In mathematics education, teacher knowledge matters. However, the amount, type and nature of knowledge required for quality mathematics teaching is remains unclear. This may be due to the ways in which teachers’ subject matter knowledge has been measured.
This study explored relationships between three aspects of teacher knowledge: knowledge for designing mathematical tasks; knowledge for solving mathematical problems; and knowledge for making judgements of student learning. Positivism was applied to establish expectations for objective, context-free generalisations throughout the research and used to attach corresponding methodologies and tools. Examining relationships between aspects of teacher knowledge required the selection, testing, development and use of instruments to gain insights into aspects of teacher knowledge before correlations among them could be tested. This necessitated the selection of content that could illuminate conceptual, rather than procedural, knowledge.
All data were gathered in a single day from a group of 64 participants teaching 10 to 12 year old students in a large metropolitan schooling system in New South Wales. Relationships between aspects of teacher knowledge were identified and tested using measures of statistical association before correlations among all three aspects were studied simultaneously. Strong correlations were identified between teachers’ understandings of mathematics, the level of challenge in the tasks they designed and their noticing of higher levels of student achievement. Stronger subject matter knowledge, to the extent that teachers could solve more complex, unfamiliar, non-routine problems, was predictive of higher levels of pedagogical knowledge.
Australia aspires to increase the proportion of students studying higher levels of mathematics. It is argued that teachers’ understandings of mathematical content are foundational to their development of aspects of pedagogical content knowledge essential for effective teaching. Without increasing the knowledge of the key stakeholders responsible for student learning, changing the syllabus, raising professional standards and testing students may not lead to higher levels of achievement in mathematics.