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This article describes a multi-method research project examining the use of various freely available online collections and projects, such as Project Gutenberg, the Internet Archive, and Creative Commons-licensed ebooks, by public libraries. This research begins with the questions: what are libraries doing with freely available materials? Are there barriers to incorporating them into the collection? What role are librarians playing in expanding access and awareness of these resources? (Contains 2 figures.)

In this article, Heather C. Hill and Pam Grossman discuss the current focus on using teacher observation instruments as part of new teacher evaluation systems being considered and implemented by states and districts. They argue that if these teacher observation instruments are to achieve the goal of supporting teachers in improving instructional practice, they must be subject-specific, involve content experts in the process of observation, and provide information that is both accurate and useful for teachers. They discuss the instruments themselves, raters and system design, and timing of and feedback from the observations. They conclude by outlining the challenges that policy makers face in designing observation systems that will work to improve instructional practice at scale.

Background/Context: Since 2002, U.S. federal funding for educational research has favored the development and rigorous testing of interventions designed to improve student outcomes. However, recent reviews suggest that a large fraction of the programs developed and rigorously tested in the past decade have shown null results on student outcomes and, often, intermediate variables. Scholars reporting on null results often explain such results by citing factors they informally identified while they either delivered or observed the program. Purpose/Objective/Research Question/Focus of Study: In this paper, we argue for a more systematic approach to examining null results, and develop a framework for evaluating null results based on the policy implementation literature. We then illustrate this approach by examining why one professional development program failed to show impacts on measures of teaching and student learning in a recent study. Setting: The professional development program took place in a mid-sized urban school district on the East Coast. The provider was fully scaled up, capable of providing professional development in most U.S. locations. Research Design: The main study of this program was conducted as a cluster randomized trial with 105 teachers in 18 schools. Here, we engage in a qualitative case study, using multiple sources of evidence to assess the likelihood that specific reasons for null results are valid. Data Collection and Analysis: The case study sources of evidence include observations of professional development; teacher surveys and logs; transcribed videos of teachers' mathematics instruction; and teacher interviews. Findings/Results: Our analysis suggested that null impacts could result from district priorities and instructional guidance that compete with professional development goals; weaknesses in the intervention as well as its fit to teachers' needs; and the difficulty of implementing ambitious instructional practice. Conclusions/Recommendations: Our findings suggest the need for further elaboration of the null-results framework. They also suggest that professional development providers consider both (a) both the organizations in which programs operate and (b) fit of the program to teachers' needs as potential barriers to success.

Multiple-choice assessments are frequently used for gauging teacher quality. However, research seldom examines whether results from such assessments generalize to practice. To illuminate this issue, we compare teacher performance on a mathematics assessment, during mathematics instruction, and by student performance on a state assessment. Poor performance on the written assessment predicted poor classroom performance; likewise, strong performance on the written assessment predicted strong classroom performance. However, classroom performance of teachers in the middle of the written assessment distribution varied considerably. These results also held true using student outcomes as a criterion, leading to implications for both research and policy. (Contains 3 tables and 4 figures.)

In recent years, interest has grown in using classroom observation as a means to several ends, including teacher development, teacher evaluation, and impact evaluation of classroom-based interventions. Although education practitioners and researchers have developed numerous observational instruments for these purposes, many developers fail to specify important criteria regarding instrument use. In this article, the authors argue that for classroom observation to succeed in its aims, improved observational systems must be developed. These systems should include not only observational instruments but also scoring designs capable of producing reliable and cost-efficient scores and processes for rater recruitment, training, and certification. To illustrate how such a system might be developed and improved, the authors provide an empirical example that applies generalizability theory to data from a mathematics observational instrument. (Contains 4 tables, 3 figures and 4 notes.)

Measurement scholars have recently constructed validity arguments in support of a variety of educational assessments, including classroom observation instruments. In this article, we note that users must examine the robustness of validity arguments to variation in the implementation of these instruments. We illustrate how such an analysis might be used to assess a validity argument constructed for the Mathematical Quality of Instruction instrument, focusing in particular on the effects of varying the rater pool, subject matter content, observation procedure, and district context. Variation in the subject matter content of lessons did not affect rater agreement with master scores, but the evaluation of other portions of the validity argument varied according to the composition of the rater pool, observation procedure, and district context. These results demonstrate the need for conducting such analyses, especially for classroom observation instruments that are subject to multiple sources of variation. (Contains 7 tables and 5 footnotes.)

