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 author wants her students to see any new mathematics--fractions, negative numbers, algebra--as logical extensions of what they already know. This article describes two students' efforts to make sense of their conflicting interpretations of 1/2 × -6, both of which were compelling and logical to them. It describes how discussion, constructing…

The authors asked fifth-grade and eighth-grade students to pose stories for number sentences involving the addition and subtraction of integers. In this article, the authors look at eight stories from students. Which of these stories works for the given number sentence? What do they reveal about student thinking? When the authors examined these…

Just as athletes stretch their muscles before every game and musicians play scales to keep their technique in tune, mathematical thinkers and problem solvers can benefit from daily warm-up exercises. Jessica Shumway has developed a series of routines designed to help young students internalize and deepen their facility with numbers. The daily use…

A considerable body of research exists on students' understanding of decimal fractions and the prevalence and persistence of common misconceptions related to this understanding. Results from major studies such as the National Assessment of Educational Progress (NAEP) in the United States and the Concepts in Secondary Mathematics and Science (CSMS)…

Action research (AR) is defined by Macintyre to be: "an investigation, where, as a result of rigorous self-appraisal of current practice, the researcher focuses on a problem,or a topic or an issue which needs to be explained, and on the basis of information, plans, implements, then evaluates an action then draws conclusions on the basis of…

Children's natural curiosity about numbers, big and small can lead to exploring place-value ideas. But how can these abstract concepts be experienced more concretely? This article presents some practical approaches for conceptualising very small numbers using linear models, area models, volume models, and diagrams.

This book provides a landscape of learning that helps teachers recognize, support, and celebrate their students' capacity to structure their worlds algebraically. It identifies the models, contexts, and landmarks that facilitate algebraic thinking in young students and provides insightful and practical methods for teachers, math supervisors, and…

Described is a study designed to extend a theoretical model of children's progression from a perceptual to an abstract concept of number. The implications of this research for the design of mathematics curricula are discussed. (CW)

Arithmetic programming for students with mild mental disabilities requires a comprehensive perspective that includes attention to curriculum, instruction, and appraisal. Arithmetic computation should not dominate educational programming, but should be included in ways that are functionally relevant and meaningfully presented within a framework of…

Seventh-grade students were tested to uncover arithmetic errors. Answers and intermediate steps were analyzed and models to represent students' behavior were developed. Certain errors were common across students. Others were tied to the format of the test item. Some superficial understandings of mathematical concepts were exposed. (Author/DC)

This competency analysis profile contains eight lists of mathematics skills that have been identified by employers and verified by math-certified instructors as being core competencies for eight groups of occupational areas. Each list is organized into subsections dealing with the following: numbers and number relations, measurement, data analysis…

The papers presented in these proceedings are organized into seven categories: (1) number and number operations (13 papers); (2) spatial representation and geometrical understanding (10 papers); (3) developing and/or using models of mathematical learning (15 papers); (4) mathematical concept formation (17 papers); (5) the mathematical learning…

This document is intended to help Australian technical and further education instructors in New South Wales (TAFE NSW) identify teaching principles and learning activities that they can use to help adult learners master the mathematics processes, knowledge, and skills needed to perform basic measurement tasks in today's workplace. The materials…