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David C Geary - One of the best experts on this subject based on the ideXlab platform.
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preschool deficits in cardinal knowledge and executive function contribute to longer term Mathematical Learning disability
Journal of Experimental Child Psychology, 2019Co-Authors: Felicia W Chu, Mary K Hoard, Kristy Vanmarle, Lara Nugent, John E Scofield, David C GearyAbstract:Abstract In a preschool through first grade longitudinal study, we identified groups of children with persistently low mathematics achievement (n = 14) and children with low achievement in preschool but average achievement in first grade (n = 23). The preschool quantitative developments of these respective groups of children with Mathematical Learning disability (MLD) and recovered children and a group of typically achieving peers (n = 35) were contrasted, as were their intelligence, executive function, and parental education levels. The core characteristics of the children with MLD were poor executive function and delayed understanding of the cardinal value of number words throughout preschool. These compounded into even more substantive deficits in number and arithmetic at the beginning of first grade. The recovered group had poor executive function and cardinal knowledge during the first year of preschool but showed significant gains during the second year. Despite these gains and average mathematics achievement, the recovered children had subtle deficits with accessing magnitudes associated with numerals and addition combinations (e.g., 5 + 6 = ?) in first grade. The study provides unique insight into domain-general and quantitative deficits in preschool that increase risk for long-term Mathematical difficulties.
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insights from cognitive science on Mathematical Learning
2017Co-Authors: David C Geary, Daniel B Berch, Robert J Ochsendorf, Kathleen Mann KoepkeAbstract:Abstract Research in the cognitive sciences has yielded unique and critical insights into how the human mind represents, processes, and learns Mathematical concepts and procedures. The chapters throughout this volume illustrate these insights for complex arithmetic, rational numbers, algebra, geometry, and trigonometry. In this chapter, we review and discuss several basic themes, such as the importance of prior knowledge for Learning that cut across most or all of the other chapters, and highlight several challenges to translating these findings into instructional approaches and policies.
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fact retrieval deficits in low achieving children and children with Mathematical Learning disability
Journal of Learning Disabilities, 2012Co-Authors: David C Geary, Mary K Hoard, Drew H BaileyAbstract:Using 4 years of mathematics achievement scores, groups of typically achieving children (n = 101) and low achieving children with mild (LA-mild fact retrieval; n = 97) and severe (LA-severe fact retrieval; n = 18) fact retrieval deficits and Mathematically Learning disabled children (MLD; n = 15) were identified. Multilevel models contrasted developing retrieval competence from second to fourth grade with developing competence in executing arithmetic procedures, in fluency of processing quantities represented by Arabic numerals and sets of objects, and in representing quantity on a number line. The retrieval deficits of LA-severe fact retrieval children were at least as debilitating as those of the children with MLD and showed less across-grade improvement. The deficits were characterized by the retrieval of counting string associates while attempting to remember addition facts, suggesting poor inhibition of irrelevant information during the retrieval process. This suggests a very specific form of working memory deficit, one that is not captured by many typically used working memory tasks. Moreover, these deficits were not related to procedural competence or performance on the other Mathematical tasks, nor were they related to verbal or nonverbal intelligence, reading ability, or speed of processing, nor would they be identifiable with standard untimed mathematics achievement tests.
