Bivariate developmental relations between calculations and word problems: A latent change approach

Abstract

The relation between 2 forms of mathematical cognition, calculations and word problems, was examined. Across grades 2–3, performance of 328 children (mean starting age 7.63 [SD=0.43]) was assessed 3 times. Comparison of a priori latent change score models indicated a dual change model, with consistently positive but slowing growth, described development in each domain better than a constant or proportional change model. The bivariate model including change models for both calculations and word problems indicated prior calculation performance and change were not predictors of subsequent word-problem change, and prior word-problem performance and change were not predictors of subsequent calculation change. Results were comparable for boys versus girls. The bivariate model, along with correlations among intercepts and slopes, suggest calculation and word-problem development are related, but through an external set of overlapping factors. Exploratory supplemental analyses corroborate findings and provide direction for future study.

Developmental dynamics between reading and math in elementary school

“…Newer methodological approaches, such as the latent change score model, can assist in elucidating the reading‐math dynamics (Ferrer & McArdle, 2010; McArdle, 2009). The model has been successfully applied in the reading (e.g., Quinn, Wagner, Petscher, & Lopez, 2015) as well as math literature (e.g., Gilbert & Fuchs, 2017) to study the co‐development of only reading related or math related components. The bivariate latent change score model simultaneously models three types of change across two constructs: a constant change for each construct (i.e., linear growth), a proportional change for each construct (i.e., time‐point to time‐point change), and coupling effects between the constructs (i.e., development in one construct influences subsequent development in the other construct).…”

Exploring academic and cognitive skills impacting retention and acquisition of word‐problem knowledge gained during or after intervention

“…In addition to single‐digit operations, we included double‐digit addition and subtraction due to their significance in solving word problems that involve larger numbers and multiple steps. Proficiency in manipulating numbers enhances understanding of numerical relations, which is crucial for accurately solving word problems (Gilbert & Fuchs, 2017; Lin, 2021). Finally, we used a measure of numeration because such foundational knowledge forms the basis for more advanced mathematical reasoning and problem solving.…”

El rol del vocabulario en la resolución de problemas aritméticos: Un metaanálisis

“…La relación entre el vocabulario y la resolución de problemas aritméticos está documentada. Sin embargo, los estudios que la describen difieren en cuanto a las medidas utilizadas para evaluar el conocimiento que tienen los niños de las palabras (Gilbert & Fuchs, 2017;Purpura & Ganley, 2014). Debido a que, cuando se busca resolver un problema aritmético se construye un modelo de situación de la descripción del mismo que implica la identificación de los componentes relevantes de la narración y las relaciones entre ellos, sería esperable que no bastase con el reconocimiento de las etiquetas de las palabras, sino que hiciera falta un conocimiento mayor del significado de las mismas.…”