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 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…

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 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)

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)

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)

This report describes an investigation in England of some of the problems children experience with fractions. In particular, the restricted view that some children have of fractions is investigated. The methodology involved a large number of interviews with secondary school children (aged 12-14). The results of these interviews led to the design…

This booklet is a catalog of error patterns found in basic arithmetic and algebra courses. It is intended to be used as a resource by instructors and tutors teaching these concepts. The material is divided into major concept headings with subheadings. The error patterns are named and given a brief general description followed by a specific example…

Two major ways to view the numbers to 100 are counting by ones and grouping by tens and ones. Research suggests that early understanding of numbers comes from counting and that place value instruction cannot be hurried. (PK)

Children in grades four and five had instruction on fractions with a continuous manipulative aid to help transfer their knowledge to tasks with a discrete manipulative aid. Results suggest that discrete-embodiment tasks are more difficult than continuous-embodiment tasks. (MNS)

Children's responses to an alternative model over three lessons were described and their learning assessed in a posttest. Their responses and performances were compared to that of a similar group of children learning through a conventional number line model. The two models were compared from practical and theoretical viewpoints. (Author/CW)

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…

This publication is an abstracted compilation of 15 investigations selected from other journals. The information includes purpose, rationale, research design and procedures, findings, interpretations, abstractor's comments, and references. This journal includes the following reports: (1) "A Constructivist Approach to Numeration in Primary…