Many teachers have designed lessons for students who will be working in groups to discuss and solve a problem. After investing time in constructing an interesting problem, creating strategically designed groups, and introducing the problem carefully, teachers may be left wondering how to help students collaborate to make sense of 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.…

The revised standards, like the earlier social studies standards published in 1994, continue to be structured around the ten themes of social studies. However, the revised standards offer a sharper focus on: (1) Purposes; (2) Questions for Exploration; (3) Knowledge: what learners need to understand; (4) Processes: what learners will be capable of…

Presents some ideas about how teachers can foster mathematical communication by encouraging students to find multiple solutions to problems. Discusses three problems that help develop communication ability in mathematics. Views communication of multiple solutions as an instructional strategy to help students make sense of mathematics. (KHR)

Discusses the difference between a generic chemistry problem (one which can be solved using an algorithm) and a harder chemistry problem (one for which there is no algorithm). Encourages teachers to help students recognize these categories of problems so they will be better able to find solutions. (TW)

Argues that there is a sense of surprise and wonder that can result from looking back at problem solutions and there is a potential for then creating unexpected, even memorable, alternative solutions. Example problems with routine solutions and alternative approaches uncovered while "looking back" at the solution are given. (PK)

Presented is a set of mathematics problems associated with the characteristics, production, and consumption of chicken eggs. Student assignment sheets are included. (CW)

Differentiates between problems, exercises and algorithms. Discusses the role of algorithms in solving problems and exercises in chemistry. Suggests that very real differences exist between solving problems and exercises, and that problem solving steps can be and should be taught in chemistry education. (TW)

Proposes methods to teach the more difficult concepts of linear algebra. Examines features of the Linear Algebra Curriculum Study Group Core Syllabus, and presents problems from the core syllabus that utilize the mathematical process skills of making conjectures, proving the results, and communicating the results to colleagues. Presents five…

Norms govern the criteria by which students decide what is good and what is not good, and align their learning trajectories accordingly.We found that the high-school students' norm is to produce working, but not necessarily error-free, programs and to argue for their correctness solely on the basis of a few executions. Therefore, they prefer…

Describes four methods to structure estimation activities that enable students to make connections between their understanding of numbers and extensions of those concepts to estimating. Presents activities that connect estimation with other curricular areas, other mathematical topics, and real-world applications. (MDH)

Described is the use of a commercial computer software package, "Dust," to enhance mathematical learning in the classroom. Samples of mathematics problems presented in this game which is a simulation of an adventure in outer space are presented. (CW)

Describes the method to solve problems called T-E-M-T-T: trial, error, and modified trial through technology. The method integrates students' skills of estimation, mental computation, and appropriate choice of calculator use. Includes 2 activities for each of grades K-4 and 5-8 that illustrate the method. (MDH)