A study of New Zealand secondary school students using four self-report inventories of conceptions of assessment found four robust independent measurement models. Four structural models mapped the conceptions of assessment to mathematics achievement taking into account student ethnicity and student sex. The conceptions that assessment makes students accountable and was beneficial for students loaded positively on achievement, while the conceptions that assessment is fun and assessment is ignored had negative loadings on achievement. These findings are consistent with self-regulation theory and formative assessment, suggesting that students who use assessment to take responsibility for their learning by using assessment formatively will attain increased mathematics outcomes. (Contains 4 figures and 1 footnote.)