Proportional Reasoning: Student Knowledge and Teachers' Pedagogical Content Knowledge

Abstract

This report considers the responses of 1205 students to two chance and data problems involving proportional reasoning and the interventions suggested by 44 teachers for four typical incomplete or inappropriate student responses. Students' responses reflect the relative difficulty of the two items, whereas the teachers' suggested interventions display a wide range of pedagogical content knowledge, including aspects of content knowledge and knowledge of students as learners. Rubrics are provided for both students' and teachers' responses and analysis supports the view that teachers find it difficult to assist students without directly telling them the answer. Suggestions are made for assisting teachers to improve feedback for students.