Predicate calculus and program semantics
Predicate calculus and program semantics
On the shape of mathematical arguments
On the shape of mathematical arguments
Teaching calculation and discrimination: a more effective curriculum
Communications of the ACM
A logical approach to discrete math
A logical approach to discrete math
Algebra of programming
Elements of a Relational Theory of Datatypes
Proceedings of the IFIP TC2/WG 2.1 State-of-the-Art Report on Formal Program Development
Interfacing Program Construction and Verification
FM '99 Proceedings of the Wold Congress on Formal Methods in the Development of Computing Systems-Volume II
Doing High School Mathematics Carefully
Doing High School Mathematics Carefully
Communications of the ACM - Self managed systems
Recounting the Rationals: Twice!
MPC '08 Proceedings of the 9th international conference on Mathematics of Program Construction
Puzzled: Understanding relationships among numbers
Communications of the ACM - Security in the Browser
Students' feedback on teaching mathematics through the calculational method
FIE'09 Proceedings of the 39th IEEE international conference on Frontiers in education conference
Using domain-independent problems for introducing formal methods
FM'06 Proceedings of the 14th international conference on Formal Methods
Designing an algorithmic proof of the two-squares theorem
MPC'10 Proceedings of the 10th international conference on Mathematics of program construction
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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.