Computer Algebra Systems (CAS) in Upper Secondary School Mathematics – with emphasis on CAS Assisted Proofs in Textbooks
Professor Morten Misfeldt, IND-KU
In this talk I will describe some of the problems and discussions that are related to the use of CAS in upper secondary school. The talk will consist of two parts. First an overview of different ways to look at the potentials and challenges that CAS use brings to upper secondary teaching and secondly a zoom in on the use of CAS in textbook-proofs. The latter part is based on a paper recently published in Redimat by Uffe Thomas Jankvist and Me. In this paper we have scanned 33 upper secondary school mathematics textbooks, and found 38 instances of CAS assisted proofs. These proofs are of three types: complete outsourcing of the proof to CAS; partial outsourcing of the proof to CAS; and additional verification of the proof’ correctness by CAS. Analyses of examples of each of these types are provided. The analyses make use of a distinction between epistemic, pragmatic and justificational mediations. Results suggest both potential problems with using CAS as an integrated part of deductive mathematical proofs in textbooks, since it appears to promote undesired proof schemes with the students, and difficulties with understanding these problems using the constructs of epistemic and pragmatic mediations that are often adopted in the literature regarding CAS use in mathematics teaching and learning.
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