How do engineering students without a strong knowledge base reason and form ideas about electricity wit= hin a task-based learning context?

Karen E. Bledsoe, , Oregon State University

A= bstract<= o:p>

The purpose of this study was to examine conceptions held by first year undergraduate electrical engineering students around the concepts of current, voltage, and resistance in simple = and complex circuits as they enter a task-based learning environment, and how t= heir prior knowledge interacted with their reasoning skills as they worked to so= lve the problems presented in the tasks. While the study involved students with both high and low knowledge, this paper focuses on two students who entered= the course with low prior knowledge. The study contributed to an overall model = of how students use their prior knowledge to reason within task-based learning environments and how, in turn, reasoning within a task affects their concep= ts.

Introduction

Task-structured curricula are anchored in a task, problem, or project, which requires student to reason across content areas rather than work through an established series of cont= ent topics. The effectiveness of task-structured curriculum has been the subjec= t of a great deal of research, most of which has drawn ambiguous conclusions (Al= banese & Mitchell, 1993). Tests of content knowledge alone sometimes show that students taught in traditional settings have a slight advantage over those taught in a task-based setting (for example, Saunders, et al., 1990), but in other cases show insignificant differences between the two groups (for exam= ple, Enarson & Cariaga-Lo, 2001). Students taught in a task-based context of= ten show an advantage in long-term knowledge retention (Breton, 1999), and may = also be better able to apply their knowledge to real-world problems (Vernon & Blake, 1993). Students engaged in problem-based learning often show a great= er improvement in problem-solving skills over their traditional counterparts, = as might be expected when problem solving was part of the daily problem-based learning context (Hmelo, 1998).

Inconclusive results of studies = on knowledge outcomes, and possible negative consequences, have not inhibited = the promotion of task-based learning as a means of teaching reform. Because of = the high costs of developing and implementing task-based curricula, educators m= ay want to know whether the methods are truly advantageous, and whether there = are any disadvantageous effects.

However, the question, “Do= es task-based learning improve test scores?” may be the wrong question to ask. At the very least, it is overly-simplistic. Task-based learning is a v= ery different way of learning from traditional lecture-practice-test teaching a= nd creates different cognitive demands. It is reasonable to hypothesize that students engaged in task-based learning may be thinking, reasoning, and experiencing conceptual change differently from students in other learning contexts. Capturing these differences is often difficult, as conceptual mod= els and reasoning skills require more than a standardized test or a survey to measure. Furthermore, any discussion of generic “students” is oversimplified, as student enter a task-based course with a wide range of p= rior knowledge and reasoning skills. They often work in groups where the collect= ive knowledge allows the group to achieve tasks of greater complexity than any = one member could achieve individually.

A better question to ask, then, = may be: “How do student learn content knowledge and reason with that cont= ent knowledge within task-based contexts?” Answering this question requir= es a rich description of student learning, mental representations, conceptual change, and reasoning as students struggle with solving problems and comple= ting tasks. as well as the dynamics involved in the social construction of knowl= edge. The results of many studies around these questions may then be compared with studies involving similar questions about students learning by didactic methods.

Research Questions

This study was developed to help fill the gap in knowledge about how students and reason within task-based learning contexts. Specifically, this study examined lear= ning and reasoning among first-year electrical engineering students as they work= ed to complete tasks and solve problems in a project-based lab component of on= e of their required courses. The questions guiding the research were:=

1. What phenomenographic categories of common knowledge regarding direct-curre= nt electrical circuits are constructed by first-year electrical engineering students?

2. What relationship exists between a student’s prior conceptual understanding of electrical circuits and the student’s reasoning processes while solving problems involving circuits?

3. How does a student’s meaningful learning change as the student grappl= es with a series of complex problems?

This paper will look specificall= y at two students who entered the course with low prior knowledge.

A Proposed Model

Whitehead (192= 9) proposed a model of learning within a task-based setting. The knowledge tha= t a student brings to a task consists of prior knowledge held before instructio= n, and any direct instruction just prior to the task. What emerges is two sets= of knowledge: “meaningful” knowledge that the individual values and uses spontaneously in the task and similar tasks, and “inert” knowledge that may be recalled if asked for, such as on an exam, but is not used spontaneously. Hence “inert” and “meaningful” knowledge are related to both retention and transfer of knowledge. Figure 1 illustrates Whitehead’s model.

Fi= gure 1: A diagram of learning based on Whitehead’s (1929) concept of inert and meaningful learning.

