Investigates mathematical phenomena with students through a dialog between teacher and students in an inquiry-based mathematics class. (KHR)

Suggests that trivialized versions of constructivism are promulgated due to misunderstandings of vocabulary adopted by its advocates. Discusses specifics of frustrations in an effort to communicate the insights and implications of radical and social constructivist theories to preservice and practicing teachers. Presents a classroom episode to show…

Indirectly, instructor behavior provided two models for using a multitrait-multimethod matrix. Students who formulated their own concept, created empirical indicators, and assessed convergent and discriminant validity had better results than those who, influenced by classroom authority dynamics, followed a poorly formulated concept with a…

Describes the Inquiry "I" which is designed as a learning tool for scientific inquiry. Explains the steps of prior knowledge, logical argument, experimental design, procedure, data collection, data transformation, results, and new knowledge. Uses guided and open inquiry approaches. (YDS)

Discusses a class on subtraction or difference-finding, problems such as "There are eight white flowers and five red flowers, how many more white flowers are there than red flowers?" used in the teaching of Japanese first grade children. Describes three instances of introductory teaching of "difference-finding" problems in the…

Describes the Virtual Solar System (VSS) course which is one of the first attempts to integrate three-dimensional (3-D) computer modeling as a central component of introductory undergraduate education. Assesses changes in student understanding of astronomy concepts as a result of participating in an experimental introductory astronomy course in…

Investigates the relationship between traditional physics textbook problem solving and conceptual understanding. Reports that students had many of the well-known conceptual difficulties with basic mechanics and that there was little correlation between the number of problems solved and conceptual understanding. (Contains 21 references.)…

Presents a framework for incorporating classroom strategies that advance children's thinking through eliciting student responses, supporting conceptual understanding, and extending children's mathematical thinking. (KHR)

Clarifies features of Smith et al.'s attentional learning account of object naming, arguing that Booth and Waxman's findings address tenets not in the attentional learning account while not addressing one of the central tenets of the attentional learning account. Suggests that the debate about the nature of children's language and cognition would…

Responds to Smith et al.'s work on relations between perceptual, conceptual, and linguistic knowledge in early word learning and discusses treatment of evidence. Asserts that Smith et al.'s commentary fails to engage data presented and their implications. Asserts that learners seamlessly integrate perceptual, linguistic, and conceptual information…

Examines students' thinking about an open-ended National Assessment of Educational Progress (NAEP) task through written and oral explanations. (YDS)

Addresses the role that mathematical definitions can play in the middle grades mathematics classroom and focuses on the concept of angle as it was introduced to 6th grade students. Describes a traditional approach and an alternative approach to teaching the concept of angle. Illustrates students' concept images of angle. (KHR)

Describes four learning characteristics that make learning and doing mathematics difficult for students with special needs. Discusses instructional strategies that make learning and doing mathematics attainable for these students in the context of a vignette based on real-life experiences. (YDS)

Discusses examples from research of how students' misconceptions underlie their difficulties in interpreting kinematics graphs, possible underlying causes, and promising remedies. (KHR)

Assesses students' geometric thinking through an action research task that uses problems from the National Assessment of Educational Progress (NAEP). Improves students' conceptual understanding of geometric properties and measurement by exploring complex figures, perimeter, and area concepts. (YDS)