Abstract
Teaching formal methods in software construction has often been a concern of several computer science educators. In our opinion, the origin of most of the difficulties in learning formal methods in computer science and software engineering does not lie in computer science courses but in the mathematical background of the students. Moreover, there are numerous obstacles to learning basic concepts noted by both computer science and mathematics educators. To change this situation it is necessary to integrate the work of mathematics and computer science educators. That is, the main focus should be the creation of new educational approachs nourished by two components: a theoretical one (formally introducing discrete mathematics concepts) and an experimental one (implementing those concepts in a suitable programming language).
In this paper, using examples from a discrete mathematics course for high school teachers, we describe the main characteristics of our approach.
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References
Asiala, M., Dubinsky, E., et al.: A Framework for Research and Curriculum Development in Undergraduate Mathematics Education. Research in Collegiate Mathematics Education II, CBMS Issues in Mathematics Education 6, 1–32 (1999)
Ben-Ari, M.: Constructivism in Computer Science Education. Journal of Computers in Mathematics and Science Teaching (2001)
Dubinsky, E., Lewin, P.: Reflective Abstraction and Mathematics Education: The Genetic Decomposition of Induction and Compactness. The Journal of Mathematical Behavior 5, 55–92 (1986)
Dörfler, W.: Forms and Means of Generalization in Mathematics (1991) (unpublished)
Ernest, P.: Social Constructivism as a Philosophy of Mathematics: Radical Constructivism Rehabilitated (2000) (unpublished)
Michael, B.: How Do Children Learn Mathematics? Research and Reform in Mathematics Education. In: Talk in Conference Curriculum Wars: Alternative Approaches to Reading and Mathematics, Harvard University, Cambridge (1999)
Schoenfeld Alan, H.: Making Mathematics Work for All Children: Issues of Standards, Testing, and Equity. Educational Researcher 31(1) (2002)
Jean, P., Garcia, R.: Psychogenesis and the History of Sciences. Columbia University Press, New York (1980)
Jean, P., Beth, E.: Mathematical Epistemology and Psychology. D. Reidel Publishing Company, Dordrecht (1966)
Jean, P., et al.: Recherches sur la Généralisation. Presses Universitaires de France (1978)
Jean, P.: L’équilibration des Structures Cognitives, Probl‘eme Central du Développement. Presses Universitaires de France (1975)
Bird, R., Wadler, P.: Introduction to Functional Programming. Prentice-Hall, Englewood Cliffs (1988)
Ralph-Johan, B., von Joakim, W.: Structured Derivations: a Method for Doing High-School Mathematics Carefully. TUCS Technical Report No 246 (1999)
Viera, K.: Proulx: The Role of Computer Science and Discrete Mathematics in the High School Curriculum. DIMACS Series in Discrete mathematics and Theoretical Computer Science, vol. 36 (1997)
da Rosa, S., Cirigliano, G.: Ensayo sobre Matemática aplicada a Computación. Congreso Iberoamericano de Educación Superior en Computación (1999) (in Spanish)
da Rosa, S., Cirigliano, G.: Ensayo sobre Matemática aplicada a Computación. Congreso Iberoamericano de Educación Superior en Computación (1999) (in Spanish)
da Rosa, S.: The Role of Discrete Mathematics and Programming in Education. In: Workshop: Functional and Declarative Programming in Education (2002)
Henderson, P.B.: Functional and Declarative Languages for Learning Discrete Mathematics. In: Workshop: Functional and Declarative Programming in Education (2002)
Page, R.L.: Software is Discrete Mathematics. In: ICFP 2003 (2003)
Tucker, A.B.: Fundamentals of Computing I: Logic, Problem Solving, Programs and Computers. Mc Graw-Hill Series in Computer Science (1995)
Abelson, H., Sussman, G.J., Sussman, J.: Structure and Interpretation of Computer Programs. The MIT Press, Cambridge (1996)
Hall, C., O’Donnell, J.: Discrete Mathematics using a Computer. Springer, Heidelberg (2000)
Felleisen, M., Findler, R.B., Flat, M., Krishnamurthi, S.: How to Design Programs. In: An Introduction to Computing and Programming, The MIT Press, Cambridge (2003)
Hartel, P.H., von Es, B., Tromp, D.: Basic Proof Skills of Computer Science Students. In: Hartel, P.H., Plasmeijer, R. (eds.) FPLE 1995. LNCS, vol. 1022, Springer, Heidelberg (1995)
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da Rosa, S. (2004). Designing Algorithms in High School Mathematics. In: Dean, C.N., Boute, R.T. (eds) Teaching Formal Methods. TFM 2004. Lecture Notes in Computer Science, vol 3294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30472-2_2
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DOI: https://doi.org/10.1007/978-3-540-30472-2_2
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