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Dr Tianrui Shen


Tianrui Shen studied for a full-time PhD on numerical cognition with Dr Denes Szucs (2006-2009). Prior to this, Tianrui worked as a teacher and course developer on mind abacus for two years and received his Masters degree in psychology and education in 2005 from the Faculty of Education, University of Cambridge. His PhD interest was in visuo-spatial processing mechanisms of mental abacus calculation, together with its developmental effect on a learner's fundamental representations and numerical abilities.

PhD: The abacus representation and our innate mathematical abilities

Abstract:  Mathematics is usually thought of as something profound and difficult that has to be acquired through extensive experience and exercises. However evidence from developmental, cross-cultural, comparative and neuroscience has revealed that we are born to be equipped with certain number senses, which represents the quantity in the form of analogue magnitudes or object-files. However, these innate numerical representations are found to be accurate only within small numerosities. Thus to functionalize exact numerical operations over the integer list, we turned to exact verbal and later on symbol representation system. The transition from primitive to new system may not be smooth, and it may cause our very first fear about mathematics.

Abacus, a nonverbal bead representation system in the Oriental cultures, is probably suggestive to a smoother transition. It resembles our primitive non-verbal number representations in its organisation, yet provides the same precision level as the language-based exact number representation as well as the support for arithmetic algorithms. An extensive literature reports the fact that youngsters who learn abacus are found to have higher calculation speed and capacity, as well as more confidence and interest in mathematics. Why? Is this because mental abacus representation provide a better bridge for the gap between innate numerical representations and exact symbol representation?

Consequently, the current study aims to investigate the potential link between mental abacus representation, object-file representation and analogue magnitude representation through our innate numerical abilities, subitizing and numerosity discrimination. The link, if any, would be beneficial to the improvement of our early year mathematical education.