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Recent standards reform documents across the globe have called for statistical literacy by the end of high school. Thus, it is important for teachers to develop a deep understanding of the content. Despite the relatively thick literature base connecting students' content knowledge and reasoning, research on these connections among practicing teachers is in critical need. Our study contributes to this lack of research by examining the knowledge structures and statistical reasoning--and possible ways knowledge structures supported reasoning--of a stratified purposeful sample of nine middle and secondary mathematics teachers as they responded to released items from the Levels of Conceptual Understanding in Statistics (LOCUS) assessment during two 60-90 minute task-based clinical interviews. Knowledge structures were categorized as compatible-connected, incompatible-connected, and incompatible-disconnected. Teachers with less incompatible knowledge elements in their structures engaged more frequently in reasoning coded as sound. However, teachers frequently engaged in both sound and unsound forms of reasoning on the same task item. Implications are offered for teacher education and future research.

Through the lenses of statistical investigations and cognitive demands, we examined bivariate data tasks offered in US high school mathematics textbook series--a popular representative of three curriculum types: traditional, integrated, and hybrid. We developed a framework grounded in literature of association topics for the inclusion and exclusion of tasks. Using the "Guidelines for Assessment and Instruction of Statistics Education" (GAISE) framework, textbook tasks were coded for four investigation components (formulate questions, collect data, analyze data, and interpret results) and levels of statistical sophistication, as well as levels of cognitive demand as suggested by the Mathematical Complexity framework. Across the three series 582 statistical association tasks, all components of statistical investigation were evident with different levels of treatment: (a) all questions for statistical investigations were provided by textbook authors; (b) tasks rarely afforded student opportunities to collect data; and (c) nearly all of the tasks required students to analyze data and most required them to interpret results. Tasks in the integrated series were more numerous (n = 246) and required higher levels of mathematical complexity and statistical sophistication than tasks in the traditional and hybrid series. The vast majority of tasks were coded at the GAISE Level B for analyze data and interpret results and moderate level for mathematical complexity. Further analyses show the concordance between the developmental levels for statistical sophistication and mathematical complexity. Suggestions for curriculum development, content analysis, and future research are provided.

We examined the effect of curriculum organization in US high schools where students could freely choose to study mathematics from textbooks that employed one of two types of content organization, an "integrated" approach or a (traditional) "subject-specific" approach. The study involved 2,242 high school students, enrolled in either Course 3 or Algebra 2, in 10 schools in 5 geographically dispersed states. Taking account of curriculum implementation and students' prior mathematics learning, we analyzed two end-of-year outcome measures: a test of common objectives and a standardized achievement test. Our hierarchical linear models with three levels showed that students in the integrated curriculum scored significantly higher than those in the subject-specific curriculum on the common objectives test. In both outcome measures, gender and prior achievement were significant student-level predictors. In the standardized achievement test, ethnicity was a moderating factor. At the teacher-level, in addition to curriculum type, teachers' orientation and free and reduced lunch eligibility were significant moderating factors. Opportunity to learn, implementation fidelity, teacher experience, and professional development were not significant predictors.

The authors examined curricular effectiveness in high schools that offered parallel paths in which students were free to study mathematics using 1 of 2 content organizational structures, an integrated approach or a (traditional) subject-specific approach. The study involved 3,258 high school students, enrolled in either Course 2 or Geometry, in 11 schools in 5 geographically dispersed states. Students in the integrated curriculum scored significantly higher than those in the subject-specific curriculum on the standardized achievement test. Significant student-level predictors included prior achievement, gender, and ethnicity.

This study examined the effect of 2 types of mathematics content organization on high school students' mathematics learning while taking account of curriculum implementation and student prior achievement. Hierarchical linear modeling with 3 levels showed that students who studied from the integrated curriculum were significantly advantaged over students who studied from a subject-specific curriculum on 3 end-of-year outcome measures: Test of Common Objectives, Problem Solving and Reasoning Test, and a standardized achievement test. Opportunity to learn and teaching experience were significant moderating factors.

The current era of common curriculum standards, increased accountability, and rapid expansion of technology within a complex and highly charged political context has influenced changes in assessment practices in mathematics classrooms. This research commentary situates high-stakes assessments in a historical context, discusses recent advances in assessment tools and related technologies, makes recommendations related to future research efforts, and outlines potential challenges and opportunities associated with these recommendations.

One method to investigate classroom quality is for a person to observe what is happening in the classroom. However, this method raises practical and technical concerns such as how many observations to collect, when to collect these observations and who should collect these observations. The purpose of this study is to provide empirical evidence to address these concerns using a particular middle school mathematics classroom observation tool. Data included multiple ratings of mathematics classrooms from 69 middle school teachers within 11 districts that were analyzed using generalizability theory. Findings suggest that raters trained to use this particular measure required 3 observations to consistently capture habitual classroom environments. Implications for investigating classroom quality using this and other classroom observation tools should be guided by decisions about the specific purpose of the observation tool, as well as budget and practical considerations.

The NCTM Research Committee developed this article to address a distinctly important activity that links research and practice: writing research-based articles for practitioner journals. Six guiding principles are described. (Contains 6 figures.)

