Develops covariational reasoning and proposes a framework for describing mental actions when interpreting and representing dynamic function events. Investigates calculus students' ability to reason about covarying quantities in dynamic situations. Suggests that curriculum and instruction should emphasize moving students to a coordinated image of…

Examines in-service secondary school mathematics teachers' conceptions of proof. Suggests that teachers recognize the variety of roles that proof plays in mathematics. Noticeably absent, however, was a view of proof as a tool for learning mathematics. Many of the teachers held limited views of the nature of proof in mathematics and demonstrated…

Presents a case study in which two 8th grade students developed knowledge for modeling a physical device called a winch. Demonstrates that students have and can use criteria for evaluating algebraic representations. Explains how students can develop modeling knowledge by coordinating criteria with knowledge for generating and using algebraic…

Supports the use of a science experiment option in the high school curriculum to enhance student learning. Presents a science experiment rubric and connects the use of science projects with standards. (DDR)

This article discusses strategies for encouraging the gifted child's brain to make the most of learning opportunities. Strategies include offering programming enrichment classes, accelerated classes, and teachers trained in differentiating instruction. The importance of providing enrichment, challenges, and feedback are stressed and the game…

Advocates a constructivist approach to learning mathematics in which children are given ample time to think and reflect about numbers and exchange ideas with peers. Teachers should construct a classroom environment in which children invent methods to solve problems. Every child's thinking must be assessed in order to guide each to a higher level…

Uses Muybridge's sequence of photos of a moving cat to examine how one might picture changes in the cat's velocity. Classroom implications include building on personally enacted physical experience and recognizing uncertainty as fundamental. Concludes that carefully examined case examples are essential in teaching students to learn and reason…

Explores ways that colleges and universities can become learning communities in all of their dimensions. Discusses the five disciplines of the learning organization (personal mastery, mental models, shared vision, team learning, and systems thinking) and ways to adhere to these disciplines. Describes leadership roles and the importance of vision.…

Considers the relationship of teacher questioning to resultant student questions in a whole language, literature-based classroom. Finds that the teacher provided numerous opportunities for students to continually formulate questions, helping students to master the difficult art of asking questions at different levels of inquiry. (RS)

The construct validity of the Category Test (W. C. Halstead, 1947) was studied for 308 adults with heterogeneous cognitive dysfunction. Factor analysis indicated that Category subtests load on three factors distinct from intelligence: (1) symbol recognition/counting; (2) spatial position reasoning; (3) and proportional reasoning. Clinical…

Investigates students' abilities to draw inferences. Introduces cognitive conflict in the form of video clips of reasoning expressed by students. Documents change with regard to the levels of observed response for the protocol and the use of displayed variation in the graphs. Analyzes change associated with the presentation of cognitive conflict.…

Discusses several solutions--correct and incorrect--for a "Food for Thought" problem from the May 2000 issue. Emphasizes the importance of proportional reasoning. (KHR)

This article describes how one secondary writing teacher integrated two computer-assisted strategies into her writing curriculum to enable students to use writing as a means of thinking. Strategies involved providing feedback on other students' writing and on addressing issues of interest in online synchronous chats. Application with students who…

Three studies examined the age at which children start to use external symbols to aid their memory and how external symbol use affects both memory performance and information allocation strategies. Findings with children in grades 1, 3, 5, and 7 suggest that in mid-childhood, children begin to distribute information actively between internal and…

This study investigated students' mathematics achievement, estimation ability, use of estimation strategies, and academic self-perception with 135 students (n=135) in grades 4, 6, or 8, either with learning disabilities (LD), average achievers, or intellectually gifted. Students with LD differed significantly from average achievers in their use of…