If the prospective students of probability lack a background in mathematical proofs, hands-on classroom activities may work well to help them to learn to analyze problems correctly. For example, students may physically roll a die twice to count and compare the frequency of the sequences. Tools such as graphing calculators or Microsoft Excel®…

This article describes a classroom activity with college sophomores in a methods-of-proof course in which students reasoned about absolute value inequalities. The course was designed to meet the needs of both mathematics majors and secondary school mathematics teaching majors early in their college studies. Asked to "fix" a false…

In the criminal justice system, defendants accused of a crime are presumed innocent until proven guilty. Statistical inference in any context is built on an analogous principle: The null hypothesis--often a hypothesis of "no difference" or "no effect"--is presumed true unless there is sufficient evidence against it. In this…

Calculus instruction is an important topic for high school and college teachers alike. A prime target for attention is integration, which, unfortunately, students too often treat as a rote procedure. Understanding the integral better will support students' application of their mathematical knowledge to science, technology, and engineering…

Over the past five years, the Mathematical Association of America, with support from the National Science Foundation, has explored the teaching of mainstream Calculus 1 at the postsecondary level, where by "mainstream" we mean those courses that can be used as part of the prerequisite stream to more advanced postsecondary mathematics. We…

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…

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…

Much of what is taught, especially in college, is designed to support other disciplines. To determine the current mathematical needs of twenty-three partner disciplines, the Mathematical Association of America (MAA) conducted the Curriculum Foundations Project (Ganter and Barker 2004; Ganter and Haver 2011), as discussed in the appendix…

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…

The Common Core State Standards (CCSS) provide teachers with the expectations and requirements that are meant to prepare K-12 students for college and the workforce (CCSSI 2010b). The Common Core State Standards for Mathematical Practice (SMPs) emphasize the development of skills and conceptual understanding for students to become proficient in…

Statistical studies are referenced in the news every day, so frequently that people are sometimes skeptical of reported results. Often, no matter how large a sample size researchers use in their studies, people believe that the sample size is too small to make broad generalizations. The tasks presented in this article use simulations of repeated…

The quadrilaterals problem is a particularly rich task, applicable to in-service teachers as well as to the students they teach. The ways in which students engage in this task, the strategies they use, and the mathematics that results align well with this "MT" Focus Issue on flexible mathematical thinking. The authors offer their observations of…

The activity of posing and solving problems can enrich learners' mathematical experiences because it fosters a spirit of inquisitiveness, cultivates their mathematical curiosity, and deepens their views of what it means to do mathematics. To achieve these goals, a mathematical problem needs to be at the appropriate level of difficulty,…

In the early 1990s, after a long series of disappointing results on national and international mathematics achievement tests the National Science Foundation (NSF) funded the development of thirteen complete mathematics programs at the elementary school, middle school, and secondary school levels. Many teachers were quite happy with the new…