Describing the what and why of students' difficulties in Boolean logic

ACM Transactions on Computing Education

Volumn 12, Issue 1, 2012, Pages

  Herman, Geoffrey L ^a   Loui, Michael C ^a   Kaczmarczyk, Lisa ^b   Zilles, Craig ^a  

^a University of Illinois at Urbana Champaign   (United States)

^b NONE

Author keywords

Human Factors; Languages; Verification

Indexed keywords

ASSESSMENT TOOL; BOOLEAN EXPRESSIONS; BOOLEAN LOGIC; COMPUTER ENGINEERS; COMPUTER SCIENTISTS; CONCEPT INVENTORIES; DIGITAL LOGIC DESIGN; PROPOSITIONAL LOGIC;

FORMAL LOGIC; HUMAN ENGINEERING; LOGIC DESIGN; QUERY LANGUAGES; SCAFFOLDS; TEACHING; VERIFICATION;

STUDENTS;

EID: 84859417818     PISSN: 19466226     EISSN: None     Source Type: Journal    
DOI: 10.1145/2133797.2133800     Document Type: Article

References (71)

1. ALMSTRUM, V. 1999. The Propositional Logic Test as a diagnostic tool for misconceptions about logical operations. J. Comput. Math. Sci. Teach. 18, 3, 205-224.
2. ALMSTRUM, V. L. 1993. Limitations in the understanding of mathematical logic by novice computer science students. Ph.D. thesis, University of Texas at Austin.
3. ALMSTRUM, V. L. 1996. Investigating student difficulties with mathematical logic. In Teaching and Learning Formal Methods, C. N. Dean and M. G. Hinchey Eds., Academic Press, 131-160.
4. ALMSTRUM, V. L., HENDERSON, P. B., HARVEY, V., HEEREN, C.,MARION, W., RIEDESEL, C., SOH, L.-K., AND TEW, A. E. 2006. Concept inventories in computer science for the topic discrete mathematics. In Proceedings of the 11th Annual SIGCSE Conference on Innovation and Technology in Computer Science Education (ITiCSE'06). 163-167.
5. ANDERSON, J. R., REDER, L. M., AND SIMON, H. A. 1998. Radical constructivism and cognitive psychology. In Brookings Papers on Education Policy, D. Ravitch Ed., Brookings Institution, 227-255. (A more complete version, is available online http://act.psy.cmu.edu/ACT/papers/misapplied-abs- ja.html.)
6. BEN-ARI, M. 2005. The Concorde doesn't fly anymore. In Proceedings of the Technical Symposium on Computer Science Education (SIGCSE'05).
7. BRANSFORD, J. D., BROWN, A. L., AND COCKING, R. R. 1999. How People Learn: Brain, Mind, Experience, and School. National Academy Press, Washington, D.C.
8. CAREY, S. 1999. Sources of conceptual change. In Conceptual Development: Piaget's Legacy, E. K. Scholnick, K. Nelson, S. Gelman, and P. Miller Eds., Erlbaum, Manwah, NJ, 293-326.
9. CHENG, P. W. AND HOLYOAK, K. J. 1985. Pragmatic reasoning schemas. Cog. Psych. 17, 391-416.
10. CHENG, P. W., HOLYOAK, K. J., NISBETT, R., AND OLIVER, L. 1986. Pragmatic vs. syntactic approaches to training deductive reasoning. Cog. Psych. 18, 293-328.
11. CHI, M. T. H., FELTOVICH, P. J., AND GLASER, R. 1981. Categorization and representation of physics problems by experts and novices. Cog. Sci. 5, 121-152.
12. CLEMENT, J. 1982. Algebra word problem solutions: Thought processes underlying a common misconception. J. Res. Math. Ed. 33, 1, 16-30.
13. CLEMENT, J. 1993. Using bridging analogies and anchoring intuitions to deal with students' preconceptions in physics. J. Res. Sci. Teach. 30, 10, 1241-1257.
14. CLEMENT, J. 2004. A call for action (research): Applying science education research to computer science instruction. Comp. Sci. Ed. 14, 4, 343-364.
