Poverty, neglect, or family stress can make it especially difficult for young children to develop the self-discipline and habits of mind they will need to succeed in the classroom and beyond. Armed with research and a commitment to the whole child, Washington state has transformed the way its agencies work together and in partnership with…

In the 21st century, a deep understanding of mathematics, and the ability to apply that understanding, is more important than it has ever been. In Montgomery County (Maryland) Public Schools (MCPS), and across the country, mathematics instruction is changing to provide students with the skills and knowledge they need for success in college and the…

The Common Core State Standards Initiative, in its aim to align diverse state curricula and improve educational outcomes, calls for K-12 teachers in the United States to engage all students in mathematical problem solving along with reading and writing complex text through the use of rigorous academic content. Until recently, most teacher…

Creative and critical thinking have been identified by Isaksen, Dorval, and Treffinger (2000) as the ability to "perceive gaps, challenges, or concerns; think of many varied or unusual possibilities; or elaborate and extend alternatives," as well as make meaningful connections that include analyzing, evaluating, and developing options.…

This note gives a power series solution to the pendulum equation that enables to investigate the system in an analytical way only, i.e. to avoid numeric methods. A method of determining the number of the terms for getting a required relative error is presented that uses bigger and lesser geometric series. The solution is suitable for modelling the…

We give an irredundant axiomatization of the complete ordered field of real numbers. In particular, we show that all the field axioms for multiplication with the exception of the distributive property may be deduced as "theorems" in our system. We also provide a complete proof that the axioms we have chosen are independent.

Computers are very good at solving certain types combinatorial problems, such as fitting sets of polyomino pieces into square or rectangular trays of a given size. However, most puzzle-solving programs now in use assume orthogonal arrangements. When one departs from the usual square grid layout, complications arise. The author--using a computer,…

The basis of a good mechanical puzzle is often a puzzling mechanism. This article will introduce some new puzzling mechanisms, like two knots that engage like gears, a chain whose links can be interchanged, and flat gears that do not come apart. It illustrates how puzzling mechanisms can be transformed into real mechanical puzzles, e.g., by…

Hyperbolic geometry occurs on hyperbolic planes--the most commonly cited one being a saddle shape. In this article, the author explores negative hyperbolic curvature, and provides a detailed description of how she constructed two hyperbolic paraboloids. Hyperbolic geometry occurs on surfaces that have negative curvature. (Contains 11 figures and 4…

In the late seventies, Guy Brousseau set himself the goal of verifying experimentally a theory he had been building up for a number of years. The theory, consistent with what was later named (nonradical) constructivism, was that children, in suitable carefully arranged circumstances, can build their own knowledge of mathematics. The experiment,…

The Lorentz velocity addition formula for one-dimensional motion presents a number of problems for beginning students of special relativity. In this paper we suggest a simple rewrite of the formula that is easier for students to memorize and manipulate, and furthermore is more intuitive in understanding the correction necessary when adding…

A problem addressed infrequently in beginning physics courses is that of a moving body with changing mass. Elementary texts often have footnotes referring to jet planes and rockets but rarely do they go further. This omission is understandable because calculations with variable mass generally require the tools of calculus. This paper presents a…

This little problem arose because I was frustrated with the standard electromagnetism texts, which show the magnetic field due to a current-bearing wire outside the wire [proportional to] 1/r and inside [proportional to] r. However, they never point out that the moving electrons must be influenced by the magnetic field created by the other moving…

Mediation has become common in many areas of society, including marital dissolution, community disputes, governmental agencies, and business and industry. Though higher education has been slower than society to adopt mediation services, campus mediation is becoming increasingly more common. This article explains why mediation is a viable…

Visualizing complex roots of a quadratic equation has been a quest since the inception of the Argand plane in the 1800s. Many algebraic and numerical methods exist for calculating complex roots of an equation, but few visual methods exist. Following on from papers by Harding and Engelbrecht (A. Harding and J. Engelbrecht, "Sibling curves and…