Based on a synthesis of the literature, a model for problem posing cognitive processes was formulated, and validated. The major constructs incorporated in this framework were the situations in which problem posing occurs. For each situation, four cognitive processes were established: the editing of problems based on iconic or symbolic stimuli, the…

The Purposeful Algebraic Activity Project is a longitudinal study of the development of pupils' algebraic activity in the early years of their secondary schooling. Analysis of data from a spreadsheet-based teaching programme and from semi-structured interviews leads us to identify three features of the spreadsheet environment that appear to shape…

Our study concerns the analysis of teacher and student activities. Secondary school 6th grade students were confronted, for the first time, with solving equations. We used our cognitive models of students and experts (in algebraic calculations) for analyzing the teaching process and the cognitive functioning of students. Our model led us to…

"Focus on Basics" is the quarterly publication of the National Center for the Study of Adult Learning and Literacy. It presents best practices, current research on adult learning and literacy, and how research is used by adult basic education teachers, counselors, program administrators, and policymakers. "Focus on Basics" is dedicated to…

Even in early grades, a large gap in skills exists between students from economically advantaged and disadvantaged families. Evidence suggests that a substantial share of this skills gap emerges during the summer months, when school is not in session. Children from disadvantaged families experience greater losses in skills during summer vacations…

This study investigated the attitudes toward statistics of graduate students who used a computer program as part of the instruction, which allowed for an individualized, self-paced, student-centered, activity-based course. The twelve sections involved in this study were offered in the spring and fall 2001, spring and fall 2002, spring and fall…

The purpose of this paper is to share the strategies that children invented to solve problems involving division of fractions in the absence of algorithmic instruction. The data come from two sources, the first being a teaching experiment and the second being the regular classroom practice of this teacher/researcher. It was found that when the…

We present results from a study which investigated the influence of dynamic geometry-based activities in the development of proving skills (in geometry) in high-school students (15-16 years of age). After a 12-week course on Cabri and the writing of conjectures and proofs, students were asked to write and prove conjectures based on their…

This technical report describes a study that was undertaken to compare the content of three mathematics assessments conducted in 2003: the NAEP fourth-and eighth-grade assessments; the Trends in International Mathematics and Science Study (TIMSS), which also assessed mathematics at the fourth-and eighth-grade levels; and the Program for…

All children are entitled to a solid education in the United States. There is a good reason for this: For generations, education has been the most reliable path to a better life. A good education offers a better quality of life, including access to good jobs and careers. Getting a good education is even more important today than in the past as…

After the No Child Left Behind Act was signed into practice, states were required to implement stringent accountability systems including standards-based reform efforts and annual testing of students. Academic content standards define what students should know for each subject at each grade level and annual state assessments assess students'…

This study sought to ascertain children's perceptions of the value and usefulness of mathematics. Children were interviewed with open-ended and structured questions about the uses of mathematics. Findings indicated that children at the kindergarten through third-grade levels are positive about mathematics and their abilities to do mathematics.…

Examines the varying opinions on school readiness within a broad context and, more specifically, in relation to mathematics learning. Focuses on the kinds of mathematical experiences children should have before entering formal schooling and suggestions for parents of young children. Specific areas examined include: (1) national standards as a road…

Reviews current research on brain-behavior relationships in disabilities of arithmetic and mathematical reasoning from both a neurological and a neuropsychological perspective. Defines developmental dyscalculia and the developmental importance of right versus left hemisphere integrity for the mediation of arithmetic learning and explores…

Analyzes the current state of mathematics assessment as applied to individuals with learning disabilities. An overview of the development of mathematics assessment is provided and specific strategies for conducting math evaluations are described, including portfolios, criterion-referenced tests, curriculum-based measurement, observations, and…