The alignment of curriculum components of Cambridge IGCSE international mathematics

Abstract

This thesis investigates the alignment among the Cambridge IGCSE International Mathematics 0607 Extended syllabus, a widely used textbook, and past examination papers. The focus is placed on the topic of functions, which constitutes a central component of the curriculum. A systematic item to learning objective mapping was first conducted to examine the extent to which textbook and assessment items reflect the official syllabus learning objectives. Items were then categorized by cognitive demand using the framework of Stein and Smith (1998). To quantify alignment between the textbook and assessments, Porter’s Alignment Index (PAI) (Porter, 2002) was applied, with Kazemi’s (2022) extension used to capture categories of misalignment. The analysis revealed notable discrepancies in coverage and emphasis. Several textbook items could not be mapped to any learning objective, often requiring skills or transformations not explicitly included in the curriculum. Assessments, in contrast, concentrated heavily on a limited set of learning objectives, particularly those related to function notation, and graphical calculator skills, while paying less attention to others. The application of PAI provided a numerical measure of alignment between the textbook and assessments, while Kazemi’s (2022) framework further highlighted patterns of misalignment, such as overrepresentation of specific objectives and cognitive demands. These findings underscore the importance of careful textbook selection, teacher preparation, and curriculum monitoring to ensure that instruction, materials, and assessments work together to promote coherent student learning.