This note presents an alternative approach to the reasoning process and derivation of the hypergeometric probability mass function (pmf), and contrasts it with a binomial model. It utilizes the essential concept of sampling without replacement directly in the development of the mass function.

This article presents a neat way to approximate the measure of an angle using a ruler and discusses the accuracy of various versions of the method.

We answer a geometric question that was raised by the carpenter in charge of erecting helical stairs in a 10-story hospital. The explanation involves the equations of lines, planes, and helices in three-dimensional space. A brief version of the question is this: If A and B are points on a cylinder and the line segment AB is projected radially onto…

This article describes a geometrical solution to a problem that is usually solved geometrically as an example of how alternative solutions may enrich the teaching and learning of mathematics. (Contains 11 figures.)

While the author was searching the web, he came across an article by Michael Keyton of IMSA (Illinois Mathematics and Science Academy) called "Theorems of mystery". The phrase is Keyton's own, and he defines such a theorem as "a result that has considerable structure with minimal hypotheses." The simplest of his 10 examples is one that many…

The number [pie] [approximately] 3.14159 is defined to be the ratio C/d of the circumference C to the diameter d of any given circle. In this article, the author looks at some surprising and unexpected places where [pie] occurs, and then thinks about some ways of remembering all those digits in the expansion of [pie].

The author first saw Trevor Fletcher's film on the cardioid as an undergraduate in 1959. When he saw Fletcher's cardioid film once again, the author was vividly reminded of his first experiences of animated mathematics nearly 50 years before. He discovered that the idea of using mental pictures to develop dynamic images came from work by the Swiss…

Teachers want and need students to excel in the classroom. Cooperative learning is one method recognized to address this. Numerous researchers have shown that cooperative learning leads to improved skills in teamwork and communication in other fields (Johnson and Johnson, 2007; Slavin, 1995). Cooperative learning used in this study showed that the…

In this paper we describe the learning process of a group of experienced chemistry teachers in a specially designed workshop on molecular symmetry and continuous symmetry. The workshop was based on interactive visualization tools that allow molecules and their symmetry elements to be rotated in three dimensions. The topic of continuous symmetry is…

Teachers are expected to possess not only the necessary knowledge and training to support mathematical content but also the pedagogical skills to support the learning needs of all students. Coteaching can provide solutions for general educators in diverse mathematics environments through collaboration with a special educator. This teaming can have…

The purpose of this study was to determine the changes in the mathematics curriculum for grades 5-8 in the Republic of Serbia after the break-up of SFRY. In particular, the research sought to identify the changes in the mathematics curriculum in terms of curriculum content and learning objectives, textbooks, and high school entrance examination…

The study compared the effects of dynamic geometry software and physical manipulatives on the spatial visualisation skills of first-year pre-service mathematics teachers. A pre- and post-test quasi-experimental design was used. The Purdue Spatial Visualisation Test (PSVT) was used for the pre- and post-test. There were three treatment groups. The…

After a test is developed, most content validation analyses shift from ascertaining domain definition to studying domain representation and relevance because the domain is assumed to be set once a test exists. We present an approach that allows for the examination of alternative domain structures based on extant test items. In our example based on…

The "Foundations" (English/language arts, mathematics, social emotional skills, approaches to play and learning, science, social studies, creative arts, and physical health and growth) are Indiana's early learning development framework and are aligned to the 2014 Indiana Academic Standards. This framework provides core elements that…

Symmetry is one of the fundamental concepts in Geometry. It is a Mathematical concept, which can be very well connected with Art and Ethnography. The aim of the article is to show how to link the geometrical concept symmetry with interculturality. For this mosaics from different countries are used.