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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.

Children begin to form mathematical concepts at an early age and many of these concepts are linked to measurement experiences. Often mathematics education in pre-school and at the beginning of school is focused on numbers. In order to acknowledge children’s mathematical concepts and to build on them, a mathematics intervention program that focused on measurement replaced the usual mathematics curriculum for 40 children entering their first year of school in Australia. This chapter presents the results of the children’s performance on a one-to-one task-based interview that tested their number knowledge at the beginning and end of the school year. In addition, two case studies and some classroom stories from the intervention are described. Findings indicate that a measurement-based curriculum can stimulate the development of children’s number knowledge and their number sense.