A synthesis of cognitive science research on the mental number line, and its relation to the pedagogical use of number lines in the teaching of elementary arithmetic in the Foundation Phase of schooling

Master Thesis


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In this paper, I examine how biologically endowed computational systems help to frame our experiences as it relates to using the number line in school mathematics. This study is a synthesis of the research findings in cognitive science and mathematics education to elucidate the mechanisms that underpin the connection between the mental number line in humans and its relation to the growth of mathematical knowledge in young children. This reported research drawn together here shows how we draw on core domain knowledge (the object tracking system (OTS), the approximate number line (ANS) and the mental number line (MNL) to construct mathematical ideas. The OTS allows us to track individual items, which provides us with the notion of exact number and the ANS creates an intuitive number sense from which we intuit that a collection can be assigned a cardinal value. Language mediates the integration of knowledge of the ANS and OTS to overcome the limits of the core systems and build the exact number system. I review the literature to investigate spatial numerical associations and the properties of the internal number line and to clarify the relationship between cognitive development, cultural factors and education. The synthesis concludes by using the ideas of representations and structure preservation to examine how closely the number line aligns with our natural intuitions about magnitude and number and the implications this has on education. I argue that educators need to understand how biologically innate conceptions of number guide subsequent learning and provides us with a foundation for domains such as mathematics. This insight will enable educators to select teaching models that build on from our intuitive notions of number and understand why certain concepts are difficult for children to understand.