Neural correlates of arithmetic calculation strategies

Rosenberg‐Lee, Miriam; Lovett, Marsha C.; Anderson, John R.

doi:10.3758/cabn.9.3.270

Cited by 44 publications

(41 citation statements)

References 51 publications

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“…Shit!" These exception problems have been a focus of our attention because they pose challenges to modeling in the ACT-R theory (Anderson et al, 2004), which has been successfully applied to neuroimaging data from more routine mathematical problem solving (e.g., Anderson, 2005;Anderson, Carter, Fincham, Ravizza, & Rosenberg-Lee, 2008;Rosenberg-Lee, Lovett, & Anderson, 2009). Anderson (2007) described an ACT-R model that dealt with the behavioral data from these pyramid problems.…”

Section: Pyramid Experimentsmentioning

confidence: 99%

Discovering the Sequential Structure of Thought

Anderson

Fincham

2013

Cognitive Science

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Multi-voxel pattern recognition techniques combined with Hidden Markov models can be used to discover the mental states that people go through in performing a task. The combined method identifies both the mental states and how their durations vary with experimental conditions. We apply this method to a task where participants solve novel mathematical problems. We identify four states in the solution of these problems: Encoding, Planning, Solving, and Respond. The method allows us to interpret what participants are doing on individual problem-solving trials. The duration of the planning state varies on a trial-to-trial basis with novelty of the problem. The duration of solution stage similarly varies with the amount of computation needed to produce a solution once a plan is devised. The response stage similarly varies with the complexity of the answer produced. In addition, we identified a number of effects that ran counter to a prior model of the task. Thus, we were able to decompose the overall problem-solving time into estimates of its components and in way that serves to guide theory.

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Section: Pyramid Experimentsmentioning

confidence: 99%

Discovering the Sequential Structure of Thought

Anderson

Fincham

2013

Cognitive Science

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“…However, number series and letter series completion tasks are solved differently. Evidences demonstrated that different strategies (by definition, a strategy is a goal-directed procedure under the deliberate control of the participant (Rosenberg-Lee and Anderson, 2009)) were employed in number series and letter series completion tasks, in which each item in one has a same-rule counterpart in the other (Quereshi, 2001), and number series tasks are easier and more familiar than letter series tasks (Quereshi & Seitz, 1993;Quereshi & Smith, 1998). This has been confirmed by a recent pilot study with post-test oral report in our group, in which subjects are required to solve the two kinds of series completion tasks comprising items based on identical rules.…”

Section: Introductionmentioning

confidence: 99%

Different strategies in solving series completion inductive reasoning problems: An fMRI and computational study

Liang

Jia

Taatgen

et al. 2014

International Journal of Psychophysiology

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Neural correlate of human inductive reasoning process is still unclear. Number series and letter series completion are two typical inductive reasoning tasks, and with common core component of rule induction. Previous studies have demonstrated that different strategies are adopted in number series and letter series completion tasks even the underlying rules are identical. In the present study, we examined cortical activation as a function of two different reasoning strategies for solving series completion tasks. The retrieval strategy, used in number series completion tasks, involves direct retrieving of arithmetic knowledge to get the relations between items. The procedural strategy, used in letter series completion tasks, requires counting a certain number of times to detect the relations linking two items. The two strategies require essentially the equivalent cognitive processes, but have different working memory demands (the procedural strategy incurs greater demands). The procedural strategy produced significant greater activity in areas involved in memory retrieval (dorsolateral prefrontal cortex, DLPFC) and mental representation/maintenance (posterior parietal cortex, PPC). An ACT-R model of the tasks successfully predicted behavioral performance and BOLD responses in DLPFC and PPC. The present findings support a general-purpose dualprocess theory of inductive reasoning regarding the cognitive architecture.

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“…17, 18), and visual regions that are active in studies of mathematical problem solving that involve visual scanning (e.g., ref. 19). The negatively weighted regions seem less interpretable; some are in white matter, for example.…”

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Neural imaging to track mental states while using an intelligent tutoring system

Anderson

Betts²,

Ferris³

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

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Hemodynamic measures of brain activity can be used to interpret a student's mental state when they are interacting with an intelligent tutoring system. Functional magnetic resonance imaging (fMRI) data were collected while students worked with a tutoring system that taught an algebra isomorph. A cognitive model predicted the distribution of solution times from measures of problem complexity. Separately, a linear discriminant analysis used fMRI data to predict whether or not students were engaged in problem solving. A hidden Markov algorithm merged these two sources of information to predict the mental states of students during problem-solving episodes. The algorithm was trained on data from 1 day of interaction and tested with data from a later day. In terms of predicting what state a student was in during a 2-s period, the algorithm achieved 87% accuracy on the training data and 83% accuracy on the test data. The results illustrate the importance of integrating the bottom-up information from imaging data with the top-down information from a cognitive model.T his article reports a study of the potential of using neural imaging to facilitate student modeling in intelligent tutoring systems, which have proven to be effective in improving mathematical problem solving (1, 2). The basic mode of operation of these systems is to track students as they solve problems and offer instruction based on this tracking. These tutors individualize instruction by two processes, called "model tracing" and "knowledge tracing." Model tracing uses a model of students' problem solving to interpret their actions. It tries to diagnose the student's intentions by finding a path of cognitive actions that match the observed behavior of the student. Given such a match, the tutoring system is able to provide real-time instruction individualized to where that student is in the problem. The second process, knowledge tracing, attempts to infer a student's level of mastery of targeted skills and selects new problems and instruction suited to that student's knowledge state. Although the principle of individualizing instruction to a particular student holds great promise, the practice is limited by the ability to diagnose what the student is thinking. The only information available to a typical tutoring system comes from the actions that students take in the computer interface. Inferences based on such impoverished data are tenuous at best, and brain imaging data might provide a useful augmentation. Recent research has reported a variety of successes in using brain imaging to identify what a person is thinking about (e.g., refs. 3-6) and identifying when mental states happen (e.g., refs. 7-9).Although the methods described here could extend to knowledge tracing, this article will focus on model tracing where the goal is to identify the student's current mental state. Two features of the intelligent tutoring situation shaped our approach to the problem: (i) Given that instruction must be made available in real time, inferences about mental state ca...

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Neural correlates of arithmetic calculation strategies

Cited by 44 publications

References 51 publications

Discovering the Sequential Structure of Thought

Discovering the Sequential Structure of Thought

Different strategies in solving series completion inductive reasoning problems: An fMRI and computational study

Neural imaging to track mental states while using an intelligent tutoring system

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