Undergraduate Engineering Students’ Representational Competence of Circuits Analysis and Optimization: An Exploratory Study

William Sanchez; Alejandra J. Magana; Peter Bermel

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Conference: 2016 ASEE Annual Conference & Exposition
Location: New Orleans, Louisiana
Publication Date: June 26, 2016
Start Date: June 26, 2016
End Date: June 29, 2016
ISBN: 978-0-692-68565-5
ISSN: 2153-5965
Conference Session: Classroom Practice III: Student-Centered Instruction
Tagged Division: Educational Research and Methods
Page Count: 11
DOI: 10.18260/p.27091
Permanent URL: https://peer.asee.org/27091
Download Count: 678

Paper Authors

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William Sanchez Purdue University, West Lafayette

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Alejandra J. Magana Purdue University, West Lafayette orcid.org/0000-0001-6117-7502

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Alejandra Magana is an Associate Professor in the Department of Computer and Information Technology and an affiliated faculty at the School of Engineering Education at Purdue University. She holds a B.E. in Information Systems, a M.S. in Technology, both from Tec de Monterrey; and a M.S. in Educational Technology and a Ph.D. in Engineering Education from Purdue University. Her research is focused on identifying how model-based cognition in STEM can be better supported by means of expert technological and computing tools such as cyberinfrastructure, cyber-physical systems, and computational modeling and simulation tools.

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Peter Bermel Purdue University, West Lafayette orcid.org/0000-0001-7140-0667

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DR. PETER BERMEL is an assistant professor of Electrical and Computer Engineering at Purdue University. His research focuses on improving the performance of photovoltaic, thermophotovoltaic, and nonlinear systems using the principles of nanophotonics. Key enabling techniques for his work include electromagnetic and electronic theory, modeling, simulation, fabrication, and characterization.

Dr. Bermel is widely-published in both scientific peer-reviewed journals and publications geared towards the general public. His work, which has been cited over 3500 times, includes the following topics:
* Understanding and optimizing the detailed mechanisms of light trapping in thin-film photovoltaics
* Fabricating and characterizing 3D inverse opal photonic crystals made from silicon for photovoltaics, and comparing to theoretical predictions
* Explaining key physical effects influencing selective thermal emitters in order to achieve high performance thermophotovoltaic systems

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Abstract

Undergraduate Engineering Students’ Representational Competence of Circuits Analysis and Optimization: An Exploratory Study (Evidence-based Practice)

Background and Motivation There is a long-standing interest and strong concentration of educational research in electricity-related concepts, due to two essential reasons: (a) electricity is one of the central areas of science curricula at all levels of education, and (b) its concepts are particularly difficult to teach and learn because they are abstract and complex. Therefore, both educators and students face several challenges through the learning process. The abstract and complex nature of electricity-related concepts makes many students generate conceptions and ideas, which may be in conflict with the formal science perspectives. Specifically in engineering education, concepts associated with electric circuits are particularly important because they are the foundation for other advanced topics and skills, such as the design of devices, circuits, and systems. However, researchers such as McDermott and Shaffer have identified that students are unable to apply formal concepts to an electric circuit. As a consequence, students may hold misconceptions about electric current, voltage, and resistance. One particular characteristic of misconceptions in science and engineering is that even after long periods of instruction, students may not demonstrate a significant improvement in their learning performance 6. A main concern for educational researchers and educators has been finding ways to improve current learning techniques to consequently improve students’ conceptual understanding. This study explores the use of multiple representations as a feasible mechanism to improve conceptual understanding of electric circuits. The guiding research question are: How effectively do students use multiple representations of electric circuits? And what is the relationship between students’ conceptual understanding of circuits and their performance on a representational task?

Theoretical Framework Model-based reasoning (MBR) is the theoretical framework that guided the design of the learning activity and its evaluation. MBR is one form of scientific cognition that investigates how scientific representations are created from existing representations. It has been documented that processes of reasoning taking place during MBR episodes can lead to concept formation, conceptual understanding or conceptual change. In practice, MBR often consists of constructing artifacts and external representations allowing learners to make their understanding explicit by creating models, also called conceptual tools. Such conceptual tools may include explicit descriptive or explanatory systems functioning as models designed specifically to reveal aspects about how students interpret specific problem-solving situations. The implications for the use of MBR as the theoretical framework for this study relate to the use of Model-Eliciting Activities (MEAs) as (a) a guideline for the development of the learning design focused emphasizing representational competence, and (b) a mechanism to identify and assess student representational competence via their produced graphical representations. Methods The participants of this study were 24 sophomore engineering students enrolled in a linear circuit analysis course offered to electrical engineering students at a Midwestern University. Students were asked to complete a homework assignment guided by principles of MEA design. The assignment consisted of having students to first analyze an electric circuit, and then optimize it in order to be able to recharge a car’s battery. Students were prompted to create and use multiple representations such as (1) diagrams and equations to identify the mathematical model of the problem, (2) simulations to represent the circuit behavior and its optimization and (3) computational tool (i.e., MATLAB) to program the model and evaluate the circuit. At the end, for each circuit (i.e., base and optimized) students were asked to explain their solution. This last question measured student conceptual understanding. Different forms of representations created by the students were analyzed independently and qualitatively. Based on the categorization of each of the different representations a rubric was developed (see Appendix A). Students’ representations were then assessed with the rubric, and students’ scores were analyzed via descriptive statistics and a correlational analysis between representations. Rubric scoring ranged from one to four where scores below 1.5 were considered as low achievement, between 1.6 to 3.5 as moderate achievement, and over 3.6 as high achievement. An additional grading criteria of “no response” was also included.