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Consequences, characteristics, and causes of Mathematical Learning disabilities and persistent low achievement in mathematics
Journal of Developmental and Behavioral Pediatrics, 2011Co-Authors: David C GearyAbstract:The goals of the review are threefold: (a) to highlight the educational and employment conse- quences of poorly developed Mathematical competencies; (b) overview the characteristics of children with Mathematical Learning disability (MLD) and with persistently low achievement (LA) in mathematics; and (c) provide a primer on cognitive science research that is aimed at identifying the cognitive mechanisms under- lying these Learning disabilities and associated cognitive interventions. Literatures on the educational and economic consequences of poor mathematics achievement were reviewed and integrated with reviews of epidemiological, behavioral genetic, and cognitive science studies of poor mathematics achievement. Poor Mathematical competencies are common among adults and result in employment difficulties and difficulties in many common day-to-day activities. Among students, ?7% of children and adolescents have MLD and another 10% show persistent LA in mathematics, despite average abilities in most other areas. Children with MLD and their LA peers have deficits in understanding and representing numerical magnitude, difficulties retrieving basic arithmetic facts from long-term memory, and delays in Learning Mathematical procedures. These deficits and delays cannot be attributed to intelligence but are related to working memory deficits for children with MLD, but not LA children. These individuals have identifiable number and memory delays and deficits that seem to be specific to mathematics Learning. Interventions that target these cognitive deficits are in development and preliminary results are promising
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predicting Mathematical achievement and Mathematical Learning disability with a simple screening tool the number sets test
Journal of Psychoeducational Assessment, 2009Co-Authors: David C Geary, Drew H Bailey, Mary K HoardAbstract:The Number Sets Test was developed to assess the speed and accuracy with which children can identify and process quantities represented by Arabic numerals and object sets. The utility of this test for predicting mathematics achievement and risk for Mathematical Learning dis- ability (MLD) was assessed for a sample of 223 children. A signal detection analysis of first grade Number Sets Test scores provided measures of children's sensitivity to number and their response bias. The sensitivity measure, d´, but not the response bias measure was predictive of third grade mathematics achievement scores, above and beyond the influence of intelligence, working memory, and first grade achievement scores. Further analyses assessed the sensitivity and specificity of the test and revealed that first grade dscores identified 2 out of 3 children diagnosed as MLD in third grade and correctly identified about 9 out of 10 children who were not at risk for MLD.
Michele M M Mazzocco - One of the best experts on this subject based on the ideXlab platform.
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impaired acuity of the approximate number system underlies Mathematical Learning disability dyscalculia
Child Development, 2011Co-Authors: Michele M M Mazzocco, Lisa Feigenson, Justin HalberdaAbstract:Many children have significant Mathematical Learning disabilities (MLD, or dyscalculia) despite adequate schooling. The current study hypothesizes that MLD partly results from a deficiency in the Approximate Number System (ANS) that supports nonverbal numerical representations across species and throughout development. In this study of 71 ninth graders, it is shown that students with MLD have significantly poorer ANS precision than students in all other mathematics achievement groups (low, typically, and high achieving), as measured by psychophysical assessments of ANS acuity (w) and of the mappings between ANS representations and number words (cv). This relation persists even when controlling for domain-general abilities. Furthermore, this ANS precision does not differentiate low-achieving from typically achieving students, suggesting an ANS deficit that is specific to MLD.
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parts and holes gaps in rational number sense among children with vs without Mathematical Learning disabilities
Developmental Science, 2008Co-Authors: Michele M M Mazzocco, Kathleen T DevlinAbstract:Many middle-school students struggle with decimals and fractions, even if they do not have a Mathematical Learning disability (MLD). In the present longitudinal study, we examined whether children with MLD have weaker rational number knowledge than children whose difficulty with rational numbers occurs in the absence of MLD. We found that children with MLD failed to accurately name decimals, to correctly rank order decimals and/or fractions, and to identify equivalent ratios (e.g. 0.5 = 1/2); they also 'identified' incorrect equivalents (e.g. 0.05 = 0.50). Children with low math achievement but no MLD accurately named decimals and identified equivalent pairs, but failed to correctly rank order decimals and fractions. Thus failure to accurately name decimals was an indicator of MLD; but accurate naming was no guarantee of rational number knowledge - most children who failed to correctly rank order fractions and decimals tests passed the naming task. Most children who failed the ranking tests at 6th grade also failed at 8th grade. Our findings suggest that a simple task involving naming and rank ordering fractions and decimals may be a useful addition to in-class assessments used to determine children's Learning of rational numbers.
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is it a fact timed arithmetic performance of children with Mathematical Learning disabilities mld varies as a function of how mld is defined
Developmental Neuropsychology, 2008Co-Authors: Michele M M Mazzocco, Kathleen T Devlin, Sarah J MckenneyAbstract:Poor fact retrieval is a frequently reported characteristic of children with Mathematical Learning disability (MLD). To better understand the nature and specificity of poor fact retrieval in MLD, in the present study, we examined eighth graders' accuracy on timed addition and multiplication problems of varying levels of difficulty. We compared the performance of 16 children with deficient math achievement (MLD), 19 children with below average (but not deficient) math achievement (LA), and 100 typically achieving (TA) children. Children in all three groups made errors. Errors made by children in the LA group were more numerous, but comparable in type, to those observed for typically developing children. Errors made by children with MLD were more numerous still, and included errors that differ qualitatively from those in the LA and TA groups. Thus the way in which performance linked to “math difficulties” differs from that of typically achieving children varies as a function of how we define math disabiliti...
