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…

We developed a web-based tool to provide students with access to old exam problems and solutions. By controlling the order in which students saw the problems, as well as their access to solutions, we obtained data about student learning by studying old exam problems. Our data suggest that in general students learn from doing old exam problems, and…

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…

We implemented a "how to study" workshop for small groups of students (6-12) for N = 93 consenting students, randomly assigned from a large introductory biology class. The goal of this workshop was to teach students self-regulating techniques with visualization-based exercises as a foundation for learning and critical thinking in two areas:…

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…

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.…

Targeted as a highly desired skill for contemporary work and life, problem solving is central to game-based learning research. In this study, middle grade students achieved significant learning gains from gameplay interactions that required solving a science mystery based on microbiology content. Student trace data results indicated that effective…

Presents some examples of drill problems turned into thinking problems. Examples include fraction problems, stretching simple problems, cone problems, and area problems. (KHR)

Comments on student responses to the three dimensional items produced by first investigating flat paper cutouts of the items. (KHR)

Discusses a problem that appeared in the September, 1999 issue of this journal and presents solutions from students in grades 2-6. The question involved using colored cubes rearranged to make different stacked towers. (KHR)

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)