A mental model is a concept that exists in students' minds and is used to describe and explain a phenomenon. This study aims to describe the transition-attempting mental model of students in understanding the concept of integers. This study uses a qualitative approach and the type of research conducted is descriptive. The subjects of this study…

To learn mathematics, historically students had no choice but to memorize fundamental facts and apply memorized algorithms. Since 1995 in the US, all states have adopted standards to govern K-12 mathematics instruction, and in most, standards have de-emphasized memorization and emphasized reasoning based on concepts. This change assumed the brain…

This article reconsiders Case's theory of central conceptual structures (CCS), examining the relation between working memory and the acquisition of quantitative CCS. The lead hypothesis is that the development of working memory capacity shapes the development of quantitative concepts (whole and rational numbers). Study I, with 779 children from…

In this article, the authors summarize results from 5 randomized controlled trials assessing the effects of intervention to improve the fraction performance of fourth-grade students at risk for difficulty in learning about fractions. The authors begin by explaining the importance of competence with fractions and why an instructional focus on…

A group of 50 good readers and a group of 50 poor readers of Grade 5 matched for age and intelligence and selected on the basis of their proficiency in reading comprehension were tested for their competence in word reading and the process of planning at three different levels, namely, perceptual, memory and conceptual in order to study the…

The purpose of the study was to determine whether individual differences in at-risk 4th graders' language comprehension, nonverbal reasoning, concept formation, working memory, and use of decimal labels (i.e., place value, point, incorrect place value, incorrect fraction, or whole number) are related to their decimal magnitude understanding.…

We report on the 1st experimental elicitation of nonbelieved memories for childhood events in adults (Study 1) and children (Study 2) using a modified false memory implantation paradigm. Participants received true (trip to a theme park) and false (hot air balloon ride) narratives and recalled these events during 2 interviews. After debriefing, 13%…

The purpose of this study was to examine the cognitive predictors of calculations and number line estimation with whole numbers and fractions. At-risk 4th-grade students (N = 139) were assessed on 6 domain-general abilities (i.e., working memory, processing speed, concept formation, language, attentive behavior, and nonverbal reasoning) and…

This study explored the Junior Brixton Test (JBT), an executive function (EF) measure for children, in comparison to the Wisconsin Card Sorting Test (WCST) in a sample of 6- to 8-year-olds, all attending the first 2 years of elementary school. Factor analyses indicated two main domains in both measures, namely concept formation and cognitive…

The main purposes of this study were to test the effects of teaching at-risk 4th graders to provide explanations for their mathematics work and examine whether those effects occur by compensating for limitations in cognitive processes. We randomly assigned 212 children to 3 conditions: a control group and 2 variants of a multicomponent fraction…

Great science teachers recognise the importance of providing children with practical, real-life experiences to develop their understanding of, and enthusiasm for, this truly inspirational subject. However, Gareth Metcalfe believes that the process by which children understand and remember their scientific experiences can be enriched. This article…

Comparing multiple solutions to a single problem is an important mode for developing flexible mathematical thinking, yet instructionally leading this activity is challenging (Stein, Engle, Smith, & Hughes, 2008). We test 1 decision teachers must make after having students solve a problem: whether to only verbally discuss students' solutions or…

Before starting school, many children reason logically about concepts that are basic to their later mathematical learning. We describe a measure of quantitative reasoning that was administered to children at school entry (mean age 5.8 years) and accounted for more variance in a mathematical attainment test than general cognitive ability 16 months…

The purpose of this study was to examine the cognitive and academic profiles associated with learning disability (LD) in reading comprehension, word reading, applied problems, and calculations. The goal was to assess the specificity hypothesis, in which unexpected underachievement associated with LD is represented in terms of distinctive patterns…

The purpose of the present study was to explore the 3rd-grade cognitive predictors of 5th-grade computational skill with rational numbers and how those are similar to and different from the cognitive predictors of whole-number computational skill. Students (n=688) were assessed on incoming whole-number calculation skill, language, nonverbal…