Abstract
The relationships with mathematics construct provides a framework for understanding the complex ways students engage with, learn, and participate in mathematics. This paper examines the construct, drawing on a longitudinal study of 31 secondary students in New Zealand. The study identified five interrelated elements that comprise students' relationships with mathematics: beliefs about mathematics, mathematical knowledge, macro-feelings, perceptions of mathematical capabilities, and habits of engagement. Findings show that these elements were highly interconnected and evolved over time as students participated in mathematics classrooms and interpreted their experiences. Students' relationships with mathematics shaped their engagement with mathematical tasks, their affective responses to challenge and success, and their ongoing participation in the subject. The construct highlights the dynamic interplay between cognitive, affective, identity-related, and social dimensions of mathematical learning and helps explain why students respond differently to similar mathematical experiences. The paper argues that the relationships with mathematics construct provides a useful lens for research, teaching, and curriculum design. By drawing attention to dimensions of learning beyond achievement alone, the construct broadens understandings of mathematical participation and learning. Ultimately, relationships with mathematics matter because they influence not only what students learn, but also how they engage with that learning and whether they continue to participate in mathematics.