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is it a fact timed arithmetic performance of children with Mathematical Learning disabilities mld varies as a function of how mld is defined
Developmental Neuropsychology, 2008Co-Authors: Michele M M Mazzocco, Kathleen T Devlin, Sarah J MckenneyAbstract:Poor fact retrieval is a frequently reported characteristic of children with Mathematical Learning disability (MLD). To better understand the nature and specificity of poor fact retrieval in MLD, in the present study, we examined eighth graders' accuracy on timed addition and multiplication problems of varying levels of difficulty. We compared the performance of 16 children with deficient math achievement (MLD), 19 children with below average (but not deficient) math achievement (LA), and 100 typically achieving (TA) children. Children in all three groups made errors. Errors made by children in the LA group were more numerous, but comparable in type, to those observed for typically developing children. Errors made by children with MLD were more numerous still, and included errors that differ qualitatively from those in the LA and TA groups. Thus the way in which performance linked to "math difficulties" differs from that of typically achieving children varies as a function of how we define math disabilities (MLD vs. LA). Moreover, the frequency and types of errors made by individuals varied within the MLD group, highlighting group heterogeneity even when using strict criteria to define this group of children. Finally, the types of errors made by children with MLD reflect reliance on processes other than retrieval to solve these alleged "math facts."
Sarah J Mckenney - One of the best experts on this subject based on the ideXlab platform.
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is it a fact timed arithmetic performance of children with Mathematical Learning disabilities mld varies as a function of how mld is defined
Developmental Neuropsychology, 2008Co-Authors: Michele M M Mazzocco, Kathleen T Devlin, Sarah J MckenneyAbstract:Poor fact retrieval is a frequently reported characteristic of children with Mathematical Learning disability (MLD). To better understand the nature and specificity of poor fact retrieval in MLD, in the present study, we examined eighth graders' accuracy on timed addition and multiplication problems of varying levels of difficulty. We compared the performance of 16 children with deficient math achievement (MLD), 19 children with below average (but not deficient) math achievement (LA), and 100 typically achieving (TA) children. Children in all three groups made errors. Errors made by children in the LA group were more numerous, but comparable in type, to those observed for typically developing children. Errors made by children with MLD were more numerous still, and included errors that differ qualitatively from those in the LA and TA groups. Thus the way in which performance linked to “math difficulties” differs from that of typically achieving children varies as a function of how we define math disabiliti...
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is it a fact timed arithmetic performance of children with Mathematical Learning disabilities mld varies as a function of how mld is defined
Developmental Neuropsychology, 2008Co-Authors: Michele M M Mazzocco, Kathleen T Devlin, Sarah J MckenneyAbstract:Poor fact retrieval is a frequently reported characteristic of children with Mathematical Learning disability (MLD). To better understand the nature and specificity of poor fact retrieval in MLD, in the present study, we examined eighth graders' accuracy on timed addition and multiplication problems of varying levels of difficulty. We compared the performance of 16 children with deficient math achievement (MLD), 19 children with below average (but not deficient) math achievement (LA), and 100 typically achieving (TA) children. Children in all three groups made errors. Errors made by children in the LA group were more numerous, but comparable in type, to those observed for typically developing children. Errors made by children with MLD were more numerous still, and included errors that differ qualitatively from those in the LA and TA groups. Thus the way in which performance linked to "math difficulties" differs from that of typically achieving children varies as a function of how we define math disabilities (MLD vs. LA). Moreover, the frequency and types of errors made by individuals varied within the MLD group, highlighting group heterogeneity even when using strict criteria to define this group of children. Finally, the types of errors made by children with MLD reflect reliance on processes other than retrieval to solve these alleged "math facts."
Kathleen T Devlin - One of the best experts on this subject based on the ideXlab platform.
