Graphing polar curves typically involves a combination of three traditional techniques, all of which can be time-consuming and tedious. However, an alternative method--graphing the polar function on a rectangular plane--simplifies graphing, increases student understanding of the polar coordinate system, and reinforces graphing techniques learned…

"How Much Can You Bench?" appears in the "Mathematical Lens" section of "Mathematics Teacher." "Mathematical Lens" uses photographs as a springboard for mathematical inquiry and appears in every issue of "Mathematics Teacher." This month the mathematics behind the photograph includes finding areas…

If a teacher asked their students what thinking looks like, what would they say? Would they just look at the teacher quizzically? The question is challenging because thinking is largely an invisible endeavor, and developing thoughtful students can be a daunting task. However, the job of mathematics teachers is to develop students who think about…

The Borough of Manhattan Community College (BMCC) in New York City is fourth among all community colleges in awarding degrees to minority students and in awarding degrees to African Americans. The BMCC student body is approximately 37 percent Hispanic, 33 percent black, 15 percent white, and 15 percent Asian. In addition, a significant proportion…

This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…

Educators in forty-five states and the District of Columbia are hard at work interpreting and implementing the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010). This work typically involves teacher participation in professional development activities focused on developing an understanding of the content standards as well as the…

Principles and Standards for School Mathematics (NCTM 2000) states, "Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning." The focus on reasoning and sense making with technology in the lesson presented in this article will enable students to do…

Must two triangles with equal areas and equal perimeters also be congruent? This question was introduced in "Mathematics Teacher" ("MT")by Rosenberg, Spillane, and Wulf in their article "Heron Triangles and Moduli Spaces" (2008), which also described the authors' subsequent investigation of a particular moduli…

Many preservice teachers come into teacher education programs with a rule-based view of mathematics, a view that is to a large extent indicative of their previous school experiences. In teaching preservice elementary school teachers, this author has used his instrumental understanding as the starting point for rich discussions about the…

Card sorting has the potential to provide opportunities for exploration of a variety of topics and levels. In a card-sorting task, each participant is presented with a set of cards--each of which depicts a relationship--and is asked to sort the cards into categories that make sense to him or her. The concept of function is critical to…

What does problem-based instruction do for students and teachers? The open-ended geometry problem presented in this article, along with examples of students' work on the problem, illustrates how problem-based instruction can help students develop their mathematical proficiency. Recent studies have shown that students who experience…

Problem solving is a necessary component of developing a strong mathematics curriculum that will help all students achieve their life goals, regardless of their specific academic plans. What day-to-day instructional decisions do teachers need to make if they believe that problem solving is a vehicle for learning mathematical content? In this…

Today there are many categories of mathematics literature, including fiction and poetry. Mathematics fiction appears in such anthologies as "Fantasia Mathematica" (Fadiman 1958, 1997) and "The Mathematical Magpie" (Fadiman 1962, 1997). In addition, mathematics fiction is featured at http://kasmana.people.cofc.edu/MATHFICT.…

In this article, the author describes the development and implementation of a measurement-based group activity designed to support students in understanding the connection between angle magnitude and the shape of the sine function. She explains that the benefit of this activity is that it allows students to build their trigonometric knowledge…

While teaching a methods class for preservice secondary school mathematics teachers, Christopher E. Smith found that although all students could draw a reasonably close approximation of a circle, not all could provide an entirely accurate definition of a circle. A discussion with students led him to think about ways of reintroducing students to…