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…

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.…

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…

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)

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)