Today, more than ever, teachers must work effectively and efficiently to meet seemingly contradictory demands placed on them by society. On the one hand, school personnel are tasked with attaining and publicly reporting high levels of student achievement in response to No Child Left Behind. On the other, school personnel must ensure that students…

Co-rumination, a social process between two friends, is defined as the frequent and excessive discussion of personal problems. Like body image and alcohol use, it is one of those complicated issues embedded in larger cultural realities, which makes it universally recognizable. On campus, co-rumination has deleterious side effects: it challenges…

In this article, the authors discuss how educators can engage students in real world learning using their academic knowledge and technical skills. They describe how school districts have discovered that the world of robotics can help students use technical skills to solve simulated problems found in the real world, while understanding the…

Much attention has been devoted in the literature to students' struggles with fraction division. With regard to the traditional invert and multiply algorithm, researchers and educators have examined such areas as typical errors, how to help students understand why this method works, and what alternatives are available that might be more intuitive.…

As a fifth-grade mathematics teacher, the author tries to create authentic problem-solving activities that connect to the world in which his students live. He discovered a natural connection to his students' real world at a computer camp. A friend introduced him to Alice, a computer application developed at Carnegie Mellon, under the leadership of…

Mr. Carter is about to start a two-day lesson on subtraction of integers with his sixth-grade prealgebra students. He plans to use contextualized problems that will allow his students to develop an interpretation of subtraction that involves the idea of "difference." This article outlines one way to teach students develop number line…

Although any mainstream thought is subject to theoretical challenges, the challenges to the mainstream cognitive perspective on transfer have had an unfortunate divisive effect. This article takes a pragmatic view that transfer perspectives are simply designed objects (Plomp & Nieveen, 2007), which provide different information for different…

Parents--whether they're biological parents, legal guardians, grandparents, or other family members who are primary caregivers--can be the most critical partners teachers have in their students' academic journeys. How can teachers build effective relationships that help students to succeed? This article provides ideas and methods that can help…

Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…

This article describes an after-school program at the Horace Mann School for the Deaf (HMS), the oldest public day school for deaf students in the United States, where almost half of the student body imagined and created bridge and robotic machines. The Deaf Robotics Engineering and Math Team, or the DREAM Team club, included HMS students in…

Algebraic thinking is a crucial and fundamental element of mathematical thinking and reasoning. It initially involves recognising patterns and general mathematical relationships among numbers, objects and geometric shapes. This paper will highlight how the ability to think algebraically might support a deeper and more useful knowledge, not only of…

Students sometimes have difficulty calculating the result of a voting system applied to a particular set of voter preference lists. Saari triangles offer a way to visualize the result of an election and make this calculation easier in the case of several important voting systems.

This article describes some problems of the maximum/minimum type, which are generally solved using calculus at secondary school, but which here are solved algebraically. We prove six algebraic properties and then apply them to this kind of problem. This didactic approach allows pupils to solve these problems even at the beginning of secondary…

In this article, we discuss how to use a diagrammatic approach to solve the classic sailors and the coconuts problem. It provides us an insight on how to tackle this type of problem in a novel and intuitive way. This problem-solving approach will be found useful to mathematics teachers or lecturers involved in teaching elementary number theory,…

Fermat's Last Theorem says that for integers n greater than 2, there are no solutions to x[superscript n] + y[superscript n] = z[superscript n] among positive integers. What about rational exponents? Irrational n? Negative n? See what an undergraduate senior seminar discovered.