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1. B. M. Zwickl, N. Finkelstein, and H. J. Lewandowski, “ The process of transforming an advanced lab course: Goals, curriculum, and assessments,” Am. J. Phys. 81, 6370 (2013).
2. L. C. McDermott and P. S. Shaffer, “ Research as a guide for curriculum development: An example from introductory electricity. Part I: Investigation of student understanding,” Am. J. Phys. 60(11), 9941003 (1992); printer's erratum to Part I, 61(11), 81 (1993).
3. P. S. Shaffer and L. C. McDermott, “ Research as a guide for curriculum development: An example from introductory electricity. Part II: Design of instructional strategies,” Am. J. Phys. 60(11), 10031013 (1992).
4. P. V. Engelhardt and R. J. Beichner, “ Students' understanding of direct current resistive electrical circuits,” Am. J. Phys. 72, 98115 (2004).
5. M. R. Stetzer, P. van Kampen, P. S. Shaffer, and L. C. McDermott, “ New insights into student understanding of complete circuits and the conservation of current,” Am. J. Phys. 81, 134143 (2013).
6. J. G. Getty, “ Assessing inquiry learning in a circuits/electronics course,” Proceedings of the 39th IEEE International Conference on Frontiers in Education Conference ( IEEE Press, Piscataway, NJ, 2009), pp. 817822.
7.See, for example: E. C. Sayre, M. C. Wittmann, and J. R. Thompson, “ Resource selection in nearly-novel situations,” AIP Conf. Proc. 720, 101104 (2004). In this proceedings paper, the authors reported some data on student understanding of diodes and simple diode circuits.
8.See, for example: A. O'Dwyer, “ Prior understanding of basic electrical circuit concepts by first year engineering students,” All-Ireland Society for Higher Education (AISHE) Conference, NUI Maynooth, 2009;
8. T. Ogunfunmi and M. Rahman, “ A concept inventory for an electric circuits course: Rationale and fundamental topics,” in Proceedings of the 2010 IEEE International Symposium on Circuits and Systems (ISCAS), 2010, pp. 28042807;
8. N. H. Hussain, L. A. Latiff, and N. Yahaya, “ Alternative conceptions about open and short circuit concepts,” Procedia—Soc. Behav. Sci. 56, 466473 (2012).
9. C. H. Kautz, “ Development of instructional materials to address student difficulties in introductory electrical engineering,” in Proceedings of the 40th SEFI Annual Conference 2012, Lisbon, Portugal, 2011, pp. 228235.
10. P. Coppens, M. de Cock, and C. H. Kautz, “ Student understanding of filters in analog electronics lab courses,” in Proceedings of the 40th SEFI Annual Conference, Thessaloniki, Greece, 2012.
11.See, for example: A. S. Andreatos and G. S. Kliros, “ Identifying transistor roles in teaching microelectronic circuits,” in Proceedings of 2006 IEEE Mediterranean Electrotechnical Conference, Bernalmadena, Spain, 2006, pp. 12211224;
11. A. Andreatos and G. Michalareas, “ Engineering education e-assessment with Matlab; Case study in electronic design,” in Proceedings of the 5th WSEAS/IASME International Conference on Engineering Education, Heraklion, Greece, 2008, pp. 172177.
12.See, for example: M. F. Simoni, M. E. Herniter, and B. A. Ferguson, “ Concepts to questions: Creating an electronics concept inventory exam,” in Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition, 2004;
12. T. A. Hudson, M. Goldman, and S. M. Sexton, “ Using behavioral analysis to improve student confidence with analog circuits,” IEEE Trans. Educ. 51(3), 370377 (2008).
13. A. Mazzolini, T. Edwards, W. Rachinger, S. Nopparatjamjomras, and O. Shepherd, “ The use of interactive lecture demonstrations to improve students' understanding of operational amplifiers in a tertiary introductory electronics course,” Lat. Am. J. Phys. Educ. 5(1), 147153 (2011); available at
14. L. C. McDermott, “ Millikan lecture 1990: What we teach and what is learnedClosing the gap,” Am. J. Phys. 59(4), 301315 (1991).
