The purpose of this study was to investigate the preservice secondary mathematics teachers' development of pedagogical understanding in the teaching of modular arithmetic problems. Data sources included, written assignments, interview transcripts and filed notes. Using case study and action research approaches cases of three preservice teachers…

Given that the sine and cosine functions of a real variable can be interpreted as the coordinates of points on the unit circle, the author of this article asks whether there is something similar for complex variables, and shows that indeed there is.

In this article, we present a somewhat surprising result connected with random permutations.

This article focusses on the specific learning disabilities found in schools such as Dyslexia and Dyscalculia, the influence of dyslexia on dyscalculia and the need to adopt certain strategies that help cope with this problem. Learners with multifarious language-related or arithmetic-related disabilities are found in most schools. These children…

Being a mathematician, the author started to wonder if there are any theorems in mathematics that seem very ordinary on the outside, but when applied, have surprisingly far reaching consequences. The author thought about this and came up with the following unlikely candidate which follows immediately from the definition of the area of a rectangle…

Many high-school mathematics teachers have likely been asked by a student, "Why does the cross-multiplication algorithm work?" It is a commonly used algorithm when dealing with proportion problems, conversion of units, or fractional linear equations. For most teachers, the explanation usually involves the idea of finding a common denominator--one…

Recent research has revealed new information about how preschoolers develop an understanding of counting, and offers exciting new strategies for teaching. These new strategies encourage children to problem solve and use reasoning to understand quantities and how counting works rather than simply providing them practice with counting procedures.…

Shrinky Dinks[R] are a plastic-sheet material that shrinks, hardens and thickens when heated in a traditional or toaster oven. The material was a favorite of generations, but many contemporary students and professionals in art have never had the opportunity to play with the unique media. This article discusses Shrinky Dinks and the importance of…

This study investigated introductory calculus students' spontaneous reasoning about limit concepts guided by an interactionist theory of metaphorical reasoning developed by Max Black. In this perspective, strong metaphors are ontologically creative by virtue of their emphasis (commitment by the producer) and resonance (support for high degrees of…

Mathematics is a natural part of daily life for young children as they explore and investigate the world around them. To build on these experiences, and to begin establishing a mathematical foundation, early childhood educators must not only be knowledgeable about mathematical concepts, they must also be aware of the most developmentally…

Parametric differentiation and integration under the integral sign constitutes a powerful technique for calculating integrals. However, this topic is generally not included in the undergraduate mathematics curriculum. In this note, we give a comprehensive review of this approach, and show how it can be systematically used to evaluate most of the…

Flexibility in the use of mathematics procedures consists of the ability to employ multiple solution methods across a set of problems, solve the same problem using multiple methods, and choose strategically from among methods so as to reduce computational demands. The purpose of this study was to characterize prospective elementary teachers' (n =…

It is well known that meaningful knowledge of statistics involves more than simple factual or procedural knowledge of statistics. For an intelligent use of statistics, conceptual understanding of the underlying theory is essential. As conceptual understanding is usually defined as the ability to perceive links and connections between important…

Sets of mathematics problems are generally arranged in 1 of 2 ways. With "blocked practice," all problems are drawn from the preceding lesson. With "mixed review," students encounter a mixture of problems drawn from different lessons. Mixed review has 2 features that distinguish it from blocked practice: Practice problems on…

Data from 154 interviews with students in grades 3 to 13 were analyzed to suggest a developmental progression of conceptual understanding associated with the sample space for two ordinary six-sided dice tossed simultaneously. The model was then considered in the light of responses to an extension task involving three six-sided dice with four sides…