Let I be a real interval. We call a continuous function [mu] : I x I [right arrow] [Bold R] a proper mean if it is symmetric, reflexive, homogeneous, monotonic and internal. Let f : I [right arrow] [Bold R} be a differentiable and strictly convex or strictly concave function. If a, b [image omitted] I with a [not equal to] b, then there exists a…

Making connections between various representations is important in mathematics. In this article, the authors discuss the numeric, algebraic, and graphical representations of sums of absolute values of linear functions. The initial explanations are accessible to all students who have experience graphing and who understand that absolute value simply…

This article reports that young inventors at a Maryland high school are not only learning scientific principles, but also teamwork and the tenets of patent law. Twice a week, 10 members of the Clarksburg High School's Coyote Inventors Club gather in a second-floor computer lab to peck away at building a deceptively simple device: a cable that…

"Report of a Workshop on the Scope and Nature of Computational Thinking" presents a number of perspectives on the definition and applicability of computational thinking. For example, one idea expressed during the workshop is that computational thinking is a fundamental analytical skill that everyone can use to help solve problems, design…

Despite multiple calls for reform, the curriculum for first-year college chemistry at many universities across the world is still mostly fact-based and encyclopedic, built upon a collection of isolated topics, oriented too much towards the perceived needs of chemistry majors, focused too much on abstract concepts and algorithmic problem solving,…

This paper describes a novel method for the delivery of an introductory module on survey sampling at a third-level institution. As part of the module, students undertake a practical survey that is of interest not only to themselves but also to university administrators and other module coordinators. Unlike many data collection activities used in…

Finding patterns, and making and justifying conjectures are considered the building blocks of mathematical reasoning and proof. Curriculum revisions in the United States and Australia place increased emphasis on problem solving and reasoning in the primary school curriculum. A number of curriculum resources for teachers are available but under…

In this article, the authors describe how they used student's complaints about limited salad choices in the cafeteria as the focus of a class project. Following steps of the Project Citizen protocol of the Center for Civic Education, the authors facilitated students' efforts, which included researching the problem, talking with adult…

Play has been traditionally recognized as an activity within early childhood education, but in actuality, it has substantial importance to learners at all levels. Since the idea of play is abstract and has no pre-determined outcomes, some teachers feel uneasy about allowing students to play with concepts and materials, especially with the advent…

Many empirical investigations concerning the use of computer algebra systems (CAS) and symbolic calculators (SC) are restricted to a period of only a few weeks. They do not show long-term effects on students understanding. Therefore, a long term project (2003-2012) was started to test the use of symbolic calculators in Bavarian…

A traditional abstract algebra course typically consists of the professor stating and then proving a sequence of theorems. As an alternative to this classical structure, the students could be expected to discover some of the theorems even before they are motivated by classroom examples. This can be done by using a software system to explore a…

This article presents material that has been used as a classroom activity in a calculus-based probability and statistics course. The application was used in the first few lessons of this course. Students had three previous semesters of math, including calculus (single and multivariable), differential equations, and a course in mathematical…

An nth-term problem involves a sequence. Students must determine which expression will allow them to calculate the nth position of the sequence. To solve such problems, students are to find "a rule that determines the number of elements in a step from the step number." These types of problems help students develop concepts of functions, variables,…

Proportional reasoning is perhaps one of the most important types of mathematical thinking for elementary school students to develop. It includes aspects of rational numbers, spans the entire mathematics curriculum, and is a significant foundation for mathematical proficiency. Understanding students' use of proportional reasoning is a basis on…

Although science is a creative endeavor (NRC 1996, p. 46), many students think they are not encouraged--or even allowed--to be creative in the laboratory. When students think there is only one correct way to do a lab, their creativity is inhibited. Park and Seung (2008) argue for the importance of creativity in science classrooms and for the…