The role of cognitive processes, foundational math skill, and calculation accuracy and fluency in word-problem solving versus prealgebraic knowledge.

Abstract

The purpose of this study was to examine child-level pathways in development of pre-algebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of grade 2; calculation accuracy and calculation fluency at end of grade 2; and pre-algebraic knowledge and word-problem solving at end of grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than pre-algebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students’ foundational mathematics skills or cognitive processes.

Cognitive predictors of calculations and number line estimation with whole numbers and fractions among at-risk students.

“…We administered two subtests of Double-Digit Calculation Tests (Fuchs, Hamlett, & Powell, 2003). The first subset, Double-Digit Addition, includes 20 2-digit by 2-digit addition problems with and without regrouping.…”

Cognitive and linguistic predictors of mathematical word problems with and without irrelevant information

“…To control for initial arithmetic skill, we used Math Fact Fluency (Fuchs, Hamlett, & Powell, 2003b), with four subtests: 25 single-digit addition problems with sums from 6 to 12; 25 single-digit subtraction problems with minuends from 6 to 12; 25 single-digit addition problems with sums from 5 to 18; 25 single-digit subtraction problems with minuends from 5 to 18. Students have 1 min to write answers for each subtest.…”

“…VSP and VSP-I are from Fuchs and Seethaler (2008). Arithmetic is from Math Fact Fluency (Fuchs et al, 2003b). Single-Digit Story Problems is from Jordan and Hanich (2000); adapted from Carpenter and Moser (1984), Riley et al (1983).…”

Prevention: Necessary But Insufficient? A 2‐Year Follow‐Up of an Effective First‐Grade Mathematics Intervention

“…This is the case in this study, where some children reached normalized performance, while others did not. For example, on the longitudinal WRAT‐Arithmetic measure, indexing simple and complex calculations, more than one‐third of intervention students across the two conditions met the criterion for adequate response commonly applied in the response‐to‐intervention literature (Frijters et al., ; Fuchs, Gilbert, et al., ) at end of third grade: normalized performance, with standard score of 90. We note that although dichotomizing continuous data has its drawbacks (Irwin & McClelland, ; MacCallum, Zhang, Preacher, & Rucker, ), school personnel are regularly called upon to make dichotomous service allocation decisions.…”

“…Individual differences in mathematical competencies arise early and remain stable over time (Duncan et al., ; Fuchs, Gilbert, et al., ), and are associated with quality of life and financial security in adulthood (Every Child a Chance Trust, ; Murnane, Willett, Braatz, & Duhaldeborde, ; Ritchie & Bates, ). Given these long‐term associations, there is a pressing need for programs that ameliorate the mathematical deficits of at‐risk children and that sustain intervention gains throughout schooling and into adulthood.…”