15. CLEMENT, J., LOCHHEAD, J., AND SOLOWAY, E. 1980. Positive effects of computer programming on student understanding of variables. In Proceedings of the ACM Annual Conference (ACM'80). 467-474.
16. DEER, G. W. 1969. The effects of teaching an explicit unit in logic on students' ability to prove theorems in geometry. Ph.D. thesis, Florida State University.
17. DISESSA, A. A., GILLESPIE, N. M., AND ESTERLY, J. B. 2004. Coherence vs. fragmentation in the development of the concept of force. Cog. Sci. 28, 6, 843-900. (Pubitemid 39620371)
18. DUFRESNE, R., GERACE, W., HARDIMAN, P., AND MESTRE, J. 1992. Constraining novices to perform expert-like problem analyses: Effects on schema acquisition. J. Learn. Sci. 2, 307-311.
19. EPP, S. S. 2003. The role of logic in teaching proof. Amer. Math. Month. 110, 10, 886-899. (Pubitemid 37537560)
20. ERICSSON, K. A. AND SIMON, H. A. 1984. Protocol Analysis: Verbal Reports as Data. MIT Press, Cambridge, MA.
21. EVANS, D. L., GRAY, G. L., KRAUSE, S., MARTIN, J., MIDKIFF, C., NOTAROS, B. M., PAVELICH, M., ROANCOUR, D., REED-RHOADS, T., STEIF, P., STREVELER, R., AND WAGE, K. 2003. Progress on concept inventory assessment tools. In Proceedings of the 33rd ASEE/IEEE Frontiers in Education Conference (FIC'03).
22. GLASER, B. AND STRAUSS, A. 1967. The Discovery of Grounded Theory: Strategies for Qualitative Research. Aldine, Chicago, IL.
23. GOETTING, M. M. 1995. The college student's understanding of mathematical proof. Ph.D. thesis, University of Maryland.
24. GOLDMAN, K., GROSS, P., HEEREN, C., HERMAN, G., KACZMARCZYK, L., LOUI, M. C., AND ZILLES, C. 2010. Setting the scope of concept inventories for introductory computing subjects. ACM Trans. Comput. Ed. 10, 2, 1-29.
25. GREENE, S. L., DEVLIN, S. J., CANNATA, P. E., AND GOMEZ, L. M. 1990. No ifs, ands, or ors: A study of database querying. Int. J. Man-Mach. Studies 32, 303-326.
26. HAKE, R. 1998. Interactive-engagement vs. traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses. Amer. J. Phys. 66, 64-74.
27. HARDIMAN, P. T., DUFRESNE, R. J., AND MESTRE, J. P. 1989. The relation between problem categorization and problem solving among novices and experts. Mem. Cogn. 17, 627-638.
28. HAREL, G. AND SOWDER, L. 1998. Students' proof scheme. In Research in Collegiate Mathtematics Education, Vol. III, E. Dubinsky, A. Schoenfeld, and J. Kaput Eds., American Mathematical Society, 234-283.
29. HERMAN, G. L. 2011. The development of a digital logic concept inventory. Ph.D. thesis, University of Illinois at Urbana-Champaign.
30. HERMAN, G. L. AND HANDZIK, J. 2010. A preliminary pedagogical comparison study using the Digital Logic Concept Inventory. In Proceedings of the 40th ASEE/IEEE Frontiers in Education Conference (FIC'10).
31. HERMAN, G. L., KACZMARCZYK, L., LOUI, M. C., AND ZILLES, C. 2008. Proof by incomplete enumeration and other logical misconceptions. In Proceedings of the 4th International Workshop on Computing Education Research (ICER'08). 59-70.
32. HERMAN, G. L., ZILLES, C., AND LOUI, M. C. 2009. Work in progress: Students' misconceptions about state in digital systems. In Proceedings of the 39th ASEE/IEEE Frontiers in Education Conference (FIC'09).
