Abstract: Numerical representation refers to the mental representation of a given number. Though the perspective of abstract representation has predominated for a long time, recent evidence shows the notation-dependent representation of number with the development of automatic processing paradigms and brain imaging techniques. There were two theories which assumed that the notation-independent and notation-dependent representations might coexist in the number processing. The computational model proposed that the summation coding was notation-dependent, whereas the place coding was notation-independent for both non-symbolic and symbolic number. The extension of dual code theory suggested that numerical information was represented internally by way of automatic and intentional codes. In the first stage, there was an automatic activation of the numerical quantity that was notation-dependent in the Intraparietal sulcus (IPS). Then the representation could be transferred to an on-line abstract representation on demands of tasks at the stage of intentional code. Although those assumptions were supported by extensive behavioral and neuropsychological studies, the internal mechanism and cortex of the dynamic change of numerical representation are still open questions. More attention should be devoted to numerical representation in many aspects in the future, such as developmental studies, cross-culture studies, the combination of automatic processing paradigms and neural imaging techniques, and single cell recording techniques.

Key words: numerical representation, abstract representation, notation-independent, notation-dependent, automatic processing