Interesting and engaging mathematics problems can come from anywhere. Sometimes great problems arise from interesting contexts. At other times, interesting problems arise from asking "what if" questions while appreciating the structure and beauty of mathematics. The intriguing problem described in this article resulted from the second…

"Sickle cell anemia: tracking down a mutation" is a full-day, inquiry-based, biology experience for high school students enrolled in genetics or advanced biology courses. In the experience, students use restriction endonuclease digestion, cellulose acetate gel electrophoresis, and microscopy to discover which of three putative patients…

The author shares some examples from her Bulgarian project, "Mathematics Through Experience", which approaches mathematics from a practical, real-life perspective in order to develop creative thinking: just like science! What was most important to her was to motivate her students to study maths and science by giving them a taste of how…

This paper focuses on the parameters of a semester-long project called the "Do Good" project, geared towards developing small group communication skills in undergraduate students. This project highlights participation in a social engagement project that allows students to bridge concepts learned in small group communication lectures…

This article describes how our university built a unique classroom environment specifically for active learning. This classroom changed students' experience in the undergraduate executive information technology (IT) management class. Every college graduate should learn to think critically, solve problems, and communicate solutions, but 90% of…

"Modeling Mathematical Ideas" combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students' common misconceptions in investigating and…

In this article, Ceyanes, Lockwood, and Gill use "The Geometer's Sketchpad" in a sequence of algebra lessons to introduce quadratic functions as the product of two linear functions. The lessons provide an enriched look at the creation of parabolas and allow students to experience the foundational idea that all functions are…

Stephanie Whitney teaches in the department of teacher education at DePaul University in Chicago, Illinois. Her interest is in how students reason and make sense of mathematics, and how teachers can promote this behavior. Students should engage in reasoning and sense making daily in their mathematics classes. It is often through students'…

This paper deals with ideas about dynamic presentation of photo-pictures by means of dynamic software GeoGebra in order to motivate art students to get acquainted with some specific mathematical functions. The results of the experiment include deeper understanding of the functions' nature, search of new functions for dealing with a practical…

When organic chemistry students encounter competing reactions, they are often overwhelmed by the task of evaluating multiple factors that affect the outcome of a reaction. The use of a decision tree is a useful tool to teach students to evaluate a complex situation and propose a likely outcome. Specifically, a decision tree can help students…

Formulas, problem types, keywords, and tricky techniques can certainly be valuable tools for successful counters. However, they can easily become substitutes for critical thinking about counting problems and for deep consideration of the set of outcomes. Formulas and techniques should serve as tools for students as they think critically about…

A focus on enrollments, rankings, uncertain budgets, and branding efforts to operate universities could have serious implications for discussions of sustainable solutions to complex problems and the decision-making processes of leaders. The Authentic Leadership Model for framing ill-defined problems in higher education is posited to improve the…

Sets in the game "Set" are lines in a certain four-dimensional space. Here we introduce planes into the game, leading to interesting mathematical questions, some of which we solve, and to a wonderful variation on the game "Set," in which every tableau of nine cards must contain at least one configuration for a player to pick up.

Solving equations in finite algebraically structures (semigroups with identity, groups, rings or fields) many times is not easy. Even the professionals can have trouble in such cases. Therefore, in this paper we proposed to solve in the various finite groups or fields, a binomial equation of the form (1). We specify that this equation has been…

Two contestants debate the notorious probability problem of the sex of the second child. The conclusions boil down to explication of the underlying scenarios and assumptions. Basic principles of probability theory are highlighted.