Student strategies and errors in mental computation with rational numbers in open number sentences

International audienceMental computation is an important skill for mathematics learning. This paper analyzes mental computation strategies and errors in grade 6 students with positive rational numbers in a teaching experiment based on tasks. The tasks involve the four basic operations and are done in conjunction with a discussion of strategies with the entire class. We focussed on student relational thinking and our findings suggest that open number sentences highlight the meaning of the equal sign and the importance of using properties of operations in mental computation. This is reflected in student's strategies when they use numerical relationships to compute mentally. Mental representations such as propositional representations are strongly linked to strategies based on numerical relationships