We examine student achievement of 2533 students in 10 middle schools in relation to the implementation of textbooks developed with funding from the National Science Foundation (NSF) or publisher-developed textbooks. Using hierarchical linear modeling (HLM), curriculum type was not a significant predictor of student achievement on the Balanced…

The mathematics-education community stresses the importance of real-world connections in teaching. The extant literature suggests that in actual classrooms this practice is infrequent and cursory, but few studies have specifically examined whether, how, and why teachers connect mathematics to the real world. In this study, I surveyed 62 secondary…

Developing students' ability to reason has long been a fundamental goal of mathematics education. A primary way in which mathematics students develop reasoning skills is by constructing mathematical proofs. This article presents a number of nontypical results, along with their proofs, that can be explored with students in any calculus classroom.…

This article considers why (-1)(-1) = +1 and how and why a teacher might go about explaining this concept to high school students without using pseudoreasoning. Furthermore, it provides a precise explanation, through the use of the distributive property, as to why (-1)(-1) = +1. (Contains 1 figure.)

Detracking and heterogeneous groupwork are two educational practices that have been shown to have promise for affording all students needed learning opportunities to develop mathematical proficiency. However, teachers face significant pedagogical challenges in organizing productive groupwork in these settings. This study offers an analysis of one…

The transition from arithmetic to algebra in general, and the use of symbolic generalizations in particular, are a major challenge for beginning algebra students. In this article, we describe and analyze students' learning in a "computer intensive environment" designed ad hoc and implemented in two seventh grade classrooms throughout two…

In this article I recount my experiences with a series of encounters with the catwalk task and reflect on the professional growth that these opportunities afforded. First, I reflect on my own mathematical work on the catwalk task, including my efforts to fit various algebraic models to the data. Second, I reflect on my experiences working with a…

The triangle congruence conditions are a central focus to nearly any course in Euclidean geometry. The author presents a hands-on activity that uses straws and pipe cleaners to explore and justify the triangle congruence conditions. (Contains 4 figures.)

In a previous article in this journal, simple constructions were considered to study the reflective property of a parabola and of a paraboloid. The purpose was to help middle school students understand the importance of the parabola shape and its ability to focus parallel rays. The examples demonstrated a use of the two "Cabri" products to study a…

Fractal geometry offers teachers great flexibility: It can be adapted to the level of the audience or to time constraints. Although easily explained, fractal geometry leads to rich and interesting mathematical complexities. In this article, the authors describe fractal geometry, explain the process of iteration, and provide a sample exercise.…

Under the backdrop of the investigation of rational functions and their respective curved asymptotes, the reader is invited to experience the mathematical process alongside the authors and observe the application of the NCTM Process Standards and the use of multiple representations in the investigation and solution of a problem. (Contains 9…

Many mathematics educators believe that it is insufficient for students' knowledge of the division of fractions to be limited to the invert-and-multiply algorithm, arguing that students' learning of mathematics must go beyond rote memorization of procedures. Teachers ought to carefully consider what students need to learn beyond the algorithmic…

Mastering mathematics has become more important than ever before in the United States. Students with a strong background in mathematics have an advantage over those students who struggle, when competing for jobs. In the job market, workers who have a strong mathematics and science background are more likely to be employed and earn more than those…

This content analysis examined the distribution of financial mathematical tasks (FMTs), mathematical tasks that contain financial terminology and require financially related solutions, across the National Standards in K-12 Personal Finance Education categories (JumpStart Coalition, 2007), the thinking skills as identified by "A Taxonomy for…

The California's Outstanding Math Educators' Ongoing Network (COME ON) initiative is a unique and innovative effort to support high school mathematics teachers in California. It serves as a living example of a successful model that addresses an issue critical to all of mathematics education K-18--how to sustain and strengthen those most directly…