Introduction: The present paper shows the importance of a joint use of pencil and paper activities and of technology so that students may develop a complete understanding of ratio and proportion. A previous experience with strategy use when solving ratio and proportion problems provided background. Prompted by a recognition of the cognitive…

In this article I present an activity introducing statistical concepts to engineering students to help them develop inductive reasoning and problem-solving skills.

In this article we derive all salient properties of analytic functions, including the analytic version of the inverse function theorem, using only the most elementary convergence properties of series. Not even the notion of differentiability is required to do so. Instead, analytical arguments are replaced by combinatorial arguments exhibiting…

As early as 3500 years ago, shadows of sticks were used as a primitive instrument for indicating the passage of time through the day. The stick came to be called a "gnomon" or "one who knows." Early Babylonian obelisks were designed to determine noon. The development of trigonometry by Greek mathematicians meant that hour lines…

In this article, the author responds to the paper "Exploring pre-service teachers' understanding of statistical variation: Implications for teaching and research" by Sashi Sharma (see EJ779107). In that paper, Sharma described a study "designed to investigate pre-service teachers' acknowledgment of variation in sampling and…

This note discusses the introduction of Fourier series as an immediate application of optimization of a function of more than one variable. Specifically, it is shown how the study of Fourier series can be motivated to enrich a multivariable calculus class. This is done through discovery learning and use of technology wherein students build the…

Four experiments were conducted in order to examine effects of notation--Arabic and verbal numbers--on relevant and irrelevant numerical processing. In Experiment 1, notation interacted with the numerical distance effect, and irrelevant physical size affected numerical processing (i.e., size congruity effect) for both notations but to a lesser…

In this article we propose building sets of problems rooted in the same concept, a process that allows students to develop understanding and take on increasingly complex problems. By beginning with "foundation stories" and using strategies similar to those for literary constructs, we have dramatically increased our students' mathematical…

Evert Willem Beth (1908-1964) was a Dutch logician, mathematician and philosopher, whose work mainly concerned the foundations of mathematics. Beth was among the founders of the Commission Internationale pour l'Etude et l'Amelioration de l'Enseignement des Mathematiques and was a member of the Central Committee of the International Commission on…

This article illustrates the concept of statistical independence using the example of slot machines that may be played on multiple lines.

A method is derived for the numerical evaluation of the error term arising in some Gauss-type formulae modified so as to approximate Cauchy Principal Value integrals. The method uses Chebyshev polynomials of the first kind. (Contains 1 table.)

In the present note, two Parseval-type relations involving the Laplace transform are given. The application of the relations is demonstrated in evaluating improper integrals and Laplace transforms of trigonometric functions.

The article documents student experiences with quilt blocks in a mathematics classroom. Using blocks as tools, students construct their understanding of perimeter, area, probability, and transformations. (Contains 9 figures.)

In this commentary, some remarks are offered on David Pimm, Mary Beisiegel, and Irene Meglis' article "Would the Real Lakatos Please Stand up." The commentary focuses on relatively recent developments in the philosophy of mathematics based on the work of Lakatos; on theory development in mathematics education; and offers critique on whether…

For any parent tetrahedron ABCD, centroids of selected sub-tetrahedra form the vertices of an irregularly shaped space-filling truncated octahedron. To reflect these properties, such a figure will be called an ISTO. Each edge of the ISTO is parallel to and one-eighth the length of one of the edges of tetrahedron ABCD and the volume of the ISTO is…