33. HERMAN, G. L., LOUI, M. C., AND ZILLES, C. 2010. Creating the Digital Logic Concept Inventory. In Proceedings of the 41st Annual ACM Technical Symposium on Computer Science Education (ITiCSE'10). 102-106.
34. HERMAN, G. L., LOUI, M. C., AND ZILLES, C. 2012. Flip-flops in students' conceptions of state. IEEE Trans. Ed.
35. HERMAN, G. L., LOUI, M. C., AND ZILLES, C. 2011a. Students' misconceptions about medium-scale integrated circuits. IEEE Trans. Ed. 54, 4, 637-645.
36. HERMAN, G. L., ZILLES, C., AND LOUI, M. C. 2011b. Administering a digital logic concept inventory at multiple institutions. In Proceedings of the American Society for Engineering Education Annual Conference and Exposition (ASEE'11).
37. HERMAN, G. L., ZILLES, C., AND LOUI, M. C. 2011c. How do students misunderstand number representations? Comput. Sci. Ed. 23, 3, 289-312.
38. HESTENES, D. AND HALLOUN, I. A. 1995. Interpreting the Force Concept Inventory: A response to March 1995 critique by Huffman and Heller. Phys. Teach. 33, 502-506.
39. HESTENES, D., WELLS, M., AND SWACKHAMER, G. 1992. Force Concept Inventory. Phys. Teach. 30, 141-158.
40. HOC, J. M. 1989. Do we really have conditional statements in our brain. In Studying the Novice Programmer, E. Soloway and J. C. Spohrer Eds., Lawrence Erlbaum Associates, Hillsdale, NJ, 179-190.
41. JUNGWIRTH, E. 1985. Science teaching and pupil avoidance of logical fallacies. South African J. Ed. 5, 55-60.
42. JUNGWIRTH, E. 1987. Avoidance of logical fallacies - A neglected aspect of science-education and science teacher education. Res. Sci. Technol. Ed. 5, 43-58.
43. JUNGWIRTH, E. 1990. Science teachers spontaneous, latent, or nonattendance to the validity of conclusions in reported situations. Res. Sci. Technol. Ed. 8, 103-115.
44. KIM, Y. 1995. The reasoning ability and achievement of college level students enrolled in a logic class in computer science. Ph.D. thesis, University of Texas at Austin. http://www.lib.utexas.edu/indexes/titles.php?id=114.
45. KVALE, S. 1996. Interviews: An Introduction to Qualitative Research Inquiry. Sage, Thousand Oaks, CA.
46. LEONARD, W. J., DUFRESNE, R. J., AND MESTRE, J. P. 1996. Using qualitative problem-solving strategies to highlight the role of conceptual knowledge in solving problems. Amer. J. Phys. 64, 1495-1503.
47. LONGINO, J. T., LOUI, M. C., AND ZILLES, C. 2006. Student misconceptions in an introductory digital logic design course. In Proceedings of the American Society for Engineering Education Annual Conference and Exposition (ASEE'06).
48. MCCRACKEN, M., ALMSTRUM, V., DIAZ, D., GUZDIAL, M., HAGAN, D., KOLIKANT, Y. B.-D., LAXER, C., THOMAS, L., UTTING, I., AND WILUSZ, T. 2001. A multi-national, multi-institutional study of assessment of programming skills of first-year CS students. In Proceedings of the 11th Annual SIGCSE Conference on Innovation and Technology in Computer Science Education Working Group Reports (ITiCSE'06). 125-180.
49. MERRIAM, S. B. 2009. Qualitative Research: A Guide to Design and Implementation. Jossey-Bass.
50. MILES, M. B. AND HUBERMAN, M. 1984. Qualitative Data Analysis: A Sourcebook of New Methods. Sage Publications, Thousand Oaks, CA.
51. NISBETT, R. E. 1993. Rules for Reasoning. Lawrence Erlbaum Associates, 1-12.
