The relation between complement understanding and computational skills: A random intercept cross-lagged panel model.

Abstract

Understanding of the complement principle has been proposed as closely related to computational skills, but few studies have investigated their interrelations. The present longitudinal study attempted to clarify the picture by examining their potential cross-lagged relation. Fourth graders (n = 221) in Hong Kong received 3 cognitive assessments at intervals of 6 months, consisting of multiple measures of complement understanding, a nonverbal intelligence test, and a computational skills measure. A random intercept cross-lagged panel model revealed that complement understanding significantly predicted future computational skills, but the reciprocal prediction was nonsignificant. The findings provide empirical evidence supporting the close relation between complement understanding and computational skills and call for future endeavors to examine the interrelations between computational skills and understanding of other arithmetic principles.

How are spatial ability and math related? The mediating roles of numerical magnitude knowledge, understanding of arithmetic operations, and word-problem representation.

“…On the other hand, unlike the above two components, the current study is the first to investigate the mediating role of the understanding of arithmetic operations on the relation between spatial ability and math performance. The current study not only demonstrated the association between spatial ability and the understanding of arithmetic operations suggested by previous studies (Cheng & Mix, 2014; Gilligan et al, 2020) but also confirmed the relation between the understanding of arithmetic operations and math performance, which is also in line with previous studies (Ching & Nunes, 2017; McNeil et al, 2019; Yip et al, 2023 ; Wong, 2017, 2023). The indirect effect further confirmed the mediating role of the understanding of arithmetic operations on the relation between spatial ability and math performance.…”

“…For example, Ching and Nunes (2017) found that knowledge of commutativity and complement measured in grade one significantly predicted both concurrent and future calculation and problem-solving performance, even after controlling for factors such as students' ages, intelligence, counting abilities, working memory, and autoregressor effects. A recent study by Yip et al (2023) demonstrated a similar longitudinal prediction from complement understanding to arithmetic computation among senior elementary school students. The results are consistent with another study by Wong (2017) that indicated a significant relation between the understanding of arithmetic principles and children's calculation and overall math competence.…”

The sums are larger than their natural number addends: Relation to operands understanding predicts growth in arithmetic/algebraic problem solving.

“…The current findings showed that fifth graders’ understanding of the RO principles significantly predicted the growth in arithmetic/algebraic problem solving over 2 years. These findings, together with those from other studies on arithmetic principle knowledge (Ching & Nunes, 2017; Cragg et al, 2017; Wong et al, 2021; Yip et al, 2023), illustrated how the investigation of arithmetic principle knowledge may increase our knowledge about numerical cognition (Gilmore et al, 2018; Wong, 2021). While researchers are encouraged to further explore this construct, educators may think about how students can be encouraged to discover the regularities in mathematics.…”

“…The current findings showed that fifth graders' understanding of the RO principles significantly predicted the growth in arithmetic/algebraic problem solving over 2 years. These findings, together with those from other studies on arithmetic principle knowledge (Ching & Nunes, 2017;Cragg et al, 2017;Yip et al, 2023), illustrated how the investigation of arithmetic principle knowledge may increase our This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.…”

“…As most, if not all, of the advanced mathematics topics (e.g., fractions, algebra) are built upon the four arithmetic operations, an inadequate understanding of these fundamental properties may affect students' acquisition of more advanced mathematics topics in the long run. The significant relations observed between the understanding of other arithmetic principles (e.g., commutativity and complement) and children's mathematics achievement in other studies (Ching & Nunes, 2017;Cragg et al, 2017;Yip et al, 2023) suggest that the understanding of such fundamental properties of arithmetic could be an important aspect in mathematics learning (Gilmore et al, 2018;.…”