For cell-like upper semicontinuous (usc) decompositions "G" of finite dimensional manifolds "M", the decomposition space "M/G" turns out to be an ANR provided "M/G" is finite dimensional ([Dav07], page 129). Furthermore, if "M/G" is finite dimensional and has the Disjoint Disks Property (DDP), then "M/G" is homeomorphic to "M" ([Dav07], page 181).…

Many students confuse the standard deviation and standard error of the mean and are unsure which, if either, to use in presenting data. In this article, we endeavour to address these questions and cover some related ambiguities about these quantities.

In this article, we consider the concept of rhotrices and present one-sided system of the form R[subscript n]x = b, where R[subscript n] is an n-dimensional rhotrix, x the unknown n-dimensional rhotrix vector and b the right-hand-side rhotrix vector.

A base for linear recursive sequences, such as the sequence of Fibonacci numbers, is defined within the framework of the sum of the digits of a number. Examples of bases of a number of such sequences are then outlined, and a Mobius strip is also used to illustrate the effects diagrammatically.

In this study, we show how to construct a function from the set N of natural numbers that explicitly counts the set Q[superscript +] of all positive rational numbers using a very intuitive approach. The function has the appeal of Cantor's function and it has the advantage that any high school student can understand the main idea at a glance…

By using the Cauchy-Schwarz inequality a new proof of several standard inequalities is given. A new proof of Young's inequality is given by using Holder's inequality. A new application of the above inequalities is included.

This article shows that when applying resampling methods to the problem of comparing two proportions, students can discover that whether you resample with or without replacement can make a big difference.

This paper explores how mathematicians build meaning through communicative activity involving talk, gesture and diagram. In the course of describing mathematical concepts, mathematicians use these semiotic resources in ways that blur the distinction between the mathematical and physical world. We shall argue that mathematical meaning of…

This is a study about how graphs of functions of two-variables are taught. We are interested in particular in the techniques introduced to draw and analyze these graphs. This continues previous work dedicated to students' understanding of topics of two-variable functions in multivariable calculus courses. The model of the "moments of…

In this paper, we describe the way in which traditional Indonesian games can support the learning of linear measurement. Previous research has revealed that young children tend to perform measurement as an instrumental procedure. This tendency may be due to the way in which linear measurement has been taught as an isolated concept, which is…

The Association of Teachers of Mathematics (ATM) exists for, and is run by, its members. Branch meetings are so much more than the "grass roots" of the association--it can be a powerhouse of inspiration and creativity. In this article, the authors provide commentaries on a recent branch meeting.

While hesitating to say that teachers are entering a new era for mathematics education, the author ventures that, on the basis of members' experience in the All Attainment Group, things are definitely looking up. For several years now the group has been bumping along with a quite small core group of active participants, but in the last twelve…

This article presents an extended analogy that connects infinite sequences and series to the science of genetics, by identifying power series as "DNA for a function." This analogy allows standard topics such as convergence tests or Taylor approximations to be recast in a "forensic" light as mathematical analogs of genetic concepts such as DNA…

This article describes an investigation of Buffon's coin problem and related problems with the aid of an applet. The problems are accessible at a variety of grade levels and facilitate making connections between geometry and probability.

Limits are foundational to the central concepts of calculus. However, the authors' experiences with students and educational research abound with examples of students' misconceptions about limits and infinity. The authors wanted calculus students to understand, appreciate, and enjoy their first introduction to advanced mathematical thought. Thus,…