Bransford, et = al., (1993), in discussing Whitehead’s propositions, argued that task-based instruction is more likely than didactic instruction to result in the development of meaningful knowledge. Bransford proposed that meaningful learning applied to tasks is retained, and is likely to be transferred to further tasks.

Both Whitehead’s and Bransford’s arguments are incorporated into the model in Figure 2, which served as a hypothetical model guiding this study. This model proposes that meaningful knowledge may be discerned in two instances. First, when students enter a problem space, they bring with them= a complex array of prior knowledge, some of it scientifically accurate and so= me of it not. Those with strong prior knowledge are often more successful at problem-solving (Anderson, 1987). Second, students may learn new knowledge = in a class setting before approaching a task, depending on how the curriculum is arranged.

Fi= gure 2: A proposed model of learning within task-based curricula, based on Whitehead (1929) and Bransford, et al. (1993).

Other factors besides knowledge enter the complex problem space. Students bring with them idiosyncratic interpretations of the purpose of the task (Osborne & Freyberg, 1985), a wide range of reasoning skills, attitudes toward the task and the subject, and habits of mind, including study skills and student self-efficacy.

The complex learning space is itself a learning environment in which students not only apply knowledge, but construct new knowledge. Emerging from this space is t= he student’s knowledge, now transformed. Some of the resulting knowledge will be meaningful; that is, students will spontaneously apply it to further tasks. Some will be inert: the student will be able to recall the knowledge= if asked, but will not think to use it on a related task. The model therefore describes an iterative process. Each time a student enters a task-based environment, the student brings the knowledge from prior learning, some of which will be applied to the new task.

Method<= /u>

Th= is paper reports on a portion of data collected during a larger study, to be described in Bledsoe (2007), in which students with high prior knowledge and students with low prior knowledge, as determined by a survey of electrical concepts, were interviewed and observed as they participated in a task-based laboratory section of an electrical engineering course. This paper will describe two students who entered the course with low prior knowledge, how = the concepts held by these students changed, the reasoning displayed by these students, and their self-perceived success in the course. These two students were of particular interest because of their differing degrees of success in the course.

The subjects of this study were selected from first-year engineering students enrolled in ECE 112: Introduction to Electrical and Computer Engineering, at Oregon State University. They were engaged in a project-based lab which involved the TekBots robotic platform (http://eec= s.oregonstate.edu/education/tekbots.html), where the problem required application of knowledge of electrical systems to a series of projects as students built the robot platform, learned how it functioned, and created a “bump bot” designed to back up and turn around after it bumped = into an object.

Se= ven case studies were selected from a pool of volunteers, and comprised students who scored at the low end and at the high end of scores on a survey of electrical concepts given on the first day of the lecture portion of the cl= ass. The survey, developed by the researcher, consisted of a set of questions on= DC circuits from the concept test described in Mazur (1997) and questions drawn from McDermott & van Zee (1985) and Shipstone, (1984). Each question sh= owed a diagram of a circuit and asked students to make one or more predictions a= bout the circuit. Students selected from several possible answers, and wrote an explanation of their choice in the space provided. The questions were score= d 2 if the student chose the correct response and gave a correct explanation, 1= for a correct response with an incorrect explanation, and 0 for incorrect or missing response SHAPE \* MERGEFORMAT 3D"Text

Figure 3: Sample question from the conceptual su= rvey administered at the beginning and the end of this study, and used in the ca= se study interviews.

Ca= se study students were interviewed early in the term to develop a description = of the mental conceptions they held around the concepts of current, voltage, a= nd resistance. During the interview, students were given the survey that they = had filled out. The researcher read each question and noted the student’s response, then asked if the student still held that view. Students explained their responses, then were asked to create the circuit using wires, bulbs, batteries, and resistors mounted on a board in order to test their predicti= ons. Students observed the results and attempted to explain any discrepancies. <= o:p>

St= udents were videotaped at least three times during lab as they engaged with the projects, and the researcher engaged students in conversation during lab wh= en practical. The researcher also sat in on lectures in order to observe how students were learning concepts and what language the might be expected to = use around the basic concepts.

At= the end of the term, students filled out the electrical concepts survey a second time and were interviewed to develop a description of their electrical conc= epts at the end of the term, using the same protocols as the first interview. At this time, copies of students’ lab reports were also collected. =

In= terviews and videotapes from labs were transcribed and analyzed using a phenomenogra= phic perspective, using the analytical methods described in Ebenezer & Fraser (2001). Descriptions of mutually exclusive categories of knowledge were developed from student responses, and matrices developed to track whether student conceptions changed during the term. Individual student responses w= ere used to develop a series of concept maps, which were analyzed to examine bo= th changes in student knowledge and how students used that knowledge during the reasoning process.

