Virginia Mathematics Teacher Spring 2017

The Role of Skip Counting in Children's Reasoning Jesse L. M. Wilkins and Catherine Ulrich Skip Counting and Figurative Material in Children’s Construction of Composite Units and Multiplicative Reasoning An important part of children’s graders. These solutions will be referred to throughout the article to highlight children’s ways of thinking and to make connections to

mathematical development in the elementary and middle school years is the transition from additive to multiplicative thinking. This developmental milestone affords children necessary tools for understanding more advanced mathematical concepts that is limited by additive thinking, such as fractions and proportional reasoning. An important part of this mathematical development is the construction and coordination of units, which does not occur all at once, but through several hierarchical stages (Ulrich, 2015, 2016). Understanding these stages and the nature of children’s ways of thinking about units during each stage is important for teachers as they plan and prepare instructional activities for their students. In this article we discuss the characteristic ways of thinking associated with these stages and instructional opportunities for moving children through these stages. In particular, we discuss the role of skip counting (e.g., counting by 3’s: 3, 6, 9, 12, 15, 18, 21…) as both an indicator of, and as a way to foster, children’s construction and coordination of units throughout these stages of development. We also discuss the placement of skip counting within Virginia’s mathematics Standards of Learning and Curriculum Framework (Virginia Department of Education [VDOE], 2009) and potential extensions and understandings that could be helpful for curriculum development for elementary-aged children. Moreover, we discuss the distinction between a child understanding, e.g., 5 × 3 as the result of their skip counting by 3s, from a child who has truly developed a multiplicative understanding of 5 × 3 as 5 times as much as 3. To motivate and facilitate our discussion of the ideas outlined above we first discuss several solutions to the task in Figure 1 produced by sixth

You have baked 39 cupcakes and you will put the cupcakes in boxes of three. How many boxes will you fill?

(a)

(b)

(d)

(c)

(e) (f) Figure 1 . Examples of sixth graders’ solutions to the Cupcake Task

Virginia Mathematics Teacher vol. 43, no. 2

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