The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical…

We define and describe how subitizing activity develops and relates to early quantifiers in mathematics. Subitizing is the direct perceptual apprehension and identification of the numerosity of a small group of items. Although subitizing is too often a neglected quantifier in educational practice, it has been extensively studied as a critical…

As America's Great City Schools implement the Common Core State Standards (CCSS), they have a unique opportunity to integrate strategies for teaching, intervening, and supporting the nation's urban students in a way that will ensure they have the literacy, numeracy, behavioral, and engagement skills necessary to be successful in college and…

The chapters in this book reflect the work of science and mathematics educators who have worked for many years at the international level. As members of the International Consortium for Research in Science and Mathematics Education, their work provides readers with issues, models, practices, and research results that have applicability and…

Research on computational estimation and mental computation has received a considerable amount of attention from mathematics educators during the past decade. These proceedings resulted from a meeting to explore dimensions of number sense and its related fields. The participants came from three groups: mathematics educators actively pursuing…

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…

Four experiments were conducted to study explanations of why children make relative number judgments inconsistent with their counting. Results are discussed in relation to judgments children make when they use matching, and in light of Klahr and Wallace's (1973) account of number development. (PCB)

Compares the effects of a part-part-whole curriculum for teaching the concept of number in the kindergarten to the effects of the standard curriculum. Describes the curriculum and instruction used. Overall, the treatment curriculum was successful in aiding development of basic number concepts. (YP)

This book contains 15 essays written between 1969 through 1983. The essays included are: (1) "Semantic Analysis of Verbs in Terms of Conceptual Situations"; (2) "'Because' and the Concepts of Causation"; (3) "The Development of Language as Purposive Behavior"; (4) "Adaptation and Viability"; (5) "On the…

The 5-stage model of Ross was used to examine the role of instruction in facilitating children's acquisition of place value knowledge. Compares children from 2 samples on 10 tasks designed to reveal their thinking about place value. Discusses implications for theory and classroom. (YP)

This study explored the ability of 14 individuals with autism to generate a unique series of digits. Individuals with autism were more likely to repeat previous digits than comparison individuals, suggesting they may exhibit a shortfall in response inhibition. Results support the executive dysfunction theory of autism. (Contains references.)…

An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.

To investigate the effect on young children's coding of spatial information, an array of boxes was varied in number, size, and arrangement and was shown to 20 toddlers. Only the number of boxes defining the left and right sides of the array influenced performance; that is, multiple boxes were associated with the use of external objects as spatial…

Reports the third grade and seventh grade results of the fourth mathematics assessment of the National Assessment of Educational Progress. Summarizes the major results of the performance on number, operations, and word problem items. Some examples of data are given. (PK)

Investigates whether elementary school students can construct operations of thought for integers and integer addition crucial for understanding elementary algebra. Two sixth graders were taught using a computer. Results included both students being able to construct mental operations for negating arbitrary integers and determining sign and…