The goal of this study is to uncover the successes and challenges that preservice teachers are likely to experience as they unpack lesson-level mathematical learning goals (i.e., identify the subconcepts and subskills that feed into target learning goals). Unpacking learning goals is a form of specialized mathematical knowledge for teaching, an…

Debates about the future of school mathematics in the United States often center on whether standards-based instruction is improving or undermining students' achievement. Critical for making progress in these debates is information about the actual nature of classroom practice in U.S. classrooms. This article focuses on one key element of…

Addresses the role that research can and should play in shaping standards, by distinguishing between values and research problems, and by calibrating appropriate expectations for research. Illustrates research contributions to current debates with brief summaries of some findings that are relevant to the standards set by the National Council of…

Nine children were tested to determine the appropriateness of Piaget's part-whole fraction concept interpretation for both the discrete case and the continuous cases of length and area. (MP)

A theory is proposed for how students develop competence with the written symbols of decimal fractions. Competence is viewed as the cumulative and sequential mastery of four separate cognitive processes. The theory was tested with small groups of students, most of whom were able to acquire the first two processes. (MNS)

Logical reasoning ability and information processing capacity are investigated in terms of the effects of these cognitive capacities on children's ability to learn concepts of linear measurement. (MP)

The subjects were 47 first-grade children from three classrooms in a Lexington, Kentucky public school. Results indicate that the position of the unknown set in a verbal problem substantially determines whether or not a problem can be modeled successfully by children of this age. (MP)

This study investigated the relationship between several Piagetian abilities and an information processing capacity, and first-grade children's performance on verbal addition and subtraction problems. Results pointed to a sometimes small but consistent relationship between possession of a cognitive ability and solving an arithmetic problem. (MP)

Investigates issues of conceptual understanding in teaching and learning mathematics provided conceptually based instruction on place value and two-digit addition and subtraction without regrouping in four first grade classrooms. Conventional textbook-based instruction was provided in two first grade classrooms. Experimental-group students scored…