Pseudo abstract composition: the case of language concatenation

ABSTRACT

Composition is a fundamental problem solving heuristic. In computer science, it primarily appears in program design with concrete objects such as language constructs. It also appears in more abstract forms in higher-level courses. One such form is that of language concatenation in the Computational Models course. This concatenation involves the composition of two specifications of infinite sets (source languages) into a third one, and requires both abstraction and non-deterministic conception. In this paper, we illuminate behaviors of advanced high school students, with such composition. Students who encountered difficulties offered pseudo solutions, which enclosed only "surface" features and observations. We orderly display their solutions, discuss them, and offer suggestions for educators to cope with this phenomenon.

References

1. Armoni, M. and Gal-Ezer, J. (2006). Introducing non-determinism, Journal of Computers in Mathematics and Science Teaching, 25(4), 325--359.
2. Armoni M. and Gal-Ezer, (2006). Reduction -- an abstract thinking pattern: the case of the computational models course, SIGCSE'06, 389--394.
3. Armoni, M. and Gal-Ezer, J. (2007). Non-determinism: an abstract concept in computer science studies, Computer Science Education, 17(4), 243--262.
4. Astrachan, O., Berry, G., Cox, L., and Mitchener, G. (1998). Design patterns: an essential component of CS Curricula. SIGCSE'98, 153--160.
5. Hazzan, O. (1999). Reducing abstraction level when learning abstract algebra concepts, Educational Studies in Mathemartics, 40, 71--90.
6. Hazzan, O. (2003). How students attempt to reduce abstraction in the learning of mathematics and in the learning of computer science, Computer Science Education 13(2), 95--122.
7. Muller, O., Ginat, D., and Haberman, B. (2007). Pattern-oriented instruction and its influence on problem decomposition and solution construction, ITiCSE'07, 151--155.
8. Polya, G. (1954). How to Solve It. Princeton University Press.
9. Schank, P. K., Linn, C. M., and Clancy, J. M. (1993). Supporting Pascal programming with an on-line template library and case studies, International Journal of Man-Machine Studies, 38(6), 1031--1048.
10. Schoenfeld, A. E. (1992). Learning to think mathematically: problem solving, metacognition, and sense making in mathematics, in Grouws D. A. (ed.), Handbook of Research on Mathematics Teaching and Learning, 334--370.
11. Soloway, E. (1986). Learning to program=learning to construct mechanisms and explanations. Communications of the ACM, 29(9), 1031--1048.
12. Sphorer, J., Soloway, E., and Pope, E. (1985). A goal/plan analysis of buggy Pascal programs. Human-Computer Interaction, 1(2), 163--207.
13. Wing, J. (2006). Computational thinking. Communications of the ACM, 49(3), 33--35..

Index Terms

• Social and professional topics

  • Professional topics

    • Computing education

      • Computing education programs

        • Computer science education

        • Information science education