An integral, either definite or improper, cannot always be computed by elementary methods, such as reversed usage of differentiation formulae. Graphical properties, in particular symmetries, can be useful to compute the integral, via an auxiliary computation. We present graded examples, then prove a general result. (Contains 4 figures.)

A triple (x,y,z) of natural numbers is called a Primitive Pythagorean Triple (PPT) if it satisfies two conditions: (1) x[squared] + y[squared] = z[squared]; and (2) x, y, and z have no common factor other than one. All the PPT's are given by the parametric equations: (1) x = m[squared] - n[squared]; (2) y = 2mn; and (3) z = m[squared] +…

Australian teachers in Church related schools have begun to use the term "spiritual intelligence" in their educational discourse. Is it accurate to describe spirituality as a form of intelligence? This paper explores whether the notion of spiritual intelligence is plausible. It addresses this firstly by discussing the notion of spiritual…

This article describes the variety of strategies that can be used to determine the probability that a player wins a tennis game, given a probability of 60 percent that he or she wins each point. The article suggests strategies for using the problem in 9-12 classrooms.

This article outlines an engineering problem requiring the use of a specialized trigonometric formula, and offers an answer to that age-old classroom question, "When are we gonna have to use this"?

This article describes the rich thinking that can go into solving a difficult equation. The authors also give some sources for challenging mathematical problems.

Many research students go through periods where their research seems to stall, their motivation drops, and they seem unable to make any progress. As supervisors, we attempt to remain alert to signs that our student's progress has stalled. Drawing on cognitive strategies, this article explores a problem-solving model supervisors can use to identify…

This article proposes that student-written math riddles can provide worthwhile mathematical tasks that support the learning of important concepts as they engage and challenge children. It describes procedures for guiding students as they create math riddles for their classmates to solve.

This article describes some benefits of using problem posing in the classroom, and provides suggestions to teachers for how to begin implementing this strategy.

The results of an action research project in which young children in one classroom are encouraged to solve and pose their own problems in their first year at school are described. The progress of these children supports the finding that kindergarten children could solve a variety of quite difficult word problems on their own.

Describes a Palestinian school, the Ashtar School for Theater Education and Training, that has designed a program to stimulate young people to define problems in new ways and then develop solutions. The school coordinates programs in high schools and universities and takes into account the gaps in the present curriculum of Palestinian secondary…

Simple nongraphing calculators can be powerful tools to enhance students' conceptual understanding of mathematics concepts. Students have opportunities to develop (1) a broad repertoire of problem-solving strategies by observing multiple solution strategies; (2) respect for other students' abilities and ways of thinking about mathematics; (3) the…

Accommodations influence the measurement of student proficiency. However, with discrepant research findings, it is difficult to evaluate the effects of these practices on the measurement of performance of students with special needs. In this article, we present results from an experimental study investigating the effects of item characteristics…

Research in the disciplines of education, science education, and environmental education has a rich history. While research in Education for Sustainable Development (ESD) may be related to these traditions, there is a need for ESD to carve a new niche that promotes high quality and effective ESD programmes. With an eye towards practice and applied…

In this article, Judith V. Boettcher provides ten core learning principles that can guide technology-enhanced teaching as well as more traditional forms of instruction. Drawn from both traditional pedagogical theory as well as current research about how people learn, the ten principles integrate these findings in a helpful set of guidelines that…