Abstract
Argumentation and proof are two main ingredients in strategies for developing mathematical skills and structured reasoning. This paper reports on a research project aimed at ‘refactoring’ school Mathematics in other to achieve a higher degree of mathematical literacy. In a sense this builds on a number of ‘lessons’ learnt from the practice of Computing Science. We further argue that mathematical fluency, broadly understood as the ability to reason in terms of abstract models and the effective use of logical arguments and mathematical calculation, became a condition for democratic citizenship and sustainable development.
Collaboration with João Ferreira, at Teeside University, and Roland Backhouse, at Nottingham University, in the context of the MathIS project, is greatly acknowledged. The authors express their gratitude to Paulo Silva who developed the teaching scenario on logarithms from which some examples discussed in the paper were taken. This work is partially funded by ERDF - European Regional Development Fund through the COMPETE Programme (operational programme for competitiveness) and by National Funds through the FCT (Portuguese Foundation for Science and Technology) within projects MathIS, FCOMP-01–0124-FEDER-007254, and Professional Practices of Teachers of Mathematics, PTDC/CPECED/098931/2008.
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Notes
- 1.
The attentive reader will recognise this property as the categorial definition of the universal arrow associated to a product construction [2], but such a formal setting is unnecessary for our purposes here. Reference [16] provides, however, an introduction to categorial arguments most suitable for didactical practice and research.
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Barbosa, L.S., Martinho, M.H. (2014). Mathematical Literacy as a Condition for Sustainable Development. In: Cerone, A., et al. Information Technology and Open Source: Applications for Education, Innovation, and Sustainability. SEFM 2012. Lecture Notes in Computer Science(), vol 7991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54338-8_5
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