Beautiful connections are established between seemingly unrelated mathematical territories, Fibonacci-Lucas numbers and hyperbolic trigonometric functions.

This article provides detailed analysis, from a radical constructivist perspective, of a sequence of letter-writing exchanges between a preservice secondary mathematics teacher and a high school student. This analysis shows the ways in which the preservice teacher gained understanding of the high school student's mathematics and attempted to pose…

Technology can support the study of math in a variety of ways. Through class Web sites, blogs or wikis, teachers can communicate the math standards, the goals needed to achieve the standards, homework assignments, projects, tests, and helpful Web sites for parents and students. The online site becomes an extension of the class. There are plenty of…

This paper reports a study of the classroom assessment practices of 12 sixth form college mathematics teachers in Malta. It explores the extent to which these teachers are knowledgeable about their students' learning of mathematics and the implications that this has for their classroom practices. It reveals that these teachers' knowledge of their…

The purpose of this study was to explore gender differences in mathematics achievement as demonstrated by performance on the mathematics subsection of a nationwide high school entrance examination in Turkey. In this study, the cities in Turkey were separated into five groups according to their level of economic development. The analysis was based…

This article presents a lesson for studying minority and women's contributions to the field of mathematics in the middle school classroom. This lesson may be able to stem the tide of the shrinking number of students entering the field of mathematics by helping them become interested in its history. Nonetheless, this project encourages students to…

This study documents problem solving approaches that high school students develop as a result of using systematically Cabri-Geometry software. Results show that the use of the software becomes an important tool for students to construct dynamic representations of the problems that were used to identify and examine different mathematical relations.…

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

This article shares an assessment tool that uses student-written word problems to provide meaningful information regarding the depth of mathematical understanding. Students' word problems representing 6 [division] 1/2 were classified using the scoring categories described in the NAEP. By categorizing the problems, students' levels of understanding…

We analyse the stability of the spring inverted pendulum with the vertical oscillations of the suspension point. An important factor in the stability analysis is the interaction between radial and oscillating modes. In addition to the small oscillations near the upper position, the nonlinearity of the problem leads to the appearance of limit-cycle…

This article describes and shares an innovative pedagogical practice that holds promise in contributing to the teaching and learning of proportions in middle school. The teaching and learning of mathematics with understanding framework was used as a vehicle to help 21 seventh grade students reason proportionally. The findings of this unit suggest…

This article describes a semester-long pen-pal project in which preservice teachers composed mathematical problems and the middle school students worked for solutions. The college students assessed the solution and the middle school students provided feedback regarding the problem itself. (Contains 6 figures.)

To guide problem-solving activities in the classroom, this article presents a strategy similar to the reading model found in literature circles. The goal of mathematics circles is to provide guidance and structure to problem-solving activities so that students can internalize the strategies needed for them to develop into mathematicians. (Contains…

The concept of "revoicing" has recently received a substantial amount of attention within the mathematics education community. One of the primary purposes of revoicing is to promote a deeper conceptual understanding of mathematics by positioning students in relation to one another, thereby facilitating student debate and mathematical…

One way to teach Pythagoras' Theorem is through use of puzzles. Marshall (2004:1) points out that, "in creating their individual solutions to puzzles, students may reveal mathematical thinking on which approaches to the standard curriculum could be based." This article describes a puzzle-like spatial structuring activity related to…