Abstract Children’s multiplicative thinking as the visualization of equal group structures and the enumeration the composite units was the subject of this study. The results were obtained from a small sample of Australian children (n = 18) in their first year of school (mean age 5 years 6 months) who participated in a lesson taught by their classroom teacher. The 12 Little Ducks problem stimulated children to visualize and to draw different ways of making equal groups. Fifteen children (83 %) could identify and create equal groups; eight of these children (44 %) could also quantify the number of groups they formed. These findings show that some young children understand early multiplicative ideas and can visualize equal group situations and communicate about these through their drawings and talk. The study emphasises the value of encouraging mathematical visualization from an early age; using open thought-provoking problems to reveal children’s thinking; and promoting drawing as a form of mathematical communication.

中文翻译：

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调查青年学生的乘法思维：12只小鸭子问题

摘要 儿童乘法思维作为平等群体结构的可视化和复合单元的枚举是本研究的主题。结果来自一小部分澳大利亚儿童（n = 18），他们在第一年（平均年龄 5 岁 6 个月）参加了课堂老师教授的课程。12 只小鸭子问题激发了孩子们的想象和绘制不同的方法来组成平等的群体。15 名儿童 (83 %) 可以识别和创建平等的群体；其中 8 名儿童 (44%) 也可以量化他们组成的团体数量。这些发现表明，一些幼儿理解早期的乘法思想，可以想象平等的群体情况，并通过他们的绘画和谈话进行交流。该研究强调了从小就鼓励数学可视化的价值；用开放的发人深省的问题来揭示孩子的想法；并促进绘画作为一种数学交流形式。