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parts and holes gaps in rational number sense among children with vs without Mathematical Learning disabilities
Developmental Science, 2008Co-Authors: Michele M M Mazzocco, Kathleen T DevlinAbstract:Many middle-school students struggle with decimals and fractions, even if they do not have a Mathematical Learning disability (MLD). In the present longitudinal study, we examined whether children with MLD have weaker rational number knowledge than children whose difficulty with rational numbers occurs in the absence of MLD. We found that children with MLD failed to accurately name decimals, to correctly rank order decimals and/or fractions, and to identify equivalent ratios (e.g. 0.5 = 1/2); they also 'identified' incorrect equivalents (e.g. 0.05 = 0.50). Children with low math achievement but no MLD accurately named decimals and identified equivalent pairs, but failed to correctly rank order decimals and fractions. Thus failure to accurately name decimals was an indicator of MLD; but accurate naming was no guarantee of rational number knowledge - most children who failed to correctly rank order fractions and decimals tests passed the naming task. Most children who failed the ranking tests at 6th grade also failed at 8th grade. Our findings suggest that a simple task involving naming and rank ordering fractions and decimals may be a useful addition to in-class assessments used to determine children's Learning of rational numbers.
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is it a fact timed arithmetic performance of children with Mathematical Learning disabilities mld varies as a function of how mld is defined
Developmental Neuropsychology, 2008Co-Authors: Michele M M Mazzocco, Kathleen T Devlin, Sarah J MckenneyAbstract:Poor fact retrieval is a frequently reported characteristic of children with Mathematical Learning disability (MLD). To better understand the nature and specificity of poor fact retrieval in MLD, in the present study, we examined eighth graders' accuracy on timed addition and multiplication problems of varying levels of difficulty. We compared the performance of 16 children with deficient math achievement (MLD), 19 children with below average (but not deficient) math achievement (LA), and 100 typically achieving (TA) children. Children in all three groups made errors. Errors made by children in the LA group were more numerous, but comparable in type, to those observed for typically developing children. Errors made by children with MLD were more numerous still, and included errors that differ qualitatively from those in the LA and TA groups. Thus the way in which performance linked to “math difficulties” differs from that of typically achieving children varies as a function of how we define math disabiliti...
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is it a fact timed arithmetic performance of children with Mathematical Learning disabilities mld varies as a function of how mld is defined
Developmental Neuropsychology, 2008Co-Authors: Michele M M Mazzocco, Kathleen T Devlin, Sarah J MckenneyAbstract:Poor fact retrieval is a frequently reported characteristic of children with Mathematical Learning disability (MLD). To better understand the nature and specificity of poor fact retrieval in MLD, in the present study, we examined eighth graders' accuracy on timed addition and multiplication problems of varying levels of difficulty. We compared the performance of 16 children with deficient math achievement (MLD), 19 children with below average (but not deficient) math achievement (LA), and 100 typically achieving (TA) children. Children in all three groups made errors. Errors made by children in the LA group were more numerous, but comparable in type, to those observed for typically developing children. Errors made by children with MLD were more numerous still, and included errors that differ qualitatively from those in the LA and TA groups. Thus the way in which performance linked to "math difficulties" differs from that of typically achieving children varies as a function of how we define math disabilities (MLD vs. LA). Moreover, the frequency and types of errors made by individuals varied within the MLD group, highlighting group heterogeneity even when using strict criteria to define this group of children. Finally, the types of errors made by children with MLD reflect reliance on processes other than retrieval to solve these alleged "math facts."
Mary K Hoard - One of the best experts on this subject based on the ideXlab platform.
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preschool deficits in cardinal knowledge and executive function contribute to longer term Mathematical Learning disability
Journal of Experimental Child Psychology, 2019Co-Authors: Felicia W Chu, Mary K Hoard, Kristy Vanmarle, Lara Nugent, John E Scofield, David C GearyAbstract:Abstract In a preschool through first grade longitudinal study, we identified groups of children with persistently low mathematics achievement (n = 14) and children with low achievement in preschool but average achievement in first grade (n = 23). The preschool quantitative developments of these respective groups of children with Mathematical Learning disability (MLD) and recovered children and a group of typically achieving peers (n = 35) were contrasted, as were their intelligence, executive function, and parental education levels. The core characteristics of the children with MLD were poor executive function and delayed understanding of the cardinal value of number words throughout preschool. These compounded into even more substantive deficits in number and arithmetic at the beginning of first grade. The recovered group had poor executive function and cardinal knowledge during the first year of preschool but showed significant gains during the second year. Despite these gains and average mathematics achievement, the recovered children had subtle deficits with accessing magnitudes associated with numerals and addition combinations (e.g., 5 + 6 = ?) in first grade. The study provides unique insight into domain-general and quantitative deficits in preschool that increase risk for long-term Mathematical difficulties.
