For many children, fraction skills pose a serious obstacle to the attainment of more complex mathematical procedures in elementary school and beyond. The present application focuses on the problem of growth in fraction skills in math disabled (MD) and normally achieving children. The acquisition of math skills in children is influenced by a host of social (e.g., social competence in the classroom) cognitive (e.g., intelligence, attention, and memory), and mathematical knowledge (e.g., conceptual and factual) factors. To date, few studies have examined math disabilities from a longitudinal perspective, and many do not differentiate between children with and without MD.
Aim 1 is to determine the defining characteristics of children who experience difficulties in acquiring fraction skills. To that end, study 1 will provide the most comprehensive comparison of MD children and normally achieving children with respect to fraction-relevant outcomes. During the first year of this proposed project, measures of working memory and intelligence, teacher ratings of on-task behavior during math class, two kinds of mathematical knowledge (i.e., conceptual and factual), and three fraction outcomes: computation, estimation, and word problem solving, of MD 4th grade children and normally achieving children will be assessed.
Aim 2 will be to examine the influences of cognitive, behavioral, and mathematical knowledge factors with respect to growth in the three fraction outcomes. To that end, study 2 is proposed to be a longitudinal study with MD and normally achieving children. During the second year of this proposed project, the same outcomes will be assessed again with the same cohort of MD and normally achieving children that composed the fourth grade sample in study 1. Both the stability of cognitive, behavioral, and mathematical knowledge outcomes, and the factors that predict emerging variability in fraction outcomes in both ability groups will be examined. The longitudinal design will allow for strong conclusions to be made concerning causal relations between the predictors and growth in fraction outcomes. The proposed research has practical as well as theoretical value. The findings will increase our knowledge of the nature and processes of mathematical thinking in the domain of fractions. Also, the research will provide valuable information with which to promote readiness among children at risk for mathematical failure, and lay the foundation for ongoing programmatic investigations of fraction skills. ? ?
| Hecht, Steven A; Vagi, Kevin J (2012) Patterns of strengths and weaknesses in children's knowledge about fractions. J Exp Child Psychol 111:212-29 |
| Hecht, Steven A; Vagi, Kevin J (2010) Sources of Group and Individual Differences in Emerging Fraction Skills. J Educ Psychol 102:843-859 |
