We present and discuss three examples of misapplication of the notion of conditional probability. In each example, we present the problem along with a published and/or well-known incorrect--but seemingly plausible--solution. We then give a careful treatment of the correct solution, in large part to show how careful application of basic probability…

The purpose of this paper is to re-examine the relationships between mathematical problem solving and learning mathematics. After introducing a diagram representing the notion of problem solving, four types of problem solving approaches used in mathematics classrooms will be distinguished according to which aspect of that diagram is attended to.…

There are four Euclidean centres of a triangle--the circumcentre, the centroid, the incentre and the orthocentre. In this article, the authors prove the following: if the centre is the incentre (resp. orthocentre) then there exists a triangle with given distances of its vertices from its incentre (resp. orthocentre). They also consider uniqueness…

People are inclined to desire proof of theories if they have developed a certain philosophical style when they are quite young. It is a style that questions the authority for things, so that they can hold fast to what is good. Regarding mathematical proof, this author argues that it is only those who are prepared to take their own authority for…

The author has always been fascinated by the title identity. It's charming and simple, as well as easy to believe after pressing a few calculator keys. Several fine proofs have appeared in the literature, including several proofs without words. His own earlier proof is trigonometric, and he has often been dissatisfied with not being able to…

Technology is a powerful tool in assisting students in problem solving by allowing for multiple representations. The vignette offered in this article provides insight into ways to solve open-ended problems using multiple technologies.

Algebra has been identified as the foundational course for all other mathematics courses. Yet, research has shown that African-American students are low achievers in all strands of mathematics (NCES, 2001). Computers, on the other hand, have been marketed as an instructional tool to teach and reinforce classroom instructions. This study…

We study four non-Newtonian fluid mechanics problems using Mathematica[R]. Constitutive equations describing the behavior of power-law, Bingham and Carreau models are recalled. The velocity profile is obtained for the horizontal flow of power-law fluids in pipes and annuli. For the vertical laminar film flow of a Bingham fluid we determine the…

Gaps between teaching practices and research recommendations have been well documented. One challenge for research is in understanding the processes and systems that promote a bridging of these gaps. A year-long study with four primary teachers documented ten support mechanisms, or connection levers, that the teachers raised as important for…

A holiday quilt project in a kindergarten classroom becomes a focus for exploring patterns, shapes, measurement, spatial relationships, and number sense. Cooperative group work, problem solving, and communication of mathematical ideas enhance the completion of the project. (Contains 5 figures.)

The perspective of situated learning offers a theoretical framework for understanding the dialectical relations between the social and the individual dimensions of classroom microculture. The purpose of this article is to show how sociomathematical norms constructed during whole-class discussions provide a reference for the elaboration of…

Fjellstedt and Sulzer-Azaroff (1973) used differential reinforcement of short latencies to decrease a child's latency to comply with instructions. We replicated this contingency with a young man diagnosed with Asperger syndrome across two tasks (question answering and math problem solving). We added a differential reinforcement contingency to…

The study investigated the effects of two reflection support programs on elementary school mathematics teachers' pedagogical problem solving view. Sixty-two teachers participated in a professional development program. Thirty teachers were assigned to the self-questioning (S_Q) training and thirty two teachers were assigned to the reflection…

A majority of studies on learning disabilities have focused on elementary grades. Although problems with learning disabilities are life-affecting only a few studies focus on deficits in adults. In this study adults with isolated mathematical disabilities (n = 101) and adults with combined mathematical and reading disabilities (n = 130) solved…

Recognition of the importance of (special) children's learning of mathematics in an active fashion has increased rapidly since the beginning of the 1980s. This book presents current ideas and trends in the teaching of mathematics and aims at giving an overview of new developments in the field of (special) mathematics and showing how researchers…