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 forum is focused on thinking about and with algorithms as a way of unifying all one's mathematical endeavors. The lead article by Maurer presents examples and discussion of this point. Responses, often disagreeing with his views, are by Douglas, Korte, Hilton, Renz, Smorynski, Hammersley, and Halmos. (MNS)

This paper describes the Structure-Mapping Engine (SME), a cognitive simulation program for studying human analogical processing. SME is based on Gentner's Structure-Mapping theory of analogy, and provides a "tool kit" for constructing matching algorithms consistent with this theory. This flexibility enhances cognitive simulation studies by…

Sixteen Brazilian third graders aged 8-13 were given problems involving multidigit computation. School-taught algorithms were likely to be used in school-taught problems, with little carry-over to real problem situations, but resulted in more incorrect answers. (MNS)

Use of low-stress algorithms to reduce the cognitive load on students is advocated. The low-stress algorithm for addition developed by Hutchings is detailed first. Then a variation on the usual algorithm is proposed: adding from left to right, writing the partial sum for each stage. Next, a "quick addition" method for adding fractions proposed by…

This review of the literature and annotated bibliography summarizes the available research relating to teaching programming to high school students. It is noted that, while the process of programming a computer could be broken down into five steps--problem definition, algorithm design, code writing, debugging, and documentation--current research…

The author argues that children not only can but should create their own computational algorithms and that the teacher's role is "merely" to help. How children in grades K-3 add and subtract is the focus of this article. Grouping, directionality, and exchange are highlighted. (MNS)

The ideas and techniques involved in learning about fractions were investigated with students in grades 1-12, in the first 3 years of colleges, in community college mathematics courses, and in graduate school. Also included were some high school mathematics teachers, some mathematicians, and some retired persons. Part I provides the rationale and…

In one school, algorithmic development has been infused in the mathematics curriculum. An example of what occurs in mathematics classes since the teachers began using the computer is given, with two students' conjectures included as well as the algebraic justification. (MNS)

Computational strategies and estimating abilities of 466 Japanese students were tested and interviews with a subsample of that group were used to compare with a theoretical model based on a sample from the United States. Results of the comparison of computational and estimating abilities are presented. (CW)

Activities are given to assist students in seeing a rationale for the difficult algorithms we teach for fractions. Both interpretations of fractions and operations with fractions are discussed. (MNS)

Examines the hypothesis that there are preliminary stages in problem solving that are often neglected in teaching chemistry. Discusses correlations calculated between the student's ability to handle disembedding and cognitive restructuring tasks in the spatial domain and ability to solve chemistry problems. (TW)

The concept of multiplication is described and illustrated using several different representational systems. A conceptual approach to teaching mathematics is compared with the procedural approach commonly found in the school curriculum. Four different methods of representing the multiplication process with numbers larger than ten are presented:…

Traditional methods of teaching addition include algorithms that involve right-to-left procedures. This article describes efficient procedures for left-to-right addition and subtraction involving computation and computational estimation that reflect children's natural behaviors observed during activities with unifix cubes. (MDH)

The educational background of students termed "limited English proficient" (LEP) is discussed, with consideration of how that background might affect the LEP student's learning of arithmetic. Reasons why knowledge of background is important are first noted. Then examples of different ways to read and write numerals and differing subtraction and…