Algebraic Thinking: A Case Study on Assessment in Calculus Course

Abstract

This article presents a case study investigating the role of algebraic thinking in assessment within a calculus course. Algebraic thinking constitutes a fundamental aspect of mathematical proficiency and plays a critical role in the comprehension and application of calculus concepts. The aim of this study is to explore the effectiveness of various assessment strategies in promoting and evaluating students' algebraic reasoning within the context of calculus instruction. The research methodology involved collecting data from a sample of calculus students through multiple assessment instruments, including problem-solving tasks, written examinations, and semi-structured interviews. This study focuses on students’ abilities to manipulate algebraic expressions, solve equations, and generalise patterns within calculus problems. The findings from this case study reveal both the strengths and limitations of different assessment methods in capturing students' algebraic thinking skills. The results indicate that traditional assessment formats, such as written exams, tend to evaluate procedural knowledge rather than conceptual understanding and flexibility in applying algebraic techniques within calculus. Conversely, performance-based assessments, such as problem-solving tasks and interviews, offer a richer insight into students’ algebraic reasoning. The implications of this study underscore the importance of integrating algebraic thinking into the teaching and assessment practices of calculus. Educators are encouraged to incorporate open-ended problem-solving tasks and reflective assessments that prompt students to apply algebraic methods creatively and analytically. By fostering and evaluating algebraic thinking in calculus, instructors can deepen students’ understanding of the subject matter and enhance their overall mathematical proficiency.