Programming-languages as a conceptual framework for teaching mathematics

Abstract

Formal mathematical methods remain, for most high school students, mysterious, artificial and not a part of their regular intuitive thinking. The authors develop some themes that could lead to a radically new approach. According to this thesis, the teaching of programming languages as a regular part of academic progress can contribute effectively to reduce formal barriers. This education can also be used to enable pupils to access an accurate understanding of some key mathematical concepts. In the field of heuristic knowledge for technical problem solving, experience of programming is no less valuable: it lends itself to promote a discussion of relations between formal procedures and the comprehension of intuitive problem solving and provides examples for the development of heuristic precepts (formulating a plan, subdividing the complexities, etc.). The knowledge gained in programming can also be used for the discussion of concepts and problems of classical mathematics. Finally, it can also facilitate the expansion of mathematical culture to topics in biological and physical sciences, linguistics, etc. The authors describe a programming language called 'Logo' adapted to objectify an enduring framework of mathematical experimentation.

Bridging Primary Programming and Mathematics: Some Findings of Design Research in England

“…Early research also highlighted the potential of expressing mathematical ideas as computer programs (Feurzeig et al 1969;Hatfield and Kieren 1972). Noss and Hoyles (1996, pg.…”

Collaboration, Collusion and Plagiarism in Computer Science Coursework

“…The idea that young learners should be taught to program, and that doing so has far reaching benefits, originated with the Logo Project [4], [5]. Papert found that "when a child learns to program, the process of learning is transformed.…”

Transferring Skills at Solving Word Problems from Computing to Algebra Through Bootstrap

“…Logo was designed explicitly to teach mathematics, and many researchers have studied it as a vehicle for algebra (e.g., [5,6]). Pea and Kurland [9] found no evidence of improved mathematical reasoning among students who had been exposed to more than 30 hours of instruction in Logo, and later questioned the entire expectation of transfer into algebra.…”