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…

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…

Discusses flaws in the Apple IIe Applesoft random number generator, RND, and reports results of frequency and serial correlation tests of the generator. Suggestions of seeds that yield sequences of numbers which pass fundamental screening tests for randomness are presented. (Author/LRW)

Explores in three experiments development of three linguistic aspects of "more" in children's speech. Experiment 1 examined nature of early semantic content of "more;" Experiment 2, the child's differentiation of mass "more" from count "more"; and Experiment 3, the child's use of "more" as a…

Proposes the hypothesis that preschoolers have number concepts based on the numbers 1-5 rather than on the decimal structure. Results suggest that children understand numbers to 5 as a privileged anchor. Proposes a new model for a representational system of numbers. (Author/DR)

Comparison of 15 English children (mean age 7.5 years) with specific language difficulties and 12 similar children with mathematical difficulties found few differences in their ability to process 2- and 3-digit numbers. Results suggest that a language difficulty may underlie delayed performance in mathematics. (DB)

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)

Presented is a brief overview of Japanese education followed by specific ideas about important considerations in the teaching of mathematics in elementary grades. Examples are given for teaching flexibility in mathematical thinking. (RH)

Discussed are the results of interviews with 63 Australian children (interviewed in English) and 62 Nigerian children (62 interviewed in English and 60 interviewed in Yoruba) to determine how they used number concepts in discussing five demonstrations manipulating physical matter. Differences between the two groups are considered. (RH)

The study compared two methods of teaching an initial place value skill: a concrete, semiconcrete, abstract teaching sequence and an abstract-only presentation. Learning-disabled elementary and middle school students (N=24) using the concrete to abstract teaching sequence performed significantly better on three posttests than students taught the…

Compared performance of Malaysian children with that of English children on a test into the understanding of number concepts. Findings indicate that difficulties of Malaysian children may be quite different from those of English children. Among the difficulties identified were misconceptions about the order of operation in division and…

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…