Teachers' beliefs about the teaching, learning and assessment of mathematics and their relationships with both students' achievement, and teachers' summative judgments

Teachers in New Zealand are required to make judgments of students’ achievement in reading, writing and mathematics against the National Standards and to report these to the Ministry of Education annually (Ministry of Education, 2009b, 2013). The process for making these judgments is complex and there are many factors that contribute to the variability of teachers’ judgments (Smaill, 2013; Ward & Thomas, 2013, 2015). It is likely that the beliefs teachers hold about effective pedagogy in mathematics, about the primary purpose of assessment and about the nature of students’ ability in mathematics will contribute to the variability of teachers’ judgments against the mathematics standards.

This research explored the beliefs teachers hold about four elements of effective pedagogy in mathematics; the extent to which teachers endorse a discrete approach, a connectionist approach, a procedural approach and a conceptual pedagogical approach. Teachers’ beliefs about the primary purpose of assessment and the nature of students’ ability in mathematics were also explored.

The purpose of this research was to elucidate relationships between teachers’ beliefs and their application of assessment criteria when making summative judgments of students’ achievement in mathematics. An additional purpose was to elucidate any relationships between these elements of teachers’ beliefs and increased students’ achievement and in mathematics.

The degree to which teachers are conservative in their application of assessment criteria when making “at the standard” judgments of students’ achievement was found to be related to a coherent set of beliefs. Increased students’ achievement was found to be only weakly related to teachers’ beliefs about the nature of students’ mathematical ability.