Contributions of domain-general cognitive resources and different forms of arithmetic development to pre-algebraic knowledge.

Abstract

The purpose of this study was to investigate the contributions of domain-general cognitive resources and different forms of arithmetic development to individual differences in pre-algebraic knowledge. Children (n=279; mean age=7.59 yrs) were assessed on 7 domain-general cognitive resources as well as arithmetic calculations and word problems at start of 2nd grade and on calculations, word problems, and pre-algebraic knowledge at end of 3rd grade. Multilevel path analysis, controlling for instructional effects associated with the sequence of classrooms in which students were nested across grades 2–3, indicated arithmetic calculations and word problems are foundational to pre-algebraic knowledge. Also, results revealed direct contributions of nonverbal reasoning and oral language to pre-algebraic knowledge, beyond indirect effects that are mediated via arithmetic calculations and word problems. By contrast, attentive behavior, phonological processing, and processing speed contributed to pre-algebraic knowledge only indirectly via arithmetic calculations and word problems.

Working memory components that predict word problem solving: Is it merely a function of reading, calculation, and fluid intelligence?

“…The findings some ways, matched our findings, except that we did not find that reading completely mediated the influence of WM on problem-solving accuracy. In a later study, Fuchs et al (2012) administered a battery of nonverbal reasoning, language, attention behavior, WM, phonological processing, and processing speed measures as well as calculation measures to children in the second and third grade. In this study, predictions were made to word problem-solving performance.…”

Sources of individual differences in emerging competence with numeration understanding versus multidigit calculation skill.

“…In terms of visuospatial reasoning , structured interviews suggest that numeration understanding depends on children’s ability to recognize the structure of mathematical representations in visuospatial arrays (Gray, Pitta, & Tall, 2000; Mulligan & Mitchelmore, 2009; Pitta-Pantazzi, Gray, & Christou, 2004; Young-Loveridge, 2002). Also, pattern recognition at kindergarten predicts mathematics achievement through eighth grade (Claessens & Engel, 2013); visuospatial reasoning predicts other forms of mathematics learning, such as arithmetic, word problem learning, and general mathematics achievement (Fuchs, Geary, Compton, Fuchs, Hamlett, & Bryant, 2010; Fuchs, Geary, Compton, Fuchs, Hamlett, Seethaler, et al, 2010; Fuchs, Geary, et al, 2013; Li & Geary, 2013; H. L. Swanson & Beebe-Frankenberger, 2004); and visuospatial reasoning tasks, like the ones included in intelligence tests, are central to the kinds of highly symbolic learning reflected in numeration understanding (e.g., Fuchs et al, 2012). Further, a role for such reasoning makes sense because the recursive groupings that underlie our numeration system are typically depicted in terms of spatial configurations.…”

“…Attentive behavior in the classroom is a robust predictor across many forms of mathematical cognition and learning, including simple arithmetic, multidigit addition and subtraction, and word problems (Fuchs et al, 2005, 2006; Geary, Hoard, & Nugent, 2012), prealgebra (Fuchs et al, 2012), and fractions (Hecht & Vagi, 2010; Jordan et al, 2013; Vukovic et al, 2012). The multicomponent nature of operating in the numeration system and the need to attend in careful and sustained ways to lengthy explanations about numeration concepts suggest the importance of attentive behavior.…”

“…This literature has focused on different forms of mathematics learning, including calculations (e.g., Andersson, 2008; DeStefano & LeFevre, 2004; Geary, 2011), word problems (e.g., Andersson, 2007; Fuchs et al, 2006; Fuchs, Geary, Compton, Fuchs, Hamlett, & Bryant, 2010; Fuchs, Geary, Compton, Fuchs, Hamlett, Seethaler, et al, 2010; H. L. Swanson & Beebe-Frankenberger, 2004), fractions (e.g., Hecht & Vagi 2010; Jordan et al, 2013; Vukovic et al, 2012), algebra (e.g., Fuchs et al, 2012; Lee, Ng, Bull, Pe, & Ho, 2011; Tolar, Lederberg, & Fletcher, 2009), and general mathematics achievement (e.g., De Smedt, Janssen, et al, 2009; De Smedt, Verschaffel, & Ghesquière, 2009). …”

Longer bars for bigger numbers? children’s usage and understanding of graphical representations of algebraic problems

“…Regarding the cognitive factors that influence children's success in algebra, there has been a number of recent studies on both domain-general and domain-specific correlates of algebraic performance (e.g., Fuchs et al, 2012;Lee, Ng, Bull, Pe, & Ho, 2011;Tolar, Lederberg, & Fletcher, 2009;Wei, Yuan, Chen, & Zhou, 2012). On the specific influence of using diagrams, there is a large body of research that examined whether students learn better when text is accompanied by diagrams (Mayer, 1989(Mayer, , 2002 or when students generate the diagrams themselves (Meter & Garner, 2005).…”