Abstract: Numerical competence is one of the basic components of individual understanding the empirical world. It represents one of the basic components of mathematical cognition. Investment on numerical competence can help us to understand the foundation of human mathematics cognition thoroughly. Although there are plentiful evidences to support that animals have numerical competence, studies have found that from lower animals to mammals, many of them have the approximate number representation ability and precise number representation ability.However，those results can only prove that human beings and animals have a a common mathematical cognitive basis. Compared to animals, the human ability is unique in that human beings have a complete number concepts. Human beings not only have the ability to represent and count quantity ，but also have the ability to carry out mathematical operations, to obtain the numerical competence, has a complete number concept system. Human beings are born with two number representation systems-approximate number system and precise number system. Both systems can not provide support for the precise representation of numbers beyond 3 or 4, therefore they are not the only basis for the formation of numbers competence.It remians unlcear about how the unique mathematical ability of human beings develop on the foundation of cognitive basis? What kind of cognitive mechanisms contribute to the development of numerical competence from numerosity representation to number representation? Then requires more complex cognitive mechanisms to support it. Debates on these issues continue from the view of traditional cognitive science and second-generation cognitive science. Based on the representation-computing paradigm, the traditional cognitive science holds that mind is a processor to deal with meaningless symbols in accordance with certain rules and the cognition is a process that information is captured through the calculation of symbolic systems mentally. Traditional cognitive science can not provide a powerful explanation for the acquisition of human advanced numerical competence. On the contrary, the second-generation of cognitive science poses a challenge that the conceptual representation is not an independent, abstract, arbitrary, and amodal symbols representation, but representation constructed by external perception, internal states, and actions mutually. In addition, it provided two cognitive mechanisms for number conceptual representation. We mainly provided theoretical supports and empirical evidences for the acquisition of human numerical competence under embodied cognition perspective. In recent years, there has been a new interpretation of brain structure and function in the field of cognitive neuroscience - the Neural Reuse Hypothesis may be a revelation of the overlap between quantity and space. Future studies should further uncover the cognitive neural mechanism of numerical competence. The study of number spatial metaphor still has broad exploration space. In addition, future research needs to proceed from the perspective of specific knowledge, to further explore how to better enable students to understand the mathematical concepts in teaching.

Key words: Embodied Cognition/Numerical Competence/Number Representation/Conceptual Metaphor

摘要： 数能力是数学认知的基本成分。与动物所具有的基本数能力不同，人类不仅具备数量表征能力，更重要的是还拥有对数概念进行表征的数表征能力。虽然具身认知与离身认知都对数概念的表征问题进行了解释，但二者却存在明显理论分歧。具身认知观点主要从具身数量表征和数能力发展的具身认知机制两方面为人类独特数能力的获得提供了理论支撑及实证证据。这启示人们需要重视具身学习在数能力形成实践中的关键作用，重视具身数量表征在数学教学中的作用，仍需进一步揭示其内在的心理和神经基础。

关键词: 具身认知/数能力/数表征/概念隐喻