In this article, the classic problem of finding three ways to determine the probability that the pieces of a stick randomly broken in two places will form a triangle is analyzed anew. To be useful in the classroom, an application must be incorporated into an often-crowded curriculum. What is nice about this triangle problem is that it fits in…

In this paper we report on a small-scale comparative examination of prospective elementary teachers' beliefs about problem-solving in Cyprus and England. First year undergraduate students (13 from Cyprus and 14 from England) from a well-regarded university in each country were qualitatively interviewed at the commencement of their respective…

Learning through meaningful problem solving is integral in any successful mathematics program (Carpenter et al. 1999). The National Council of Teachers of Mathematics (NCTM) promotes the use of problem solving as a means to deepen understanding of all content areas within mathematics (NCTM 2000). This article describes a first-grade lesson that…

A basic level of literacy and numeracy is essential for full participation in modern societies. While very few people in most of the advanced countries could be regarded as illiterate or innumerate, recent studies have shown that there are, in fact, significant numbers of people with poor skills, and that low levels of skills are associated with…

In the teaching of physics at upper secondary school level (K10-K12), the students are generally taught to solve problems analytically, i.e. using the dynamics describing a system (typically in the form of differential equations) to compute its evolution in time, e.g. the motion of a body along a straight line or in a plane. This reduces the scope…

This study examined a random stratified sample (n = 62) of prospective teachers' work across eight institutions on three tasks that utilized dynamic statistical software. The authors considered how teachers utilized their statistical knowledge and technological statistical knowledge to engage in cycles of investigation. This paper characterizes…

We study the greenhouse effect on a model satellite consisting of a tungsten sphere surrounded by a thin spherical, concentric glass shell, with a small gap between the sphere and the shell. The system sits in vacuum and is heated by sunlight incident along the "z"-axis. This development is a generalization of the simple treatment of the…

This study examined how types of tasks influenced student activities/thinking and defined the role of Seatwork in mathematics lessons. It used 60 lessons from the TIMSS videotaped Study. These data indicated that practice was the most prevalent form of tasks in the U.S. In Germany, students completed mathematical calculations after a complex…

A Graphing Calculator (GC) is one of the most portable and affordable technology in mathematics education. It quickens the mechanical procedure in solving mathematical problems and creates a highly interactive learning environment, which makes learning a seemingly difficult subject, easy. Since research on the use of GCs for the teaching and…

Transfer is typically thought of as requiring individuals to "see" what is the same in the deep structure between a new target problem and a previously encountered source problem, even though the surface features may be dissimilar. We propose that experts can "see" the deep structure by considering the first-order interactions…

The issues that prompt this study are based on current research indicating the positive effects of inquiry learning on the cognitive development of children. The purpose of this case study was to understand the effects of inquiry learning on the academic achievement and bilingual verbal ability of 5th grade bilingual students in a French/English…

There is growing worldwide interest in Japanese lesson study as a model for professional learning, with large-scale adaptations of lesson study taking place in many countries. This paper describes how teachers and researchers collaborated in a lesson study project carried out in three Victorian schools. It describes Japanese lesson study and the…

A study was conducted at the Technical University Berlin involving students who twice failed the written examination in the first semester course Linear Algebra for Engineers in order to better understand the reasons behind their failure. The study considered student understanding in terms of Bloom's taxonomy and the ways in which students…

Education systems worldwide must strive to support the teaching of a set of New Media Literacies (NMLs). These literacies respond to the need for educating human capital within participatory cultures in a highly technologized world. In this paper, we present Collboard, a constructivist problem solving activity for fostering the development of…

The purpose of this study was to examine children's mathematical understandings related to participation in tithing (giving 10% of earnings to the church). Observations of church services and events, as well as interviews with parents, children, and church leaders, were analyzed in an effort to capture the ways in which mathematical problem…