conceptions that were important rather than reaching the right answer The interviewer s role was to listen attentively and ask questions only to further clarify views as described in Ebenezer and Fraser 2001 Rather than asking What is voltage which tends to elicit a recital of textbook definitions questions began with phra ses such as How do you explain in order to uncover the subjects own ideas This helped elicit if then propo sitions from subjects such as If the current is flowing in A Springer Fig 2 Sample question from the conceptual survey administered at the start and at the end of the course J Sci Educ Technol 4 Observe the circuit below which includes a dry cell two bulbs and a switch Circle as many of the following that will happen when the switch is closed and explain in the space below A will get brighter A will get dimmer or go out B will get brighter B will get dimmer or go out this direction then what we should see is this bulb lighting up first Researcher observations on students engaged in lab tasks captured evidence of concept use and conceptual change Students were videotaped at work and the tapes were later transcribed for an
64. ut that They might be a negative Because you know direction will be changing In this AM was referring to the direction that the robot would be moving stating the purpose of the exercise as We re probably going to have to put like switches on here so we can turn it left or right That d be my guess AM also commented on how voltage of resistors adds up in a circuit During this observation AM also made the comment that he was having difficulty understanding the lessons in lecture on digital logic stating that they went right over my head He tended to ascribe his failure to understand entirely to the difficulty of the subject matter and did not appear to be changing his learning strategies to increase his understanding Yet in addition to understanding and applying basic electrical concepts students needed some elementary understanding of digital logic to be able to use diodes and bipolar junction transistors as digital switches to make the robot carry out its function as a bump bot A Springer J Sci Educ Technol In the final interview AM described his limited success with his bump bot The motor ran and the wheels turned but it did not successfully negotiate a maze as he thought it should AM s approach was largely trial and error AM used schematics from the lab to construct the basic plan for the bump bot When it came to constructing the circuitry to make it respond as desired when bumpi
65. vey while MJ scored 8 on the pre survey and 16 on the post survey Their post survey scores were similar to JF s pre survey score of 15 and lower than TA s pre survey score of 23 Both JF and TA scored 24 on the post survey However looking at actual performance in the lab suggests that the knowledge needed to predict the out comes of simple circuits on the surveys was only one aspect of the knowledge skills and habits necessary to success in the problem based lab particularly on the final bump bot problem Furthermore the survey outcomes did not distinguish between problem solving approaches that later influenced success in problem solving in the lab The nature of meaningful knowledge of electrical con cepts that subjects applied to problem solving also differed JF s hands on try it and see style derived from a knowl edge that consisted of previous practice and recalled out comes from past experience He applied that knowledge to the pre survey recalling for example a series circuit that he had once wired that had resulted in bulbs that were dimmer than desired In lab as well the knowledge that JF applied consisted of examples recalled from his prior background lecture and prior labs From his construction experience JF derived what Cook and Brown 1999 referred to as knowing In contrast with knowledge about actions knowing is action or an aspect of action JF was able to successfully perform certain act
66. vides a framework to examine changes in student knowledge over time Methods The students in this study were engaged in a first year electrical engineering course at a state research university on the west coast of the United States The course was taught during winter quarter During the fall quarter stu dents had been introduced to the school of engineering learned some basic electrical concepts learned to solder circuits and constructed a small circuit board During the winter term students reviewed the concepts of current voltage and resistance in greater detail then applied these concepts to complex problems in class The term concluded with an introduction to digital logic The researcher did not participate in instruction The lab portion of the course employed a hands on robotics platform for learning called TekBots Oregon State University 2007 Students purchased the kit at the beginning of the term and used it throughout the term in solving both structured and open ended problems Labs met once a week for the 10 weeks of the term A maximum of 24 students attended each lab The lab sections were supervised by two or more graduate teaching assistants For most assignments students could work alone if they chose but most students elected to work with other students at their workbenches Each lab assignment took 2 weeks to complete The first assignment was highly structured consisting of the instructions for ass
67. y TA explained We re going to have like this is what pointing to battery three volts total on the circuit here So each bulb is going to have the change in voltage is going to be one and a half volts across each one Um I guess it s because the voltage drop is equal and the way they re made up the resistance should be about equal Um all that s saying is the current s going to be the same which I already said TA described current as the flow of electrons through wires Interestingly in his interview he did not explicitly connect the idea of voltage as pressure with the idea of voltage as the force pushing electrons through the wires though this concept came out later during lab observations TA also described resistance as something that restricts the flow of electrons In the final interview TA explicitly connected voltage resistance and current He stated that in a circuit where resistance was 0 voltage was also 0 If voltage was 0 then current should also be 0 TA s responses during the inter view were highly focused on the problem revealing only a small part of the knowledge that he had expressed during lab on the same concepts His written responses on the final survey however revealed knowledge that was not expressed in the interview In general TA seemed to express more through written words than spoken In both interviews TA tended to view each circuit as a mathematical problem to b

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