In this paper, we aim to contribute to the discussion of the role of the human body and of the concrete artefacts and signs created by humankind in the constitution of meanings for mathematical practices. We argue that cognition is both embodied and situated in the activities through which it occurs and that mathematics learning involves the…

This article presents different approaches to a problem, dubbed by the author as "the consecutive pages problem". The aim of this teaching-oriented article is to promote the teaching of abstract concepts in mathematics, by selecting a challenging amusement problem and then presenting various solutions in such a way that it can engage the attention…

By working through well-designed tasks, students can expand their thinking about mathematical ideas and their approaches to solving mathematical problems. They can come to see the value of looking at tasks from different perspectives and of using different representations. This article discusses four tasks that encourage high school students and…

The mathematical topic of inverse functions is an important element of algebra courses at the high school and college levels. The inverse function concept is best understood by students when it is presented in a familiar, real-world context. In this article, the authors discuss some misconceptions about inverse functions and suggest some…

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. Nonroutine tasks encourage students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions. This…

This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos--satisfying an axiom sin[superscript 2] + cos[superscript 2] = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two…

Recent years have witnessed a growing interest in interdisciplinary teaching and learning in the elementary grades. Teachers are increasingly looking for ways to help their students integrate literacy instruction with content area learning. This article highlights some of the similarities between reading comprehension and mathematical…

In this paper we describe the results that we have obtained while integrating algorithm visualization (AV) movies (strongly tightened with the other teaching material), within a first-year undergraduate course on algorithms and data structures. Our experimental results seem to support the hypothesis that making these movies available significantly…

A visual approach to understanding the chain rule and related derivative formulae, for functions from R to R and from C to C, is presented. This apparently novel approach has been successfully used with several audiences: students first studying calculus, students with some background in linear algebra, students beginning study of functions of a…

Solving problems in different ways is strongly advised for mathematics learning and teaching. There is, however, little data available on the examination of teachers' openness to and evaluation of different solutions to the problems. In this paper, the author examines classroom teachers' openness to different solutions (or to what extent they…

This article deals with a brief history of Fibonacci's life and career. It includes Fibonacci's major mathematical discoveries to establish that he was undoubtedly one of the most brilliant mathematicians of the Medieval Period. Special attention is given to the Fibonacci numbers, the golden number and the Lucas numbers and their fundamental…

In late October 1967, the USS Scorpion was lost at sea, somewhere between the Azores and Norfolk Virginia. Dr. Craven of the U.S. Navy's Special Projects Division is credited with using Bayesian Search Theory to locate the submarine. Bayesian Search Theory is a straightforward and interesting application of Bayes' theorem which involves searching…

Communicating and collaborating online are becoming common requirements in education. The specialized notations and symbols necessary for some content areas where mathematical expressions are part of the conversation require that users select appropriate communication tools. The purpose of this article is to describe tools that can be used for…

One of the difficulties in any teaching of mathematics is to bridge the divide between the abstract and the intuitive. Throughout school one encounters increasingly abstract notions, which are more and more difficult to relate to everyday experiences. This article examines a familiar approach to thinking about negative numbers, that is an…

Graphing utilities, such as the ubiquitous graphing calculator, are often used in finding the approximate real roots of polynomial equations. In this paper the author offers a simple graphing technique that allows one to find all solutions of a polynomial equation (1) of arbitrary degree; (2) with real or complex coefficients; and (3) possessing…