Working memory components as predictors of children's mathematical word problem solving

This study determined the working memory (WM) components (executive, phonological loop, and visual–spatial sketchpad) that best predicted mathematical word problem-solving accuracy of elementary school children in Grades 2, 3, and 4 (N = 310). A battery of tests was administered to assess problem-solving accuracy, problem-solving processes, WM, reading, and math calculation. Structural equation modeling analyses indicated that (a) all three WM components significantly predicted problem-solving accuracy, (b) reading skills and calculation proficiency mediated the predictive effects of the central executive system and the phonological loop on solution accuracy, and (c) academic mediators failed to moderate the relationship between the visual–spatial sketchpad and solution accuracy. The results support the notion that all components of WM play a major role in predicting problem-solving accuracy, but basic skills acquired in specific academic domains (reading and math) can compensate for some of the influence of WM on children’s mathematical word problem solving.     

Health numeracy and cognitive decline in advanced age

ABSTRACT

The study aimed at investigating health numeracy in cognitively well performing healthy participants aged from 50 to 95 years as well as in participants with cognitive impairment, but no dementia (CIND). In cognitively well performing participants (n = 401), demographic variables and cognitive abilities (executive functions, reading comprehension, mental calculation, vocabulary) were associated with health numeracy. Older age, lower education, female gender as well as lower cognitive functions predicted low health numeracy. The effect of older age was partly mediated by executive functions and calculation abilities. Participants with CIND (n = 51) performed significantly lower than healthy controls in health numeracy. The findings suggest that cognitively well performing old individuals have difficulties in understanding health-related numerical information. The risk of misunderstanding health-related numerical information is increased in persons with CIND. As these population groups are frequently involved in health care decisions, particular attention has to be paid to providing numerical information in comprehensible form.     

The role of strategies in deciding advantageously in ambiguous and risky situations

In decision situations of everyday life, the potential positive or negative consequences of a decision are often specified and the associated probabilities are known or they are principally calculable ("decisions under risk"). On the basis of correlations reported in patient studies, it has been recently proposed that decisions under risk involve strategic components, i.e. calculation of the risk, as well as emotional processes, i.e. processing feedback from previous decisions. However, the potential impact of calculative strategies on decision-making under risk has not been investigated systematically, so far. In the current study, we examined 42 healthy subjects (21 females) with the Game of Dice Task measuring decisions under risk, and a questionnaire assessing strategy application in items comparable to the choices in the Game of Dice Task. In addition, the subjects performed the Iowa Gambling Task, examining decision-making under ambiguity, and a neuropsychological test battery focusing on executive functions. Results indicate that deciding advantageously in a decision-making task with explicit and stable rules is linked to applying calculative strategies. In contrast, individuals who decide intuitively prefer risky or disadvantageous choices in the Game of Dice Task. Applying calculative strategies was correlated with executive functions but not with performance on the Iowa Gambling Task. The results support the view that calculative processes and strategies may improve decision-making under explicit risk conditions.     

An electro-physiological temporal principal component analysis of processing stages of number comparison in developmental dyscalculia

Developmental dyscalculia (DD) still lacks a generally accepted definition. A major problem is that the cognitive component processes contributing to arithmetic performance are still poorly defined. By a reanalysis of our previous event-related brain potential (ERP) data (Soltész et al., 2007) here our objective was to identify and compare cognitive processes in adolescents with DD and in matched control participants in one-digit number comparison. To this end we used temporal principal component analysis (PCA) on ERP data. First, PCA has identified four major components explaining the 85.8% of the variance in number comparison. Second, the ERP correlate of the most frequently used marker of the so-called magnitude representation, the numerical distance effect, was intact in DD during all processing stages identified by PCA. Third, hemispheric differences in the first temporal component and group differences in the second temporal component suggest executive control differences between DD and controls.     

Working memory and access to numerical information in children with disability in mathematics

The relationship among working memory, mathematic ability, and the cognitive impairment of children with difficulties in mathematics was examined. A group of children with difficulties in mathematics (MD) was compared with a group of children with a normal level of achievement matched for vocabulary, age, and gender (N = 49). The children were required to perform a variety of working memory and short-term memory tasks that had been administered 1 year previously. Moreover, the children were asked to perform tasks designed to provide information about speed of articulation. The results suggest a general working memory deficit in children with MD, specifically in the central executive component of Baddeley's model and primarily in the ability to inhibit irrelevant information. However, the MD children were not impaired in speech rate and counting speed tasks, which mainly involve the role of the articulatory loop.     

