Classroom assessment techniques to assess Chinese students’ sense of division

Abstract

This paper is about an explorative study of the use of classroom assessment techniques (CATs) by primary school mathematics teachers in China. Six female teachers and 216 third-grade students from two schools in Nanjing were involved. The focus was on assessing whole number arithmetic. Teachers’ use of the CATs was investigated through lesson observations, feedback forms, interviews, and reports. In this paper we zoom in on one CAT in which students had to solve division problems without making use of the standard division algorithm, being the only procedure they had been taught. From the solutions teachers can infer whether their students really had deep understanding of the division operation. Only a few students could apply a solution strategy without using the standard algorithm. All teachers were initially unsure about what information they were supposed to find with this CAT and did not know how to deal with the results afterwards.