15. L. C. McDermott, “ Oersted medal lecture 2001: Physics education researchThe key to student learning,” Am. J. Phys. 69(11), 11271137 (2001).
16. P. R. L. Heron, “ Empirical investigations of learning and teaching, Part I: Examining and interpreting student thinking,” in Enrico Fermi Summer School on Physics Education Research, edited by E. F. Redish and M. Vicentini (Italian Physical Society, Varenna, Italy, 2003), pp. 341350.
17. P. Horowitz and W. Hill, The Art of Electronics, 2nd ed. ( Cambridge U. P., NY, 1991).
18. T. C. Hayes and P. Horowitz, Student Manual for the Art of Electronics ( Cambridge U.P., NY, 1992).
19. G. S. Tombras, Introduction to Electronics, 2nd ed. ( Diavlos Books, Athens, 2006).
20. E. J. Galvez, Electronics with Discrete Components ( John Wiley & Sons, Hoboken, NJ, 2013).
21. A. J. Diefenderfer and B. E. Holton, Principles of Electronic Instrumentation, 3rd ed. ( Brooks/Cole, Belmont, CA, 1994).
22. On the tasks in this study, we have often noted significant performance differences between UA and the other two institutions. We speculate that they may be related to systemic factors at UA including larger class sizes (200+), less laboratory time (labs every other week), and lower course attendance.
23. It is possible that some of the UA students were more attentive to the relationship between the voltage across and the current through an ohmic resistor.
24. See, for example, Ref. 2.
25. These graduate students were either working as TAs in the electronics course or just beginning research in electronics.
26.Such behavior is consistent with a “knowledge in pieces” or resources model of student thinking (in which, for example, a student might draw upon a more informal notion that “increased resistance leads to less result”) and dual process theories of reasoning. See, for example: D. Hammer, “ Student resources for learning introductory physics,” Phys. Educ. Res., Am. J. Phys. Suppl. 68(7), S52S59 (2000);
26. D. Hammer, “ Misconceptions or p-prims: How may alternative perspectives of cognitive structure influence instructional perceptions and intentions?,” J. Learn. Sci. 5(2), 97127 (1996);
26. A. diSessa, “ Towards an epistemology of physics,” Cognit. Instruct. 10(2–3), 105225 (1993);
26. M. Kryjevskaia, M. R. Stetzer, and N. Grosz, “ Answer first: Applying the heuristic-analytic theory of reasoning to examine student intuitive thinking in the context of physics,” Phys. Rev. ST Phys. Educ. Res. 10, 020109 (2014).
27.A similar phenomenon has been reported in Ref. 5.
28.Many electronics texts show and discuss the rails when first introducing the op-amp, but subsequently omit them from diagrams and discussions when covering the canonical op-amp circuits. This was generally true for the texts and materials used in this study, although both Galvez and Tombras explicitly discuss rail currents at least once when covering the canonical circuits.
29. L. C. McDermott, P. S. Shaffer, and the Physics Education Group at the University of Washington, Tutorials in Introductory Physics, 1st ed. ( Prentice Hall, Upper Saddle River, NJ, 2002);
29. L. C. McDermott, P. S. Shaffer, Instructor's Guide ( Prentice Hall, Upper Saddle River, NJ, 2003).

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The research reported in this article represents a systematic, multi-year investigation of student understanding of the behavior of basic operational-amplifier (op-amp) circuits. The participants in this study were undergraduates enrolled in upper-division physics courses on analog electronics at three different institutions, as well as undergraduates in introductory and upper-division electrical engineering courses at one of the institutions. The findings indicate that many students complete these courses without developing a functional understanding of the behavior of op-amp circuits. This article describes the most prevalent conceptual and reasoning difficulties identified (typically after lecture and hands-on laboratory experience) as well as several implications for electronics instruction that have emerged from this investigation.


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