E. Paul Torrance, a pioneer in creative education, and his associates founded the Future Problem Solving Program (now FPSPI, or Future Problem Solving Program International) in the mid-1970s as a competitive, interscholastic program and as a curriculum project integrating creative problem-solving and future studies. Since its founding, the program…

Proportional reasoning is an important cornerstone in children's mathematical development. This sort of reasoning has been shown to develop across the early years of schooling (ages 8 to 10) through the middle years (ages 11-14). In the early years, children tend to use additive reasoning to generate solutions to problems, while later comparisons…

The Catholic Higher Education Collaborative (CHEC) is committed to fostering effective partnerships that generate innovative responses to the critical current condition of Catholic schooling. Beginning in 2008, national CHEC conferences were organized by member institutions to energize the movement and begin a national conversation aimed at…

Trees transport water from roots to crown--a height that can exceed 100 m. The physics of tree hydraulics can be conveyed with simple fluid dynamics based upon the Hagen-Poiseuille equation and Murray's law. Here the conduit structure is modelled as conical pipes and as branching pipes. The force required to lift sap is generated mostly by…

What is, or should be, the role of ethics in giftedness? In this article, I consider why ethical behavior is much harder to come by than one would expect. Ethical behavior requires completion of a series of eight steps to action, the failure of any one of which may result in a person, even one who is ethically well trained, to act in a manner that…

Decision making is the most common kind of problem solving. It is also an important component skill in other more ill-structured and complex kinds of problem solving, including policy problems and design problems. There are different kinds of decisions, including choices, acceptances, evaluations, and constructions. After describing the centrality…

All children are born with the gifts of curiosity and creativity--and an insatiable appetite for asking questions to find out about the world in which they live. Fostering these questions and developing inquisitive and investigating minds is one of the essential roles of parent and teacher, and the processes of enquiry are the necessary routes for…

In this article, we present an integer sequence approach to solve the classic water jugs problem. The solution steps can be obtained easily by additions and subtractions only, which is suitable for manual calculation or programming by computer. This approach can be introduced to secondary and undergraduate students, and also to teachers and…

A newspaper numbers game based on simple arithmetic relationships is discussed. Its potential to give students of elementary algebra practice in semi-"ad hoc" reasoning and to build general arithmetic reasoning skills is explored. (Contains 3 figures, 7 tables and 3 notes.)

The blue-eyed islanders puzzle is an old and challenging logic puzzle. This is a narrative of an experience introducing a variation of this puzzle on the first day of classes in a liberal arts mathematics course for non-majors. I describe an exercise that was used to facilitate the class's understanding of the puzzle.

There are, it seems, few instances when "unintended consequences" are regarded as having a positive and beneficial effect. Here a well-used activity takes on a "life of its own" as a result of the enthusiasm of the learners. The outcome provides insights for all those involved, including the "teacher". Maybe it is…

"Probability is a difficult concept to teach, because children and adults find it counterintuitive." This is impetus to consider the detailed planning of a set of lessons with a "mixed", in many senses, group of fourth graders. Can the use of prior experience, and the knowledge associated with that experience, make probability a concept that is…

Learners are all different and teachers are all different, so why do we often ignore this reality when trying to explain, or demystify, some aspect of mathematics in the classroom? Enabling learning can be challenging, demanding of creativity, and needy of alternatives if understanding is the real goal. Here the authors offer ideas that are aimed…

Sociodrama is an arts-based, action-oriented tool of individual and collective social exploration and creative problem solving that allows participants to explore and find potential resolutions to issues of concern and conflict in their lives. This article describes how Early Years educators can begin to implement basic sociodrama into their…

Teachers have used graphic organizers successfully in teaching the writing process. This paper describes graphic organizers and their potential mathematics benefits for both students and teachers, elucidates a specific graphic organizer adaptation for mathematical problem solving, and discusses results using the "four-corners-and-a-diamond"…