Classroom Observation of Mathematics Teachers’ Use of Instructional Materials in Teaching Geometry in Selected Technical Secondary Schools in Muhanga District, Rwanda

Abstract

This paper reports the classroom-observation component of a broader qualitative study of how mathematics teachers use instructional materials to teach and learn geometry in selected Technical Secondary Schools (TSS) in Muhanga District, Rwanda. While teachers' accounts of practice are useful, self-reports can overstate the consistency and quality of classroom implementation, so this paper focuses on what was directly observed in real geometry lessons. Anchored in an interpretivist paradigm and a qualitative case-study design, the study observed twenty geometry lessons taught by ten mathematics teachers purposively drawn from five TSS representing urban, semi-urban, and rural contexts. A structured observation checklist, informed by constructivism, Vygotsky's Zone of Proximal Development, and Gagné's Nine Events of Instruction, was used to record the presence, type, and quality of instructional-material use at successive stages of each lesson. The researchers analysed the observation data using narrative analysis, reconstructing each lesson as a chronological account and comparing the accounts across lessons. The findings show that traditional geometry tools, particularly rulers, compasses, protractors, and setsquares, dominated observed lessons, while concrete hands-on materials, geometric models, and ICT-based materials were rarely present. Teachers often used materials to demonstrate constructions on the chalkboard, with learners largely copying diagrams rather than handling materials themselves; when practical activities occurred, teachers often worked with shared materials because quantities were insufficient. Across the four instructional events tracked, most lessons were rated as only moderately implemented, and assessment and feedback practices using materials were the weakest and most irregularly observed. These classroom-level findings extend prior interview-based accounts by showing a gap between teachers' stated intentions and what actually occurred during instruction, and they point to insufficient material quantities, limited ICT infrastructure, and time pressure as the principal constraints on effective classroom use.