Results How effectively do students use multiple representations of electric circuits? Students were prompted to develop a total of five different representations as part of the assignment; two for the base circuit and three for the optimized circuit. Students, on average, developed 3 representations (mean=3.4, SD=1.2) and the overall score for those was rated as moderate (mean=2.9, SD=0.9). Overall performance of students’ conceptual interpretation of the circuit was identified as moderate (mean=2.0, SD=1.6). Overall results suggest that students demonstrated a good understanding of the mathematical representation of the base circuit as well as a basic explanation of its behavior. However, for the case of the optimized circuit, students were able to represent the circuit at the beginning of the optimization process at a basic level, but failed to successfully represent its mathematical model as well as the computational model. For the optimized circuit, students were not able to provide an acceptable conceptual explanation of the optimized circuit. A second analysis was performed with observations from those students who developed the two representations for the base circuit, and the three representations for the optimized circuit. To be included in this analysis, it was also required that students responded both of the conceptual questions. This analysis suggest that students who completed the five representations performed in the moderate to high achievement levels in constructing the representations and using them meaningfully for their conceptual understanding.

What is the relationship between students’ conceptual understanding of circuits and their performance on a representational task? Overall results suggest a positive correlation between number of graphical representations students developed, and their overall conceptual understanding (r=0.53, p=.006). In addition, the correlation between the quality of the representations students produced and their achievement in the conceptual questions was also analyzed. This correlation analysis suggests that there is a positive correlation between the computational representation and the conceptual understanding. In contrast, the correlation analysis suggest strong relationships between students’ representations, diagrams, mathematical and computational, and their conceptual understanding. Finally, for those students who completed both of the conceptual questions (n=14), one for each circuit, it was identified a moderate positive correlation between the number of representations they developed and their conceptual understanding (r=0.46, p=0.102); and a strong correlation between the quality of their representations (as scored with the rubric) and their explanations in their conceptual understanding (r=0.92, p less than.0001).

Conclusion and Implications Results from this exploratory study suggest that, for most of the cases, when students developed accurate representations, students also interpreted the behavior of the circuit accurately. Results also suggest that the number and quality of students’ representations are correlated with their conceptual understanding. Findings from this study are aligned from those to others who have identified the effect of the use of graphical representations in engineering education and its role in supporting conceptual understanding. The contribution of this study relates to the integration of computational representations and modeling practices for problem solving. The implications of this study relate to the evaluation of pedagogical approaches that can be integrated along with modeling and simulation practices at the undergraduate level.

Citation
Format

Sanchez, W., & Magana, A. J., & Bermel, P. (2016, June), Undergraduate Engineering Students’ Representational Competence of Circuits Analysis and Optimization: An Exploratory Study Paper presented at 2016 ASEE Annual Conference & Exposition, New Orleans, Louisiana. 10.18260/p.27091

TY - CPAPER
AB -
Undergraduate Engineering Students’ Representational Competence of Circuits Analysis and Optimization: An Exploratory Study
(Evidence-based Practice)

Background and Motivation
There is a long-standing interest and strong concentration of educational research in electricity-related concepts, due to two essential reasons: (a) electricity is one of the central areas of science curricula at all levels of education, and (b) its concepts are particularly difficult to teach and learn because they are abstract and complex. Therefore, both educators and students face several challenges through the learning process. The abstract and complex nature of electricity-related concepts makes many students generate conceptions and ideas, which may be in conflict with the formal science perspectives. Specifically in engineering education, concepts associated with electric circuits are particularly important because they are the foundation for other advanced topics and skills, such as the design of devices, circuits, and systems. However, researchers such as McDermott and Shaffer have identified that students are unable to apply formal concepts to an electric circuit. As a consequence, students may hold misconceptions about electric current, voltage, and resistance.
One particular characteristic of misconceptions in science and engineering is that even after long periods of instruction, students may not demonstrate a significant improvement in their learning performance 6. A main concern for educational researchers and educators has been finding ways to improve current learning techniques to consequently improve students’ conceptual understanding. This study explores the use of multiple representations as a feasible mechanism to improve conceptual understanding of electric circuits. The guiding research question are: How effectively do students use multiple representations of electric circuits? And what is the relationship between students’ conceptual understanding of circuits and their performance on a representational task?

