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

The relation to operands (RO) principles describe the relation between operands and answers in arithmetic problems (e.g., the sum is always larger than its positive addends). Despite being a fundamental property of arithmetic, its empirical relation with arithmetic/algebraic problem solving has seldom been investigated. The current longitudinal study aimed to address this issue. Two-hundred-and-two Chinese fifth graders (57% boys) were assessed on their RO understanding. Their arithmetic/algebraic problem solving were assessed multiple times over 2 years. Results from latent growth curve modeling showed that RO understanding predicted the growth in arithmetic/algebraic problem solving when other known predictors of arithmetic/algebraic problem solving were controlled. The findings highlight the role of RO understanding in children's mathematical development. Interventions should be developed to enhance children's RO understanding. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Cognitive predictors of children's arithmetic principle understanding.

The understanding of arithmetic principles (APs) is an important component of our conceptual mathematical knowledge, but we have limited knowledge about how children acquire APs. The current study examined this issue through a longitudinal study with 273 Chinese fourth graders. These children were assessed on various cognitive capacities (e.g., verbal and visuospatial working memory, processing speed, inhibition skill, numerical magnitude representation) in Grade 4 as well as on their AP understanding using multifaceted assessment and their arithmetic competence in Grade 5. Results from structural equation modeling suggested that verbal memory and inhibition skill directly predicted AP understanding, which in turn predicted arithmetic competence. Visuospatial working memory predicted AP understanding through numerical magnitude representation. The findings allow researchers to better account for the individual differences in AP understanding.

Multifaceted assessment of children's inversion understanding.

The current study was aimed at examining various theoretical issues concerning children's inversion understanding (i.e., its factor structure, development, and relation with mathematics achievement) using a multifaceted assessment. A sample of 110 fourth to sixth graders was evaluated in three different measures of inversion understanding: evaluation of examples, explicit recognition, and application of procedures. The participants were also evaluated on their mathematics achievement. A one-factor structure best explains inversion understanding involving different arithmetic operations. Grade-related improvements were observed in some facets of inversion understanding. Latent profile analysis using the three inversion measures revealed seven classes of children with different inversion profiles. Furthermore, classes with better inversion understanding also had higher mathematics achievers. The current findings provide evidence to support the multifaceted nature of inversion understanding, grade-related improvements in children's inversion understanding as well as the relation between inversion understanding and mathematics achievement.

The association between visual attention and arithmetic competence: The mediating role of enumeration.

The current study aimed at clarifying the nature of relation between visual attention and arithmetic competence. A group of 301 Chinese second graders was assessed. Children's visual attention was measured using two versions of a visual search task, with efficient visual search (the similarity between the target and the distractors is low) tapping automatic, stimulus-driven visual attention and inefficient visual search (the similarity between the target and the distractors is high) tapping effortful, goal-directed visual attention. Children's arithmetic competence, enumeration skills (assessed in about half of the participants), and other domain-general cognitive abilities were also assessed. The results suggest that only inefficient visual search significantly predicted children's arithmetic competence, and such a relation was mediated through their enumeration skills. The findings highlight the role of fundamental cognitive capacities in mathematics learning and provide insights into potential interventions for improving children's arithmetic competence.

The growth rates of dot enumeration ability predict mathematics achievements: A 5-year longitudinal study.

BACKGROUND: Dot enumeration is the basic mathematics competency in young children and a significant indicator of later mathematics achievement. AIM: The present study focused on (1) how children's dot enumeration ability changed as they progressed from late kindergarten years (K3) to the second year of primary school in Hong Kong (P2), and (2) the extent to which such changes are associated with students' mathematics outcomes assessed at the fourth grade, including standardized mathematics achievement, whole number magnitude understanding, and rational number concept. SAMPLE(S): Two hundred and eleven Hong Kong kindergarteners were recruited. METHODS: The participants' dot enumeration was assessed from K3 to P2. Their mathematics outcomes were assessed at P4, including standardized mathematics achievement, whole number magnitude understanding, and rational number concept. RESULTS: The changes in their dot enumeration speed reflected a linear growth pattern. Further, both the initial level and growth rate of dot enumeration predicted standardized mathematics achievement and whole number magnitude understanding 2 years later while only the latter predicted rational number concept. CONCLUSIONS: The results indicate the importance of focusing on children's growth in a specific mathematics skill, in addition to their status at one single time point. Practical implications are discussed in this article.

The roles of place-value understanding and non-symbolic ratio processing system in symbolic rational number processing.

