Early Development of Quantity to Number-Word Linkage as a Precursor of Mathematical School Achievement and Mathematical Difficulties: Findings from a Four-Year Longitudinal Study.

Abstract This article reports results of a four-year longitudinal study that investigated the impact of specific and non-specific precursors on mathematical school achievement. Preschool quantity-number competencies (QNC) predicted mathematical achievement in primary school. Furthermore, basic arithmetic fact retrieval in Grade 1 had an impact on early mathematics school achievement. The influence of socioeconomic status and number naming speed, assessed in kindergarten, became especially important at the end of Grade 4. Particularly, a subgroup of mathematically low-achieving children in Grade 4 had already performed more poorly than normal children in tasks assessing preschool QNC, number naming speed, and basic arithmetic fact retrieval, as well as nonverbal intelligence and socioeconomic status.

[1]  Karen Wynn,et al.  Children's understanding of counting , 1990, Cognition.

[2]  M. Passolunghi,et al.  The precursors of mathematics learning: Working memory, phonological ability and numerical competence. , 2007 .

[3]  W. Schneider,et al.  Individual development from 3 to 12: Findings from the Munich Longitudinal Study. , 1999 .

[4]  D. Geary Mathematical disabilities: cognitive, neuropsychological, and genetic components. , 1993, Psychological bulletin.

[5]  P. Starkey,et al.  Perception of numbers by human infants. , 1980, Science.

[6]  Christof Zoelch,et al.  Defizite numerischer Basiskompetenzen bei rechenschwachen Kindern der 3. und 4. Klassenstufe , 2004 .

[7]  Mary K. Hoard,et al.  Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. , 2004, Journal of experimental child psychology.

[8]  H. Swanson Cognitive processes that underlie mathematical precociousness in young children. , 2006, Journal of experimental child psychology.

[9]  R. Wagner,et al.  The relations between phonological processing abilities and emerging individual differences in mathematical computation skills: a longitudinal study from second to fifth grades. , 2001, Journal of experimental child psychology.

[10]  Derek H Berg,et al.  Working memory and arithmetic calculation in children: the contributory roles of processing speed, short-term memory, and reading. , 2008, Journal of experimental child psychology.

[11]  U. Goswami,et al.  Picture Naming Deficits in Developmental Dyslexia: The Phonological Representations Hypothesis , 1997, Brain and Language.

[12]  B. Butterworth The development of arithmetical abilities. , 2005, Journal of child psychology and psychiatry, and allied disciplines.

[13]  David C. Geary,et al.  Numerical and arithmetical deficits in learning-disabled children: Relation to dyscalculia and dyslexia , 2001, Aphasiology.

[14]  Kelly S. Mix,et al.  Amount Versus Number: Infants' Use of Area and Contour Length to Discriminate Small Sets , 2001 .

[15]  K. McGilly,et al.  Classroom lessons: Integrating cognitive theory and classroom practice. , 1994 .

[16]  Julie E. Dockrell,et al.  Children's developing numerical notations: The impact of input display, numerical size and operational complexity , 2005 .

[17]  R H Logie,et al.  Counting on working memory in arithmetic problem solving , 1994, Memory & cognition.

[18]  Kelly S. Mix,et al.  Do preschool children recognize auditory-visual numerical correspondences? , 1996, Child development.

[19]  Wolfgang Schneider,et al.  Relations of Television Viewing and Reading: Findings From a 4-Year Longitudinal Study , 2007 .

[20]  Kelly S. Mix,et al.  Numerical abstraction in infants: another look. , 1997, Developmental psychology.

[21]  K. Aunola,et al.  Developmental Dynamics of Math Performance From Preschool to Grade 2 , 2004 .

[22]  Alan D. Baddeley,et al.  Reading and Working Memory. , 1982 .

[23]  Patrick Lemaire,et al.  The Role of Working Memory Resources in Simple Cognitive Arithmetic , 1996 .

[24]  Stanislas Dehaene,et al.  Approximate quantities and exact number words: dissociable systems , 2003, Neuropsychologia.

[25]  M. Wolf,et al.  Naming, reading, and the dyslexias: A longitudinal overview , 1984, Annals of dyslexia.

[26]  Nancy C. Jordan,et al.  Number sense growth in kindergarten: a longitudinal investigation of children at risk for mathematics difficulties. , 2006, Child development.

[27]  K. Fuson Children's Counting and Concepts of Number , 1987 .

[28]  J. Piaget The Child's Conception of Number , 1953 .

[29]  E. Spelke,et al.  Infants' Discrimination of Number vs. Continuous Extent , 2002, Cognitive Psychology.

[30]  K. Stanovich Matthew effects in reading: Some consequences of individual differences in the acquisition of literacy. , 1986 .

[31]  Karen Wynn,et al.  Addition and subtraction by human infants , 1992, Nature.

[32]  S. Dehaene Varieties of numerical abilities , 1992, Cognition.

