Results 1  10
of
40
Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability
 Child Development
, 2007
"... Using strict and lenient mathematics achievement cutoff scores to define a learning disability, respective groups of children who are math disabled (MLD, n 5 15) and low achieving (LA, n 5 44) were identified. These groups and a group of typically achieving (TA, n 5 46) children were administered a ..."
Abstract

Cited by 16 (5 self)
 Add to MetaCart
Using strict and lenient mathematics achievement cutoff scores to define a learning disability, respective groups of children who are math disabled (MLD, n 5 15) and low achieving (LA, n 5 44) were identified. These groups and a group of typically achieving (TA, n 5 46) children were administered a battery of mathematical cognition, working memory, and speed of processing measures (M 5 6 years). The children with MLD showed deficits across all math cognition tasks, many of which were partially or fully mediated by working memory or speed of processing. Compared with the TA group, the LA children were less fluent in processing numerical information and knew fewer addition facts. Implications for defining MLD and identifying underlying cognitive deficits are discussed. Diagnostic criteria and thus the percentage of children with a learning disability in mathematics (MLD)
Promoting broad and stable improvements in lowincome children’s numerical knowledge through playing number board games
 Child Development
, 2008
"... Theoretical analyses of the development of numerical representations suggest that playing linear number board games should enhance young children’s numerical knowledge. Consistent with this prediction, playing such a game for roughly 1 hr increased lowincome preschoolers ’ (mean age 5 5.4 years) pr ..."
Abstract

Cited by 13 (4 self)
 Add to MetaCart
Theoretical analyses of the development of numerical representations suggest that playing linear number board games should enhance young children’s numerical knowledge. Consistent with this prediction, playing such a game for roughly 1 hr increased lowincome preschoolers ’ (mean age 5 5.4 years) proficiency on 4 diverse numerical tasks: numerical magnitude comparison, number line estimation, counting, and numeral identification. The gains remained 9 weeks later. Classmates who played an identical game, except for the squares varying in color rather than number, did not improve on any measure. Also as predicted, home experience playing number board games correlated positively with numerical knowledge. Thus, playing number board games with children from lowincome backgrounds may increase their numerical knowledge at the outset of school. Children vary greatly in the mathematical knowledge they possess when they enter school. These differences in initial mathematical knowledge appear to have large, longterm consequences. Proficiency in mathematics at the beginning of kindergarten is strongly predictive of mathematics achievement test scores years later: in elementary school, in middle school, and even in high school (Duncan et al., 2007; Stevenson & Newman, 1986). This pattern is consistent with the general finding that initial knowledge is positively related to learning (Bransford, Brown, & Cocking, 1999), but the relations in math are unusually strong and persistent. For example, they were considerably stronger than the relations between initial and subsequent reading proficiency in the same six longitudinal studies reviewed by Duncan et al. (2007; average standardized beta coefficients of.34 vs..16). Given the strong and persistent relation between early and later mathematical proficiency, it is especially unfortunate that preschoolers and kindergartners from lowincome families enter school with far less numerical knowledge than peers from more affluent families. Being clear on the locus of this gap is crucial for understanding it. On nonverbal numerical
Sex differences in intrinsic aptitude for mathematics and science? A critical review
 American Psychologist
, 2005
"... for assistance, and Nora Newcombe and Elliott Blass for advice and comments on the manuscript. Above all, I am grateful to Ariel Grace and Kristin Shutts for their unending support and afterhours labor on this project. Draft, 4/20/05. This paper has not yet been peer reviewed. Please do not copy or ..."
Abstract

Cited by 11 (2 self)
 Add to MetaCart
for assistance, and Nora Newcombe and Elliott Blass for advice and comments on the manuscript. Above all, I am grateful to Ariel Grace and Kristin Shutts for their unending support and afterhours labor on this project. Draft, 4/20/05. This paper has not yet been peer reviewed. Please do not copy or cite without author's permission. This report considers three prominent claims that boys and men have greater natural aptitude for highlevel careers in mathematics and science. According to the first claim, males are more focused on objects and mechanical systems from the beginning of life. According to the second claim, males have a profile of spatial and numerical abilities that predisposes them to greater aptitude in mathematics. According to the third claim, males show greater variability in mathematical aptitude, yielding a preponderance of males at the upper end of the distribution of mathematical talent. Research on cognitive development in human infants and preschool children, and research on cognitive performance by students at all levels, provides evidence against these claims. Mathematical and scientific reasoning develop from a set of biologically based capacities that males and females share. From these capacities, men and women appear to develop equal talent for mathematics and science.
