Exploring the mental strategies of Year 9 students

This paper reports on a study with eight Year 9 students from a low decile secondary school. Four of the students were high achievers in mathematics (from a mathematics extension class), and four were low achievers in mathematics (from a mathematics applied [MAP) class]. Tasks from the diagnostic interview of the Numeracy Development Project (Numeracy Project Assessment: NumPA) were used to assess the students' mathematics understanding. Additional tasks to explore students' recognition of the connectedness of related mathematics problems were also used. High achieving students differed from low achieving students in a number of ways, including: the number of questions they could answer, the speed with which they found solutions to the problems, the ease with which they explained their mental strategies, and their overall confidence levels. Most of the students from both groups expressed a preference for using pen­and-paper, and many of those who used mental strategies simply carried out a formal written algorithm in their heads. Most students recognised the connection between related mathematics questions and used that information to solve subsequent problems. The only student not to recognise the connectedness of related problems was a low achieving student.