Strategy choice for arithmetic verification: effects of numerical surface form

Canadian university students (n=48) solved simple addition problems in a true/false verification task with equations in digit format (3+4=8) or written English format (three+four=eight). Participants reported their solution strategy (e.g. retrieval or calculation) after each trial. Reported use of calculation strategies was much greater with word (41%) than digit stimuli (26%), and this difference was exaggerated for numerically larger problems. Word-format costs on reaction time (RT) were correspondingly greater for large than for small problems, but this Format×Size RT effect was bigger for true than for false equations. The results demonstrate that surface format affects central, rather than only peripheral, stages of cognitive arithmetic.     

计算的脑科学研究及其对数学教育的启示

脑科学研究发现,简单心算主要涉及算术事实的提取,依赖于左半球的语言中枢,而复杂心算激活了左侧顶—额叶网络和双侧颞下回,与视觉空间表征和视觉表象加工有关;精算主要激活左额叶下部区域,而估算激活了两半球更大的区域。在计算过程中所激活的脑区受年龄发展与个体差异以及训练的影响。研究对有效地促进儿童计算能力的发展提供了重要启示。     

Differentiating core and co-opted mechanisms in calculation: The neuroimaging of calculation in aphasia

The role of language in exact calculation is the subject of debate. Some behavioral and functional neuroimaging investigations of healthy participants suggest that calculation requires language resources. However, there are also reports of individuals with severe aphasic language impairment who retain calculation ability. One possibility in resolving these discordant findings is that the neural basis of calculation has undergone significant reorganization in aphasic calculators. Using fMRI, we examined brain activations associated with exact addition and subtraction in two patients with severe agrammatic aphasia and retained calculation ability. Behavior and brain activations during two-digit addition and subtraction were compared to those of a group of 11 healthy, age-matched controls. Behavioral results confirmed that both patients retained calculation ability. Imaging findings revealed individual differences in processing, but also a similar activation pattern across patients and controls in bilateral parietal cortices. Patients differed from controls in small areas of increased activation in peri-lesional regions, a shift from left fronto-temporal activation to the contralateral region, and increased activations in bilateral superior parietal regions. Our results suggest that bilateral parietal cortex represents the core of the calculation network and, while healthy controls may recruit language resources to support calculation, these mechanisms are not mandatory in adult cognition.     

Magnitude processing and complex calculation is negatively impacted by mathematics anxiety while retrieval‐based simple calculation is not

Mathematics anxiety (MA) refers to the experience of negative affect when engaging in mathematical activity. According to Ashcraft and Kirk (2001), MA selectively affects calculation with high working memory (WM) demand. On the other hand, Maloney, Ansari, and Fugelsang (2011) claim that MA affects all mathematical activities, including even the most basic ones such as magnitude comparison. The two theories make opposing predictions on the negative effect of MA on magnitude processing and simple calculation that make minimal demands on WM. We propose that MA has a selective impact on mathematical problem solving that likely involves processing of magnitude representations. Based on our hypothesis, MA will impinge upon magnitude processing even though it makes minimal demand on WM, but will spare retrieval‐based, simple calculation, because it does not require magnitude processing. Our hypothesis can reconcile opposing predictions on the negative effect of MA on magnitude processing and simple calculation. In the present study, we observed a negative relationship between MA and performance on magnitude comparison and calculation with high but not low WM demand. These results demonstrate that MA has an impact on a wide range of mathematical performance, which depends on one's sense of magnitude, but spares over‐practiced, retrieval‐based calculation.     

The exact vs. approximate distinction in numerical cognition may not be exact, but only approximate: How different processes work together in multi-digit addition

Two types of calculation processes have been distinguished in the literature: approximate processes are supposed to rely heavily on the non-verbal quantity system, whereas exact processes are assumed to crucially involve the verbal system. These two calculation processes were commonly distinguished by manipulation of two factors in addition problems: the identity of the target and the distance of the distractor. However, in all previous studies, these two factors were not manipulated independently. In this fMRI study, we could disentangle the two factors by using a different (two-digit) number stimulus set. Both behavioral and neurofunctional data suggest that the cognitive processes involved could be best explained by the (independent) factors target and distractor distance. Based on these data we suggest that the exact/approximate distinction does not seem to be as generally valid as previously assumed. We conclude that this study may be a starting point for a closer examination of the experimental, procedural and strategic conditions of when the exact/approximate distinction is valid and when it is not.