Developmental progression of subtraction strategies : a comparison of mathematically normal and mathematically disabled children

ABSTRACT This study was designed to investigate the character and extent of differences between mathematically disabled children (MD children) and their mathematically normal peers as reflected in the use of task‐specific strategies for solving basic fact problems in subtraction as children move up through primary school, that is from the 1st to 7th grade. The pattern of development showed the MD children as being characterized by: (1) use of back‐up strategies only, (2) use of primary back‐up strategies, (3) small degree of variation in the use of strategy variants and (4) limited degree of change in the use of strategies from year to year through the primary school. Early and striking convergence of the developmental curves supported the suggestion that the acquisition of strategy skills by MD children follows a sequence that is fundamentally different (not only delayed) from that observed in normal achievers. The findings highlight the MD children's need for mathematics instruction to shift from comput...

[1]  T. P. Carpenter,et al.  Learning and teaching with understanding. , 1992 .

[2]  M. Montague,et al.  Cognitive Strategy Instruction in Mathematics for Students with Learning Disabilities , 1997, Journal of learning disabilities.

[3]  M. Pressley,et al.  Good information processing: What it is and how education can promote it , 1989 .

[4]  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 .

[5]  Susan R. Goldman,et al.  Extended Practice of Basic Addition Facts: Strategy Changes in Learning-Disabled Students , 1988 .

[6]  Eric A. Jenkins,et al.  How Children Discover New Strategies , 1989 .

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

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

[9]  W. Schneider.  Domain-specific knowledge and memory performance in children , 1993 .

[10]  Snorre A. Ostad,et al.  Developmental differences in addition strategies: a comparison of mathematically disabled and mathematically normal children. , 1997, The British journal of educational psychology.

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

[12]  Mark H. Ashcraft,et al.  The development of mental arithmetic: A chronometric approach☆ , 1982 .

[13]  R S Siegler.  Individual differences in strategy choices: good students, not-so-good students, and perfectionists. , 1988, Child development.

[14]  Jeannette E. Fleischner,et al.  Automatization and Basic Fact Performance of Normal and Learning Disabled Children , 1983 .

[15]  Nancy C. Jordan,et al.  Calculation Abilities in Young Children with Different Patterns of Cognitive Functioning , 1995, Journal of learning disabilities.

[16]  Stellan Ohlsson,et al.  An Information Processing Analysis of the Function of Conceptual Understanding in the Learning of Arithmetic Procedures. , 1988 .

[17]  R. Siegler.  The perils of averaging data over strategies: An example from children's addition. , 1987 .

[18]  James M. Moser,et al.  The Acquisition of Addition and Subtraction Concepts in Grades One through Three. , 1984 .

[19]  J. Flavell.  Speculations about the nature and development of metacognition , 1987 .

[20]  Ann Dowker,et al.  Estimation Strategies of Four Groups , 1996 .

[21]  A. Brown.  Metacognition, executive control, self-regulation, and other more mysterious mechanisms , 1987 .

[22]  M. Ashcraft.  Cognitive arithmetic: A review of data and theory , 1992, Cognition.

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