Students' Comparison of Their Trigonometric Answers with the Answers of a Computer Algebra System

TL;DR

This study explores how students compare their trigonometric solutions with computer algebra system answers, focusing on their recognition of equivalence and correctness, and analyzing their reasoning processes in educational settings.

Contribution

It investigates students' ability to identify and explain differences between their solutions and CAS outputs in the context of trigonometric equations, highlighting educational implications.

Findings

Students notice various differences between solutions.

Students can recognize some forms of equivalence.

Students explain differences and similarities in their own words.

Abstract

Comparison of answers offered by a computer algebra system (CAS) with answers derived by a student without a CAS is relevant, for instance, in the context of computer-aided assessment (CAA). The issues of identity, equivalence and correctness emerge in different ways and are important for CAA. These issues are also interesting if a student is charged with the task of comparing the answers. What will happen when students themselves are encouraged to analyse differences, equivalence and correctness of their own answers and CAS answers? What differences do they notice foremost? Would they recognise equivalence/non-equivalence? How do they explain equivalence/non-equivalence? The paper discusses these questions on the basis of lessons where the students solved trigonometric equations. Ten equations were chosen with the aim to ensure that the expected school answer and the CAS answer would differ in various ways. Three of them are discussed more thoroughly in this paper.