A mathematics classroom that reflects the vision of NCTM's "Principles and Standards for School Mathematics" will have the teacher posing problems, asking questions that build on students' thinking, and encouraging students to explore different solutions. In teaching about area, it is not sufficient to give students the…

For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…

At a time when the debate continues over whether homework is overused, optional, or essential or favors well-off students over those with little home support, teachers must understand ways in which effective homework strategies can help narrow the achievement gap. Vatterott (2009, p. 94) argues convincingly that the "old paradigm" of…

Planning a lesson can be similar to planning a road trip--a metaphor the authors use to describe how they applied research and theory to their lesson planning process. A map and mode of transportation, the Common Core State Standards for Mathematics (CCSSM) and textbooks as resources, can lead to desired destinations, such as students engaging in…

How can the key concept of equivalent expressions be addressed so that students strengthen their representational fluency with symbols, graphs, and numbers? How can research inform the synergistic use of both paper-and-pencil analysis and computer algebra systems (CAS) in a classroom learning environment? These and other related questions have…

Unit conversion need not be boring. If students see that the skill is necessary, both their motivation to learn and their appreciation of the process can be enhanced. As a result, students become actively engaged and construct understanding and computational skills that they will retain over time. The activity described here makes use of scale…

In 1996, a new proof of the Pythagorean theorem appeared in the "College Mathematics Journal" (Burk 1996). The occurrence is, perhaps, not especially notable given the fact that proofs of the Pythagorean theorem are numerous in the study of mathematics. Elisha S. Loomis in his treatise on the subject, "The Pythagorean…

Most people who are attracted to STEM-related fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®,…

Shapedoku is a new type of puzzle that combines logic and spatial reasoning with understanding of basic geometric concepts such as slope, parallelism, perpendicularity, and properties of shapes. Shapedoku can be solved by individuals and, as demonstrated here, can form the basis of a review for geometry students as they create their own. In this…

After serving as a high school math teacher in Maryland for three years, the author moved to teaching sixth-grade math. His high school background led him to differentiate differently than his colleagues. The article discusses his observations and his conclusions and offers a plan to implement changes in the way mathematics is taught through…

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…

John Lamb, a professor of mathematics education and a teacher of high school precalculus, describes how he developed a way to use the elements of the game Angry Birds® as a platform to engage his students with the concepts of parabolas and vectors. The game could be categorized as a type of microworld game in which students interact with the…

KenKen® is the new Sudoku. Like Sudoku, KenKen requires extensive use of logical reasoning. Unlike Sudoku, KenKen requires significant reasoning with numbers and operations and helps develop number sense. The creator of KenKen puzzles, Tetsuya Miyamoto, believed that "if you give children good learning materials, they will think and learn and…