Research shows that students often struggle with understanding empirical sampling distributions. Using hands-on and technology models and simulations of problems generated by real data help students begin to make connections between repeated sampling, sample size, distribution, variation, and center. A task to assist teachers in implementing…

In recent years, the term "quantitative literacy" has become a buzzword in the mathematics community. But what does it mean, and is it something that should be incorporated into the high school mathematics classroom? In this article, the authors will define quantitative literacy (QL), discuss how teaching for QL differs from teaching a traditional…

Exploring and deriving proofs of closed-form expressions for series can be fun for students. However, for some students, a physical representation of such problems is more meaningful. Various approaches have been designed to help students visualize squares of sums and sums of squares; these approaches may be arithmetic-algebraic or combinatorial…

In this article, the author considers many of the common answers to the student question "When am I ever going to use this?" and points out ways in which students may be dissatisfied with these answers. He then suggests a change in perspective with respect to the handling of this and similar questions. In particular, he proposes that, if teachers…

The National Council of Teachers of Mathematics (NCTM), through its Connections Standard, highlights the importance of "the opportunity for students to experience mathematics in a context." Seeing how mathematics can be used to describe real-world phenomena can motivate students to learn more mathematics. Connecting mathematics to the real world…

An introduction to hypothesis testing using a mathematician's claim that his dog knows calculus and can intuit a minimum path.

Discusses the distribution of primes and focuses directly on one particular recurring pattern among them. (Author/NB)

Benjamin Banneker, a self-taught African American mathematician, kept a journal containing a number of mathematical puzzles. Explores four of these puzzles, 200 years later, with the aid of 21st century technology. (Author/NB)

Describes the use of a purposefully designed set of problems borrowed from a variety of critical thinking activity books and selected to motivate, excite, and engage students in the learning process. Helps students develop a deeper, more conceptual understanding of mathematics by incorporating these problems into a beginning algebra course.…

Presents the technique of mind mapping and points out its special fitting as a pedagogical tool for mathematics education. Discusses possible applications of mind mapping in mathematics education together with their advantages and limitations. (Author/NB)

Recounts a high school teacher's recognition of forces that impede the success of high school students in higher-level mathematics courses. (Author/NB)

Explores logarithms of negative numbers spurred by an unanticipated result given by a calculator. Shares the perspectives of the teacher and the teacher-as-learner. (Author/NB)

Discusses the merits of cooperative learning in the classroom and the effects of implementing cooperative learning in a high school geometry classroom. (Author/NB)

The values of a polynomial with integer coefficients can be computed using a graphing calculator, but it is impossible to see the formula itself. Suggests finding this formula from numerical data and describes the unusual way to solve this problem with one calculation only. (Author/NB)

Introduces the concept of function using graphs or pictorial representations of functions. Presents four activities for grade levels 8-14 that use the natural progression from qualitative graphs to quantitative graphs to tables to equations for introducing the theme of distance from an object as a function of time. (Author/NB)