"Drawing Conclusions" explores the use of juxtaposed visual representations (JVRs) to help preservice teachers grapple with abstract concepts, theories, or complex controversies in education. Acting as both a learning tool and an intellectual spark, JVRs are two simple contrasted sketches that students produce on a divided sheet of…

Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.

The Common Core State Standards (CCSSI 2010) for Mathematical Practice have relevance even for those not in CCSS states because they describe the habits of mind that mathematicians--professionals as well as proficient school-age learners--use when doing mathematics. They provide a language to discuss aspects of mathematical practice that are of…

Empirical arguments rely on examples without necessarily addressing all cases. Students should be skeptical of empirical evidence and should seek more secure arguments for generalizations, such as those that explain why a generalization is true for all cases. Generalizing on the basis of patterns in data is an important mathematical practice;…

"Modeling Mathematical Ideas" combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students' common misconceptions in investigating and…

Most students in America can graduate from high school without ever analyzing a piece of art. Perhaps these students will take an art history or an art appreciation course in college that may incorporate a few references to literature and history. Math or science connections will most likely remain entirely absent. Why do we treat art analysis…

Science classes are full of abstract or challenging concepts that are easier to understand if an analogy is used to illustrate the points. Effective analogies motivate students, clarify students' thinking, help students overcome misconceptions, and give students ways to visualize abstract concepts. When they are used appropriately, analogies can…

Includes a dandelion poem that is designed to stimulate elementary students' creativity and abstract-thinking skills. Offers several exercises to go with the poem: creating mental pictures, drawing first images, and performing for better understanding. A reproducible for creating a dandelion-shaped poem is included. (SM)

Describes the use of chess instruction to develop abstract thinking skills and problem solving among gifted students. Offers suggestions for starting school chess programs, teaching and evaluating chess skills, and measuring the success of both student-players and the program in general. (PB)

Encourages teachers to listen more carefully to what students say. Discusses two modes of reasoning in an effort to understand more deeply what students hear and the styles of reasoning that they might use in mathematics. (Contains 12 references.) (ASK)

Presents a model for teaching reasoning using technology in the contexts of algebra and geometry. (MKR)

Presents research findings and teaching implications of mathematics as reasoning and students' reasoning abilities in mathematics. (20 references) (MKR)

Describes the different types of reasoning in scientific research activity. Outlines three different but complementary ways to integrate history into the presentation of science. Considers and illustrates the close historical relationship between mathematics and physics. (Contains 50 references.) (ASK)

Undergraduate biology programs are currently undergoing reform to involve students in biomedical research. Engaging students in more active, hands-on experiments allows students to discover scientific principles for themselves, and to develop techniques of critical thinking and problem solving. This models the world of real scientific research,…

This paper uses data from two mathematics lessons to explore the nature of progressive discourse and examine critical features of teacher actions that contribute to mathematics classrooms functioning as communities of inquiry. Features found to promote progressive discourse include a focus on the conceptual elements of the curriculum and the use…