Young children communicating their

mathematical thinking and

understanding

Ross Ó Corráin and Liz Dunphy

Key Aim: Mathematical Proficiency

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Adaptive Reasoning

Capacity for logical thought, reflection, explanation, and justification.

… the justification of one’s work. This justification can be both formal and informal. Individuals clarify their reasoning by talking about concepts and procedures and giving good reasons for the strategies that they are employing. (US National Research Council, 2001, pp. 116-113)

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Standards for Early Childhood

Mathematics Education

Recommendation 14

As important as mathematical content are general mathematical processes such as problem solving , reasoning and proof, communication, connections, and representation; specific mathematical processes such as organising information, patterning and composing ; and habits of mind such as curiosity, imagination, inventiveness, persistence, willingness to experiment, and sensitivity to patterns. All should be involved in a high-quality mathematics program.

(Clements, Sarama and DiBiase 2004, p. 3)

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Mathematizing is Key

…children interpreting and expressing their everyday experiences in mathematical form and understanding the relations between the two (Ginsburg, 2009)

…generalising concepts and situations first understood on an intuitive and informal level in the context of every day activity into mathematical terms… (National Research Council, 2009)

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Key Implication from Research Report

Connecting, communicating, reasoning

argumentation, justifying, representing, problem solving and generalising should permeate all learning and teaching activities …

These processes are implicated in mathematization.

(Research Report No. 17, Chapter 1)

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Towards A Change in Emphasis

Towards a revision of mathematics learning and teaching with the youngest children?

A change in pedagogy towards one that emphasises mathematization.

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Researching Mathematization

How can the teacher support young children’s ability to mathematize?

• Research participants: My class

• Methodology: Action Research

• Instruments: Video, observation notes, video journal, children’s mathematical representations

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Strategies

Supporting mathematization through…

• Children’s mathematical representations (drawing, mark-making, writing, photographs)

• Engaging contexts for mathematical tasks (helping teacher, Talking Tom application)

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Egg box Task

Strategy: Supporting mathematization through mathematical representations

• Children given egg box (6 spaces) and 2 eggs

• Find as many ways as possible the 2 eggs can be arranged in box

• Keep track of answers with paper and pencil

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Egg box Transcript

• Read in pairs

• What role does teacher play in supporting mathematizing?

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Katie

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Lizzy

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Fergie

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Tower Task

Strategies: Supporting mathematization through meaningful mathematical context and digital photography

• Children set measurement task by Talking Tom

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Tower Task

Video: How does digital photography support mathematization in this clip?

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In Summary

Successful mathematization came through a combination of …

• A meaningful context for mathematical tasks : Talking Tom

• The role of teacher

• Digital photographs

• Small group work

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References

Task Source: Cook, G., Jones, L., Murphy, C. & Thumpston, G. (1997). Enriching early mathematical learning. Buckingham: Open University Press

Digital Resource: Talking Tom application www.talkingtom.com

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