We give an example of a student project that experimentally explores a topic in random graph theory. We use the "Combinatorica" package in "Mathematica" to estimate the minimum number of edges needed in a random graph to have a 50 percent chance that the graph is connected. We provide the "Mathematica" code and compare it to the known theoretical…

The usual formula for variance depending on rounding off the sample mean lacks precision, especially when computer programs are used for the calculation. The well-known simplification of the total sums of squares does not always give benefit. Since the variance of two observations is easily calculated without the use of a sample mean, and the…

The present paper deals with the problem of non-selective harvesting of a prey-predator system in which both the prey and the predator species obey the law of logistic growth and each predators functional response to the prey approaches a constant as the prey population increases. Boundedness of the exploited system is examined. The existence of…

Principals need to get away from traditional beliefs that equate math success solely with rote knowledge of math facts and the ability to calculate. Today, math instruction also is being directed to student understanding of essential concepts. Principals must learn what to look for when they visit math classrooms to make sure it is being taught…

In this article, the author discusses the perils of adhering to a data-driven model of instruction, and discusses how writing center coaches can become involved with all academic disciplines represented at their schools--even those with which they are not familiar--in order to help students learn how to think about the things they are studying and…

We examine the behavior of the curvature function associated with most common families of functions and curves, with the focus on establishing where maximum curvature occurs. Many examples are included for student illustrations. (Contains 18 figures.)

In this paper, results of a questionnaire about continuity of functions are analysed. The tested students attend Novi Sad grammar school. The aim of this test was to check the student's theoretical and visual knowledge of continuous functions at the end of their high school education. The questions were given with and without the graphs of…

This article classifies and describes a selection of mathematical fiction. It also provides some practical activities teachers or parents can use to help make the mathematics more explicit and engaging for their children. Not many people, apart from primary teachers, are aware of mathematical fiction or mathematical picture storybooks, although…

Young students often struggle with abstract concepts in mathematics, causing primary teachers to continue to search for ways to help teach such concepts. "Principles and Standards for School Mathematics" (NCTM, 2000) recommends using concrete models and physical materials before moving on to more abstract ideas. However, some children…

Perimeter and area are important real-world concepts in their own right, and their relationship certainly is no less important. This relationship can be intuitively challenging for both children and adults. In this article, the author explores the relationship between perimeter and area with students from grades 4 to 6. The study of perimeter-area…

The authors discuss proportional reasoning as a challenging yet central concept for students in the middle grades that lays a foundation for mathematics studied later in high school. Four types of proportional reasoning problems are discussed: (1) Part-part-whole (comparing a subset (part) of a whole with its complement (other part) or the whole…

Recently, the author has been fortunate to be a visitor in a number of classrooms in the United States, England and Europe. On one such visit to an Elementary School in Columbia, Missouri, the teachers accepted him into their normal classrooms for their normal lessons. He moved between three classes: Grade 1, Grade 2 and Grade 4. A snapshot…

Automaticity in math facts has been of considerable interest to special educators for decades. A review of the intervention literature suggests at least two common approaches to developing automaticity in facts. One is grounded in the use of strategies for teaching facts, the other emphasizes the use of timed practice drills. Recent research…

We describe a principled way of imposing a metric representing dissimilarities on any discrete set of stimuli (symbols, handwritings, consumer products, X-ray films, etc.), given the probabilities with which they are discriminated from each other by a perceiving system, such as an organism, person, group of experts, neuronal structure, technical…

Stevens postulated that we can use the responses of a participant in a ratio scaling experiment directly to construct a psychophysical function representing the participant's sensations. Although Stevens' methods of constructing measurement scales are widely used in the behavioral sciences, the problem of which scale type is appropriate to…