Re= asoning was described according to a cognitive model of reasoning by way of mental modeling, derived from Nersissian (1998). This view arises from psychologic= al literature on semantic reasoning, which plays a larger role in human reason= ing than the traditional inductive-deductive models allow (Craik, 1943). Vandierendonck and de Vooght (1996) also argue that humans tend to solve problems, including simple logic problems, by constructing mental models in memory rather than using classical rules of argument. This perspective was valuable for this study, as traditional accounts of reasoning do not support conceptual change. Nersessian (1992) argues for an explanation of conceptual change through the problem-solving process, noting that records of this pro= cess capture processes that comprise model-based reasoning. Chi, et al. (1989) a= nd Chi (1992) employ a similar approach, using student self-explanations and “think aloud” methods as a means of tracking student reasoning = and conceptual change. Reasoning and conceptual change are, in this model, intertwined, and reasoning consists largely of the application of current concepts to a specific problem.

Findings

Two of the case study students b= egan the course with low prior knowledge. While it might be expected that studen= ts with low prior knowledge would not perform as well as students with high pr= ior knowledge in a task-based setting, the results, as exemplified by these two students, were not that simple.

Subject AM was male, age 19. AM = had studied electricity in a prior physics course, and had built his own comput= er, so he had some prior knowledge of electrical concepts and electronics. Howe= ver, out of a possible score of 24 on the survey, AM scored 6. The highest math class that AM had taken was MTH 252, Integral Calculus.

Subject MJ was female, age 23. MJ could think of no prior courses where she had studied electrical concepts, = and had no prior experience with electronics. Her score on the initial survey w= as 8 out of 24. However, she had an aptitude for math and had been counseled by = an advisor to try electronics as a major. The highest math class that MJ had t= aken was MTH 256, Applied Differential Equations.

Question 1: What phenomenographic categories of common knowledge regarding direct-current electrical circuits= are constructed by first-year electrical engineering students?

Transcriptions of surveys and conceptual interviews at the beginning and end of the term were examined and coded for instances of student statements regarding current, voltage, and resistance. Codes were sorted= and merged to form a hierarchical set of phenomenographic categories of knowled= ge, which were used to describe student concept development over the course of = the term.

Primary concep= t: the nature of current

Lecture notes provided for the c= lass explicitly stated that current consists of electrons in motion through material. The phrase “current consists of moving electrons” was printed in bold face at the t= op of the class notes for the first day of class. How students interpreted and us= ed this phrase may have depended on their understanding of what electrons are. Students who viewed them as solid particles tended to have a material view = of current, while students who thought less about moving electrons and more ab= out the effects of current tended to view current in more energetic terms. Thus= two phenomenographic categories emerged:

1. Current is material or quasi-material: This view was accompanied by the belief that current could = be “used up” like a fuel by circuit elements, or could even be dam= med up behind resistors. The analogies used in lecture, in which current was compared to water flowing in pipes, may have reinforced this view.

2. Current is energy: Subjects holding this view often defined current as the flow of electrons, but when describing current in an actual circuit, tended to use energy-related terms involving the use or dissipation of energy, power, or electricity.

AM’s initial conception of current was highly material. In explaining how the light bulb in the circuit board lit up, AM described light as being caused by a chemical reaction bet= ween “power” and chemicals in the bulb:

I: Okay, so inside the bulb itse= lf, what’s happening?

AM: The power’s mixing with whatever’s inside, um, the, (turns to I) the chemical that’s in= side it.

I: Okay. And when you say power, what do you mean when you say power?

AM: Electron flow. (AM, initial interview)

By the end of the term, AM’= ;s views of current still contained material elements. He talked less about current and more about voltage in the final interview, but did not distingu= ish clearly between the two concepts:

AM: Um, well, say if this was li= ke one light bulb (pointing to A and B). It would have to equal the same amoun= t as coming into this one (pointing to C). Amount of what, I don’t know. Voltage, or current. Um, so, they’re going to equal the same. And, bu= t, this one (A and B) has to divide it, because they’re in parallel, so = both of them are a lot dimmer than that (C). (AM, final interview)

MJ began the term with a material view of current, and struggled at the beginning of the term with the ideas = that current is shown flowing one direction, while electrons flow in the opposite direction. For a student with a material view of current, this apparent conflict makes no sense:

MJ: That's something that I'm ki= nd of confused -- I think the electrons are going from negative to positive, b= ut the way we always draw it is, you know, the current is always flowing from positive to -- er, I mean it's going into the positive direction, so (pause= s) I'm not really sure. I think it goes like this (moving hand clockwise).