Beyond hemispheric dominance: Brain regions underlying the joint lateralization of language and arithmetic to the left hemisphere
 J. Cogn. Neurosci.,inpress
, 2009
"... & Language and arithmetic are both lateralized to the left hemisphere in the majority of righthanded adults. Yet, does this similar lateralization reflect a single overall constraint of brain organization, such an overall ‘‘dominance’ ’ of the left hemisphere for all linguistic and symbolic operati ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
& Language and arithmetic are both lateralized to the left hemisphere in the majority of righthanded adults. Yet, does this similar lateralization reflect a single overall constraint of brain organization, such an overall ‘‘dominance’ ’ of the left hemisphere for all linguistic and symbolic operations? Is it related to the lateralization of specific cerebral subregions? Or is it merely coincidental? To shed light on this issue, we performed a ‘‘colateralization analysis’ ’ over 209 healthy subjects: We investigated whether normal variations in the degree of left hemispheric asymmetry in areas involved in sentence listening and reading are mirrored in the asymmetry of areas involved in mental arithmetic. Within the language network, a regionofinterest analysis disclosed partially dissociated patterns of lateralization, inconsistent with an overall ‘‘dominance’’ model. Only two of these areas presented a lateralization during sentence listening and reading which correlated strongly with the lateralization of two regions active during calculation. Specifically, the profile of asymmetry in the posterior superior temporal sulcus during sentence processing covaried with the asymmetry of calculationinduced activation in the intraparietal sulcus, and a similar colateralization linked the middle frontal gyrus with the superior posterior parietal lobule. Given recent neuroimaging results suggesting a late emergence of hemispheric asymmetries for symbolic arithmetic during childhood, we speculate that these colateralizations might constitute developmental traces of how the acquisition of linguistic symbols affects the cerebral organization of the arithmetic network. &
Playing linear number board games—but not circular ones —improves lowincome preschoolers’ numerical understanding
 Journal of Educational Psychology
, 2009
"... A theoretical analysis of the development of numerical representations indicated that playing linear number board games should enhance preschoolers ’ numerical knowledge and ability to acquire new numerical knowledge. The effect on knowledge of numerical magnitudes was predicted to be larger when th ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
A theoretical analysis of the development of numerical representations indicated that playing linear number board games should enhance preschoolers ’ numerical knowledge and ability to acquire new numerical knowledge. The effect on knowledge of numerical magnitudes was predicted to be larger when the game was played with a linear board than with a circular board because of a more direct mapping between the linear board and the desired mental representation. As predicted, playing the linear board game for roughly 1 hr increased lowincome preschoolers ’ proficiency on the 2 tasks that directly measured understanding of numerical magnitudes—numerical magnitude comparison and number line estimation—more than playing the game with a circular board or engaging in other numerical activities. Also as predicted, children who had played the linear number board game generated more correct answers and better quality errors in response to subsequent training on arithmetic problems, a task hypothesized to be influenced by knowledge of numerical magnitudes. Thus, playing linear number board games not only increases preschoolers ’ numerical knowledge but also helps them learn from future numerical experiences.
An evolutionary perspective on learning disability in mathematics
 Developmental Neuropsychology
"... A distinction between potentially evolved, or biologicallyprimary forms of cognition, and the culturallyspecific, or biologicallysecondary forms of cognition that are built from primary systems is used to explore mathematical learning disability (MLD). Using this model, MLD could result from defi ..."
