Pre-University Mathematics Teachers’ Design of Instructional Materials: A Case Study of the Vectors Instructional Materials from a Pre-University Institution in Singapore - Zhen Han Hans Tan; Tin Lam Toh; Zulkardi; Putri Ratu Ilma Indra (Mathematics Education Journal, 2026)
A unique feature of pre-university mathematics education in Singapore, compared to primary and secondary level mathematics, is that there are no available textbooks. Consequently, each pre-university institution designs their own instructional materials (lecture notes and practice worksheets), based on their teachers’ interpretation of the syllabus and curriculum. In this paper, we present a case study of the instructional materials of one topic Vectors from a pre-university institution. We examine how mathematical problem solving was presented in the instructional materials. We identified three features of the instructional materials that develop mathematical problem solving competencies in students: (1) the use of concrete pictorial representations to facilitate students’ understanding of abstract concepts and expose them to a mode of representation (i.e., concrete pictorial representation) to fall back on whenever necessary; (2) the steps in Polya’s Problem Solving Model were implicitly introduced to students in the form of question prompts in the worked examples; and (3) worked examples and self-review questions were heavily used in the lecture notes. Some implications to teachers’ design of instructional material are presented in the paper.