I: So what is it that actually g= oes?

MJ: Electrons.=

I: Okay, and they go...

MJ: That's the current. (MJ, ini= tial interview)

The only way that MJ could recon= cile the two conflicting ideas was to let go of her views of flowing electrons a= nd view current in terms if its mathematical relationships with voltage and resistance:

It's changing the current, becau= se the current through all three of them has to be the same because they're al= l in series, but the current, let's see -- since V=3DIR, 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. (MJ, final interview, explaining the effects of resistors on either side of a bulb.)

Primary concep= t: the nature of voltage

While students had an intuitive sense of current as something that flowed like water, voltage was a far more elusive concept. Lecture notes described voltage as an electromotive force = that pushes electrons through a substance. The notes again used a water flow mod= el, using differences in pressure at two ends of a narrow bit of hose as an ana= logy for differences in electrical potential on either side of a resistor. Sever= al phenomenographic categories of knowledge emerged from student responses:

1. No concept of voltage: While = both students described in this paper had initial concepts around voltage, two o= thers interviewed simply had no idea of what voltage was in the initial interview= s.

2. Voltage is current or is like current: In spite of the lecture instructor describing examples of this misconception in class, several students described voltage in current-like terms, such as describing voltage flowing through a circuit.

3. Voltage is a measure of curre= nt: Through instruction, students learned that voltage is not current, but some students still struggled to understand exactly what voltage was. Students u= sed multimeters in class to measure current and voltage, and some seemed to bel= ieve that voltage was a measure of some quality of current or of current itself.=

4. Voltage is pressure or “push”: This concept was used in the lecture notes as an analog= y to help students understand voltage. While not strictly scientifically accurat= e, it served as a useful model as students made predictions about their lab ta= sks and the interview tasks. This may have been drawn from the water pipe analo= gy, since the class notes compared voltage with measuring pressure in the pipe.=

5. Voltage is potential energy: = This concept, while more scientifically accurate, was the most difficult for students to understand. Those who described voltage as potential energy eit= her used the “push” concept to make predictions about where current would flow, or discarded the idea of current entirely and described circuit= s in terms of mathematical relationships.

In the initial interview, AM see= med confused by the concept of voltage, and tended to describe voltage in terms that he also applied to current. Though he wasn’t fully satisfied with this explanation, he nevertheless went back to it as he struggled to define= the term:

I: For instance, you measure vol= tage in lab.

AM: Right.

I: So what do you picture yourse= lf measuring?

AM: (long pause) The — num= ber of electrons at a give moment? (Looks back at interviewer)

I: Okay. So when it says it̵= 7;s such-and-such volts, or when you measure so many volts across a resistor, we’re measuring electrons with them?

AM: Uh, no. (thinks) Hm... The current would be the flow of electrons, and R, resistance is how many elect= rons are being held back, er, not how many, it’s just, just a number. I me= an, 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. (AM, initial interview= )

By the end of the term, AM reali= zed that voltage was not current, and moved to a conception of voltage as a mea= sure of current:

I: Or when you were measuring voltage in lab. What was it that you felt you were measuring? ...

AM: I’m going to say it’s the change of, um, like electrons flowing. Not flowing. Just the like either the drop or the increase between one point and the other. (AM, final interview)

Early in the term, MJ was forming models of voltage as a source of pressure to move current:

I: Yeah, basically what is it th= at -- that the meter’s actually measuring. What is it that those numbers mean?

M: Well, it’s not measuring the current, it’s measuring the pressure of the current. The um, way he explained it in class= was relating it to water, where the quantity of the water is the current and th= en the pressure of the water is the voltage, you know, the pressure of the current. (MJ, first observation)

In the final interview, MJ had m= oved to talking about voltage as potential energy when asked for a definition, w= hile her spontaneous explanations involved voltage in its mathematical relation = to current and resistance:

I: Okay, so what is voltage?

