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…

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)

This study systematically examined developmental changes in the flexibility of preschool children's counting skills by assessing their use of counting to solve different kinds of quantitative problems at several preschool age levels. Three principal kinds of quantitative problems were considered: (1) quantifying a given set; (2) generating a set…

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)

Eleven retarded children with mental ages (MA) less than 4.5 years were examined to evaluate whether there is a critical MA for learning basic counting principles and how an understanding of counting develops. Results are discussed in terms of individual needs. (MNS)

A model is proposed in which the quantification of inverse proportionality is developed beyond the initial qualitative relation. Based on a task analysis, the model was tested with 36 eleven-year-old students in a training experiment using a balance task. (MNS)

This case study of a 30-year-old woman with a developmental learning disability (including anomia, auditory processing problems, difficulty in learning reading and spelling skills, and a poor sense of number) suggests that all these impairments may be explained in terms of a sequential processing deficit. (Author/DB)

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…

This study addressed the problem of promoting generalization of knowledge in people with mental handicaps, by presenting an approach based on the idea that certain cognitive representations of strategies and related concepts are common to solving a wide variety of problems. The surface context of these problems may vary considerably, but all will…

The goal of books in this series is to present work that is on the growing tip of research in cognitive development. The theme of this volume is children's logical and mathematical cognition, a field in which Piaget's influence has been extensive. In the first of the six chapters, Acredolo presents a new theory of the cognitive bases for…

Teaching sequences designed to develop strategies for comparing numerals in grade two (in France) were analyzed. Children's strategies were noted, and an experiment confirmed underlying misconceptions concerning number. (MNS)

Three models are compared in terms of detail, scope, attention to individual differences, and how they deal with qualitative change and semantic processing. Two are information-processing models of arithmetical word problem-solving performance, and the third is a model of children's counting types and thinking strategies. (MNS)

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…

This resarch identified K-6 children's (N=1202) and teachers' (N=54) perceptions of what constitutes doing or using mathematics. Perceptions were documented by a questionnaire which included items reflecting the six major strands of the K-6 syllabi and explicit and implicit use of numbers and operations as both facilitating and distracting…

This study documented the spontaneously derived strategies that children use which may play a key role in the transition from counting to recall of number facts. For these strategies, the child uses a small set of known number facts to derive the solution to unknown number facts. How training in the use of derived strategies influences the…