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Large–Scale Studies in Mathematics Education, edited by James A. Middleton, Jinfa Cai, and Stephen Hwang, presents mathematics education research covering a broad range of topics using a variety of data sources and analysis techniques. By spotlighting this work, the editors hope to encourage the use of large–scale data sets, which they argue are underutilized by mathematics education researchers. Middleton, Cai, and Hwang contend that “large scale studies can be both illuminative—uncovering patterns not yet seen in the literature, and critical—changing how we think about teaching, learning, policy, and practice” (p. 12). With its inclusion of studies using large–scale data sets and expository papers concerning methodological considerations, the book effectively challenges the reader to consider issues of scale. The book has 18 chapters organized into four sections on curriculum, teaching, learning, and methodology. Although the volume is organized by these areas of interest, we suggest that prospective readers peruse chapters in all sections. As the book editors note, the boundaries between sections are far from clear–cut, and readers may find work relevant to their area of interest throughout the book.

This study examined the relationship between high school mathematics curricula and student achievement and course-taking patterns over 4 years of college. Three types of curricula were studied: National Science Foundation (NSF)-funded curricula, the University of Chicago School Mathematics Project curriculum, and commercially developed curricula. The major result was that high school mathematics curricula were unrelated to college mathematics achievement or students' course-taking patterns for students who began college with precalculus (college algebra) or a more difficult course. However, students of the NSF-funded curricula were statistically more likely to begin their college mathematics at the developmental level.

In the study reported here, I examined the diagrams that mathematically capable high school students produced in solving applied calculus problems in which a diagram was provided in the problem statement. Analyses of the diagrams contained in written solutions to selected free-response problems from the 1996 BC level Advanced Placement Calculus Examination provided insight into the various ways that students modified these diagrams and constructed new diagrams. I investigated relationships between the frequency or nature of the diagrams produced by high- and low-scoring male and female students and students' problem-solving success. Females, who were less successful in problem solving, produced more diagrams than males. Diagrams constructed or modified by males tended to be simpler than the more elaborate versions produced by females.

In this experimental study, prospective elementary school teachers enrolled in a mathematics course were randomly assigned to (a) concurrently learn about children's mathematical thinking by watching children on video or working directly with chil-dren, (b) concurrently visit elementary school classrooms of conveniently located or specially selected teachers, or (c) a control group. Those who studied children's mathematical thinking while learning mathematics developed more sophisticated beliefs about mathematics, teaching, and learning and improved their mathematical content knowledge more than those who did not. Furthermore, beliefs of those who observed in conveniently located classrooms underwent less change than the beliefs of those in the other groups, including those in the control group. Implications for assessing teachers' beliefs and for providing appropriate experiences for prospective teachers are discussed.

Enacting the vision of NCTM's Principles and Standards for School Mathematics depends on effective teacher professional development. This 7-year study of 48 projects in the National Science Foundation's Local Systemic Change Through Teacher Enhancement Initiative investigates the relationship between professional development and teachers' attitudes, preparedness, and classroom practices in mathematics. These programs included many features considered to characterize effective professional development: content focus, extensive and sustained duration, and connection to practice and to influences on teachers' practice. Results provide evidence of positive impact on teacher-reported attitudes toward, preparedness for, and practice of Standards-based teaching, despite the fact that many teachers did not participate in professional development to the extent intended. Teachers' perception of their principals' support for Standards-based mathematics instruction was also positively related to these outcomes.

After surveying high-attaining 14-and 15-year-old students about proof in algebra, we found that students simultaneously held 2 different conceptions of proof: those about arguments they considered would receive the best mark and those about arguments they would adopt for themselves. In the former category, algebraic arguments were popular. In the latter, students preferred arguments that they could evaluate and that they found convincing and explanatory, preferences that excluded algebra. Empirical argument predominated in students' own proof constructions, although most students were aware of its limitations. The most successful students presented proofs in everyday language, not using algebra. Students' responses were influenced mainly by their mathematical competence but also by curricular factors, their views of proof, and their genders.

Many studies in mathematics education research occur with a nonrepresentative sample and are never replicated. To challenge this paradigm, I designed a large-scale study evaluating student conceptions in group theory that surveyed a national, representative sample of students. By replicating questions previously used to build theory around student understanding of subgroups, cyclic groups, and isomorphism with over 800 students, I establish the utility of replication studies to (a) validate previous results, (b) establish the prevalence of various student conceptions, and (c) reexamine theoretical propositions. Data analyzed include 1 round of open-ended surveys, 2 rounds of closed-form surveys, and 30 follow-up interviews. I illustrate the potential of replication studies to refine theory and theoretical propositions in 3 ways: by offering alternate interpretations of student responses, by challenging previous pedagogical implications, and by reevaluating connections between theories

If you are aware of the results given in the media reports about the Third International Mathematics and Science Study (TIMSS), you probably know that fourth graders from the United States (U.S.) scored above the international average in mathematics and that eighth and twelfth graders scored below average (Mullis et al. 1997). As an educator, you are aware of the dangers of looking only at averages of test scores. Rich information can be gleaned from the TIMSS data that will help us learn more about what our students know and are able to do. The data from a large-scale study, such as the TIMSS, often raise questions about what the numbers really mean. This article addresses one such question that arose from examining part of the third- and fourth-grade TIMSS data. The process that we used may be as valuable as the information that we found. Perhaps this process will help you answer questions that arise as you reflect on the TIMSS results.