"Mathematical Thinking: From Assessment Items to Challenging Tasks" is a compilation of 36 problem-based lessons that encourage students to engage in productive struggle and deep thinking. Its 36 full-length lessons for grades 2-8 are each inspired by an actual test item from the National Assessment of Educational Progress (NAEP).…

Encouraging students to reason with quantitative relationships can help them develop, understand, and explore mathematical models of real-world phenomena. Through two examples--modeling the motion of a speeding car and the growth of a Jactus plant--this article describes how teachers can use six practical tips to help students develop quantitative…

Introduces five approaches--problem solving/problem based learning, authentic assessment, writing and communication skills, peer and self evaluation, and fostering curiosity. Suggests that these approaches bring critical thinking to the learning process. (Contains 15 references.) (YDS)

Research reveals that successful problem solvers must possess comprehensive knowledge, and more importantly, have appropriate knowledge organization and understanding. A new taxonomy of medical problems is recommended, and it is suggested that the traditional hypothetico-deductive strategy for problem-based learning be replaced by scheme-driven…

Provides a brief overview of "Principles and Standards for School Mathematics" and outlines some important messages related to grades pre-K-5. (Author)

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)

This article describes the factors to which the classroom teacher needs to attend to enhance the mathematical problem-solving abilities of students. Emphasis is placed upon the means necessary to develop the attribute of being a problem solver, rather than focusing on the goal of becoming a problem solver. (JJK)

Discusses experiences with the use of problem-based learning as applied to knowledge-rich biochemistry courses. Concludes that problem-based learning is not only effective in promoting habits of mind that support higher order thinking but also a powerful vehicle for conveying knowledge by imparting separate bits of knowledge as interconnected…

This guide features a problem-based learning (PBL) unit specifically designed for student-centered learning of new and meaningful content on diseases. Students grapple with a complex and changing problem that requires higher level thinking skills in an environment in which students work both individually and in collaboration with others. Includes…

Lends support to the idea that the quality of the cases used in problem-based learning affects the nature of student learning in this context. Outlines seven principles adapted from research on learning and cognition that can help guide case design. Contains 22 references. (DDR)

Presents longitudinal analyses of the mathematical achievement and beliefs of three groups of elementary pupils. The groups were designated according to those students who had received two years of problem-centered mathematics instruction, those who had received one year, and those who had received textbook instruction. Results indicate that the…

This text explores teaching techniques and adaptations that have proven effective in teaching mathematics concepts and skills to students with learning disabilities. This fourth edition, consistent with the standards developed by the National Council of Teachers of Mathematics, 2000, continues to emphasize problem solving, number sense, student…

In a world with increasingly global economies and competition, students need to learn how to think critically and analytically, and to apply the imagination to solve complex problems. Problem-based learning (PBL) does just that, helping students identify problems, pose questions, research answers, report results, and create a stake in learning.…

This text, designed for both preservice and inservice educators, promotes critical thinking and problem solving across the curriculum. Chapter 1 presents information from personal observations and national studies to support the conclusion that educators need to spend more time creating environments that foster thoughtfulness. Chapter 2 defines…