The recent publication of two important documents, "Focus in High School Mathematics: Reasoning and Sense Making" and the "Common Core State Standards for Mathematics" (CCSSM), provides a timely opportunity to take stock of the various recommendations and policies aimed at improving the quality of students' high school mathematics education in the United States. In this article, the authors capitalize on this opportunity to reflect on national trends in high school mathematics, to highlight current calls and efforts for improving high school mathematics and research on which these recommendations are based, and to suggest areas for which further research is needed. They first present data that provide an overview of the current state of high school mathematics in the United States--data that also underscore concerns about issues of equity as well as the transition from high school to college. Next, they use this overview as the background against which they consider recent recommendations, policies, and reform efforts aimed at improving high school mathematics and research cited to support these efforts. Finally, they propose an agenda for research that is needed to further explore the prospects and possibilities for improving the success of all students in high school mathematics. (Contains 1 table and 1 figure.)

We examined how middle school students reason about results from a computer-simulated die-tossing experiment, including various representations of data, to support or refute an assumption that the outcomes on a die are equiprobable. We used students' actions with the software and their social interactions to infer their expectations and whether or not they believed their empirical data could be used to refute an assumption of equiprobable outcomes. Comparisons across students illuminate intricacies in their reasoning as they collect and analyze data from the die tosses. Overall, our research contributes to understanding how students can engage in informal hypothesis testing and use data from simulations to make inferences about a probability distribution. (Contains 7 figures and 2 tables.)

We examine student achievement of 2533 students in 10 middle schools in relation to the implementation of textbooks developed with funding from the National Science Foundation (NSF) or publisher-developed textbooks. Using hierarchical linear modeling (HLM), curriculum type was not a significant predictor of student achievement on the Balanced Assessment in Mathematics (BAM) or TerraNova Survey (TNS) after controlling for student-level variables. However, the Standards-Based Learning Environment (SBLE) moderated the effect of curriculum type. Students were positively impacted on the "BAM" by NSF-funded curricula when coupled with either Moderate or High Levels of SBLE. There was no statistically significant impact of NSF-funded curricula on students in classrooms with a Low level of SBLE, and the relationship between publisher-developed textbooks and SBLE was not statistically significant. Moreover, there was no significant impact of either curriculum type when coupled with varying levels of SBLE on the "TNS" as the dependent measure. (Contains 3 figures, 5 footnotes, and 5 tables.)

We analyze probability content within middle grades (6, 7, and 8) mathematics textbooks from a historical perspective. Two series, one popular and the other alternative, from four recent eras of mathematics education (New Math, Back to Basics, Problem Solving, and Standards) were analyzed using the Mathematical Tasks Framework (Stein, Smith, Henningsen, & Silver, 2000). Standards-era textbook series devoted significantly more attention to probability than other series; more than half of all tasks analyzed were located in Standards-era textbooks. More than 85% of tasks for six series required low levels of cognitive demand, whereas the majority of tasks in the alternative series from the Standards era required high levels of cognitive demand. Recommendations for future research are offered. (Contains 6 figures and 3 tables.)

The No Child Left Behind Act of 2001 (NCLB, 2002) elevates the importance of educational research and thereby provides opportunities for mathematics education researchers in its support for and funding of rigorous research studies and its requirement of effective, research-based practices. At the same time, by demanding more of overburdened teachers and administrators, NCLB may exacerbate a long-standing gulf between educational research and practice. We use our recent experiences with conducting school-based research to illustrate how educational research can be impeded by the added demands of NCLB and other factors in the current climate. In addition, we hope to begin a dialogue that will encourage researchers and practitioners to work together to capitalize on NCLB's increased emphasis on educational research to create a systematic approach to bridging the research-practice gulf.

In this paper is reported the extent of textbook use by 39 middle school mathematics teachers in six states, 17 utilizing a textbook series developed with funding from the National Science Foundation (NSF-funded) and 22 using textbooks developed by commercial publishers (publisher-generated). Results indicate that both sets of teachers placed significantly higher emphasis on Number and Operation, often at the expense of other content strands. Location of topics within a textbook represented an oversimplified explanation of what mathematics gets taught or omitted. Most teachers using an NSF-funded curriculum taught content intended for students in a different (lower) grade, and both sets of teachers supplemented with skill-building and "practice" worksheets. Implications for documenting teachers' "fidelity of implementation" (National Research Council, 2004) are offered. (Contains 3 tables and 7 figures.)

A study involving 44 New Jersey early intervention programs estimated the cost of services. Variables affecting cost were: types of staff providing services, time allocations of providers, services setting and type, wage rates, and staff-child ratio. A fee-for-service system is discussed as a way to increase incentives for efficiency. (Contains references.) (Author/CR)

Uses data from the Third International Mathematics and Science Study to determine trends in calculator use among 13-year-olds in Japan, the United States, and Portugal. Indicates relatively high levels of calculator use for U.S. and Portugal, and no calculator use for Japan. Reports a statistically significant negative relationship between students' frequency of calculator use and student performance in Japan. (Contains 21 references.) (Author/ASK)

Discusses a framework for assessing middle school students' thinking in conditional probability and independence. Establishes four levels of thinking from subjective to numerical reasoning for both constructs. Students (n=15) from grades 4-8 were interviewed. Profiles reveal that levels of probabilistic thinking were stable across the two constructs. (AIM)