Recent years have witnessed a growing interest in interdisciplinary teaching and learning in the elementary grades. Teachers are increasingly looking for ways to help their students integrate literacy instruction with content area learning. This article highlights some of the similarities between reading comprehension and mathematical…

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 large body of research has shown that for novice learners, instruction that relies more heavily on worked examples than on problem solving, is more effective for learning as shown by higher test performance. Moreover, this beneficial effect is often obtained with less acquisition time and lower cognitive load during acquisition and test phase.…

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…

We focus on a major difficulty in solving combinatorial problems, namely, on the verification of a solution. Our study aimed at identifying undergraduate students' tendencies to verify their solutions, and the verification strategies that they employ when solving these problems. In addition, an attempt was made to evaluate the level of efficiency…

Answers to mathematical problems come in all forms and most come with a variety of questions. Students often forget to ask questions once they have found an answer. This paper suggests that students would always benefit by questioning answers.

Back-of-the-envelope problems call for approximate calculations of quantities that can be related to information in a person's knowledge but are not solved precisely. These problems provide an opportunity for the study of processes and the role of general knowledge in ill-defined problem solving. Subjects with advanced and intermediate knowledge…

Students in adult basic education/general educational development classes need skills in analyzing and solving programs, extending beyond those learned through word problems in the mathematics curriculum. The following strategies can help students broaden their problem-solving skills: (1) act it out, (2) construct a table, (3) draw a picture, (4)…

Explains an application of mathematical modeling within a school setting as well as progressive use of graphing calculators in mathematical modeling. Analyzes students' performances in the process of problem-solving using the problem of baton-passing in relay races. Discusses students' use of their mathematical knowledge and ideas when they used…

Describes the "Two-Eight" instructional model for students who have arithmetic computational skills but lack the ability to select appropriate strategies to solve problems. Offers examples showing the replacement of the actual values used in a word problem with the simple numeric values of 2 and 8 to create a parallel, solvable problem. (DMM)

This project addressed the question: What knowledge and processes enable individuals to construct and modify representations of novel, nonroutine problems? The theoretical goal was to extend the information-processing theory of problem solving to include processes that have been characterized as restructuring of problems and productive thinking by…

This book is designed to help adults gain the range of math skills they need to succeed in life and work and on standardized tests, including the GED. It is expected to help students overcome math anxiety, discover math as interesting and purposeful, and develop good number sense. Lessons are organized around four strands: (1) skill lessons that…

Describes a beginning algebra course that places stronger emphasis on learning to solve problems and introduces topics using real world applications. Students learn estimating, graphing, and algebraic algorithms for the purpose of solving problems. Indicates that applications motivate students by appearing to be a more relevant topic as well as…

Students with language and learning disabilities may have difficulty solving mathematics word problems. Use of a sequential checklist, identifying clues and keywords, and illustrating a problem can all help the student identify and implement the correct computational process. (DB)