Do subitizing deficits in developmental dyscalculia involve pattern recognition weakness?

The abilities of children diagnosed with developmental dyscalculia (DD) were examined in two types of object enumeration: subitizing, and small estimation (5–9 dots). Subitizing is usually defined as a fast and accurate assessment of a number of small dots (range 1 to 4 dots), and estimation is an imprecise process to assess a large number of items (range 5 dots or more). Based on reaction time (RT) and accuracy analysis, our results indicated a deficit in the subitizing and small estimation range among DD participants in relation to controls. There are indications that subitizing is based on pattern recognition, thus presenting dots in a canonical shape in the estimation range should result in a subitizing‐like pattern. In line with this theory, our control group presented a subitizing‐like pattern in the small estimation range for canonically arranged dots, whereas the DD participants presented a deficit in the estimation of canonically arranged dots. The present finding indicates that pattern recognition difficulties may play a significant role in both subitizing and subitizing deficits among those with DD.     

The Impact of Cognitive Diversity on Crisis Negotiations

This paper reports on a series of experiments designed to assess the impact of grouping decision makers by level of cognitive complexity on the outcomes they attain in crisis negotiations. The participants—University of Maryland undergraduates who took roles in a simulated international hostage crisis—used a computer decision support system and a controlled network environment for communications. The goal of the experiments was to better understand the dynamics that lead certain types of groupings to have greater success in negotiations, and that lead certain groups of adversaries to achieve more mutually beneficial outcomes such as compromise and agreement. The findings point to a positive relationship between the level of homogeneity in cognitive complexity among decision makers and the achievement of positive outcomes in crisis negotiations.     

Brain hyper‐connectivity and operation‐specific deficits during arithmetic problem solving in children with developmental dyscalculia

Developmental dyscalculia (DD) is marked by specific deficits in processing numerical and mathematical information despite normal intelligence (IQ) and reading ability. We examined how brain circuits used by young children with DD to solve simple addition and subtraction problems differ from those used by typically developing (TD) children who were matched on age, IQ, reading ability, and working memory. Children with DD were slower and less accurate during problem solving than TD children, and were especially impaired on their ability to solve subtraction problems. Children with DD showed significantly greater activity in multiple parietal, occipito‐temporal and prefrontal cortex regions while solving addition and subtraction problems. Despite poorer performance during subtraction, children with DD showed greater activity in multiple intra‐parietal sulcus (IPS) and superior parietal lobule subdivisions in the dorsal posterior parietal cortex as well as fusiform gyrus in the ventral occipito‐temporal cortex. Critically, effective connectivity analyses revealed hyper‐connectivity, rather than reduced connectivity, between the IPS and multiple brain systems including the lateral fronto‐parietal and default mode networks in children with DD during both addition and subtraction. These findings suggest the IPS and its functional circuits are a major locus of dysfunction during both addition and subtraction problem solving in DD, and that inappropriate task modulation and hyper‐connectivity, rather than under‐engagement and under‐connectivity, are the neural mechanisms underlying problem solving difficulties in children with DD. We discuss our findings in the broader context of multiple levels of analysis and performance issues inherent in neuroimaging studies of typical and atypical development.     

Intentional and automatic processing of numerical information in mathematical anxiety: testing the influence of emotional priming

ABSTRACT

Current theoretical approaches suggest that mathematical anxiety (MA) manifests itself as a weakness in quantity manipulations. This study is the first to examine automatic versus intentional processing of numerical information using the numerical Stroop paradigm in participants with high MA. To manipulate anxiety levels, we combined the numerical Stroop task with an affective priming paradigm. We took a group of college students with high MA and compared their performance to a group of participants with low MA. Under low anxiety conditions (neutral priming), participants with high MA showed relatively intact number processing abilities. However, under high anxiety conditions (mathematical priming), participants with high MA showed (1) higher processing of the non-numerical irrelevant information, which aligns with the theoretical view regarding deficits in selective attention in anxiety and (2) an abnormal numerical distance effect. These results demonstrate that abnormal, basic numerical processing in MA is context related.     

Comparative judgments of symbolic and non-symbolic stimuli yield different patterns of reaction times

Are different magnitudes, such as Arabic numerals, length and area, processed by the same system? Answering this question can shed light on the building blocks of our mathematical abilities. A shared representation theory suggested that discriminability of all magnitudes complies with Weber's law. The current work examined this suggestion. We employed comparative judgment tasks to investigate different types of comparisons — conceptual comparison of numbers, physical comparison of numbers and physical comparison of different shapes. We used 8 different size ratios and plotted reaction time as a function of these ratios. Our findings suggest that the relationship between discriminability and size ratio is not always linear, as previously suggested; rather, it is modulated by the type of comparison and the type of stimuli. Hence, we suggest that the representation of magnitude is not as rigid as previously suggested; it changes as a function of task demands and familiarity with the compared stimuli.     

Postulates for revising BDI structures

The process of rationally revising beliefs in the light of new information is a topic of great importance and long-standing interest in artificial intelligence. Moreover, significant progress has been made in understanding the philosophical, logical, and computational foundations of belief revision. However, very little research has been reported with respect to the revision of other mental states, most notably propositional attitudes such as desires and intentions. In this paper, we present a first attempt to formulate a general framework for understanding the revision of mental states. We develop an abstract belief-desire-intention model of agents, and introduce a notion of rationality for this model. We then present a series of formal postulates characterizing the processes of adding beliefs, desires, and intentions, updating costs and values, and removing beliefs, desires, and intentions. We also investigate the computational complexity of several problems involving the abstract model and comment on algorithms for revision.     

Manipulating Games by Sharing Information

We address the issue of manipulating games through communication. In the specific setting we consider (a variation of Boolean games), we assume there is some set of environment variables, the values of which are not directly accessible to players; the players have their own beliefs about these variables, and make decisions about what actions to perform based on these beliefs. The communication we consider takes the form of (truthful) announcements about the values of some environment variables; the effect of an announcement is the modification of the beliefs of the players who hear the announcement so that they accurately reflect the values of the announced variables. By choosing announcements appropriately, it is possible to perturb the game away from certain outcomes and towards others. We specifically focus on the issue of stabilisation: making announcements that transform a game from having no stable states to one that has stable configurations.