Socioeconomic variation, number competence, and mathematics learning difficulties in young children.

As a group, children from disadvantaged, low-income families perform substantially worse in mathematics than their counterparts from higher-income families. Minority children are disproportionately represented in low-income populations, resulting in significant racial and social-class disparities in mathematics learning linked to diminished learning opportunities. The consequences of poor mathematics achievement are serious for daily functioning and for career advancement. This article provides an overview of children's mathematics difficulties in relation to socioeconomic status (SES). We review foundations for early mathematics learning and key characteristics of mathematics learning difficulties. A particular focus is the delays or deficiencies in number competencies exhibited by low-income children entering school. Weaknesses in number competence can be reliably identified in early childhood, and there is good evidence that most children have the capacity to develop number competence that lays the foundation for later learning.

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

[2]  S. Lubienski,et al.  A Clash of Social Class Cultures? Students' Experiences in a Discussion-Intensive Seventh-Grade Mathematics Classroom , 2000, The Elementary School Journal.

[3]  D. Geary,et al.  Reflections of evolution and culture in children's cognition. Implications for mathematical development and instruction. , 1995, The American psychologist.

[4]  H. Ginsburg,et al.  SES, ethnic, and gender differences in young children's informal addition and subtraction: A clinical interview investigation , 2004 .

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

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

[7]  Nancy C. Jordan,et al.  Early math matters: kindergarten number competence and later mathematics outcomes. , 2009, Developmental psychology.

[8]  Lisa Feigenson,et al.  Tracking individuals via object-files: evidence from infants' manual search , 2003 .

[9]  Julie Sarama,et al.  Experimental Evaluation of the Effects of a Research-Based Preschool Mathematics Curriculum , 2008 .

[10]  Ted S. Hasselbring,et al.  Developing Math Automaticity in Learning Handicapped Children: The Role of Computerized Drill and Practice. , 1988 .

[11]  A. Karmiloff-Smith Development itself is the key to understanding developmental disorders , 1998, Trends in Cognitive Sciences.

[12]  E. Spelke,et al.  Large number discrimination in 6-month-old infants , 2000, Cognition.

[13]  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.

[14]  Snorre A. Ostad,et al.  Developmental Differences in Solving Simple Arithmetic Word Problems and Simple Number-fact Problems: A Comparison of Mathematically Normal and Mathematically Disabled Children , 1998 .

[15]  Geoffrey B. Saxe,et al.  Social processes in early number development. , 1987 .

[16]  J. Sarama,et al.  Young Children's Concepts of Shape. , 1999 .

[17]  Kelly S. Mix,et al.  The Development of Young Children’s Early Number and Operation Sense and its Implications for Early Childhood Education , 2006 .

[18]  J. Hiebert Conceptual and procedural knowledge : the case of mathematics , 1987 .

[19]  Janellen Huttenlocher,et al.  Preschool children's mathematical knowledge: The effect of teacher "math talk.". , 2006, Developmental psychology.

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

[21]  Nancy C. Jordan,et al.  Using Kindergarten Number Sense to Predict Calculation Fluency in Second Grade , 2008, Journal of learning disabilities.

[22]  A. Lillard,et al.  The early years. Evaluating Montessori education. , 2006, Science.

[23]  B. Fuller,et al.  What is “appropriate practice” at home and in child care?: Low-income mothers' views on preparing their children for school☆ , 1995 .

[24]  Susan C. Levine,et al.  Assessing early arithmetic abilities: Effects of verbal and nonverbal response types on the calculation performance of middle-and low-income children , 1994 .

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

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

[27]  L. Resnick,et al.  Psychology of Mathematics for Instruction , 1981 .

[28]  A. Lillard,et al.  Evaluating Montessori Education , 2006, Science.

[29]  David C. Geary,et al.  External validation of the strategy choice model for addition , 1989 .

[30]  Daniel B. Berch,et al.  Making Sense of Number Sense , 2005, Journal of learning disabilities.

[31]  D. Geary,et al.  A componential analysis of an early learning deficit in mathematics. , 1990, Journal of experimental child psychology.

