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Transition to School: Supporting Children’s Engagement in Mathematical Thinking Processes

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Mathematics and Transition to School

Part of the book series: Early Mathematics Learning and Development ((EMLD))

Abstract

Internationally, mathematising is now a key focus in mathematics education for children aged 3–8 years (Perry and Dockett, Handbook of International Research in Mathematics Education, 2008; National Research Council (NRC), Mathematics Learning in Early Childhood: Paths Towards Excellence and Equity, 2009). For young children mathematising involves going back and forth between abstract mathematics and real situations in the world around them (NRC, Mathematics Learning in Early Childhood: Paths Towards Excellence and Equity, 2009). It helps children to make sense of mathematics by connecting it to their everyday lives. While mathematical thinking processes associated with mathematising begin in early childhood (Paley, Molly is Three: Growing Up in School, 1986; Tizard and Hughes, Young Children Learning, 2002), educators may not always recognise and promote children’s engagement with these processes (Dunphy, International Journal of Early Years Education, 17(1), 3–16, 2009). In this chapter I present examples of children involved in mathematising. The discussion addresses issues that arise in supporting mathematisation during the transition to school, as well as directions for future research.

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Correspondence to Liz Dunphy .

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Appendix 1: Details of Tasks

Appendix 1: Details of Tasks

1.1 Task 5: How Many Now? (Objects Present)

Look at these nice presents. Let’s pretend that they are Coco’s presents. How many has he?

Children were asked to count out a linear array of birthday presents (e.g. 4) and say how many. They then were asked to remove one and say how many now. They were also asked to add one to another array (e.g. 5) that they had counted and state how many now.

4:

Count/Remove one (Repeat with 7)

3:

Count/Add one (Repeat with 5)

1.2 Task 6: Understanding of Part–Part–Whole Relationships (Objects Present)

Let’s play a game with Coco’s presents. First we had better count them to see how many. (Confirm 5)

Children were shown Coco’s presents (5) and invited to play a hiding game with these. They first counted the items to confirm that there were five. I then suggested a game of Hide some/ See some. While the child’s eyes were closed I hid some of the objects and left some visible. We played a number of rounds until the various combinations were exhausted i.e., 1 and 4, 3 and 2, 5 and 0, 4 and 1, 2 and 3, 0 and 5.

(Show first amount, hide second).

1.3 Task 8: One More Than/One Less Than a Given Numeral (Objects Not Present)

Listen carefully while I tell you what happened about his presents.

E.g. Coco had 4 presents and he got 1 more. How many now?

This was explored with the numbers 3, 7, 6 and 9.

Also less explored through the suggestion that we pretend he had x amount of presents but that one got lost.

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Dunphy, L. (2015). Transition to School: Supporting Children’s Engagement in Mathematical Thinking Processes. In: Perry, B., MacDonald, A., Gervasoni, A. (eds) Mathematics and Transition to School. Early Mathematics Learning and Development. Springer, Singapore. https://doi.org/10.1007/978-981-287-215-9_18

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