An encoding-complex approach to numerical cognition in Chinese-English bilinguals

Abstract We present a model of the cognitive architecture of basic numerical skills in adult Chinese-English bilinguals. The model is based on data reported by Campbell, Kanz, and Xue (1999) and combines Dehaene and Cohen's triple-code theory with Campbell and Clark's encoding-complex approach to modeling number processing. Participants were required to name, add or multiply Arabic or Mandarin numerals and to respond in English or Chinese. They also performed magnitude comparisons on pairs of Arabic or Mandarin numerals. The proposed model of their performance on this set of tasks assumes 1) that number processing is modular with respect to representational code (e.g., visual, visuo-spatial, verbal) rather than with respect to numerical function, 2) task-specific communication between representational codes is interactive rather than additive, and 3) memory for arithmetic facts is at least partially language-based and our Chinese-English bilinguals possessed both Chinese and English-language number-fact representations. We provide new analyses of the arithmetic data and a review of research on the role of language in simple arithmetic to substantiate our claims about linguistic codes for number-fact memory. Human numerical competence evolves from infancy out of innate perceptual and conceptual processes to eventually encompass a broad range of complex number-processing skills in adulthood (Geary, 1995; Lakoff & Nunez, 2000). Critical component skills include the ability to comprehend and produce written and spoken numbers, to count by various increments, and to retrieve, calculate, or estimate the results of both simple and complex arithmetic problems. Numerical understanding emerges through the functional and conceptual integration of these diverse numerical activities. The question of how to conceptualize the organization of cognitive systems underlying basic numerical skills has been the focus of much theoretical debate over the last 15 years (Butterworth, 1999; Dehaene, 1997). Here, we present a model of the organization of basic numerical cognition in Chinese-English bilinguals. The model is based on the results of an experiment reported by Campbell, Kanz, and Xue (1999; henceforth C, K, & X); specifically, the model represents an encoding-complex approach to these data (Campbell, 1992, 1994; Campbell & Clark, 1988, 1992; Clark & Campbell, 1991). We were motivated by three main considerations in pursuing this project. First, the original report of the data did not attempt to provide an overarching theoretical framework for the entire set of complex findings, whereas that is the focus of this paper. Second, the original article presented dozens of detailed analyses. Here, we identify and focus on phenomena that are most theoretically important, including results of new analyses. Third, we provide a review of research on language and arithmetic in order to substantiate a key assumption of the model - that arithmetic memory involves a linguistic representation, although not necessarily exclusively. We will begin by reviewing three different approaches to the architecture of basic numerical skills. Following this, we summarize the C, K, & X experiment, and then describe the model and how it accounts for the number-processing performance of Chinese-English bilinguals. Architectures for Numerical Cognition Abstract-Code Model Figure 1 depicts the model of number processing proposed by Michael McCloskey and his colleagues (see McCloskey, 1992; McCloskey & Macaruso, 1994, 1995; see also Cipolotti & Butterworth, 1995, for reviews of related work). According to the model, number processing is comprised of three types of cognitive systems: comprehension systems for encoding number input, calculation processes, and response production systems. In this view, the architecture of number processing is modular with respect to numerical function (i.e., comprehend, calculate, produce). …