Several factors seem important to understand the nature of mathematical learning. Byrnes and Miller combined these factors into the Opportunity-Propensity model. In this study the model was used to predict the number-processing factor and the arithmetic fluency in grade 4 (n = 195) and grade 5 (n = 213). Gender, intelligence and affect (positive…

Despite the vast research on the early predictors of mathematics achievement, little research has investigated the predictors of various domains of mathematics (e.g., geometry, statistics). The purpose of the present study was to examine the predictive relation between first-grade early numeracy and computation skills and third-grade mathematics…

To understand mathematics, children must interpret mathematics symbols. In this study, we designed a brief assessment of mathematics symbols for children in the elementary grades. For each of 23 symbols, children identified the symbol, provided the meaning of the symbol, and used the symbol. We assessed 297 children in Grades 1, 3, and 5. Internal…

The number of opportunities to respond (OTR) and spacing (massed or distributed practice) of practice sessions are important variables to consider in instructional design. The purpose of this pilot study was to compare the impact of these variables on trajectories of mathematics fluency. Second- and third-grade students (N = 112) were randomly…

This study examined cognitive precursors of hierarchical mathematical development. Six-year-old children (n = 258) were assessed on number skills, cognitive skills, and arithmetic 1 year prior to school entry. Skills in advanced arithmetic and advanced mathematics were assessed in Grades 3 and 6, respectively. Path analyses were computed and…

This study examined the predictive relationship of a brief computation measure administered in the fall, winter, and spring of first, second, and third grade with the mathematic portion of a state-mandated academic achievement test administered in the spring of third grade. The relationship between mathematical achievement and resource…

Purpose: The purpose of this descriptive study is to investigate why some elementary children have difficulties mastering addition and subtraction calculation tasks. Design/methodology/approach: The researchers have examined error types in addition and subtraction calculation made by 697 Portuguese students in elementary grades. Each student…

This study was designed to deepen insights on whether word-problem (WP) solving is a form of text comprehension (TC) and on the role of language in WPs. A sample of 325 second graders, representing high, average, and low reading and math performance, was assessed on (a) start-of-year TC, WP skill, language, nonlinguistic reasoning, working memory,…

According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 second-grade students, we administered: (1) measures of calculations and…

The purpose of this study was to assess the value of dynamic assessment (DA; degree of scaffolding required to learn unfamiliar mathematics content) for predicting 1st-grade calculations (CAs) and word problems (WPs) development, while controlling for the role of traditional assessments. Among 184 1st graders, predictors (DA, Quantity…

Using multitrait, multimethod data, and confirmatory factor analysis, the current study examined the effects of arithmetic item formatting and the possibility that across formats, abilities other than arithmetic may contribute to children's answers. Measurement hypotheses were guided by several leading theories of arithmetic cognition. With a…

Numerical processing has been extensively studied by examining the performance on basic number processing tasks, such as number priming, number comparison, and number line estimation. These tasks assess the innate "number sense," which is assumed to be the breeding ground for later mathematics development. Indeed, several studies have…

The purpose of this study was to assess the relative contribution of teacher and tutor ratings of inattentive behavior in two different instructional settings in predicting students' performance on fraction concepts and whole-number calculations. Classroom teachers rated each student's attentive behavior in a whole-class setting and tutors rated…

Developmental predictors of children's fraction concepts and procedures at the end of fourth grade were investigated in a 2-year longitudinal study. Participants were 357 children who started the study in third grade. Attentive behavior, language, nonverbal reasoning, number line estimation, calculation fluency, and reading fluency each…

The purpose of this investigation was to determine the relationship between the acquisition of conservation skills and achievement in mathematics. The conservation skills measured were numbered, mass, area and volume. Mathematics achievement was measured by the Computation, Concepts, Problem-Solving and Total Mathematics scores on the Metropolitan…