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)

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)

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…

Notes that almost all computer engineering textbooks present algorithms using only verbal methods. Poses that engineering students' ability to handle graphic representation is crucial yet information is presented verbally. Summarizes the results of 12 replications on learner preference for graphic or verbal algorithmic techniques. (MVL)

Defines M-demand as the maximum number of schemes that the subject must activate simultaneously in the course of executing a task. Discusses the effect of M-demand on problem solving. Uses algorithms to reduce M-demand. Describes the role of algorithms in problem solving. (MVL)