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Microsoft word - bera2009_0144.docWhy does competence in basic calculation matter? Why do primary children differ in it?
Richard Cowan1, Chris Donlan2, Donna-Lynn Shepherd1, Rachel Cole-Fletcher1 1Institute of Education University of London, London, United Kingdom, 2University College London, London,United Kingdom Differences between children in mathematical progress in primary school have long been acknowledged to be considerable (Cockcroft, 1982). Substantial curriculum reorganisation in recent yearsdoes not appear to have reduced them (Brown, Askew, Millett, & Rhodes, 2003). Basic calculation – theaddition of single digit numbers and corresponding subtractions- is a very simple component of integerarithmetic. Most children can do some basic calculations when they start school but at school they develop intheir knowledge of numerical principles and number facts and the strategies they use to solve problems.
Several studies indicate that basic calculation proficiency covaries with more general arithmetic proficiency(Durand, Hulme, Larkin, & Snowling, 2005; Geary & Brown, 1991; Hecht, Torgesen, Wagner, & Rashotte,2001; Siegler, 1988) and children identified as making unusually poor progress consistently showdeficiencies in basic calculation (Geary, Hoard, Byrd-Craven, & DeSoto, 2004; Jordan, Hanich, & Kaplan,2003; Landerl, Bevan, & Butterworth, 2004).
Why basic calculation proficiency is related to more general arithmetical attainment is uncertain. It could be that this reflects the importance of basic calculation competence for further progress in arithmetic.
An alternative is that the same factors that cause children to differ in basic calculation also affect educationalprogress more generally. Such factors include parental support and socio-emotional functioning (Sacker,Schoon, & Bartley, 2002) as well as general cognitive factors such as language skills (Cowan, Donlan,Newton, & Lloyd, 2005), working memory functioning (Gathercole & Pickering, 2000), and speed ofinformation processing (Bull & Johnston, 1997). There might also be specific numerical factors that explainthe connection between basic calculation and arithmetic. These include counting sequence knowledge(Donlan, Cowan, Newton, & Lloyd, 2007), number sense (Griffin, Case, & Siegler, 1994), as well as thecapacity measures in a dyscalculia screener (Butterworth, 2003).
Our study explored these issues with a sample of Year 3 children attending mainstream schools (M age = 8: 1, N=147) and their teachers. Teachers rated each child’s socio-emotional functioning, parentalsupport, and general mathematical progress. The children were individually assessed on standardisedmeasures of working memory, speed of information processing, vocabulary, and understanding of grammar.
Three aspects of basic calculation competence were assessed: number fact knowledge, strategy efficiency,and knowledge of number principles. All children were tested using the dyscalculia screener and other tasksassessed counting sequence knowledge and number sense.
All three basic calculation measures correlated substantially with each other and with teachers’ ratings of overall mathematical progress. They also correlated with the general factors (parental support,socio-emotional functioning, working memory, information processing speed, and language skills) and thespecific numerical factors. Significant correlations remained between basic calculation components andoverall progress even when the general and specific factors were partialled out. This indicates that therelation between basic calculation competence and general proficiency is not just due to it being affected bythe same factors.
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Bull, R., & Johnston, R. S. (1997). Children's arithmetical difficulties: Contributions from processing speed, item identification, and short-term memory. Journal of Experimental Child Psychology, 65, 1-24.
Butterworth, B. (2003). Dyscalculia Screener. London: Nelson.
Cockcroft, W. (1982). Mathematics counts. London: HMSO.
Cowan, R., Donlan, C., Newton, E. J., & Lloyd, D. (2005). Number skills and knowledge in children with specific language impairment. Journal of Educational Psychology, 97, 732-744.
Donlan, C., Cowan, R., Newton, E. J., & Lloyd, D. (2007). The role of language in mathematical development: Evidence from children with Specific Language Impairments. Cognition, 103, 23-33.
Durand, M., Hulme, C., Larkin, R., & Snowling, M. (2005). The cognitive foundations of reading and arithmetic skills in 7-to 10-year-olds. Journal of Experimental Child Psychology, 91, 113-136.
Gathercole, S. E., & Pickering, S. J. (2000). Working memory deficits in children with low attainments in the national curriculum at 7 years of age. British Journal of Educational Psychology, 70, 177-194.
Geary, D. C., & Brown, S. C. (1991). Cognitive addition: Strategy choice, and speed-of-processing differences in gifted, normal, and mathematically disabled children. Developmental Psychology, 27,398-406.
Geary, D. C., Hoard, M. K., Byrd-Craven, J., & DeSoto, M. C. (2004). Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children withmathematical disability. Journal of Experimental Child Psychology, 88, 121-151.
Griffin, S. A., Case, R., & Siegler, R. S. (1994). Rightstart: providing the central conceptual prerequisites for first formal learning of arithmetic to students at risk for school failure. In K. McGilly (Ed.), Classroomlessons: Integrating cognitive theory and classroom practice (pp. 25-49). Cambridge, Mass: MIT.
Hecht, S. A., Torgesen, J. K., Wagner, R. K., & Rashotte, C. A. (2001). The relations between phonological processing abilities and emerging individual differences in mathematical computation skills: alongitudinal study from second to fifth grades. Journal of Experimental Child Psychology, 79, 192-227.
Jordan, N. C., Hanich, L. B., & Kaplan, D. (2003). A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics andreading difficulties. Child Development, 74, 834-850.
Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental dyscalculia and basic numerical capacities: a study of 8-9-year-old students. Cognition, 93, 99-125.
Sacker, A., Schoon, I., & Bartley, M. (2002). Social inequality in educational achievement and psychosocial adjustment throughout childhood: magnitude and mechanisms. Social Science & Medicine, 55, 863-880.
Siegler, R. S. (1988). Individual differences in strategy choices: Good students, not-so-good students, and perfectionists. Child Development, 59, 833-851.
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