Designing a Pre-Calculus Learning Module for Pre-Service Mathematics Teachers through the Hypothetical Learning Trajectory Approach

Abstract

The study identified several learning obstacles (LO) experienced by students in Calculus I, particularly misconceptions related to algebraic concepts, graphical representations of functions, absolute values, inequalities, exponents, logarithms, and trigonometry. These obstacles negatively affect students’ conceptual readiness for learning Calculus. This study aims to develop an HLT-based pre-calculus module for 41 prospective mathematics teachers at a state university in Indonesia. The instruments included a diagnostic test, interview guidelines, and expert validation forms for the module. Data were collected through literature review, analysis of learning obstacles based on diagnostic test and interview results, and expert validation of the module. The pre-calculus module was developed using the 4D model (Define, Design, Develop, Disseminate), and the data were analyzed using a descriptive qualitative approach. Expert validation results indicated that the module’s content, language, and presentation achieved validity scores above 80% across all aspects. Considering the effectiveness of the HLT framework, the module is expected to support scaffolding, reduce misconceptions, and map students’ conceptual thinking trajectories. Furthermore, it is expected to serve as an independent learning resource that supports a logical transition from algebraic prerequisites to Calculus I concepts.