Here, we investigate what loci are produced when a square of side-length one is allowed to rotate around a square of side-length n, where n is a whole number. We find that if i = 1, 2, 3 or 4 (mod 4), the loci obtained for n [congruent to] i (mod 4) all have the same symmetry and we show how the perimeter of each class can be determined. We also…

This article provides an overview of vertex-edge graphs as an essential topic in the high school mathematics curriculum, including rationale, recommendations, and sample applications. A classroom-ready activity with full teacher notes is also included. (Contains 1 table and 9 figures.)

This article describes instructional activities designed to help students develop an understanding of the multiple relationships between fractions and percents and unit price as they develop their mental-math abilities. (Contains 4 figures.)

This is a study of David, a senior enrolled in a high school precalculus course. David's understandings of functions and periodicity was explored, through clinical interviews and contextualized through classroom observations. Although David's precalculus class was traditional his understanding of periodic functions was unconventional David engaged…

The use of tablet PCs in teaching is a relatively new phenomenon. A cross between a notebook computer and a personal digital assistant (PDA), the tablet PC has all of the features of a notebook with the additional capability that the screen can also be used for input. Tablet PCs are usually equipped with a stylus that allows the user to write on…

The purpose of this case study was to (a) examine the main and interaction effects of gender, race and class-type on mathematics achievement, mathematics attitudes and sources of mathematics self-efficacy, (b) investigate teacher-student interactions in the single-sex mathematics classes and (c) investigate perspectives about single-sex…

This case study evaluated the significance of implementing an enrichment mathematics course during the summer to rising African American ninth graders entitled, "Geometry Honors Preview." In the past, 60 to 70 percent of African American students in this school district had withdrawn from Geometry Honors by the second academic quarter. This study…

"Streaming" for mathematics remains a contentious issue and particular forms of the practice have been considered inequitable. In the study reported here, the focus was on the extent to which streaming is used for mathematics at years 7-10 in Victorian secondary schools. Also of interest were the forms of streaming adopted and the…

The Mathematics Education Debate is an assignment designed for and implemented in an undergraduate mathematics methods course for prospective secondary school mathematics teachers. For the assignment, students read and analyze current research and policy reports related to mathematics education, prepare and present their positions, offer…

Engaging all students in grade-level mathematics is often a challenge for teachers, especially in diverse urban classrooms. Too often in her role of supporting the development of effective practices with middle school teachers, the author observes traditional classroom instructors presenting information and demonstrating procedures. In this…

This article focuses on a secondary mathematics teacher education program where traditional field placements are prevalent in grades 9-12. Traditional, for this article, is defined as and comprised of: (a) straight-rowed desks in classrooms, (b) explicitly direct instruction (teacher-centered classrooms), (c) predominantly repetition of low-level…

Recent attention to low student achievement in mathematics has brought attention at the national, state, and local level to the shortage of "Highly Qualified" mathematics teachers. However, current policy and practice fall short of ensuring that the most qualified--as in effective--mathematics teachers support the learning of the…

This article presents the results of a three-year study that explores students' performance on patterning tasks involving prealgebra and algebra. The findings, insights, and issues drawn from the study are intended to help teach prealgebra and algebra. In the remainder of the article, the authors take a more global view of the three-year study on…

Taking advantage of pedagogical opportunities afforded by new technology requires appropriately designed lessons. This article reports on the use of "lesson study" to research principles for the design of a lesson aiming to take advantage of multiple representations. The lesson, for year 10 students who had personal access to TI-Nspire, focused on…

This article presents an analysis of how students' dispositions toward learning shift and change over time through their engagement with particular classroom practices and identifies classroom practices that support the development of more productive dispositions. An analysis of 4 purposefully selected students from 2 different classrooms reveals…