The research presented in this dissertation involves a quantitative study of mathematics teachers' knowledge of formative assessment. Formative assessment is understood as a process in which both teachers and students actively become the agents of the process, responsible for their own knowledge and practice. In this process, formally gathered evidence is used to formulate feedback and inform decisions; and informal evidence (e.g. observation, conversations) is used to generate teacher and peer-feedback to improve learning (Hargreaves, 2005; Wiliam & Leahy, 2015).

The focus of the study is on mathematics teachers in state secondary schools in the Brazilian Federal District. The research design employs survey methodology with a structured e-questionnaire. The questionnaire was designed based on six domains of knowledge extracted from existing research literature. The several piloting phases, and a field test conducted with a larger sample, demonstrate the validity and reliability of the instrument and provide information about mathematics teachers' knowledge of formative assessment.

The evidence shows that teachers in the Federal District did relatively better in terms of interpreting evidence of students' learning and helping students to use assessment information. On the other hand, they had a relatively lower performance in terms of choosing/developing assessment methods (e.g. classroom activities, discussions) to elicit evidence of students' learning. The overall performance of teachers in the Federal District was lower than that of teachers sampled from the other states of Brazil.

The original contribution of this research is methodological in the development, piloting and application of a new instrument to assess mathematics teachers' knowledge of formative assessment; and to knowledge in providing information and a unique insight into Brazilian mathematics teachers' knowledge of formative assessment. There are important implications for policy and practice, focussing on teachers' professional development with regards to formative assessment and clarifying Brazilian teachers' roles as assessors.