BACKGROUND: While it has been widely demonstrated that children's and adolescents' understanding of rational number plays an important role in their mathematics achievement, we have limited knowledge about the cognitive correlates of this understanding. AIMS: The current study aimed at examining whether children's non-symbolic ratio processing and their understanding of place-value structure of whole numbers play a role in their understanding of fractions and decimals and whether their roles are different for fractions versus decimal understanding. SAMPLE: A sample of 124 fourth graders was tested. METHODS: Participants were tested on their symbolic rational number processing, non-symbolic ratio processing, place-value understanding of whole numbers, mathematics achievement, as well as a series of domain-general and domain-specific cognitive skills related to symbolic rational number processing. RESULTS: The findings suggest that, while the understanding of place value of whole numbers significantly predicted the understanding of both fractions and decimals, non-symbolic ratio processing specifically predicted the understanding of fractions, but not decimals. CONCLUSIONS: The findings highlight the roles of place-value understanding and non-symbolic ratio processing in the acquisition of symbolic rational numbers.

The unique role of executive function skills in predicting Hong Kong kindergarteners' reading comprehension.

BACKGROUND: Word reading and linguistic comprehension skills are two crucial components in reading comprehension, according to the Simple View of Reading (SVR). Some researchers have posited that a third component should be involved in reading and understanding texts, namely executive function (EF) skills. AIM: This study was novel in two ways. Not only did we tested EF skills as a predictor of reading comprehension in a non-alphabetic language (i.e., Chinese) to extend the theoretical model of SVR, we also examined reading comprehension further in kindergarten children (age 5) in Hong Kong, in the attempt to reveal possible early precursors of reading comprehension. SAMPLE(S): A group of 170 K3 kindergarteners was recruited in Hong Kong. METHODS: Children's word reading was assessed. Their linguistic comprehension was assessed with phonological awareness, verbal short-term memory, and vocabulary knowledge. Using a structured observation task, Head-Toes-Knees-Shoulders (HTKS), we measured their composite scores for EF skills. RESULTS: Head-Toes-Knees-Shoulders performance predicted unique variance in children's Chinese reading comprehension concurrently beyond word reading and a set of linguistic comprehension skills. CONCLUSIONS: The results highlight the important role of EF skills in beginning readers' reading comprehension.

Is conditional reasoning related to mathematical problem solving?

The current study aimed to investigate the relation between conditional reasoning, which is a common type of logical reasoning, and children's mathematical problem solving. A sample of 124 fourth graders was tested for their conditional reasoning skills and their mathematical problem solving skills, as well as a list of control variables (e.g., IQ, working memory, reading) and potential mediators (number sentence construction and computation). The children's ability to make modus ponens (MP) inferences significantly predicted their mathematical problem solving skills, even after controlling for the potential confounding variables. The relation was mediated by the number sentence construction skills. The findings, in addition to supporting the link between conditional reasoning and mathematics, further indicate that the ability to process relations may be the mechanism underlying the relation. Theoretical and practical implications are discussed.

The unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement.

The current study examined the unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement. A sample of 124 fourth graders was tested on their arithmetic operation understanding (as reflected by their understanding of arithmetic principles and the knowledge about the application of arithmetic operations) and their precision of rational number magnitude representation. They were also tested on their mathematics achievement and arithmetic computation performance as well as the potential confounding factors. The findings suggested that both arithmetic operation understanding and numerical magnitude representation uniquely predicted children's mathematics achievement. The findings highlight the significance of arithmetic operation understanding in mathematics learning.

The underlying number-space mapping among kindergarteners and its relation with early numerical abilities.

People map numbers onto space. The well-replicated SNARC (spatial-numerical association of response codes) effect indicates that people have a left-sided bias when responding to small numbers and a right-sided bias when responding to large numbers. This study examined whether such spatial codes were tagged to the ordinal or magnitude information of numbers among kindergarteners and whether it was related to early numerical abilities. Based on the traditional magnitude judgment task, we developed two variant tasks-namely the month judgment task and dot judgment task-to elicit ordinal and magnitude processing of numbers, respectively. Results showed that kindergarteners oriented small numbers toward the left side and large numbers toward the right side when processing the ordinal information of numbers in the month judgment task but not when processing the magnitude information in the number judgment task and dot judgment task, suggesting that the left-to-right spatial bias was probably tagged to the ordinal but not magnitude property of numbers. Moreover, the strength of the SNARC effect was not related to early numerical abilities. These findings have important implications for the early spatial representation of numbers and its role in numerical performance among kindergarteners.