This article uses multiple theoretical perspectives to understand the synergy that occurs between linguistically diverse parents and children during reading interactions. Through the detailed analysis of code-switching during book-sharing activities in a middle-class, bilingual home, we can observe how linguistically diverse parents support the…

A project that mixes algebra with data collection, uses technology, extends into data analysis, and cooks marshmallows can excite both teachers and students. This article describes a project that intends to pique students' interest in higher mathematics, incorporate their knowledge of parabolas, and offer a meaningful mathematics experience. Using…

In this paper, we are proposing the use of forensic case studies as a means to provide students with interesting problem solving opportunities that capitalise on the popularity of several TV series and shows. It also satisfies their natural curiosity about how answers are found to seemingly complex real life problems. We begin with a very brief…

Research reflects that graduates are leaving high school deficient in math, science and problem solving skills necessary for the demands of the workforce. In order to maintain a competitive position in high tech industries and attract new business, it is important to have a system where all students develop a confidence in learning math, science…

Boulder Creek runs literally in the backyard of Donnelly Elementary School and happens to be on the EPA list of impaired water bodies. Therefore, a unique opportunity for problem solving opened the door to an exciting chance for students to become scientists, while also becoming active in their community. With the help of the Idaho Department of…

"Watch out, the stove will burn you," "Ooh, ice cream headache!" Students construct their conceptions about heat and temperature through their own intuitions about daily life experiences. As a result, misconceptions can be born from these constructed concepts. The activity described here addresses student misconceptions about thermal insulation…

Explaining emergent structure remains a challenge for all areas of cognitive science, and problem solving is no exception. The modern study of insight has drawn attention to the issue of emergent cognitive structure in problem solving research. We propose that the explanation of insight is beyond the scope of conventional approaches to cognitive…

Traditional medical school curricula have made a clear demarcation between the basic biomedical sciences and the clinical years. It is our view that a comprehensive medical education necessarily involves an increased correlation between basic science knowledge and its clinical applications. A basic anatomy course should have two main objectives:…

Some have proposed that realistic problem situations are better for learning. This issue contains two articles that examine the effects of "making it real" in computer architecture and human-computer interaction.

In this article I present an activity introducing statistical concepts to engineering students to help them develop inductive reasoning and problem-solving skills.

In this article, the author describes a project which gave students a chance to explore the idea of using "extreme" materials in a sculpture. While the process was, at times, challenging and stressful for teacher and student alike, the results proved that, with proper planning, even young students can independently demonstrate multiple solutions…

In this article we derive all salient properties of analytic functions, including the analytic version of the inverse function theorem, using only the most elementary convergence properties of series. Not even the notion of differentiability is required to do so. Instead, analytical arguments are replaced by combinatorial arguments exhibiting…

This note shows a combinatorial approach to some identities for generalized Fibonacci numbers. While it is a straightforward task to prove these identities with induction, and also by arithmetical manipulations such as rearrangements, the approach used here is quite simple to follow and eventually reduces the proof to a counting problem. (Contains…

A stopper is called "universal" if it can be used to plug pipes whose cross-sections are a circle, a square, and an isosceles triangle, with the diameter of the circle, the side of the square, and the base and altitude of the triangle all equal. Echoing the well-known result for equal cubes that is attributed to Prince Rupert, we show that it is…

If you break a stick at two random places, the probability that the three pieces form a triangle is 1/4. How does this generalize? To answer this question, we give a method for finding the probability that n randomly chosen points in a given interval fall within a specified distance of one another. We use this method to provide solutions to…