Abstract
This research captured the mathematical journeys of 31 New Zealand students over two years of their adolescence. The research framework combined a conceptualisation of identities with the notion in the affective domain of a student having a mathematical core. Specifically, this research sought to discover the nature of students’ relationships with mathematics and the role of affect and identities. It further investigated how these relationships were associated with students’ mathematical learning and how they changed over time. A qualitative research methodology with length, breadth and depth was employed that combined aspects of ethnography and grounded theory. Interviews and student questionnaires were the main tools used to collect students’ perspectives about mathematics. Classroom observations, assessment results, school documents, parent questionnaires, teacher feedback, documented student history, reports, and prizes were also used.
Students were found to have complex and dynamic relationships with mathematics. The components of these relationships were the students’ views of mathematics, their mathematical knowledge, and their feelings, identities and habits of engagement. These components were both individual and shared by the classroom community. When students engaged in mathematics, they were situated in a unique context of the moment. Each student interpreted this context individually and, negotiating with the components of their relationship with mathematics, they engaged in the mathematical task in different ways. This engagement contributed to the students’ individual experiences and performances. The meaning the students derived from these experiences reinforced or altered components of their relationship with mathematics.
The students’ journeys were journeys of change and negotiation and shaped by the broader context of their lives. Many of the students had become more negative about mathematics since leaving primary school. They considered it to be a unique subject because of its nature, difficulty, the routines of the mathematics classroom, and the boredom these routines generated. All of the students experienced tension balancing their social and academic needs. Furthermore, the students’ ability to achieve their expectations changed as they engaged in mathematics in different ways. These factors were associated with the students’ decisions about future participation in mathematics. In Year 12, when the students were aged around 16, more than half of the class chose not to continue participating in the academic stream of mathematics, thus restricting their future choices. Six of the students were no longer participating in mathematics at any level.
The students who were thriving mathematically were those who enjoyed mathematics, viewed mathematics as an important life skill, felt confident in their ability, had highly developed engagement skills, sought relational understanding, and had multiple motivational factors. The majority of the students were not thriving mathematically. They did not feel confident in their ability, had ineffective engagement skills, sought instrumental understanding, disliked mathematics, were not convinced of its importance, and had tenuous motivational factors. The continued participation of these students in mathematics was vulnerable.