[33]  A. Gagatsis,et al.  The Effects of Different Modes of Representation on the Solution of One-Step Additive Problems. , 2007 .

[34]  D. Geary,et al.  Role of Cognitive Theory in the Study of Learning Disability in Mathematics , 2005, Journal of learning disabilities.

[35]  Elsbeth Stern Development of mathematical competencies , 1999 .

[36]  R. Hoyle Structural equation modeling: concepts, issues, and applications , 1997 .

[37]  Marie-Pascale Noël,et al.  Magnitude comparison in preschoolers: what counts? Influence of perceptual variables. , 2004, Journal of experimental child psychology.

[38]  Early training: who, what, when, why, and how? , 1997 .

[39]  Fei Xu,et al.  Number sense in human infants. , 2005, Developmental science.

[40]  Mary K. Hoard,et al.  Numerical and arithmetical cognition: a longitudinal study of process and concept deficits in children with learning disability. , 2000, Journal of experimental child psychology.

[41]  Y Okamoto,et al.  Exploring the microstructure of children's central conceptual structures in the domain of number. , 2008, Monographs of the Society for Research in Child Development.

[42]  Gundel Schümer,et al.  Familiäre Lebensverhältnisse, Bildungsbeteiligung und Kompetenzerwerb , 2001 .

[43]  Ulf Andersson,et al.  Working memory deficit in children with mathematical difficulties: a general or specific deficit? , 2007, Journal of experimental child psychology.

[44]  W. Schneider,et al.  Impact of early phonological processing skills on reading and spelling in school: Evidence from the Munich longitudinal study , 1999 .

[45]  Kelly S. Mix,et al.  Number Versus Contour Length in Infants' Discrimination of Small Visual Sets , 1999 .

[46]  L. Siegel,et al.  Working memory and access to numerical information in children with disability in mathematics. , 2004, Journal of experimental child psychology.

[47]  David C. Geary,et al.  Cognitive addition: A short longitudinal study of strategy choice and speed-of-processing differences in normal and mathematically disabled children. , 1991 .

[48]  Robert S. Siegler,et al.  Rightstart: Providing the central conceptual prerequisites for first formal learning of arithmetic to students at risk for school failure. , 1994 .

[49]  T. Ahonen,et al.  Cognitive predictors of single-digit and procedural calculation skills and their covariation with reading skill. , 2007, Journal of experimental child psychology.

[50]  Lauren B. Resnick,et al.  Developing mathematical knowledge. , 1989 .

[51]  Nancy C. Jordan,et al.  A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties. , 2003, Child development.

[52]  John R. Beech,et al.  Cognitive approaches to reading , 1987 .

[53]  Detlev Leutner,et al.  PISA 2003: Der Bildungsstand der Jugendlichen in Deutschland - Ergebnisse des zweiten internationalen Vergleichs , 2004 .

[54]  L. Verschaffel,et al.  Strategic Aspects of Simple Addition and Subtraction: The Influence of Mathematical Ability. , 2004 .

[55]  H. Lee Swanson,et al.  Working Memory, Short-Term Memory, and Speech Rate as Predictors of Children's Reading Performance at Different Ages. , 2001 .

[56]  Chaitanya Ramineni,et al.  Predicting First–Grade Math Achievement from Developmental Number Sense Trajectories , 2007 .

[57]  Susan J. Hespos,et al.  Do infants understand simple arithmetic? A replication of Wynn (1992) ☆ , 1995 .

[58]  H. Swanson,et al.  The Relationship Between Working Memory and Mathematical Problem Solving in Children at Risk and Not at Risk for Serious Math Difficulties , 2004 .

[59]  André Vandierendonck,et al.  Verifying simple arithmetic sums and products: Are the phonological loop and the central executive involved? , 2001, Memory & cognition.

[60]  E. Cannon,et al.  Preschoolers' Magnitude Comparisons are Mediated by a Preverbal Analog Mechanism , 2000, Psychological science.

[61]  Erno Lehtinen,et al.  Spontaneous Focusing on Numerosity and Mathematical Skills of Young Children. , 2005 .

[62]  Mary K. Hoard,et al.  Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. , 2007, Child development.

[63]  Jacques Mehler,et al.  How do 4-day-old infants categorize multisyllabic utterances? , 1993 .

[64]  S E Antell,et al.  Perception of numerical invariance in neonates. , 1983, Child development.

[65]  S. Graham,et al.  Improving the Mathematical Problem-Solving Skills of Students with Learning Disabilities , 1992 .

[66]  Robert S. Siegler,et al.  How Children Develop , 2002 .

[67]  D. Geary,et al.  Counting Knowledge and Skill in Cognitive Addition: a Comparison of Normal and Mathematically Disabled Children , 2022 .

[68]  Brian Butterworth,et al.  Developmental dyscalculia and basic numerical capacities: a study of 8–9-year-old students , 2004, Cognition.

[69]  Russell Gersten,et al.  Early Identification and Interventions for Students With Mathematics Difficulties , 2005, Journal of learning disabilities.