**FEATURES** |

Children's Use of the Reference Point Strategy for Measurement Estimation
*Elana Joram, Anthony J. Gabriele, Myrna Bertheau, Rochel Gelman, Kaveri Subrahmanyam* Mathematics educators frequently recommend that students use strategies for measurement estimation, such as the reference point or benchmark strategy; however, little is known about the effects of using this strategy on estimation accuracy or representations of standard measurement units. One reason for the paucity of research in this area is that students rarely make use of this strategy spontaneously. In order to boost students' strategy use so that we could investigate the relationships among strategy use, accuracy of studentsâ€™ representations of standard measurement units, and estimation accuracy, 22 third-grade students received instruction on use of the reference point strategy and another 22 third-grade students received instruction on the guess-and-check procedure. Analyses reveal that childrenâ€™s strategy use predicts the accuracy of their representations of standard linear measurement units and their estimates. Relative to students who did not use a reference point, students who used a reference point had more accurate representations of standard units and estimates of length. |

Concepts and Skills in High School Calculus: An Examination of a Special Case in Japan and the United States
*Thomas W. Judson, Toshiyuki Nishimori* An investigation of above-average high school calculus students from Japan and the United States in order to determine any differences in their conceptual understanding of calculus and their ability to use algebra to solve traditional calculus problems. We examined and interviewed 18 Calculus BC students in the United States and 26 Suugaku 3 (calculus) students in Japan. Each student completed two parts of a written examination. The first part (Part I) consisted of problems emphasizing conceptual understanding but requiring little or no algebraic computation. Problems on the second part (Part II) required sound algebraic skills in addition to good conceptual understanding. Following the examination, we interviewed each student in order to assess their mathematical and educational background, their college and career plans, their thinking on the examination problems, their understanding of concepts, and their computational and reasoning skills. We found little difference in the conceptual understanding of calculus between the two groups of students, but the Japanese students demonstrated much stronger algebra skills than their American counterparts. Accepted and edited under the editorship of Edward A. Silver. |

Progressive Mathematization of Long Division Strategies in Dutch Primary Schools
*Corneilis M. van Putten, Petra A. van den Brom-Snijders, Meindert Beishuizen* Students' strategies for solving long division problems under a realistic mathematics approach (RME) at Dutch primary schools were categorized in two ways: (a) according to the level of how students created multiples of the divisor (chunking) to be subtracted from the dividend; and (b) according to their use, or nonuse, of schematic notation. These categories could be quantified on two dimensions: use of schematization and use of number relations. Just after the introduction of long division problems, students' strategies varied from no-chunking to high-level chunking. Five months later, this variation of strategies was reduced to mainly high-level chunking using a scheme. However, strategy development depended on students' prerequisite knowledge and the type of textbook used. The results from this study contribute to the efficacy of RME for the advancement of strategies and achievement in the domain of division. |