"Dimensions of possible variation" is a phrase that now occupies a safe place in the literature describing the application of education theory to education practice: "asking yourself what could be changed [in the task], while using the same approach or technique, opens up dimensions of possible variation. A set of exercises forming a sequence of…

Formerly, the "prisoners" problem was used by the author in his teaching chiefly as a process activity, with the intention of promoting certain investigative techniques: the idea of starting with a smaller problem (say, 10 prisoners, guards and cells, rather 100), and the importance of finding an effective method for displaying what was going on.…

The Pythagorean Theorem, arguably one of the best-known results in mathematics, states that a triangle is a right triangle if and only if the sum of the squares of the lengths of two of its sides equals the square of the length of its third side. Closely associated with the Pythagorean Theorem is the concept of Pythagorean triples. A "Pythagorean…

The use of student assessment data is a key component of a model of instructional coaching, Student-Focused Coaching (Hasbrouck & Denton, 2005), designed to support student achievement by engaging reading teachers in a collaborative problem-solving process to modify instructional strategies with the goal of enhanced student outcomes. In this…

The current profile of action learning in the UK has recently become clearer (Pedler et al., 2005). Using the template of what have been described as "Revans's Classical Principles", fundamental divergences have begun to emerge. Pedler et al. (2005) identified a number of variances from this template--specifically the use of permanent…

A k-dimensional integer point is called visible if the line segment joining the point and the origin contains no proper integer points. This note proposes an explicit formula that represents the number of visible points on the two-dimensional [1,N]x[1,N] integer domain. Simulations and theoretical work are presented. (Contains 5 figures and 2…

This article explores the use of problem posing in the calculus classroom using investigative projects. Specially, four examples of student work are examined, each one differing in originality of problem posed. By allowing students to explore actual questions that they have about calculus, coming from their own work or class discussion, or…

Literacy coaching, a unique and generative opportunity to engage with and learn from teachers, is currently viewed as a powerful intervention to increase student literacy achievement. This article focuses on eight principles for responsive literacy coaching. To build trusting relationships, coaches engage with teachers in literacy events, confirm…

Maryland redesigned its CTE (career and technical education) program a dozen years ago to prepare students for the 21st Century's global economy and its rapidly changing workforce needs. With 350 business and industry representatives, the state created a program whose emphasis is problem-solving and critical thinking, rather than narrow,…

Parents are concerned about their children's math learning. Teachers are concerned about math teaching. When parents see what children are bringing home under the new curriculum, it is clear that their children are not working on the same mathematics that parents remember from the time when they were in school. But, the problem goes beyond grades…

As a Response to Intervention approach begins to be utilized in our schools, there is growing confusion regarding the role of teacher assistants/paraeducators in this problem solving approach. In this article, the authors share survey and interview data from their experiences working with Rhode Island teacher assistants--both in leading teacher…

Life Skills Education (LSE) is a novel promotional program that teaches generic life skills through participatory learning methods of games, debates, role-plays, and group discussion. Conceptual understanding and practicing of the skills occurs through experiential learning in a non-threatening setting. Such initiatives provide the adolescent with…

Like never before, today's classroom teachers routinely are being asked to collaboratively analyze student data, develop or implement new mandated curricula, and assess the effectiveness of these innovations. Ironically, few preservice preparatory or in-service professional development programs actively train classroom instructors in the use of…

School attendance is an ongoing concern for administrators, particularly in middle-level and high school. Frequent absences affect student learning, test scores, and social development. Administrators who understand the causes of school refusal behavior and are aware of effective intervention strategies can help provide supportive school…

The transportation field has for many years been dominated by engineers and other technical specialists. This article describes the Sustainable Mobility Learning Lab (SMLL), a Web-based tool designed to support classroom and university outreach activities to help initiate a more inclusive, nontechnical discussion about the role of transportation…