This article describes the Adaptive Control of Thought–Rational (ACT–R) cognitive architecture (Anderson et al., 2004; Anderson & Lebiere, 1998) and its detailed application to the learning of algebraic symbol manipulation. The theory is applied to modeling the data from a study by Qin, Anderson, Silk, Stenger, & Carter (2004) in which children learn to solve linear equations and perfect their skills over a 6‐day period. Functional MRI data show that: (a) a motor region tracks the output of equation solutions, (b) (...) a prefrontal region tracks the retrieval of declarative information, (c) a parietal region tracks the transformation of mental representations of the equation, (d) an anterior cingulate region tracks the setting of goal information to control the information flow, and (e) a caudate region tracks the firing of productions in the ACT–R model. The article concludes with an architectural comparison of the competence children display in this task and the competence that monkeys have shown in tasks that require manipulations of sequences of elements. (shrink)

We present a detailed process theory of the moment‐by‐moment working‐memory retrievals and associated control structure that subserve sentence comprehension. The theory is derived from the application of independently motivated principles of memory and cognitive skill to the specialized task of sentence parsing. The resulting theory construes sentence processing as a series of skilled associative memory retrievals modulated by similarity‐based interference and fluctuating activation. The cognitive principles are formalized in computational form in the Adaptive Control of Thought–Rational (ACT–R) architecture, and our (...) process model is realized in ACT–R. We present the results of 6 sets of simulations: 5 simulation sets provide quantitative accounts of the effects of length and structural interference on both unambiguous and garden‐path structures. A final simulation set provides a graded taxonomy of double center embeddings ranging from relatively easy to extremely difficult. The explanation of center‐embedding difficulty is a novel one that derives from the model' complete reliance on discriminating retrieval cues in the absence of an explicit representation of serial order information. All fits were obtained with only 1 free scaling parameter fixed across the simulations; all other parameters were ACT–R defaults. The modeling results support the hypothesis that fluctuating activation and similarity‐based interference are the key factors shaping working memory in sentence processing. We contrast the theory and empirical predictions with several related accounts of sentence‐processing complexity. (shrink)