There is More Than One Way to Skin a Cat: An Exploration of Flexible Mental Multiplication Strategies with Pre-Service Teachers

Abstract

This research project investigates possible strategies that satisfy Australian and NSW curriculum outcomes for the Year 5 topic of mental multiplication and teaching strategies that use a flexible approach to mental multiplication that have the potential to enhance student number sense. Two cohorts of pre-service teachers (n=36) at the University of New England participated in the three phases of the project. The initial phase involved timed testing of their mental multiplication skills and untimed reflection on strategy use for the test questions. A questionnaire explored their attitudes towards, and knowledge of, mental computation in this context. Participants were introduced to a range of possible mental multiplication strategies and a teaching approach emphasising flexibility, adaptivity and multiplicative thinking. The final phase of the project sought to measure changes in the performance and attitudes of the participants who had taken part in the intervention. This was contrasted with the results and opinions of those who had only been involved in the testing and questionnaire components and not the intervention. The project uses a case study design with a mixed methods approach. <br/> The participants demonstrated a poor knowledge of, and performance in, mental multiplication at the level required of Year 5 students. Considering that the majority had experienced schooling in the last 20 years when curriculum planners had emphasised the importance of mental computation skills, there was a distinct lack of knowledge of appropriate strategies for this topic. The use of Hill, Ball and Schilling’s (2008) Mathematical Knowledge for Teaching (MKT) framework identified deficits in the participants’ knowledge of the topic and their preparedness to teach it. Whilst the intervention was well received, its short duration meant that significant gains could not be made in the participants’ own SCK. The data did show an increase in the range and flexibility of the strategies used to solve mental multiplication problems and an improvement in timed testing results. There was an attitudinal shift of the participants away from a traditional algorithmic approach to the topic towards more flexible, number sensible approaches. <br/> The research is significant as it adds to the literature concerning mental multiplication strategies and possible teaching programs in the later primary years. Whilst there is considerable research concerning mental computation, it has focussed largely on the early years of primary and, in particular, addition and subtraction. Studies of mental multiplication with pre-service and practising teachers are less common as are specific recommendations for appropriate strategies to include in teaching programs (Hartnett, 2007). Both the Australian and NESA outcomes and support documents are vague in this area with few examples of actual strategy use for mental multiplication. It is hoped that this study promotes further discussion of this topic leading to improved curriculum guidelines and flexible teaching approaches.