For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the…

Geometry students need challenges. They need to apply what they already know to new contexts. As a result, high school teacher Wayne Nirode is always looking for groups of related problems of theorems to challenge his geometry students. He came across one such group or problems when reading Jun's (2012) one-page abstract posted online for the 12th…

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…

A fundamental component of mathematical learning is spatial visualization. To improve their spatial visualization skills, students should be given opportunities to work with two- and three-dimensional objects. The authors describe two activities that use tetrahedra nested within cubes to help improve students' visualization of two- and…

Historically, calculus has displaced many algebraic methods for solving classical problems. This article illustrates an algebraic method for finding the zeros of polynomial functions that is closely related to Newton's method (devised in 1669, published in 1711), which is encountered in calculus. By exploring this problem, precalculus students…

This article allows students to apply their knowledge and experience of area and volume to find the volume of Norris Lake, a large reservoir lake in Tennessee. Students have the opportunity to demonstrate their skills in using maps and scales as well as to incorporate the use of technology in developing the solution. This project satisfied the…

A WebQuest is an inquiry-based lesson plan that uses the Internet. This article explains what a WebQuest is, shows how to create one, and provides an example. When engaged in a WebQuest, students use technology to experience cooperative learning and discovery learning while honing their research, writing, and presentation skills. It has been found…

Discusses the use of the recursive method to permutations of n objects and a problem making c cents in change using pennies and nickels when order is important. Presents a LOGO program for the examples. (YP)

Shows the potential of using interactive geometry software to produce a natural environment for formulating and pursuing questions that arise in the course of solving problems. (KHR)

Offers a cave-mapping problem and discusses how to solve it. Presents the problem and necessary geologic background and a spreadsheet algorithm to solve the problem. (KHR)

Describes the angles-of-a-star problem designed to find the sums of the measures of the angles at the vertices of a five-pointed star. Shows that a good problem may have many correct solutions. (KHR)

Presents a scenario in which two people solve a programming problem by discussing various number sequences and functions. The problem is redefined as one related to number theory and operations research. (DDR)

Presents activities on problem solving, mathematical induction, proof by induction, and use of the phrase "without loss of generality." Provides a computer application illustrating recursive and iterative functions using C language. (ASK)

Describes the results of three years of field-work and the prospects for change in algebra teaching as a consequence of using computers and calculators. Summarizes the structure of text materials, classroom organization, and students' responsibilities. (YP)

Two incidents involving novice teachers with classes in grades 7 and 10 are presented. Then considered are the nature of intuitive mathematics and contributions computers can make to such intuitive mathematics, particularly in Algebra. (MNS)