The National Council of Teachers of Mathematics (NCTM) Algebra Standard states that instructional programs at the middle grades should enable students to "represent and analyze mathematical situations and structures using algebraic symbols" (2000, p. 222). Guess and check is a powerful problem-solving strategy that can connect a conceptual…

This Annual Measurable Objective (AMO) is designed to keep Florida moving forward toward national and international competitiveness. Florida will compare its National Assessment of Educational Progress (NAEP) scores to those of the top five states and its Trends in International Mathematics and Science Study (TIMSS), Progress in International…

Algebra is considered a key gatekeeper for higher-level mathematics course-taking in high school and for college enrollment (Adelman, 2006; Gamoran & Hannigan, 2000). Yet, algebra pass rates are consistently low in many places (Higgins, 2008; Ham & Walker, 1999; Helfand, 2006), including Chicago Public Schools (CPS). This is of particular…

Systems of linear equations are used in a variety of fields. Exposure to the concept of systems of equations initially occurs at the high school level and continues through college. Attempts to unearth what students understand about the solutions of linear systems have been limited. Gaps exist in our knowledge of how students understand systems…

Since mathematics is found in every aspect of life, it is important for teachers to provide experiences that help students find connections and develop an appreciation for math and its use in their lives outside school. Slope is an excellent example of a math concept that is usually taught without context or connection. In this article, the…

There is a growing consensus that introductory physics courses should help students develop general scientific reasoning abilities that transform them into lifelong learners, preparing them for careers and citizenship in a rapidly evolving world. Despite the sometimes daunting nature of this challenge, activities developed by various physics…

In 2007 many AAPT members received a booklet that is the first chapter of a physics textbook available on a CD. This book espouses the new educational philosophy of teaching special relativity as the first item in the topic of mechanics. Traditionally, special relativity is part of one or more modern physics chapters at the end of the text, and…

While 8th grade algebra was once reserved as a course for the gifted, today, more U.S. 8th graders take algebra than any other math course. This article discusses a report from the Brookings Institution which chronicles the history of the 8th-grade algebra surge and its impact on today's low-performing students. The report indicates that many of…

Linear algebra is one of the unavoidable advanced courses that many mathematics students encounter at university level. The research reported here was part of the first author's recent PhD study, where she created and applied a theoretical framework combining the strengths of two major mathematics education theories in order to investigate the…

The solution of linear ordinary differential equations (ODEs) is commonly taught in first-year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognizing what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to…

This study examines the process of change among grade 4 teachers (students aged 9-10 years) who participated in a yearlong Teacher Quality Grant innovation program. The concerns-based adoption model (CBAM), which informed the design and implementation of the program, was used to examine the process of change. Two questions guided the…

The goal of this paper is to explore qualities of mathematical imagination in light of a classroom episode. It is based on the analysis of a classroom interaction in a high school Algebra class. We examine a sequence of nine utterances enacted by one of the students whom we call Carlene. Through these utterances Carlene illustrates, in our view,…

This article discusses the use of hand-clapping games and dances in the music classroom. In addition to their use for teaching music skills and concepts, these games can be quite useful for making cross-disciplinary connections to reinforce the eighth and ninth National Standards for Music Education (Standard 8: understanding relationships between…

One of the basic disagreements in mathematics education concerns the roles that rules and procedures, on the one hand, and concepts and principles, on the other hand, should play in students' learning of mathematics. The use of procedures and an understanding of concepts are considered to be two separate aspects of mathematical activity.…

Pattern generalization and a focus on quantities are important aspects of algebraic reasoning. This article describes two different approaches to teaching and learning linear functions for middle school students. One group focused on patterns in number tables, and the other group worked primarily with real-world quantities. This article highlights…