Problem solving and computational skill: Are they shared or distinct aspects of mathematical cognition?

Abstract

The purpose of this study was to explore patterns of difficulty in 2 domains of mathematical cognition: computation and problem solving. Third graders (n = 924; 47.3% male) were representatively sampled from 89 classrooms; assessed on computation and problem solving; classified as having difficulty with computation, problem solving, both domains, or neither domain; and measured on 9 cognitive dimensions. Difficulty occurred across domains with the same prevalence as difficulty with a single domain; specific difficulty was distributed similarly across domains. Multivariate profile analysis on cognitive dimensions and chi-square tests on demographics showed that specific computational difficulty was associated with strength in language and weaknesses in attentive behavior and processing speed; problem-solving difficulty was associated with deficient language as well as race and poverty. Implications for understanding mathematics competence and for the identification and treatment of mathematics difficulties are discussed. Keywordscalculations; word problems; cognitive predictors; mathematics Mathematics, which involves the study of quantities as expressed in numbers or symbols, comprises a variety of related branches. In elementary school, for example, mathematics is conceptualized in strands such as concepts, numeration, measurement, arithmetic, algorithmic computation, and problem solving. In high school, curriculum offerings include algebra, geometry, trigonometry, and calculus. Little is understood, however, about how different aspects of mathematical cognition relate to one another (i.e., which aspects of performance are shared or distinct, or how difficulty in one domain corresponds with difficulty in another). SuchCorrespondence concerning this article should be addressed to Lynn S. Fuchs, Peabody College, Box 228, Vanderbilt University, Nashville, TN 37203. lynn.fuchs@vanderbilt.edu. NIH Public AccessAuthor Manuscript J Educ Psychol. Author manuscript; available in PMC 2010 January 6. NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript understanding would provide theoretical insight into the nature of mathematics competence and practical guidance about the identification and treatment of mathematics difficulties.The purpose of the present study was to explore the overlap of difficulty with two aspects of primary-grade mathematical cognition and to examine how characteristics differ among subgroups with difficulty in one, the other, both, or neither. The first aspect of performance was computation, including skill with number combinations (e.g., 2 + 5; 8 − 3) and procedural computation (e.g., 25 + 38; 74 − 22). The second aspect of performance was problem solving, including one-step, contextually straightforward word problems (e.g., John had 9 pennies. He spent 3 pennies at the store. How many pennies did he have left?) and multistep, contextually more complex problems (e.g., Fred went to the ballgame with 2 friends. He left his house with $42. While at the game, he bought 5 h...

Relação entre habilidades cognitivas de processamento visual e inteligência fluida com o desempenho em aritmética

“…Estudos apontam uma relação consistente com conhecimento/compreensão (Floyd, Evans, & McGrew, 2003;Gelman & Butterworth, 2005;Swanson & Jerman, 2006), velocidade de processamento (Floyd et al, 2003;McGrew & Wedling, 2010), memória de curto prazo e memória operacional (Fuchs et al, 2008;Geary, 2007;) bem como inteligência fluida (Flanagan et al, 2006;Geray, 2007;Hale et al, 2007) e processamento visual (Geary, 2007;Hale et al, 2008).…”

Cognitive Factors' Influence on Fraction Development in Students of Varying Ability Levels

“…For example, as previously mentioned two studies (Hecht et al, 2003;Hecht & Vagi, 2010) have already examined the impact of attention on fraction performance. Results were significant in both studies but there are questions about whether the measure they used (i.e., SSRS) is actually measuring attention (Fuchs et al, 2006;Fuchs et al, 2008). If the SSRS does not measure attention then the interpretation of the results from the study changes completely.…”

“…Clearly defining the constructs examined and how the included assessments align with those constructs is an important part of this research , 2006;Fuchs et al, 2008). If the SSRS does not measure attention then the interpretation of the results from the study changes completely.…”

“…Using both prospective and cross-sectional methods, researchers studying general mathematics outcomes have linked processing speed (Fuchs et al, 2006, Fuchs et al, 2008Geary, Hoard, Byrd-Craven, Nugent, & Numtee, 2007) and working memory (Seethaler et al, 2011) to whole-number computation outcomes. Although working memory has been shown to influence calculation and wordproblem skill (Fuchs et al, 2006;Swanson, 2006;Swanson & Beebe-Frankenburger, 2004), many cognitive factors have only been linked to word problems success.…”

“…This relationship should be explored in future studies to see if there is any significance to the potential interaction. Teacher ratings of student attention have been used as a proxy for student classroom attention (e.g., Fuchs et al, 2006Fuchs et al, , 2008Hecht & Vagi, 2010), and have been found to be strongly linked to various fraction outcomes. The question has been raised as to whether the cooperation subscale of the SSRS (used in several of the cited studies) is actually capturing…”