Classroom discussion practices that can lead to reasoned participation by all students are presented and described by the authors. Their research emphasizes the careful orchestration of talk and tasks in academic learning. Parallels are drawn to the philosophical work on deliberative discourse and the fundamental goal of equipping all students to participate in academically productive talk. These practices, termed Accountable Talk SM , emphasize the forms and norms of discourse that support and promote equity and access to rigorous academic learning. They have been shown to result in academic achievement for diverse populations of students. The authors outline Accountable Talk as encompassing three broad dimensions: one, accountability to the learning community, in which participants listen to and build their contributions in response to those of others; two, accountability to accepted standards of reasoning, talk that emphasizes logical connections and the drawing of reasonable conclusions; and, three, accountability to knowledge, talk that is based explicitly on facts, written texts, or other public information. With more than fifteen years research into Accountable Talk applications across a wide range of classrooms and grade levels, the authors detail the challenges and limitations of contexts in which discourse norms are not shared by all members of the classroom community.

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The mathematics instructional approaches of effective elementary teachers in urban highpoverty schools were investigated. Approximately 99 urban elementary teachers were administered the Star Teacher Selection Interview; a total of 31 were identified as star teachers. These teachers were then administered the Instructional Practices Assessment to identify their mathematical instructional practices and the degree to which they implemented these practices. The findings indicated that the star teachers are using a variety of instructional approaches that are culturally relevant and aligned with the NCTM's Principles and Standards for School Mathematics. The highest mean ratings were associated with principles and practices related to equity and strong adherence to curriculum standards infused with personal creativity.

Findings in cognitive science suggest new approaches to teaching in science and mathematics.

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This research is concerned with patterns of reaction times that emerge when a child is taught a specific problem-solving procedure and then given extensive practice over many weeks. Preschool children who knew how to count but were unacquainted with arithmetic were taught a simple algorithm for solving single-digit addition problems and were then given extended practice. A subject performing this algorithm would generate reaction times proportional to the sum of the addends. The main finding was that, at the end of the extended practice phase, data of many subjects were best fitted by a different model predicting reaction times proportional to the minimum addend. This implies that these children are no longer using the algorithm they were originally taught. It is also interpreted as suggesting that they have invented a more efficient procedure.We are concerned in this article with the relationship of relatively skilled performance on tasks to the processes used during early phases of acquisition. In the typical information-processing experiments, performance is highly skilled and overlearned. The processes postulated are sufficient to account for skilled performance, but little is said regarding how such processes are acquired or how performance changes over time. There is no a priori reason, however, to assume that the processes used in skilled performance are identical to the processes used to solve the same problems in a relatively unpracticed state. Here we address the question of cognitive skill acquisition directly, by modeling the performance of individuals at different times in the course of their acquiring skill in procedures for solving simple addition problems. We consider in particular the relationship between the specific procedures taught to beginners