[32]  M. Fanselow,et al.  The startled seahorse: is the hippocampus necessary for contextual fear conditioning? , 1998, Trends in Cognitive Sciences.

[33]  N. Jordan,et al.  A mental model for early arithmetic. , 1994, Journal of experimental psychology. General.

[34]  Richard E Thompson,et al.  Kindergarten Predictors of Math Learning Disability , 2005, Learning disabilities research & practice : a publication of the Division for Learning Disabilities, Council for Exceptional Children.

[35]  Nancy C. Jordan,et al.  Cognitive Arithmetic and Problem Solving , 1997, Journal of learning disabilities.

[36]  S. Griffin,et al.  Building number sense with Number Worlds: a mathematics program for young children , 2004 .

[37]  Chaitanya Ramineni,et al.  Development of number combination skill in the early school years: when do fingers help? , 2008, Developmental science.

[38]  Brian Butterworth,et al.  Information processing deficits in dyscalculia. , 2007 .

[39]  C. Hirsch Curriculum and Evaluation Standards for School Mathematics , 1988 .

[40]  Nancy C. Jordan,et al.  Performance across different areas of mathematical cognition in children with learning difficulties. , 2001 .

[41]  Robert S. Siegler,et al.  A featural analysis of preschoolers' counting knowledge. , 1984 .

[42]  Nancy C. Jordan,et al.  Development of calculation abilities in young children. , 1992, Journal of experimental child psychology.

[43]  Benson Schaeffer,et al.  Number development in young children , 1974 .

[44]  E. Spelke,et al.  Language and Conceptual Development series Core systems of number , 2004 .

[45]  Julie L. Booth,et al.  Development of numerical estimation in young children. , 2004, Child development.

[46]  Herbert P. Ginsburg,et al.  Social Class and Racial Influences on Early Mathematical Thinking. , 1981 .

[47]  Arthur J. Baroody,et al.  The development of preschoolers' counting skills and principles. , 1992 .

[48]  S. Carey,et al.  How counting represents number: What children must learn and when they learn it , 2008, Cognition.

[49]  Geetha B. Ramani,et al.  Playing linear numerical board games promotes low-income children's numerical development. , 2008, Developmental science.

[50]  Susan C. Levine,et al.  Differential calculation abilities in young children from middle- and low-income families. , 1992 .

[51]  Herbert P. Ginsburg,et al.  Cognitive Analysis of Children's Mathematics Difficulties , 1984 .

[52]  S R Goldman,et al.  Information Processing and Educational Microcomputer Technology , 1987, Journal of learning disabilities.

[53]  Jeanne D. Day,et al.  Construction and Evaluation of a Number Sense Test With Head Start Children. , 2004 .

[54]  Kelly S. Mix,et al.  Multiple cues for quantification in infancy: is number one of them? , 2002, Psychological bulletin.

[55]  J. Bisanz,et al.  Preschoolers doing arithmetic: the concepts are willing but the working memory is weak. , 2000, Canadian journal of experimental psychology = Revue canadienne de psychologie experimentale.

[56]  Sara Cordes,et al.  The relative salience of discrete and continuous quantity in young infants. , 2009, Developmental science.

[57]  R. Siegler,et al.  The Development of Numerical Estimation , 2003, Psychological science.

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

[59]  E. Brannon,et al.  Quantitative competencies in infancy. , 2008, Developmental science.

[60]  Arthur J. Baroody,et al.  The Role of the Number-After Rule in the Invention of Computational Shortcuts , 1995 .

[61]  J. Sarama,et al.  Early Childhood Mathematics Education Research: Learning Trajectories for Young Children , 2009 .

[62]  Julie L. Booth,et al.  Numerical magnitude representations influence arithmetic learning. , 2008, Child development.

[63]  Susan Carey,et al.  One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles , 2007, Cognition.

[64]  N. Vaidya,et al.  Science Teaching for the 21st Century , 2002 .

[65]  Arthur J. Baroody,et al.  The Development of Counting Strategies for Single-Digit Addition. , 1987 .

