"It makes me feel proud of who I am" : developing functional thinking through culturally located tasks : a thesis presented in partial fulfilment of the requirements for the degree of Master of Education in Mathematics Education at Massey University, Manawatū, New Zealand
Success in algebra plays a major role in equity and lifelong opportunities well beyond the mathematics classroom. Nationally, and internationally, high failure rates in algebra see many non-dominant students excluded from equitable higher education, career, and economic opportunities. There appears to be limited research focused on non-dominant students and the development of algebraic thinking through culturally located tasks. This study examines the representations Māori and Pāsifika students use when engaging with contextual functional tasks, and the ways Māori and Pāsifika students generalise culturally located tasks involving functions. A design based research intervention and qualitative research methods, drawing on a Pāsifika research methodology, were selected as most appropriate for the study. Twelve 10-12 year old Māori and Pāsifika students from a low socio-economic, urban school in New Zealand participated. Students engaged in an intervention of eight lessons focused on developing functional thinking with growing patterns drawn from Māori and Pāsifika cultures. A range of data were collected and analysed, including interviews, field notes, video recorded classroom observations, and photographs of student work. Findings revealed that when Māori and Pāsifika students were given opportunities to draw on their cultures to make sense of functional relationships, they constructed increasingly sophisticated and abstract representations to identify, communicate, and justify generalisations. There was significant growth in their conceptual understanding of both contextualised and decontextualised growing patterns. Additionally, aligning tasks with non dominant students' traditions and experiences strengthened students' mathematical and cultural identities. This study offers a contribution to the literature regarding how culturally contextualised tasks support non-dominant students to engage in early algebra, in particular, the representation and generalisation of functions. To address disparities and structural inequities in mathematics education, educators must acknowledge that students bring their own cultural knowledge and strengths to the classroom, and provide opportunities for all students to learn mathematics in ways they see as relevant to their cultural identities and communities. Recognising that mathematics is inherently cultural is a key lever for equity.