James E. Tarr

Developing notions of inference using probability simulation tools

Abstract This paper focuses on how notions of inference can be fostered in middle school through the use of carefully designed tasks, open-ended software simulation tools, and social activity that focuses on making data-based arguments. We analyzed interactions between two sixth-grade students who used software tools to formulate and evaluate inferences during a 12-day instructional program that utilized Probability Explorer software as a primary investigation tool. A variety of the software tools enabled students to understand the interplay between empirical and theoretical probability, recognize the importance of using larger samples to make inferences, and justify their claims with data-based evidence.

Challenges in Conducting Large-Scale Studies of Curricular Effectiveness: Data Collection and Analyses in the COSMIC Project

We discuss several challenges encountered during data collection and analyses in the Comparing Options in Secondary Mathematics: Investigating Curricula (COSMIC) project, a 3-year longitudinal comparative study of integrated and subject-specific curricula. Previously reported findings obscure the complexities associated with conducting well-designed studies of curricular effectiveness. In this chapter, we highlight key issues in our analyses of student and teacher data, and the construction of multilevel models of student learning outcomes. We discuss how these challenges were addressed, justify our decisions, and offer implications for conducting large-scale curriculum research in mathematics education.

Addressing Measurement Issues in Two Large-Scale Mathematics Classroom Observation Protocols

In large-scale studies of mathematics achievement, many important variables are at the classroom level and therefore require the collection of classroom observation data. However, in these studies, collecting observation data is expensive, and collecting numerous observations can be cost prohibitive. In addition to these practical considerations, there are methodological and conceptual considerations to measuring instruction. This chapter raises several of these issues around measuring mathematics classroom instruction by using empirical data from two prominent observational protocols.