Abstract

Cited by 6 (4 self)
 Add to MetaCart
A distinction between potentially evolved, or biologicallyprimary forms of cognition, and the culturallyspecific, or biologicallysecondary forms of cognition that are built from primary systems is used to explore mathematical learning disability (MLD). Using this model, MLD could result from deficits in the brain and cognitive systems that support biologicallyprimary mathematical competencies, or from the brain and cognitive systems that support the modification of primary systems for the creation of secondary knowledge and secondary cognitive competencies. The former include visuospatial longterm and working memory and the intraparietal sulcus, whereas the latter include the central executive component of working memory and the anterior cingulate cortex and lateral prefrontal cortex. Different forms of MLD are discussed as related to each of the cognitive and brain systems. When viewed from the lens of evolution and human cultural history, it is not a coincidence that public schools are a recent phenomenon and emerge only in societies in which technological, scientific, commercial (e.g., banking, interest) and other evolutionarilynovel advances influence one’s ability to function in the society (Geary, 2002, 2007). From this perspective, one goal of academic learning is to acquire knowledge that is important for social or occupational functioning in the culture in which schools are situated, and learning disabilities (LD) represent impediments to the learning of one or several aspects of this culturallyimportant knowledge. It terms of understanding the brain and cognitive systems that support academic learning and contribute to learning disabilities, evolutionary and historical perspectives may not be necessary, but may nonetheless provide a means to approach these issues from different levels of analysis. I illustrate this approach for
Origins of Mathematical Intuitions  The Case of Arithmetic
 THE YEAR IN COGNITIVE NEUROSCIENCE
, 2009
"... Mathematicians frequently evoke their “intuition” when they are able to quickly and automatically solve a problem, with little introspection into their insight. Cognitive neuroscience research shows that mathematical intuition is a valid concept that can be studied in the laboratory in reduced parad ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Mathematicians frequently evoke their “intuition” when they are able to quickly and automatically solve a problem, with little introspection into their insight. Cognitive neuroscience research shows that mathematical intuition is a valid concept that can be studied in the laboratory in reduced paradigms, and that relates to the availability of “core knowledge” associated with evolutionarily ancient and specialized cerebral subsystems. As an illustration, I discuss the case of elementary arithmetic. Intuitions of numbers and their elementary transformations by addition and subtraction are present in all human cultures. They relate to a brain system, located in the intraparietal sulcus of both hemispheres, which extracts numerosity of sets and, in educated adults, maps back and forth between numerical symbols and the corresponding quantities. This system is available to animal species and to preverbal human infants. Its neuronal organization is increasingly being uncovered, leading to a precise mathematical theory of how we perform tasks of number comparison or number naming. The next challenge will be to understand how education changes our core intuitions of number.
Representations of the magnitudes of fractions
 Journal of Experimental Psychology: Human Perception and Performance
, 2010
"... We tested whether adults can use integrated, analog, magnitude representations to compare the values of fractions. The only previous study on this question concluded that even college students cannot form such representations and instead compare fraction magnitudes by representing numerators and den ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
We tested whether adults can use integrated, analog, magnitude representations to compare the values of fractions. The only previous study on this question concluded that even college students cannot form such representations and instead compare fraction magnitudes by representing numerators and denominators as separate whole numbers. However, atypical characteristics of the presented fractions might have provoked the use of atypical comparison strategies in that study. In our 3 experiments, university and community college students compared more balanced sets of singledigit and multidigit fractions and consistently exhibited a logarithmic distance effect. Thus, adults used integrated, analog representations, akin to a mental number line, to compare fraction magnitudes. We interpret differences between the past and present findings in terms of different stimuli eliciting different solution strategies.
Straightening Up: Number Line Estimates Shift from Log to Linear with Additional Information
"... It has been suggested that a developmental logtolinear shift in children’s performance on number line estimation tasks is diagnostic of their underlying representations of numerical magnitude (Siegler & Opfer, 2003). However, in the study presented herein, we were able to induce a similar logtoli ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
It has been suggested that a developmental logtolinear shift in children’s performance on number line estimation tasks is diagnostic of their underlying representations of numerical magnitude (Siegler & Opfer, 2003). However, in the study presented herein, we were able to induce a similar logtolinear shift on number line estimation tasks among adults by manipulating their familiarity with the numbers we used as stimuli. We offer this evidence as an existence proof that differences in performance on number line estimation tasks may not necessarily be indicative of fundamental differences in the formats of people’s underlying numerical magnitude representations. Rather, they may be diagnostic of differences in people’s understandings of what magnitudes are represented by symbolic numbers.
Early math matters: kindergarten number competence and later mathematics outcomes
 Developmental Psychology
, 2009
"... Children’s number competencies over 6 time points, from the beginning of kindergarten to the middle of 1st grade, were examined in relation to their mathematics achievement over 5 later time points, from the end of 1st grade to the end of 3rd grade. The relation between early number competence and m ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Children’s number competencies over 6 time points, from the beginning of kindergarten to the middle of 1st grade, were examined in relation to their mathematics achievement over 5 later time points, from the end of 1st grade to the end of 3rd grade. The relation between early number competence and mathematics achievement was strong and significant throughout the study period. A sequential process growth curve model showed that kindergarten number competence predicted rate of growth in mathematics achievement between 1st and 3rd grades as well as achievement level through 3rd grade. Further, rate of growth in early number competence predicted mathematics performance level in 3rd grade. Although lowincome children performed more poorly than their middleincome counterparts in mathematics achievement and progressed at a slower rate, their performance and growth were mediated through relatively weak kindergarten number competence. Similarly, the better performance and faster growth of children who entered kindergarten at an older age were explained by kindergarten number competence. The findings show the importance of early number competence for setting children’s learning trajectories in elementary school mathematics.