Children's mental representation of number, their number line estimations and maths achievement: exploring the role of 3D mental rotation skills

Abstract

As children’s early grasp of number is a reliable indicator of their future mathematical competence, any internal representations they develop to encode conceptual understanding, or as a framework for problem solving, are of particular interest to researchers. Although the exact nature and form of these mental models are difficult to establish, prior research has identified a directional left to right number line as the most probable internal representational schema for number magnitude. However, the extent to which these types of mental representations influence maths achievement is not clear, as there has yet to be a systematic review of the literature evidencing such links. This review set out to systematically gather, and critically examine, findings in one small area of a potentially large field of research; specifically the relationship between children’s mental representation of number magnitude and early maths achievement. Ten studies met the criterion for inclusion, each exploring the influence of mental representations through correlational data, or through training designed to enhance any such internal symbolic framework. Results indicate that internal representations of number are important for mathematical competence particularly in the early years, as notation and calculation with integers becomes increasingly symbolic. Implications for EPs were discussed including best approaches that model and encourage precision of the mental number line, such as linear board games, and awareness of specific groups that are most likely to benefit from any such intervention.

Number magnitude knowledge is a foundational concept within mathematics, observable early in life through behavioural phenomena and linked with spatial-numerical associations. The internal representation of symbolic number magnitude is thought to be a directional left to right mental number line, acting as a framework to encode conceptual understanding and to support problem solving. Accurate performance on the associated metric, the number line estimation task (NLE), has been interpreted as improved understanding of number magnitude and is reliably related to maths achievement. However, the exact role spatial skills play in the relationship between number magnitude understanding and NLE tasks is still unclear, particularly as these skills are themselves independently related to maths achievement, whilst also being influential in the proportional judgement strategies used to complete the NLE task. To investigate these relationships, 98 primary children were recruited for a RCT training 3D mental rotation skills using a computer-based tool, over ten sessions. Spatial skill and NLE performance strongly correlated with maths achievement, and although spatial training improved spatial ability, this was not significant. Unexpectedly, spatial training did not influence NLE performance. Implications for EPs include effective use of number line tasks to target weak number magnitude understanding, and benefits of providing spatial tasks to support positive maths outcomes.

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ORCID for Edward Redhead: orcid.org/0000-0002-7771-1228

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