Students often have the misconception that mathematics involves reading the problem, staring at the page, and then writing down an answer. With more than twenty years of experience working with students in eighth-grade math through college calculus, the author has been increasingly interested in how she can foster problem-solving skills in her…

Retaining mathematical knowledge is difficult for many students, especially for those who learn facts and procedures without understanding the meanings underlying the symbols and operations. Repeated practice may be necessary for developing skills but is unlikely to make conceptual ideas stick. An idea is more likely to stick if students are…

Research shows that the greatest gains in student learning in mathematics classrooms occur in classrooms in which there is sustained use of high cognitive demanding tasks throughout instruction (Boston and Smith 2009). High cognitive demanding tasks, which this article will refer to as rich tasks, are mathematics problems that are complex, less…

This article describes the A, E, I, O, U technique, designed to help teachers ensure that teaching and learning are not mutually exclusive in the classroom. Most teachers would agree that motivating average teenagers to communicate how they got an answer or justify their problem-solving strategies can be as difficult as teaching a dog to whistle.…

The students of a Mathematical Modeling and Problem Solving class investigate and explore the mathematics involved in fitting a box spring mattress up a stairwell by solving various optimization problems and by using The Geometer's Sketchpad. The results show that a very small fraction of the class was actually able to solve the problem without…

Describes a group project concerning the Calendar Problem 9 in the January, 1993 Issue of this journal, students' methods for solving the problem, and an extension of the problem. (KHR)

Presents an interesting problem intended to introduce students to an application of algebra and to help them make the transition from arithmetic to algebra. Uses different problem representations including making successive approximations, interpreting graphs, and solving equations. Discusses pedagogical issues involved. Contains 11 references.…

Introduces a special triangle for which many different problems can be posed on the basis of one unusual property. Presents three problems and considers different approaches for the first problem. Explores other mathematical problems using the "What if not?" strategy that can be used as classroom activities. (KHR)

Describes a student project that enables students to experience problem-solving strategies and construct their own understandings of the problem-solving strategies by researching the problem-solving process itself, uncovering and defining strategies that they can subsequently use to solve problems, and exploring the impact that attitude has on…

Presents several examples of investigations which demonstrate the following: (1) algebra is connected to other mathematical topics; (2) algebra is an effective tool for representing patterns and relationships; and (3) algebra is an effective tool for analyzing patterns. (DDR)

Presents four methods for solving a quadratic equation using graphing calculator technology: (1) graphing with the CALC feature; (2) quadratic formula program; (3) table; and (4) solver. Includes a worksheet for a lab activity on factoring quadratic equations. (KHR)

Discussed are some applications of mathematics involved in actuarial science which may be taught in high school mathematics classes. Described are the importance of approximate solutions, multiple answers, and selling the solution to a problem. (CW)

Described is an approach to teaching algebra in a meaningful context by using problem solving to motivate students and increase their retention. Examples of this approach are given. (CW)

Presents an approach to explaining a relation, a - b = -(b - a), that is difficult for algebra students to understand. The approach came about as a result of discussions with students in which they provided many novel explanations. (DDR)

Two ideas for teaching mathematical Concepts are presented: "Writing Study Cards for Understanding"; and "A Conceptual Approach to Solving Equations." Examples of the applications of these methods are discussed. (CW)