In fall 2013 the author taught a graduate course entitled Topics in Geometry for Middle and High School Teachers. The majority of the participants had extensive experience teaching mathematics in middle school or high school. The fact that participants were rather comfortable with the basic concepts of school geometry made it both possible and…

In this "Delving Deeper" article, the author introduces the slip-slide method for solving Algebra 1 mathematics problems. This article compares the traditional method approach of trial and error to the slip-slide method of factoring. Tools that used to be taken for granted now make it possible to investigate relationships visually,…

In this article, Strayer and Matuszewski present a six-phase strategy that teachers can use to help students develop a conceptual understanding of inferential hypothesis testing through simulation. As Strayer and Matuszewski discuss the strategy, they describe each phase in general, explain how they implemented the phase while teaching their…

Teachers facilitate math talk in the classroom, but introducing a structured discussion format called the "talking circle" can influence opportunities for equitable student participation. Drawing on his reflections over the 2013-14 academic year and reviewing his detailed teaching notes and lesson plans, Marcus Hung takes a close look at…

Learning to reason spatially is increasingly recognized as an essential component of geometry education. Generally taken to be the "ability to represent, generate, transform, communicate, document, and reflect on visual information," "spatial reasoning" uses the spatial relationships between objects to form ideas. Spatial thinking takes a variety…

In this article, mathematics teachers in the United States were asked what constitutes a high-quality mathematics lesson. The returned responses varied greatly. This same question was asked of Japanese teachers also. For a clearer picture both American and Japanese teachers were directed to comment on videotaped mathematics lessons taught in both…

This article illustrates the use of comparison as an instructional approach that can help students develop and use a variety of problem-solving strategies and approaches in the mathematics classroom. Through comparison of solution strategies, students deliberately consider the similarities and differences among methods and how different strategies…

The use of random numbers is pervasive in today's world. Random numbers have practical applications in such far-flung arenas as computer simulations, cryptography, gambling, the legal system, statistical sampling, and even the war on terrorism. Evaluating the randomness of extremely large samples is a complex, intricate process. However, the…

In this article, the author describes how he created an approach that he terms "Mathematics as a Second Language" (MSL) for teaching ELL students mathematics. The main components of MSL are vocabulary activities, journals, group work, and projects. He used MSL to teach prealgebra to ELL students, as well as to native English speakers, for two…

This set of activity sheets requires students to organize and display data with a box-and-whiskers graph. Students use the plot as a summary display to detect patterns and to highlight the important features of the data for purposes of comparison. (PK)