The role of mathematical symbols in the development of number conceptualization: The case of the Minus sign
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophical Psychology 21 (4):555 – 570 (2008)
In mathematics education, students' difficulties with negative numbers are well known. To explain these difficulties, researchers traditionally refer to obstacles raised by the concept of NEGATIVE NUMBERS itself throughout its historical evolution. In order to improve our understanding, I propose to take into consideration another point of view, based on Vygotsky's principles, which define a strong relationship between signs such as language or symbols and cognitive development. I show how it is of great interest to consider students' difficulties with negatives in the light of the use of symbols, in particular the minus sign. I describe the results of an empirical study about students' strategies in solving arithmetical equations with negatives. My analysis shows that the problems raised by the presence of negatives in the equations are attributable to students' very restricted and often inadequate use of the minus sign, which prevents them from finding a negative solution or making sense of it.
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