The authors document their experience of working with 6-year-olds over several weeks. They share some observations that arise from weekly sessions they conducted which have been under way for several years and which have been widely reported. These observations show the payoff of a problem-solving approach to learning.

The bicycle provides a context-rich problem accessible to students in a first-year physics course, encircling several core physics principles such as conservation of total energy and angular momentum, dissipative forces, and vectors. In this article, I develop a simple numerical model that can be used by any first-year physics student to…

Computer programming in undergraduate engineering education all too often begins and ends with the freshman programming course. Improvements in computer technology and curriculum revision have improved this situation, but often at the expense of the students' learning due to the use of commercial "black box" software. This paper describes the…

In this paper we report the results from a major UK government-funded project, started in 2005, to review statistics and handling data within the school mathematics curriculum for students up to age 16. As a result of a survey of teachers we developed new teaching materials that explicitly use a problem-solving approach for the teaching and…

Since mathematics is found in every aspect of life, it is important for teachers to provide experiences that help students find connections and develop an appreciation for math and its use in their lives outside school. Slope is an excellent example of a math concept that is usually taught without context or connection. In this article, the…

Mural painting provides an excellent opportunity for students to participate in a collaborative project. To many teachers, class mural projects seem intimidating because of organizational and logistical challenges. Many of these challenges can be mitigated, however, if there is plenty of discussion beforehand to organize ideas, get input from…

In this note we show the existence of a surprising analogy between quadrilaterals and tetrahedra, determining some properties that hold for both families of figures. This analogy suggests some new properties of quadrilaterals. (Contains 11 figures,)

In this article we describe the process of studying the assumptions and the conclusion of a theorem. We tried to provide the students with exercises and problems where we discuss the following questions: What are the assumptions of a theorem and what are the conclusions? What is the geometrical meaning of a theorem? What happens when one or more…

Correctly harnessed, we can blend the best of our traditional intellectual linear culture--Socrates' wisdom of the 5th century BCE--with the current digital visual culture, creating a new learning and intellectual environment consistent with the cognitive and expressive demands of the 21st century. Four elements of the 21st-century mind could be…

The null result of the Michelson-Morley experiment and the constancy of the one-way speed of light in the "rest system" are used to formulate a simple problem, to be solved by elementary geometry techniques using a pair of compasses and non-graduated rulers. The solution consists of a drawing allowing a direct visualization of all the fundamental…

Middle-school students are just beginning to recognize their place in the world. That is why this author believes it is important to incorporate their world into their art. In this article, the author discusses the "Tree of Life" project, which she developed for her students in order to make them aware of various environmental issues, and how to…

We discuss a class of trigonometric functions whose corresponding Fourier series, on a conveniently chosen interval, can be used to calculate several numerical series. Particular cases are presented and two recent results involving numerical series are recovered. (Contains 1 note.)

Recognizing the increasing popularity of skateboarding, the author has found a project that teaches design and manufacturing concepts--and, of equal importance, really gets his students motivated. He challenges them to design and build a skateboard rack that mounts easily on a bicycle. The project benefits students by teaching creativity, the…

In this note, a method of converting a rhotrix to a special form of matrix termed a "coupled matrix" is proposed. The special matrix can be used to solve various problems involving n x n and (n - 1) x (n - 1) matrices simultaneously.

Fibonacci's forgotten number is the sexagesimal number 1;22,7,42,33,4,40, which he described in 1225 as an approximation to the real root of x[superscript 3] + 2x[superscript 2] + 10x - 20. In decimal notation, this is 1.36880810785...and it is correct to nine decimal digits. Fibonacci did not reveal his method. How did he do it? There is also a…