Teachers' collective knowledge: The case of equivalent fractions

Abstract

Research on teachers' mathematical knowledge has grown significantly over the last few decades. Many studies concern teachers' knowledge by using written tests, as for students. But in reality, teachers do not work in isolation but in institutions where professional knowledge is shared. How can this shared or collective knowledge be studied systematically and precisely? With this in mind, we designed so-called hypothetical teacher tasks (HTTs) which teachers solve in pairs. Each HTT can be used to investigate teachers' knowledge of some specific mathematical piece of knowledge (like how to add fractions) and knowledge about how to teach it. We present a case from Danish and Indonesian pre-service teachers' collaborative work on one HTT about equivalent fractions. We analyse how the shared mathematical and didactical knowledge of equivalent fractions differ between the two groups. Indeed, there are visible differences. The Danish pair proposed several didactical ideas to teach equivalent fractions, while the Indonesian pair focused on the direct instruction of standard algorithm.