On Novices’ Local Views of Algorithmic Characteristics
The solution of an algorithmic task requires rigorous insight, based on the task’s characteristics. Problem solvers seek insight in diverse ways, from different points of view. Experts usually seek a global, assertional perspective. Such a perspective is not natural to many novices, who often turn to local viewpoints. However, such points of view may yield erroneous outcomes. This study displays three different facets of novices’ improper local points of view. The three facets involve local substructures, greedy traps, and unsuitable design patterns. Novices’ erroneous solutions to three colorful tasks are described and analyzed, in comparison with the desired solutions, and suggestions are made for elaborating student awareness of the need for a global, rigorous point of view in algorithmic problem solving.
KeywordsLocal Point Design Pattern Greedy Approach Local View Local Substructure
Unable to display preview. Download preview PDF.
- 1.Astrachan, O., Berry, G., Cox, L., Mitchener, G.: Design Patterns: an Essential Component of CS Curricula. In: Proceedings of the 28th SIGCSE Symposium, pp. 153–160. ACM Press, New York (1998)Google Scholar
- 2.Borasi, R.: Reconceiving Mathematics Instruction: A Focus on Errors. Ablex Pub., Greenwich (1996)Google Scholar
- 3.Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. MIT Press, Massachusetts (1991)Google Scholar
- 6.Gama, E., Helm, R., Johnson, R., Vlissides, J.: Design Patterns: Elements of Reusable Object-Oriented Software. Addison-Wesley, Reading (1995)Google Scholar
- 7.Ginat, D.: Loop invariants, Exploration of Regularities, and Mathematical Games. Int. J. of Mathematical Education in Science and Technology 32 (2001)Google Scholar
- 8.Ginat, D.: Embedding Instructive Assertions in Program Design. In: Proceedings of the 9th ITiCSE Conference, pp. 62–66. ACM Press, New York (2004)Google Scholar
- 9.Ginat, D.: Mathematical Operators and Ways of Reasoning. The Mathematical Gazette, 7–14 (2005)Google Scholar
- 11.Schoenfeld, A.: 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, pp. 334–370. Macmillan, Basingstoke (1992)Google Scholar