Hong Kong grade 6 students’ performance and mathematical reasoning in decimals tasks: procedurally based or conceptually based?

Most studies of students’ understanding of decimals have been conducted within Western cultural settings. The broad aim of the present research was to gain insight into Chinese Hong Kong grade 6 students’ general performance on a variety of decimals tasks. More specifically, the study aimed to explore students’ mathematical reasoning for their use of ‘rules’ and algorithms and to determine whether connections exist between students’ conceptual and procedural knowledge when completing decimals tasks. Results indicated that conceptual understanding for rules and procedures were built into the students’ knowledge system for most of the items concerned with place value in decimals—ordering decimals, translating fractions into decimals, the representation of place value in decimals, the concept of place value in decimals on number line and the concept of continuous quantity in decimals. However, the students were not able to provide such clear explanations for the use of algorithms for the multiplication and division items. The findings are discussed in the light of Chinese perspectives on procedural and conceptual understanding.