Problem solving lies at the core of engineering and remains central in school mathematics. Word problems are a traditional instructional mechanism for learning how to apply mathematics to solving problems. Word problems are formulated so that a student can identify data relevant to the question asked and choose a set of mathematical operations…

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…

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…

This paper discusses one step from the scientific method--that of identifying independent and dependent variables--from both scientific and mathematical perspectives. It begins by analyzing an episode from a middle school mathematics classroom that illustrates the need for students and teachers alike to develop a robust understanding of…

This paper describes the author's attempt to design assignments that engage preservice elementary teachers in original mathematical thinking. In particular, the choice of integer operations as the focus of a structured writing assignment that takes students two weeks to complete is explained and justified. Exemplary student work is quoted.…

This article will share results from research that investigated how sixth-, seventh-, and eighth-grade students who had not been exposed to formal algebraic methods approached word problems of an algebraic nature. Student use of systematic guess and check, the predominate approach taken by these students, is the focus. The goal is to consider the…

Described is a study in which elementary education students were asked to solve word problems by looking at the mathematical structure or the surface structure of the problems. Included are the methodology, data analysis, results, and discussion. The word problems used in the study are appended. (KR)

Examines the mathematical process used by students when solving physics tasks that require proportional reasoning. Investigates students' understandings and explanations of their mathematical processes. (Author/CCM)

Presents the six major components of the Directed Reading Activity strategy: Developing Vocabulary, Building Background and motivation, Setting the Purpose, Guiding Silent Reading, Questioning to Determine Comprehension, and Rereading, as applied to mathematical problem solving, resulting in a directed mathematics activity. (MDH)

Discusses how actual or planned travel experiences can form the basis for constructing realistic, challenging, and interesting problem-solving tasks for classroom use. Provides examples of how teachers and students can create travel problems for use in the classroom. The travel-problem concept is adaptable to any elementary, secondary, or…

Describes a teaching experiment that evaluated published supplemental materials used to aid preparation of lessons at the fourth grade level involving nonroutine word problems. Lists 12 insights gained that can be useful to teachers using commercially produced problem-solving materials. (MDH)

Presents examples of how students can create drawings of sets of lines whose envelopes are parabolas, cardioids, epicycloids, or hypocycloids. Provides students with experience in problem solving, reasoning, communication, and connections between numbers and geometry, between mathematics and art, and between mathematics and other applications.…

This study explored the use of writing to help students' develop schemata knowledge for algebraic thinking. Eight seventh-grade pre-algebra students participated in a teaching experiment in which they solved algebraic problems related in mathematical structure. The problems involved contexts of growth and change and size and shape. Qualitative…

Describes how problem-based learning has been adapted for use in elementary and high school settings, including initiating learning with an ill-structured problem, using the problem to structure the learning agenda, and teacher as metacognitive coach. (31 references) (Author/MKR)

Presented are the results of a survey of elementary school principals designed to determine whether problem solving and critical thinking skills are an integral part of the science curriculum in elementary schools. Curriculum orientation, amount of problem solving, and problem-solving/higher-order thinking priorities are discussed. (CW)