**FEATURES** |

A 20-Year Study of Mathematics Achievement
*Patrick Griffin, Rosemary Callingham* Monitoring educational changes over many years is problematic when there are differences in curricula, the nature of the variables being measured, and the selection of participants. Rasch measurement techniques provide a procedure that enables each of these issues to be examined. Using archived and specially collected data, tests of numeracy undertaken in Tasmania over a 20-year period, from 1978 to 1997, were equated and mapped onto the same continuum through a combination of common item and common person equating. Examination of fit to the model showed that the nature of the measured construct had not changed over this period. Although test difficulty appears to have risen over the period, student achievement was relatively unchanged. The implications of these findings for longitudinal studies of achievement are discussed. |

Students' Coordination of Geometric Reasoning and Measuring Strategies on a Fixed Perimeter Task: Developing Mathematical Understanding of Linear Measurement
*Jeffery E. Barrett, Douglas H. Clements, David Klanderman, Sarah Jean Pennisi, Mokaeane V. Polaki* This article examines students' development of levels of understanding for measurement by describing the coordination of geometric reasoning with measurement and numerical strategies. In analyzing the reasoning and argumentation of 38 Grade 2 through Grade 10 students on linear measure tasks, we found support for the application and elaboration of our previously established categorization of children's length measurement levels: (1) guessing of length values by naïve visual observation, (2) making inconsistent, uncoordinated reference to markers as units, and (3) using consistent and coordinated identification of units. We elaborated two of these categories. Observations supported sublevel distinctions between inconsistent identification (2a) and consistent yet only partially coordinated identification of units (2b). Evidence also supported a distinction between static (3a) and dynamic (3b) ways of coordinating length; we distinguish <em>integrated abstraction</em> (3b) from <em>nonintegrated abstraction</em> (3a) by examining whether students coordinate number and space schemes across multiple cases, or merely associate cases without coordinating schemes. |

Children's Mathematical Thinking in Different Classroom Cultures
*Terry Woods, Gaye Williams, Betsy McNeal* The relationship between normative patterns of social interaction and children's mathematical thinking was investigated in 5 classes (4 reform and 1 conventional) of 7- to 8-year-olds. In earlier studies, lessons from these classes had been analyzed for the nature of interaction broadly defined; the results indicated the existence of 4 types of classroom cultures (conventional textbook, conventional problem solving, strategy reporting, and inquiry/argument). In the current study, 42 lessons from this data resource were analyzed for children's mathematical thinking as verbalized in class discussions and for interaction patterns. These analyses were then combined to explore the relationship between interaction types and expressed mathematical thinking. The results suggest that increased complexity in children's expressed mathematical thinking was closely related to the types of interaction patterns that differentiated class discussions among the 4 classroom cultures. |

A Golden Means to Teaching Mathematics Effectively: A Review of The Middle Path in Math Instruction: Solutions for Improving Math Education
*Jeremy Kilpatrick*
Review A Golden Means to Teaching Mathematics Effectively: A Review of The Middle Path in Math Instruction: Solutions for Improving Math Education The Middle Path in Math Instruction: Solutions for Improving Math Education. (2004). Shuhua An. Lanham, MD: ScarecrowEducationRowman & Littlefield Education, xii + 224 pp. |