This paper discusses variation in reasoning strategies among expert mathematicians, with a particular focus on the degree to which they use examples to reason about general conjectures. We first discuss literature on the use of examples in understanding and reasoning about abstract mathematics, relating this to a conceptualisation of syntactic and…

How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…

"In Brief" focuses on K-12 mathematics and science research and implications for policymakers, educators, and researchers seeking to improve student learning and achievement This brief highlights the learning gains of 240 elementary students involved in a long-term study in Madison, Wisconsin and their remarkable ability to reason with arithmetic…

Recent research literature has highlighted the interest of both teachers and researchers in using analogies to aid students' conceptual understanding. This appears to be especially relevant in secondary chemistry education due to the many abstract concepts that are included in the curricula. This paper reviews recent literature and considers…

Reports on a study of how naive theories, age, and education relate to higher order thinking among 54 adolescents and adults. Finds that, regardless of age and education, all subjects referred to naive theories to identify causes and create remedial strategies for social problems. (CFR)

Analyzes the art criticism of nine university art education students writing about the work of Robert Rauschenberg. Identifies the students' use or nonuse of thematic unity, intertextuality, opposition, and description. These thinking strategies are primarily found in the works of three professional art critics. (MJP)

This book was written to help teachers gain a better understanding of children who are failing in school and to provide a systematic process of attacking their learning problems. The text presents workable principles for determining probable causes of learning problems and for selecting suitable, effective remedial activities. Learning problems…