Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

Holidays and seasonal activities provide excitement and a change of pace for teachers and students alike. They also offer perfect backdrops for mathematical tasks that can be related to other topics and themes in the classroom. "Problem Solving in All Seasons, Prekindergarten-Grade 2" delivers thirty-two appealing, real-world situations,…

This article illustrates the importance of one's initial thoughts in problem solving through an entertaining example.

As we typically teach in an introductory mechanics course, choosing a "good" coordinate frame with convenient axes may present a major simplification to a problem. Additionally, knowing some conserved quantities provides an extremely powerful problem-solving tool. While the former idea is typically discussed in the context of…

In this article on introductory calculus, intriguing questions are generated that can ignite an appreciation for the subject of mathematics. These questions open doors to advanced mathematical thinking and harness many elements of research-oriented mathematics. Such questions also offer greater incentives for students to think and reflect.…

The following kinematics problem was given to several students as a project in conjunction with a first-semester calculus-based physics course. The students were asked to keep a journal of all their work and were encouraged to keep even their scrap paper. The goal of the project was to expose the students to the process of doing theoretical…

A direct method is given for solving first-order linear recurrences with constant coefficients. The limiting value of that solution is studied as "n to infinity." This classroom note could serve as enrichment material for the typical introductory course on discrete mathematics that follows a calculus course.

A well-known mathematical puzzle regarding a worm crawling along an elastic rope is considered. The resulting generalizations provide examples for use in a teaching context including applications of series summation, the use of the integrating factor for the solution of differential equations, and the evaluation of definite integrals. A number of…

In 2010, State College Area School District (SCASD) in Pennsylvania, USA, agreed to help develop a virtual international classroom exchange called the Schoolwires Greenleaf program. The program's project-based curriculum paired U.S. students with Chinese learners to collaborate, foster global citizenship, and prepare students for the digital work…

In this paper different type of mathematical explanations are presented in relation to the mathematical problem of probabilities Monty Hall (card version) and the computational tool Latent Semantic Analyses (LSA) is used. At the moment the results in the literature about this computational tool to study texts show that this technique is…

Terms to be familiar with before you start to solve the test: growth factor signaling, epidermal growth factor, tyrosine protein kinase, tyrosine phosphorylation, ubiquitin, monoubiquitination, polyubiquitination, site-directed mutagenesis, transfection, expression vector, cDNA, immunoprecipitation, SDS-polyacrylamide gel electrophoresis, Western…

Memory serves critical functions in everyday life but is also prone to error. This article examines adaptive constructive processes, which play a functional role in memory and cognition but can also produce distortions, errors, and illusions. The article describes several types of memory errors that are produced by adaptive constructive processes…

How many rods does it take to brace a square in the plane? Once Martin Gardner's network of readers got their hands on it, it turned out to be fewer than Raphael Robinson, who originally posed the problem, thought. And who could have predicted the stunning solutions found subsequently for various generalizations of the problem?

We describe the calculation of the distribution of the sum of signed ranks and develop an exact recursive algorithm for the distribution as well as an approximation of the distribution using the normal. The results have applications to the non-parametric Wilcoxon signed-rank test.

Collaborative evaluation is an approach that offers, among others, many advantages in terms of access to information, quality of information gathered, opportunities for creative problem-solving, and receptivity to findings. In the last decade, collaborative evaluation has grown in popularity along with similar participatory, empowerment, and…