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…

An increasing number of high-stakes mathematics standardised tests around the world place an emphasis on using mathematical word problems to assess students' mathematical understanding. Not only do these assessments require children to think mathematically, but making sense of these tests' mathematical word problems also brings children's language…

The purpose of this review is to determine the evidence base classification of schema-based instruction (SBI) as an intervention to improve word problem-solving outcomes in mathematics for students with learning or mathematics disabilities in Grades K-12. Using the Council for Exceptional Children's quality indicators (QIs) and standards, we…

The ability to retrieve basic arithmetic facts from long-term memory contributes to individual and perhaps sex differences in mathematics achievement. The current study tracked the codevelopment of preference for using retrieval over other strategies to solve single-digit addition problems, independent of accuracy, and skilled use of retrieval…

The worked example effect indicates that examples providing full guidance on how to solve a problem result in better test performance than a problem-solving condition with no guidance. The generation effect occurs when learners generating responses demonstrate better test performance than learners in a presentation condition that provides an…

In the international literature, increasing numbers of articles and books are published about teaching and learning, with the brain in mind. For a long time, I have been sceptical about this question. However, seeing many unresolved issues in the teaching and learning of mathematics, I slowly started to study the relevant literature and have…

The use of manipulatives to teach mathematics is often prescribed as an efficacious teaching strategy. To examine the empirical evidence regarding the use of manipulatives during mathematics instruction, we conducted a systematic search of the literature. This search identified 55 studies that compared instruction with manipulatives to a control…

In school, at least in the US, we were taught to multiply by hand according to a standard algorithm. Most people find that algorithm difficult to use, and many children fail to learn it. We propose a new way to make sense of this difficulty: to treat explicit computation as perceptually supported physical and mental action. Based on recent work in…

In this study, we test an information-processing model (IPM) of problem solving in science education, namely the working memory overload model, by applying catastrophe theory. Changes in students' achievement were modeled as discontinuities within a cusp catastrophe model, where working memory capacity was implemented as asymmetry and the degree…

Arithmetic word problems are often presented accompanied by illustrations. The present study examined how different types of illustrations influence the speed and accuracy of performance of both good (n = 67) and poor arithmeticians (n = 63). Twenty-four arithmetic word problems were presented with four types of illustrations with increasing…

This collection of 58 articles from the recently-published third edition of the International Encyclopedia of Education focuses on learning, memory, attention, problem solving, concept formation, and language. Learning and cognition is the foundation of cognitive psychology and encompasses many topics including attention, memory, categorization,…

The ability to compute, problem solve, and apply concepts and skills in mathematics influences multiple decisions in our lives. The National Research Council (1989) reported that mathematics is especially evident in our technology-rich society, where number sense and problem solving skills have increased the importance and demands of advanced…

This article investigates the effect of the vitality of historical issues in collective memory on students' history learning processes and products. Forty 12th grade students of different ethnic background participated in two historical problem-solving learning tasks. The historical issues were found to differ in their vitality in collective…

Many students find it difficult to learn the kinds of knowledge and thinking required by college or high school courses in mathematics, science, or other complex domains. Thus they often emerge with significant misconceptions, fragmented knowledge, and inadequate problem-solving skills. Most instructors or textbook authors approach their teaching…

There is little data available concerning the executive functions of children with dyslexia. The small number of existing studies in this field focus on single aspects of these functions such as working memory. The aim of the present study was therefore to assess a variety of aspects of executive functioning in children with dyslexia. Forty-two…