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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. © Springer-Verlag Berlin Heidelberg 2014.

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It can be argued that participating in free/libre open source software (FLOSS) projects can have a positive effect in the contributor's learning process. The need to interact with other contributors, to read other people's code, write documentation, or use different tools, can motivate and implicitly foster learning. In order to validate this statement we design an appropriate questionnaire asking FLOSS contributors about their experience in FLOSS projects. In this paper, we illustrate how this questionnaire was designed and what we expect to learn from the answers. We conclude the paper with a preview of the results from three cases studies. © Springer-Verlag Berlin Heidelberg 2014.

Abstract
Invariants are constraints on software components which restrict their behavior in some desirable way, but whose maintenance entails some kind of proof obligation discharge. Such constraints may act not only over the input and output domains, as in a purely functional setting, but also over the underlying state space, as in the case of reactive components. This talk introduces an approach for reasoning about invariants which is both compositional and calculational: compositional because it is based on rules which break the complexity of such proof obligations across the structures involved; calculational because such rules are derived thanks to an algebra of invariants encoded in the language of binary relations. A main tool of this approach is the pointfree transform of the predicate calculus, which opens the possibility of changing the underlying mathematical space so as to enable agile algebraic calculation. The development of a theory of invariant preservation requires a broad, but uniform view of computational processes embodied in software components able to take into account data persistence and continued interaction. Such is the plan for this talk: we first introduce such processes as arrows, and then invariants as their types. © 2012 Springer-Verlag.

Abstract