Informed by decades of research and standards-based policies, there has been a growing demand for high-quality teaching and learning in mathematics and science classrooms. Achieving these ambitious goals will not be easy; students' opportunities for learning as shaped by the tasks they are assigned will matter the most. The purpose of this article…

Examines whether problem solving, decision making, and other thinking skills depend more on deep expertise in a specialty or on reflective awareness and general strategies. General and specialized knowledge function in close partnership. The partnership's nature and implications for educational practice are explored. (Author/BJV)

Transferring the skills learned in mathematics to other contexts is a problem for many students. A new heuristic model of mathematics instruction is proposed. The model would guard against the adoption of mistaken assumptions about mathematics and foster the learning of problem-solving strategies. (VM)

Argues that educators should reconsider their current commitment to problem solving as the way to promote constructionist teaching and learning and should focus on teaching important ideas developed within the disciplines. This idea-based social constructivism focuses on the possibilities of a given situation. (SLD)

Discusses two methods for developing and assessing fluid abilities. In the first method, students are asked to solve increasingly unfamiliar problems in a domain; and in the second, students are required to organize knowledge in new ways or view it from different perspectives. (SLD)