Pedagogical content knowledge and the use of examples for teaching ratio

The upper years of primary school are critical in students’ mathematical development. One of the most important concepts is proportional reasoning, which builds upon the foundation of multiplicative thinking, and is central to work in fractions and ratio. To build this understanding in the classroom, teachers need appropriate pedagogical content knowledge (PCK) to choose suitable representations and explanations that highlight mathematical concepts in a meaningful way for students. This PCK is particularly evident in the examples that teachers choose (a) to illustrate concepts initially, and (b) for students to work on during consolidation. This paper presents case studies of two Grade 6 teachers, each giving two lessons on ratio. A framework, derived from the literature, is used to examine the PCK held by the teachers. We focus closely on the examples used by the teachers, since their choice of numerical values, the contexts used, the appropriateness of the example for students, and the aspects of the example highlighted during teaching give insight into teachers’ PCK. Both teachers made appropriate numerical choices, but one made much stronger connections to other aspects of mathematics, gave more relevant contexts, and selected problems that better matched her students’ ability.