Fuzzy sets have experienced multiple expansions since their conception to enhance their capacity to convey complex information. Intuitionistic fuzzy sets, image fuzzy sets, q-rung orthopair fuzzy sets, and neutrosophic sets are a few of these extensions. Researchers and academics have acquired a lot of information about their theories and methods…

The book synergizes research on number across two disciplines--mathematics education and psychology. The underlying problem the book addresses is how the brain constructs number. The opening chapter frames the problem in terms of children's activity, including mental and physical actions. Subsequent chapters are organized into sections that…

This fourth book in the Mathematics Recovery series equips teachers with detailed pedagogical knowledge and resources for teaching number to 7 to 11-year olds. Drawing on extensive programs of research, curriculum development, and teacher development, the book offers a coherent, up-to-date approach emphasizing computational fluency and the…

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…

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…

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…

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…

Described are children's strategies in thinking about fraction order and equivalence. The data are based on two teaching experiments with fourth and fifth-grade children. Some sample activities for teaching order and equivalence are included. (RH)

The development of a quantitative concept of rational numbers was explored in interviews with 16 fourth and fifth graders in two cities. High performers used a flexible and spontaneous application of concepts of rational number order and fraction equivalence, and a reference point, while low achievers tended not to. (MNS)

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)

By varying task conditions and constraints on subjects, this study attempted to extend and refine a developmental theory of partitioning as a foundational process undergirding children's construction of a rational number. Subjects were 31 preponderantly higher-grade pupils enrolled at an elementary school in Nova Scotia, Canada. Two tasks were…

A two-year study was conducted with fourth-grade children in the context of extensive teaching experiments concerned with the learning of rational number concepts. Representational difficulties in using the number line model were investigated. While instruction in the second year attempted to resolve observed learning difficulties, the results of…

Examples are given of transcripts made from tape recordings of a teacher working with groups of 10-year-old children using calculators. Attention is focussed on the teacher's role in the interactions which take place. Suggestions are offered for the possibility of a structure of strategies available to a teacher. (Author/RH)