Preparing Students for College-Level Mathematics Through Secondary Advanced Placement Courses – IB, A-level and AP

Abstract

Students in international schools are asked to learn subjects from foreign curricula, enabling them to pursue international education in college. Three of the more common curricula chosen by parents and students are International General Certificate of Education (IGCSE), the International Baccalaureate Diploma (IB DP) and the Advanced Placement (AP). At the end of their intensive one- or two-year studies with these foreign curricula, students must take exams that not only serve as benchmarks for schools’ reputations, but also signal the students’ readiness for college mathematics. The advanced curricula also play crucial role in shaping the students’ learning styles and significantly influence their perceptions of mathematics as they enter undergraduate studies. This thesis examines the extent to which advanced high school mathematics exams (A-Level, IB and AP) prepare students for college-level mathematics by analyzing the cognitive demands of the associated exam questions. Past exam questions from May and June of 2021 2022, and 2023, published by the Cambridge International Examination (CIE), International Baccalaureate (IB), and College Board, are analyzed. The cognitive demands of these assessment papers are evaluated using two distinct frameworks: the Complexity, Abstractness, and Strategy (CAS) framework and the Mathematical Assessment Task Hierarchy (MATH) Taxonomy. This thesis reveals that all three exams contain many low-cognitive demand questions that can be solved through rote memorization and mimicry of mathematical reasoning while lacking probes for students’ conceptual understanding. As a result, these exams often fail to bridge the gap between high school and undergraduate mathematics, perpetuating misconceptions about the nature of the subject. Despite these commonalities between the programs, the findings also indicate differences between the exams, which could serve as stepping stones toward undergraduate mathematics.