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fact retrieval deficits in low achieving children and children with Mathematical Learning disability
Journal of Learning Disabilities, 2012Co-Authors: David C Geary, Mary K Hoard, Drew H BaileyAbstract:Using 4 years of mathematics achievement scores, groups of typically achieving children (n = 101) and low achieving children with mild (LA-mild fact retrieval; n = 97) and severe (LA-severe fact retrieval; n = 18) fact retrieval deficits and Mathematically Learning disabled children (MLD; n = 15) were identified. Multilevel models contrasted developing retrieval competence from second to fourth grade with developing competence in executing arithmetic procedures, in fluency of processing quantities represented by Arabic numerals and sets of objects, and in representing quantity on a number line. The retrieval deficits of LA-severe fact retrieval children were at least as debilitating as those of the children with MLD and showed less across-grade improvement. The deficits were characterized by the retrieval of counting string associates while attempting to remember addition facts, suggesting poor inhibition of irrelevant information during the retrieval process. This suggests a very specific form of working memory deficit, one that is not captured by many typically used working memory tasks. Moreover, these deficits were not related to procedural competence or performance on the other Mathematical tasks, nor were they related to verbal or nonverbal intelligence, reading ability, or speed of processing, nor would they be identifiable with standard untimed mathematics achievement tests.
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predicting Mathematical achievement and Mathematical Learning disability with a simple screening tool the number sets test
Journal of Psychoeducational Assessment, 2009Co-Authors: David C Geary, Drew H Bailey, Mary K HoardAbstract:The Number Sets Test was developed to assess the speed and accuracy with which children can identify and process quantities represented by Arabic numerals and object sets. The utility of this test for predicting mathematics achievement and risk for Mathematical Learning dis- ability (MLD) was assessed for a sample of 223 children. A signal detection analysis of first grade Number Sets Test scores provided measures of children's sensitivity to number and their response bias. The sensitivity measure, d´, but not the response bias measure was predictive of third grade mathematics achievement scores, above and beyond the influence of intelligence, working memory, and first grade achievement scores. Further analyses assessed the sensitivity and specificity of the test and revealed that first grade dscores identified 2 out of 3 children diagnosed as MLD in third grade and correctly identified about 9 out of 10 children who were not at risk for MLD.
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first grade predictors of Mathematical Learning disability a latent class trajectory analysis
Cognitive Development, 2009Co-Authors: David C Geary, Drew H Bailey, Mary K Hoard, Andrew K Littlefield, Phillip K Wood, Lara NugentAbstract:Kindergarten to third grade mathematics achievement scores from a prospective study of Mathematical development (n = 306) were subjected to latent growth trajectory analyses. The four corresponding classes included children with Mathematical Learning disability (MLD, 6% of sample), and low (LA, 50%), typically (TA, 39%) and high (HA, 5%) achieving children. The groups were administered a battery of intelligence (IQ), working memory, and Mathematical-cognition measures in first grade. The children with MLD had general deficits in working memory and IQ and potentially more specific deficits on measures of number sense. The LA children did not have working memory or IQ deficits but showed moderate deficits on these number sense measures and for addition fact retrieval. The distinguishing features of the HA children were a strong visuospatial working memory, a strong number sense, and frequent use of memory-based processes to solve addition problems. Implications for the early identification of children at risk for poor mathematics achievement are considered.
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development of number line representations in children with Mathematical Learning disability
Developmental Neuropsychology, 2008Co-Authors: David C Geary, Mary K Hoard, Lara Nugent, Jennifer ByrdcravenAbstract:Children with a Mathematical Learning disability (MLD, n = 19) and low achieving (LA, n = 43) children were identified using mathematics achievement scores below the 11th percentile and between the 11th and 25th percentiles, respectively. A control group of typically achieving (TA, n = 50) children was also identified. Number line and speed of processing tasks were administered in 1st and 2nd grade and a working memory battery in 1st grade. In both grades, the MLD children were less accurate in their number line placements and more reliant on a natural number-magnitude representational system to make these placements than were TA children. The TA children were more reliant on the school-taught linear system in both grades. The performance of the LA children was similar to that of the MLD children in first grade and to the TA children in second. The central executive component of working memory contributed to across-grade improvements in number line performance and to group differences in this performance.