Recognizing patterns is an essential skill in early mathematics education. However, first graders often have difficulties with tasks such as extending patterns of the form ABCABC. Studies show that this pattern-recognition ability is a good predictor of later pre-algebraic skills and mathematical achievement in general, or the development of…

Many students are finishing secondary school without the essential mathematical skills needed to participate in social activities. Research in mathematics education has been investigating the phenomenon of persistent low achievement in mathematics learning from various perspectives, including cognitive, affective, and social ones. Each perspective…

This study examined how two small-group discourse types (Reflective and Exploratory) supported the inclusion and enacted levels of cognitive demand of students who typically struggle with mathematics in real-world, task-based assessment activities. The study focused on 11 fifth-grade students within a larger study involving 97 fifth-grade students…

This volume, a comprehensive survey and critical analysis of today's issues in mathematics education, distills research to build knowledge and capacity in the field. The compendium is a valuable new resource that provides the most comprehensive evidence about what is known about research in mathematics education. The 38 chapters present five…

Impairments in executive function have been documented in school-age children with mathematical learning difficulties. However, the utility and specificity of preschool executive function abilities in predicting later mathematical achievement are poorly understood. This study examined linkages between children's developing executive function…

This study examined how four domain-specific skills (arithmetic procedural skills, number fact retrieval, place value concept, and number sense) and two domain-general processing skills (working memory and processing speed) may account for Chinese children's mathematics learning difficulties. Children with mathematics difficulties (MD) of two age…

This article focuses on the cognitive factors that impact on students in the middle school years experiencing learning difficulties in basic mathematics. It begins with a review of selected literature providing information about the learning difficulties in mathematics. Focus then shifts to an implementation of the "Quicksmart"…

Investigates students' abilities to draw inferences. Introduces cognitive conflict in the form of video clips of reasoning expressed by students. Documents change with regard to the levels of observed response for the protocol and the use of displayed variation in the graphs. Analyzes change associated with the presentation of cognitive conflict.…

The ideas and techniques involved in learning about fractions were investigated with students in grades 1-12, in the first 3 years of colleges, in community college mathematics courses, and in graduate school. Also included were some high school mathematics teachers, some mathematicians, and some retired persons. Part I provides the rationale and…

Two phenomena related to the quality of student responses in regard to items used in a testing situation are involved in the construction of a pupil response model. The underlying phenomenon which defines the individual's cognitive limits is termed the hypothetical cognitive structure (HCS). The second phenomenon, which is a function of not only…

Common mathematical errors of pupils as identified by the Concepts in Secondary Mathematics and Science Project are identified and traced to the use of methods invented by students rather than formally taught methods. (MP)

The research described here seeks to characterize the "managerial" aspects of expert and novice problem-solving behavior, and to describe the impact of managerial or "executive" actions on success or failure in problem solving. A framework for analyzing protocols of problem-solving sessions based on "episodes" of…

This document notes that arithmetic disabilities can occur with an otherwise normal intelligence level. Two models of explanation are given. The first emphasizes the conditions under which children learn mathematics, the second views the identification of a number of factors in the "structure of intelligence" that appear to be strongly…

The author seeks to clarify the difficulty and complexity of the things youngsters must do to learn mathematics, and to have teachers question their own views about children in redefining mathematics instruction. (MP)

Presented are transcriptions of a research panel presentation held at the annual meeting of the National Council of Teachers of Mathematics, Boston, Massachusetts, April 1979. The members of the panel are all involved in working directly with children in a clinical setting for pupils with learning disabilities in mathematics and with graduate…