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

[67]  O. Svenson,et al.  Evolution of cognitive processes for solving simple additions during the first three school years , 1983 .

[68]  Susan C. Levine,et al.  Quantitative Development in Infancy and Early Childhood , 2002 .

[69]  James M. Royer,et al.  Influences of gender, ethnicity, and motivation on mathematical performance. , 2007 .

[70]  Arthur J. Baroody,et al.  Children's Relational Knowledge of Addition and Subtraction , 1999 .

[71]  Robert S. Siegler,et al.  The relation between conceptual and procedural knowledge in learning mathematics: A review , 2021, The Development of Mathematical Skills.

[72]  C. Gallistel,et al.  The Child's Understanding of Number , 1979 .

[73]  Robbie Case,et al.  Child cognitive development: The role of central conceptual structures in the development of scientific and social thought. , 1990 .

[74]  Nancy C. Jordan,et al.  Development of calculation abilities in middle- and low-income children after formal instruction in school☆ , 1994 .

[75]  S. Dehaene,et al.  The Number Sense: How the Mind Creates Mathematics. , 1998 .

[76]  S. Dehaene,et al.  Exact and Approximate Arithmetic in an Amazonian Indigene Group , 2004, Science.

[77]  D. Geary Mathematics and Learning Disabilities , 2004, Journal of learning disabilities.

[78]  A. Su,et al.  The National Council of Teachers of Mathematics , 1932, The Mathematical Gazette.

[79]  Susan Goldin-Meadow,et al.  What makes us smart? Core knowledge and natural language , 2003 .

[80]  Nancy C. Jordan,et al.  Journal of Experimental , 2002 .

[81]  S. Carey Bootstrapping & the origin of concepts , 2004, Daedalus.

[82]  P. Gordon Numerical Cognition Without Words: Evidence from Amazonia , 2004, Science.

[83]  S. Carey,et al.  Re-visiting the competence/performance debate in the acquisition of the counting principles , 2006, Cognitive Psychology.

[84]  K. H. Canobi,et al.  Number words in young children’s conceptual and procedural knowledge of addition, subtraction and inversion , 2008, Cognition.

[85]  Catherine M. Sandhofer,et al.  Number words and number concepts: the interplay of verbal and nonverbal quantification in early childhood. , 2005, Advances in child development and behavior.

[86]  I. Miura,et al.  Mathematics achievement as a function of language , 1987 .

[87]  S. Griffin,et al.  Early intervention for children at risk of developing mathematical learning difficulties. , 2007 .

[88]  Robert S. Siegler,et al.  The Development of Numerical Understandings , 1982 .

[89]  Robert S. Siegler,et al.  Improving the Numerical Understanding of Children From Low-Income Families , 2009 .

[90]  Nancy C. Jordan,et al.  Achievement Growth in Children With Learning Difficulties in Mathematics: Findings of a Two-Year Longitudinal Study , 2002 .

[91]  Geetha B. Ramani,et al.  Promoting broad and stable improvements in low-income children's numerical knowledge through playing number board games. , 2008, Child development.

[92]  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.

[93]  J. Sherman,et al.  Development of Arithmetic Skills and Knowledge in Preschool Children , 2004 .

[94]  Snorre A. Ostad,et al.  Developmental progression of subtraction strategies : a comparison of mathematically normal and mathematically disabled children , 1999 .

[95]  W. Barbaresi,et al.  Math learning disorder: incidence in a population-based birth cohort, 1976-82, Rochester, Minn. , 2005, Ambulatory pediatrics : the official journal of the Ambulatory Pediatric Association.

[96]  David C. Geary,et al.  Reflections of evolution and culture in children's cognition: Implications for mathematical development and instruction. , 1995 .

[97]  Belinda Blevins-Knabe,et al.  Number Use at Home by Children and Their Parents and Its Relationship to Early Mathematical Performance , 1996 .

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

[99]  Julie L. Booth,et al.  Developmental and individual differences in pure numerical estimation. , 2006, Developmental psychology.