As confirmed by a series of experimental data, there are two different cognitive systems relating to mathematical skills. The first system is not based on symbols, and it is approximative; it is based on the estimation of quantities; and it involves both a simple process of comparison and a series of basic arithmetical operations like addition and subtraction. The second system is based on symbols, and it is language- and culture-dependent; it is typical of adults; and it is founded on the ability of counting, therefore on a numerical system and on all arithmetical operations. Therefore, to explain the acquisition of mathematical concepts, we must answer the two following questions. How can the concepts of approximate numerosity become an object of thought that is so accessible to our consciousness? How are these concepts refined and specified in such a way as to become numbers? Unfortunately, starting from these experimental results, there is currently no model that can truly demonstrate the role of language in the development of numerical skills starting from approximate pre-verbal skills. The aim of this book is to answer these difficult questions by turning to the dual process theories. This theoretical approach is widely used by theorists focusing on reasoning, decision making, social cognition, consciousness, etc. In this book, for the first time this theoretical approach is applied to the studies on mathematical knowledge with the aim of detailing the results brought about by psychological and neuroscientific studies conducted on numerical cognition by a few neuroscientists and laying the foun- dations of a new potential philosophical explanation on mathematical knowledge.

Dual-Process Theories of Numerical Cognition

Graziano Mario
2018

Abstract

As confirmed by a series of experimental data, there are two different cognitive systems relating to mathematical skills. The first system is not based on symbols, and it is approximative; it is based on the estimation of quantities; and it involves both a simple process of comparison and a series of basic arithmetical operations like addition and subtraction. The second system is based on symbols, and it is language- and culture-dependent; it is typical of adults; and it is founded on the ability of counting, therefore on a numerical system and on all arithmetical operations. Therefore, to explain the acquisition of mathematical concepts, we must answer the two following questions. How can the concepts of approximate numerosity become an object of thought that is so accessible to our consciousness? How are these concepts refined and specified in such a way as to become numbers? Unfortunately, starting from these experimental results, there is currently no model that can truly demonstrate the role of language in the development of numerical skills starting from approximate pre-verbal skills. The aim of this book is to answer these difficult questions by turning to the dual process theories. This theoretical approach is widely used by theorists focusing on reasoning, decision making, social cognition, consciousness, etc. In this book, for the first time this theoretical approach is applied to the studies on mathematical knowledge with the aim of detailing the results brought about by psychological and neuroscientific studies conducted on numerical cognition by a few neuroscientists and laying the foun- dations of a new potential philosophical explanation on mathematical knowledge.
SpringerBriefs in Philosophy
978-3-319-96796-7
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3128194
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