52. OWENS, B. B. AND SEILER, J. 1996. A study of the relationship between performance in propositional logic and computer science. J. Comput. Small Coll. 11, 7, 90-93.
53. PANE, J. AND MYERS, B. 2000. Tabular and textual methods for selecting objects from a group in Institute for Software Research.
54. PERKINS, D. 1999. The many faces of constructivism. Ed. Lead. 57, 3, 6-11.
55. PERKINS, D. N. AND MARTIN, F. 1986. Fragile knowledge and neglected strategies in novice programmers. In Proceedings of the 1st Workshop on Empirical Studies of Programmers. E. Soloway and S. Iyengar Eds., Norwood, NJ, 213-229.
56. PETRUSHKA, D. 1984. A study of the effect of content on the ability to do syllogistic reasoning: An investigation of transferability and the effect of practice. Ph.D. thesis, Rutgers University.
57. PIBURN, M. D. 1989. Reliability and validity of the Propositional Logic Test. Ed. Psych. Measure. 49, 667-672.
58. PIBURN, M. D. 1990. Reasoning about logical propositions and success in science. J. Res. Sci. Ed. 27, 9, 887-900.
59. REISSLEIN, M., MORENO, R., AND OZOGUL, G. 2010. Pre-college electrical and computer engineering instruction: The impact of abstract vs. contextualized representation and practice on learning. J. Eng. Ed. 99, 3, 225-235.
60. SCHOENFELD, A. H. 1992. Learning to think mathematically: Problem solving, metacognition, and sensemaking in mathematics. In Handbook for Research on Mathematics Teaching and Learning. MacMillan, New York, 334-370.
61. SELDEN, J. AND SELDEN, A. 1995. Unpacking the logic of mathematical statements. Ed. Studies Math. 29, 2, 123-151.
62. STAGER-SNOW, D. 1985. Analytical ability, logical reasoning, and attitude as predictors of success in an introductory course in computer science for non-computer science majors. Ph.D. thesis, Rutgers University.
63. STRAUSS, A. AND CORBIN, J. 1998. Basics of Qualitative Research. Sage, Thousand Oaks, CA.
64. TEW, A. E. AND GUZDIAL, M. 2010. Developing a validated assessment of fundamental CS1 concepts. In Proceedings of the 41st Annual ACM Technical Symposium on Computer Science Education (CSE'10). 97-101.
65. THE COMPUTER SOCIETY OF THE INSTITUTE FOR ELECTRICAL AND ELECTRONIC ENGINEERS AND ASSOCIATION FOR COMPUTING MACHINERY. 2001. Computing Curricula 2001, Computer Science Volume. http://www.sigcse.org/cc2001/index.html.
66. VANDEGRIFT, T., BOUVIER, D., CHEN, T.-Y., LEWANDOWSKI, G., MCCARTNEY, R., AND SIMON, B. 2010. Commonsense computing (episode 6): Logic is harder than pie. In Proceedings of the 10th Koli Calling International Conference on Computing Education Research (KOLI'10). 76-85.
67. VERSCHAFFEL, L., DECORTE, E., AND LASURE, S. 1994. Realistic considerations in mathematical modeling of school arithmetic word problems. Learn. Instruc. 4, 273-295.
68. VOSNIADOU, S. AND BREWER, W. F. 1992. Mental models of the earth: A study of conceptual change in childhood. Cog. Psych. 24, 4, 535-585.
69. WASON, P. C. 1966. New Horizons in Psychology I. Penguin, Harmondsworth, UK.
70. WEISS, R. S. 1994. Learning from Strangers: The Art and Method of Qualitative Interview Studies. The Free Press, New York, NY.
71. WOLLMAN, W. 1983. Determining the sources of error in a translation from sentence to equation. J. Res. Math. Ed. 14, 3, 169-181.