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Journal of Mathematics Education June 2010, Vol. 3, No. 1, pp.158-166 Education for All Controversy on the Essence of Numerical Surface Form Processing Mingling Zhang Shandong Administration Institute,

Common pathway perspective suggests that all computations in the surface form are the same. In particular, they argue that the relationship between the surface form of the digit and the mental processing on the digit of magnitude is one of two parallel lines of computations. According to this view, the surface form of the digit is a basis for computing the mental magnitude of the digit (e.g., the mental magnitude of a two is equal to the mental magnitude of a single), whereas the connection of the surface form of the digit to the mental magnitude of the digit is that a digit in the surface form of the digit is associated with the mental magnitude of two. The specific pathway perspective maintains that the relationship between the surface form of the digit and the mental magnitude of the digit has two components: (1) the surface form of the digit is a representation of the mental magnitude of the digit, whereas (2) this representation of the mental magnitude of the digit can only be the case when the shape of the surface form of the digit is homogenous (i.e., if the mental magnitude of the digit is represented by the same number of curves of the surface form of the digit). This view is also based on the similarity of mental computation and the operation of the surface form of the digit. Specifically, when the surface form and operation of both operations of the digit are similar to each other, the result will typically be the same (i.e., if the mental magnitude of the digit (or two) has the same shape as the mental magnitude of the surface form of the digit). However, if they are different, the result will be the same (e.g., if the two representations of the mental magnitude of the digit are different, the result will be the same, but the mental magnitude of the digit will usually be different from the mental magnitude of the surface form of the digit). Since I will be discussing these two views, I will call them the common pathway view and the specific pathway view. To provide some further detail about these views, I will discuss the theory of specific pathway first. An Introduction to Specific Pathway The theory of specific pathway claims that all computations on the surface form of the digit are the same. Specifically, it claims that the digit in the surface form can in the general case represent all the mental computations on the number.

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