Abstract
MathIS is a new project that aims to reinvigorate secondary-school mathematics by exploiting insights of the dynamics of algorithmic problem solving. This paper describes the main ideas that underpin the project. In summary, we propose a central role for formal logic, the development of a calculational style of reasoning, the emphasis on the algorithmic nature of mathematics, and the promotion of self-discovery by the students. These ideas are discussed and the case is made, through a number of examples that show the teaching style that we want to introduce, for their relevance in shaping mathematics training for the years to come. In our opinion, the education of software engineers that work effectively with formal methods and mathematical abstractions should start before university and would benefit from the ideas discussed here.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
ATX. Algoritmo de Colocação de professores (in Portuguese). ATX Software press release (November 2004)
Back, R.-J., Mannila, L., Peltomaki, M., Sibelius, P.: Structured derivations: A logic based approach to teaching mathematics. In: FORMED 2008: Formal Methods in Computer Science Education, Budapest (2008)
Back, R.-J., von Wright, J.: Mathematics with a little bit of logic: Structured derivations in high-school mathematics
Back, R.-J., von Wright, J.: Doing high school mathematics carefully. Technical report (1997)
Backhouse, R.C.: Mathematics and programming. A revolution in the art of effective reasoning. Inaugural Lecture, School of Computer Science and IT, University of Nottingham (2001)
Backhouse, R.C.: Program Construction. John Wiley and Sons, Inc., Chichester (2003)
Backhouse, R.C., Hoogendijk, P.F.: Elements of a relational theory of datatypes. In: Möller, B., Schuman, S., Partsch, H. (eds.) Formal Program Development. LNCS, vol. 755, pp. 7–42. Springer, Heidelberg (1993)
Backhouse, R.C., Verhoeven, R.: Mathspad: A system for on-line preparation of mathematical documents. Software - Concepts and Tools 18, 80–89 (1997)
Backhouse, R., Ferreira, J.F.: Recounting the rationals: Twice! In: Audebaud, P., Paulin-Mohring, C. (eds.) MPC 2008. LNCS, vol. 5133, pp. 79–91. Springer, Heidelberg (2008)
Backhouse, R., Ferreira, J.F.: On Euclid’s algorithm and elementary number theory (2009) (submitted for publication), http://joaoff.com/publications/2009/euclid-alg/
Bell, T., Witten, I.H., Fellows, M.: Computer Science Unplugged: An enrichment and extension programme for primary-aged children (December 2006), http://csunplugged.org/index.php/en/books
Bird, R., Moor, O.: The Algebra of Programming. Series in Computer Science. Prentice-Hall International, Englewood Cliffs (1997)
Boute, R.: Using Domain-Independent Problems for Introducing Formal Methods. In: Misra, J., Nipkow, T., Sekerinski, E. (eds.) FM 2006. LNCS, vol. 4085, pp. 316–331. Springer, Heidelberg (2006)
Dijkstra, E.W.: A new science, from birth to maturity. note EWD1024 (1988)
Dijkstra, E.W.: On the cruelty of really teaching computing science. note EWD1036 (1988)
Dijkstra, E.W.: On the economy of doing mathematics. note EWD1130 (1992)
Dijkstra, E.W., Scholten, C.S.: Predicate Calculus and Program Semantics. Springer, Heidelberg (1990)
Ferreira, J.F., Mendes, A.: Student’s feedback on teaching mathematics through the calculational method. In: 39th ASEE/IEEE Frontiers in Education Conference. IEEE, Los Alamitos (2009)
Gries, D., Feijen, W.H.J., van Gasteren, A.J.M., Misra, J.: Beauty is our Business. Springer, Heidelberg (1990)
Gries, D., Schneider, F.: A Logical Approach to Discrete Mathematics. Springer, Heidelberg (1993)
Gries, D.: Improving the curriculum through the teaching of calculation and discrimination. Communications of the ACM 34(3), 45–55 (1991)
Guba, E., Lincoln, Y.: Competing paradigms in qualitative research. In: Denzin, N., Lincoln, Y. (eds.) Handbook of qualitative research, pp. 105–117. Sage, London (1994)
Honsberger, R.: In Polya’s Footsteps: Miscellaneous Problems and Essays (Dolciani Mathematical Expositions). The Mathematical Association of America (October 1997)
ME. Declaração sobre o processo de colocação de professores para o ano lectivo 2004-05 (in Portuguese). Government press release (September 2004)
Mendes, A.: Work in progress: Structure editing of handwritten mathematics. In: 38th ASEE/IEEE Frontiers in Education Conference. IEEE, Los Alamitos (2008)
Michalewicz, Z., Michalewicz, M.: Puzzle-based Learning: Introduction to Critical Thinking, Mathematics, and Problem Solving, 1st edn. Hybrid Publishers (2008)
OCDE Report. Education at a clance: OCDE indicators 2006. OCDE Publishing, Paris (2006)
DIMACS Symposium. Teaching logic and reasoning in an illogical world. Technical report, Rutgers University (1996)
van Gasteren, A.J.M.: On the Shape of Mathematical Arguments. LNCS, vol. 445. Springer, Heidelberg (1990)
Verhoeven, R., Backhouse, R.C.: Towards tool support for program verification and construction. In: Wing, J.W.J., Davies, J. (eds.) FM 1999 - Int. Formal Methods Symposium. LNCS, vol. 1709, pp. 1128–1146. Springer, Heidelberg (1999)
Wilf, H.S.: Can there be research in mathematical education? http://www.math.upenn.edu/~wilf/website/PSUTalk.pdf
Wing, J.M.: Computational thinking. Commun. ACM 49(3), 33–35 (2006)
Winkler, P.: Puzzled: Understanding relationships among numbers. Commun. ACM 52(5), 112 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ferreira, J.F., Mendes, A., Backhouse, R., Barbosa, L.S. (2009). Which Mathematics for the Information Society?. In: Gibbons, J., Oliveira, J.N. (eds) Teaching Formal Methods. TFM 2009. Lecture Notes in Computer Science, vol 5846. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04912-5_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-04912-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04911-8
Online ISBN: 978-3-642-04912-5
eBook Packages: Computer ScienceComputer Science (R0)