Theoretical Framework
Model-based reasoning (MBR) is the theoretical framework that guided the design of the learning activity and its evaluation. MBR is one form of scientific cognition that investigates how scientific representations are created from existing representations. It has been documented that processes of reasoning taking place during MBR episodes can lead to concept formation, conceptual understanding or conceptual change. In practice, MBR often consists of constructing artifacts and external representations allowing learners to make their understanding explicit by creating models, also called conceptual tools. Such conceptual tools may include explicit descriptive or explanatory systems functioning as models designed specifically to reveal aspects about how students interpret specific problem-solving situations.
The implications for the use of MBR as the theoretical framework for this study relate to the use of Model-Eliciting Activities (MEAs) as (a) a guideline for the development of the learning design focused emphasizing representational competence, and (b) a mechanism to identify and assess student representational competence via their produced graphical representations.
Methods
The participants of this study were 24 sophomore engineering students enrolled in a linear circuit analysis course offered to electrical engineering students at a Midwestern University. Students were asked to complete a homework assignment guided by principles of MEA design. The assignment consisted of having students to first analyze an electric circuit, and then optimize it in order to be able to recharge a car’s battery. Students were prompted to create and use multiple representations such as (1) diagrams and equations to identify the mathematical model of the problem, (2) simulations to represent the circuit behavior and its optimization and (3) computational tool (i.e., MATLAB) to program the model and evaluate the circuit. At the end, for each circuit (i.e., base and optimized) students were asked to explain their solution. This last question measured student conceptual understanding.
Different forms of representations created by the students were analyzed independently and qualitatively. Based on the categorization of each of the different representations a rubric was developed (see Appendix A). Students’ representations were then assessed with the rubric, and students’ scores were analyzed via descriptive statistics and a correlational analysis between representations. Rubric scoring ranged from one to four where scores below 1.5 were considered as low achievement, between 1.6 to 3.5 as moderate achievement, and over 3.6 as high achievement. An additional grading criteria of “no response” was also included.

Results
How effectively do students use multiple representations of electric circuits?
Students were prompted to develop a total of five different representations as part of the assignment; two for the base circuit and three for the optimized circuit. Students, on average, developed 3 representations (mean=3.4, SD=1.2) and the overall score for those was rated as moderate (mean=2.9, SD=0.9). Overall performance of students’ conceptual interpretation of the circuit was identified as moderate (mean=2.0, SD=1.6).
Overall results suggest that students demonstrated a good understanding of the mathematical representation of the base circuit as well as a basic explanation of its behavior. However, for the case of the optimized circuit, students were able to represent the circuit at the beginning of the optimization process at a basic level, but failed to successfully represent its mathematical model as well as the computational model. For the optimized circuit, students were not able to provide an acceptable conceptual explanation of the optimized circuit.
A second analysis was performed with observations from those students who developed the two representations for the base circuit, and the three representations for the optimized circuit. To be included in this analysis, it was also required that students responded both of the conceptual questions. This analysis suggest that students who completed the five representations performed in the moderate to high achievement levels in constructing the representations and using them meaningfully for their conceptual understanding.

What is the relationship between students’ conceptual understanding of circuits and their performance on a representational task?
Overall results suggest a positive correlation between number of graphical representations students developed, and their overall conceptual understanding (r=0.53, p=.006). In addition, the correlation between the quality of the representations students produced and their achievement in the conceptual questions was also analyzed. This correlation analysis suggests that there is a positive correlation between the computational representation and the conceptual understanding. In contrast, the correlation analysis suggest strong relationships between students’ representations, diagrams, mathematical and computational, and their conceptual understanding.
Finally, for those students who completed both of the conceptual questions (n=14), one for each circuit, it was identified a moderate positive correlation between the number of representations they developed and their conceptual understanding (r=0.46, p=0.102); and a strong correlation between the quality of their representations (as scored with the rubric) and their explanations in their conceptual understanding (r=0.92, p less than.0001).

Conclusion and Implications
Results from this exploratory study suggest that, for most of the cases, when students developed accurate representations, students also interpreted the behavior of the circuit accurately. Results also suggest that the number and quality of students’ representations are correlated with their conceptual understanding. Findings from this study are aligned from those to others who have identified the effect of the use of graphical representations in engineering education and its role in supporting conceptual understanding. The contribution of this study relates to the integration of computational representations and modeling practices for problem solving. The implications of this study relate to the evaluation of pedagogical approaches that can be integrated along with modeling and simulation practices at the undergraduate level.

AU - William Sanchez
AU - Alejandra J. Magana
AU - Peter Bermel
CY - New Orleans, Louisiana
DA - 2016/06/26
PB - ASEE Conferences
TI - Undergraduate Engineering Students’ Representational Competence of Circuits Analysis and Optimization: An Exploratory Study
UR - https://peer.asee.org/27091
DO - 10.18260/p.27091
ER -