Date of Award


Degree Type


Degree Name

Master of Education


School of Education


Education and Arts

First Advisor

Professor Mark Hackling

Second Advisor

Dr Paul Swan


Mathematical competence is a key capability for success in adult life, and yet many students do not achieve functional levels of numeracy during their school lives. Furthermore, many teachers report that they lack the confidence in teaching mathematics that they have for teaching literacy. Research indicates that it is possible to predict which students are likely to have difficulties in mathematics as early as the Pre-Primary year, and interventions can be provided which are effective in minimising such difficulties. The assumption framing this project is that raising teachers’ understanding of and thus sensitivity to markers of the skills most predictive of mathematical success in the early years will result in teachers planning more targeted and responsive learning programs and positively influence classroom practice.

A professional learning intervention focussed on raising professional knowledge about the sequence of number development and the predictors of mathematical difficulties was provided to teachers of five to eight-year-old students. Tools were provided which focussed on linear tracks (board games) as an external model of number magnitude. The study utilised a pre-test post-test design and surveys, teacher interviews, reflective discussions and student estimation tests to examine effects on four outcomes: teacher self-efficacy beliefs, confidence for teaching number and aspects of Pedagogical Content Knowledge; and, student estimation skills.

The data revealed that the intervention was successful in improving teacher self-efficacy beliefs and confidence, particularly with regard to planning and providing intervention for students with mathematical difficulties. Teachers’ Pedagogical Content Knowledge was improved, particularly with regard to understanding the sequence of number skills development and building mental representations of number, but the extent to which this was reflected in changes to classroom practice differed markedly between teachers. The teachers who made the greatest changes taught in the Pre-Primary year and were those who reported the most substantial changes in Pedagogical Content Knowledge. The study indicates that board game use could be beneficial in raising the accuracy of student number line estimation when combined with such changes in teacher PCK and associated practice.

Although the research supporting the use of board games to develop mental number line representations is compelling, teachers who did not experience a shift in thinking tended to use these as additional tools to complement existing programs, with little noticeable effect. The implications of these findings are discussed with regard to planning professional learning interventions for teachers which are narrow in focus, supported by a small number of specific classroom tools which can be used within existing whole-class or rotational structures, and targeted towards inducing particular changes in thinking.