Linear functions are an essential part of school and university education. Nevertheless, this topic is challenging for many students--especially in STEM topics. In this article, we contribute to the understanding of learning difficulties in the context of mathematical and physical problems. Here, we present the results of an eye-tracking study on…

There is a growing awareness that many children are not developing fast and accurate retrieval-based strategies for solving single-digit addition problems. In this study we individually assessed 166 third and fourth grade children to identify a group of children (called accurate-min-counters) who frequently solved simple single-digit addition…

The focus of this article is the well documented association between low working memory capacity and difficulty with mathematical word-problem solving. We begin by describing a model that specifies how various cognitive resources, including working memory, contribute to individual differences in word-problem solving and by then summarizing…

Recent studies have concluded that children's development of private speech (private speech internalization) is related to and important for developing mathematical ability. In this article, we review a project consisting of studies exploring the cognitive factors that may underlie differences between the use of private speech by children with…

The focus of this article is the well documented association between low working memory capacity and difficulty with mathematical word-problem solving. We begin by describing a model that specifies how various cognitive resources, including working memory, contribute to individual differences in word-problem solving and by then summarizing…

Cognitive strategies are important tools for children with math difficulties (MD) in learning to solve word problems. The effectiveness of strategy training, however, depends on working memory capacity (WMC). Thus, children with MD but with relatively higher WMC are more likely to benefit from strategy training, whereas children with lower WMC may…

Recent intervention studies directed to improve problem solving accuracy in children with math difficulties (MD) have found support for teaching cognitive strategies. This study addresses the question: What role does working memory capacity (WMC) play in strategy outcomes for children with MD? Four prediction models can be applied to strategy…

This article provides an overview of some perspectives about special issues in classroom mathematical teaching and learning that have stemmed from the huge explosion of research in children's mathematical thinking stimulated by Piaget. It concentrates on issues that are particularly important for less-advanced learners and for those who might be…

We used functional magnetic resonance imaging (fMRI) to explore the patterns of brain activation associated with different levels of performance in exact and approximate calculation tasks in well-defined cohorts of children with mathematical calculation difficulties (MD) and typically developing controls. Both groups of children activated the same…

As teachers of higher education, we expect students to enter college with some understanding of what it means to be an effective learner and the ability to apply effective learning strategies. Unfortunately, many students do not develop effective learning strategies unless they receive explicit instruction and the opportunity to apply these…

Sixth grade students (N=8) identified as poor spellers significantly benefited from remedial instruction involving structural word analysis and self-questioning strategy, suggesting that effective spelling instruction involves conveying knowledge of phonics and the linguistic structure of words (domain specific knowledge) and knowledge of spelling…

Argues that student comprehension difficulties are often diagnosed as reading problems, even though the problem extends to other learning skills. Considers the issue of comprehension in the context of reading, and examines aspects of the issue that extend to teacher communications. Suggest ways to help students understand social studies material.…

Empirical findings on the efficiency of memory processes in exceptional children are outlined. Cognitive deficits are considered to be central to many academic and social skill problems of children with mental retardation and learning and behavior problems. In response, educators and psychologists have devised ways of training such students to use…

New conceptions of learning, analogy, and capacity have fundamentally changed scientists' view of cognitive development. New conceptions of learning help to explain how representations of the world are acquired. New models of analogical reasoning have suggested that logical inferences are often made by mapping a problem into a mental model, or…

This article uses a cognitive problem-solving model to explore the application of hypermedia authoring software to mathematics in general and to mathematical problem solving in particular. Hypermedia is presented as a method of exploring alternative solution processes to remediate or prevent learning problems. (JDD)