This article describes the technique of introducing a new variable in some calculus problems to help students master the skills of integration and evaluation of limits. This technique is algorithmic and easy to apply.

The aim of this study is to explain students' ability to transfer their knowledge about mathematical series to the problems that they encounter. The data of the study were obtained by using two different tests, namely "Problem Solving Test (PST)" and "Series Character Identification Test (SCT)" which were developed by the…

The National Council of Teachers of Mathematics calls for an increased emphasis on proof and reasoning in school mathematics curricula. Given such an emphasis, mathematics teachers must be prepared to structure curricular experiences so that students develop an appreciation for both the value of proof and for those strategies that will assist them…

In its mathematics standards, National Council of Teachers of Mathematics (NCTM) states that problem solving is an integral part of all mathematics learning and exposure to problem solving strategies should be embedded across the curriculum. Furthermore, by high school, students should be able to use, decide and invent a wide range of strategies.…

A central goal of secondary mathematics is for students to learn to use powerful algebraic strategies appropriately. Research has demonstrated student difficulties in the transition to using such strategies. We examined strategies used by several thousand 8th-, 9th-, and 10th-grade students in five different school systems over three consecutive…

Interspersing easy problems among challenging problems has been shown to both increase students' preference for completing math worksheets and the fluency with which they complete challenging problems. Although early research examining the interspersal procedure in mathematics was conducted with college-age students, there are a growing number of…

Discusses how to express an n factorial as a product of powers of primes. Provides two examples and answers. Presents four related suggestions. (YP)

Determines which chessboards contain a chromatic rectangle having all four corners the same color for any black-white coloring. Expands the problem to a three color problem. (YP)

Analyzes fifth graders' approaches for solving the problem of the distance to the horizon. Describes determining the area bounded by the horizon. (YP)

Examines the students' understanding of mathematical structure and the relationship between problem solving and the identification of the structure in 13 word problems. Multidimensional scaling and hierarchical cluster analysis were used to assess how subjects organized word problems in their minds. (YP)

Shows that the ratio of the area of the quadrilateral formed by joining the kth points to the area of the original quadrilateral is constant whether it is convex or concave quadrilateral. Presents many geoboard or dot paper diagrams and geometrical expresssions. (YP)

Presents four examples on arithmetic mean and harmonic mean. Provides solution of each of the examples and instructional activities related to the examples. Lists eight references on mathematical problem solving. (YP)

A project in which students can develop their understanding of mathematical concepts through the collaborative writing of word problems is discussed. Worksheets for project requirements and daily requirements are provided. A Thanksgiving project is proposed. The use of a fashion modeling problem in the statistics classroom is described. (CW)

Presented is a lesson in which the patterns that occur within and between sequences of polygonal numbers present an opportunity for students to analyze, represent, and generalize relationships. Materials, objectives, levels, and directions for this activity are discussed. Worksheets to accompany the activities are provided. (CW)

Discusses making tessellations by using a polyomino. Illustrates the various ways for various shapes of polyomino. Provides several diagrams and instructional guides. (YP)