MJ: It's the change in potential from here to here (pointing to resistor on diagram) or from here to here or wherever you're measuring it from. Change in electric potential. (MJ, initi= al interview)

MJ: They're both getting the same voltage from the battery doing it like this. And this way the voltage to ea= ch of them can only be equal to the voltage across the battery it can't be -- = and since the resistance of each of them is assumed to be equal, then this is, = this (bulbs in series) can only get half of the voltage of the battery and this = can get the other half. But this way (bulbs in parallel) they can each have the full voltage of the battery. (MJ, initial interview, describing series and parallel circuits.)

Primary concep= t: the nature of resistance

Like voltage, resistance was a difficult concept for all students. The class notes in the second week introduced the concept of resistance while introducing Ohm’s Law. The notes relied on a water analogy, comparing wires to fire hoses and resistor= s to drinking straws: forcing the water in a fire hose through a drinking straw slows the flow of water considerably. There was also a molecular explanation involving the speed at which electrons can diffuse through materials. The target concept in the notes appeared to be loss of kinetic energy. However, However, the phrase from the notes that students appeared to assimilate the most was, “...a resistor is a component that purposefully impedes or opposes the flow of electrons.” This definition was used during the lecture, indicating a target concept of impeding the flow of current.

All subjects were familiar with = the phrase “the path of least resistance,” and used it on an interv= iew problem involving two bulbs wired in series, with a switch bypassing one of= the bulbs. Subjects correctly predicted that the bypassed bulb would dim or go = out when the switch was pressed because the switch had less resistance than the bypassed bulb. However, not all subjects predicted that the second bulb wou= ld get brighter at the same time that the bypassed bulb went out, indicating limitations to their knowledge of the effects of resistance on the circuit = as a whole.

Three phenomenographic categorie= s of knowledge emerged:

1. Resistance is holding back of current: This view often accompanied a material view of current. The resist= or was viewed as an impediment, like a traffic cop holding back traffic, or a = dam in a stream holding back water. One student, not described at length in this paper, believed that a bulb “behind” a resistor should get brig= hter if the resistance was increased because more current would pool behind the resistor, making more available to the bulb.

2. Resistance is the restriction= of current: This differs from the first concept in that current is not seen as being physically held back, but that its flow is somehow restricted in its flow. In the water model analogy offered in class, resistors were compared = with a narrow bit of hose, which causes an increase in pressure of the water flo= wing through. Students using this model thought that resistance should slow down= the current.

3. Resistance is the dissipation= of energy: While students using other descriptions sometimes spoke of energy dissipation, only one student, not described at length in this paper, used dissipation of energy as his primary means of describing resistance.

AM began and ended the term with= the idea that resistance involves holding back or blocking current. Interesting= ly, this concept was challenged in the initial interview when AM observed the results of changing the resistance on either side of a bulb, and AM was abl= e to offer a different explanation:

I: Yeah. So why does it get dimm= er when you put the larger resistor in? What is the resistor doing?=

AM: It’s holding back some= of the — electricity.

I: Okay. And then when you incre= ase the other one, what happens?

AM: Gets dimmer! Okay.

I: Why is that?...

AM: Maybe because it — I figured the current is set — (quietly )back and forth — (unhooks wires and tries the two resistors for R2 again, comparing resulting brightn= ess of the bulb)

I: What if instead of a resistor, that was another light bulb in that circuit? Would that make the bulb dimme= r?

AM: Yeah.

I: So does that help you explain= it?

AM: All right. So you have the w= hole total over the whole thing. Obviously if I took out this resistor (R1) that would be bright, put that one in and it’s dim, but this one is dim, because it has to — divide through the whole circuit — whatever power’s going through it.

I: So does it make a difference = what order the elements are in?

AM: I would think so, but maybe = not? (thinks for a while) From this I’m thinking no. (AM, initial intervie= w)

Furthermore, though AM’s understanding of what resistance is didn’t change, his practical understanding of what resistance does did change, as he was able to correct= ly predict that a bulb would dim regardless of which side of the bulb the resistance was increased.

Concepts held by these two stude= nts are summarized in Table 1.

Table 1

Su= mmary of categories of knowledge held by the two case study students at the initi= al and final interviews .

Concepts	AM, initial	AM, final	MJ, initial	MJ, final
Current	Current is material or quasi-material	X	X	X
Current is energy				X
Voltage	Voltage is current	X
Voltage is a measure of current		X
Voltage is pressure or “push”			X
Voltage is potential energy				X
Resistance	Resistance is the holding back of current	X	X
Resistance is the restriction of current			X	X
Resistance is the dissipation of energy