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Structured Derivations: a Method for Doing HighSchool Mathematics Carefully
, 1999
"... We show how solutions to typical problems of High School and firstyear University Mathematics can be written using structured derivations. Such a derivation extends the calculational proof format with subderivations that allow inferences to presented at different levels of detail. They also constit ..."
Abstract

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We show how solutions to typical problems of High School and firstyear University Mathematics can be written using structured derivations. Such a derivation extends the calculational proof format with subderivations that allow inferences to presented at different levels of detail. They also constitute a new paradigm where the whole solution process is viewed as an object that can be discussed and manipulated. By using structured derivations and a minimal amount of logical syntax, we can write solution to typical problems in not only algebra and equation solving but also in, e.g., real analysis. We argue why structured derivations give students a better grasp of problem solutions and better possibilities to reread and discuss solutions afterwards, as compared with traditional informal approaches to writing down solutions.
Which Mathematics for the Information Society?
"... Abstract. MathIS is a new project that aims to reinvigorate secondaryschool 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 c ..."
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Abstract. MathIS is a new project that aims to reinvigorate secondaryschool 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 selfdiscovery 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. We are all shaped by the tools we use, in particular the formalisms we use shape our thinking habits, for better or for worse, and that means we have to be very careful in the choice of what we learn and teach, for unlearning is really not possible. — E. W. DIJKSTRA in [15] 1