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

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. 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.

受试对象在符合五年级学生要求的心算乘法技能上，知识储备与实操表现均欠佳。尽管过去20年间课程规划者一直强调心算技能的重要性，且多数受试对象均接受过该时期的学校教育，但他们对该主题的适宜教学策略仍明显缺乏认知。借助希尔（Hill）、鲍尔（Ball）与希林（Schilling）于2008年提出的教学用数学知识（Mathematical Knowledge for Teaching, MKT）框架分析后，可发现受试对象在该主题知识及教学准备方面均存在不足。尽管教学干预方案广受好评，但因持续时长过短，受试对象自身的专门内容知识（Specialized Content Knowledge, SCK）未能获得显著提升。不过研究数据确实显示，受试对象用于解决心算乘法问题的策略在广度与灵活性上均有所提升，且限时测试成绩也得到改善。同时，受试对象的态度也发生了转变：从依赖传统算法式教学思路，转向更具灵活性的数感导向型方法。本研究具有重要学术价值，其补充了有关小学高年级阶段心算乘法策略与潜在教学方案的相关文献。尽管当前有关心算的研究数量颇丰，但大多聚焦于小学低年级阶段，尤其是加减法领域。针对职前与在职教师的心算乘法研究较为少见，有关教学方案中应纳入的适宜策略的具体建议同样匮乏（Hartnett, 2007）。澳大利亚教育部门与新南威尔士州教育标准局（NESA）的相关成果文件及支持材料在此领域均表述模糊，且鲜有针对心算乘法实际策略应用的示例。本研究希望能推动该主题的进一步讨论，助力完善课程指南与灵活化教学方法。