This paper draws on four case studies to perform a cross-case analysis investigating the unique and joint contribution of mathematical knowledge for teaching (MKT) and curriculum materials to instructional quality. As expected, it was found that both MKT and curriculum materials matter for instruction. The contribution of MKT was more prevalent in the richness of the mathematical language employed during instruction, the explanations offered, the avoidance of errors, and teachers' capacity to highlight key mathematical ideas and use them to weave the lesson activities. By virtue of being ambitious, the curriculum materials set the stage for engaging students in mathematical thinking and reasoning; at the same time, they amplified the demands for enactment, especially for the low-MKT teachers. The analysis also helped develop three tentative hypotheses regarding the joint contribution of MKT and the curriculum materials: when supportive "and" when followed closely, curriculum materials can lead to high-quality instruction, even for low-MKT teachers; in contrast, when unsupportive, they can lead to problematic instruction, particularly for low-MKT teachers; high-MKT teachers, on the other hand, might be able to compensate for some of the limitations of the curriculum materials and offer high-quality instruction. This paper discusses the policy implications of these findings and points to open issues warranting further investigation. (Contains 1 table.)

This paper examines the contribution of mathematical knowledge for teaching (MKT) and curriculum materials to the implementation of lessons on integer subtraction. In particular, it investigates the instruction of three teachers with differing MKT levels using two editions of the same set of curriculum materials that provided different levels of support. This variation in MKT level and curriculum support facilitated exploring the distinct and joint contribution of MKT and the curriculum materials to instructional quality. The analyses suggest that MKT relates positively to teachers' use of representations, provision of explanations, precision in language and notation, and ability to capitalize on student contributions and move the mathematics along in a goal-directed manner. Curriculum materials set the stage for attending to the meaning of integer subtraction and appeared to support teachers' use of representations, provision of explanations, and precision in language and notation. More critically, the findings suggest that less educative curriculum materials, coupled with low levels of MKT, can lead to problematic instruction. In contrast, educative materials can help low-MKT teachers provide adequate instruction, while higher MKT levels seem to enable teachers to compensate for curriculum limitations. (Contains 2 notes, 3 tables and 3 figures.)

The set of papers presented in this issue comprise a multiple-case study which attends to instructional resources--teacher knowledge and curriculum materials--to understand how they individually and jointly contribute to instructional quality. We approach this inquiry by comparing lessons taught by teachers with differing mathematical knowledge for teaching who were using either the same or different editions of a US "Standards"-based curriculum. This introductory paper situates the work reported in the next four case-study papers by outlining the analytic framework guiding the exploration and detailing the methods for addressing the research questions. (Contains 3 notes, 1 figure and 2 tables.)

This paper documents the ways mathematical knowledge for teaching (MKT) and curriculum materials appear to contribute to the enactment of a 7th grade "Connected Mathematics Project" lesson on comparing ratios. Two teachers with widely differing MKT scores are compared teaching this lesson. The comparison of the teachers' lesson enactments suggests that MKT appears to contribute to the mathematical richness of the lesson, teacher ability to capitalize on student ideas, and capacity to emphasize and link key mathematical ideas; yet the relationship of MKT to whether and how students participated in mathematical reasoning was more equivocal. Curriculum materials seemed to contribute to instructional quality, in that the novel tasks contained in the curriculum laid the groundwork for in-depth student problem-solving experiences; they also prevented the low-MKT teacher from making a mathematical error. At the same time, these ambitious materials influenced enactment because of the difficulties they caused teachers: the lesson's tasks needed to be "repaired" to enable students to engage with the main mathematical ideas, and off-track student responses to these tasks required remediation. Only the higher-MKT teacher was successfully able to meet the challenge, a finding suggestive of the confluence of MKT and the curriculum materials in informing instructional quality. (Contains 1 note, 1 table and 2 figures.)

Several studies have documented prospective teachers' (PSTs) difficulties in offering instructional explanations. However, less is known about PSTs' learning to provide explanations. To address this gap, we trace changes in the explanations offered by a purposeful sample of PSTs before and after a mathematics content/methods course sequence. Consistent with prior research, our study reveals the limitations in PSTs' explanations at their entrance to the course sequence. It also documents PSTs' progress in providing explanations, thus providing existence proof that this practice is learnable. Using evidence from multiple sources, we also propose a component entailed in this learning--learning how to unpack one's thinking through the use of representations as explanatory tools--and four factors associated with it, including PSTs' subject-matter knowledge, active and deliberate reflection on practice, productive images for engaging in this work, and productive dispositions about engaging in this practice. We discuss the implications of our findings for teacher education and offer directions for future research. (Contains 4 figures, 3 tables, and 5 footnotes.)

Value-added models have become popular in research and pay-for-performance plans. While scholars have focused attention on some aspects of their validity (e.g., scoring procedures), others have received less scrutiny. This article focuses on the extent to which value-added scores correspond to other indicators of teacher and teaching quality. The authors compared 24 middle school mathematics teachers' value-added scores, derived from a large (N = 222) district data set, to survey- and observation-based indicators of teacher quality, instruction, and student characteristics. This analysis found teachers' value-added scores correlated not only with their mathematical knowledge and quality of instruction but also with the population of students they teach. Case studies illustrate problems that might arise in using value-added scores in pay-for-performance plans. (Contains 7 notes, 7 tables and 1 figure.)

This study uses data from an experimental employment program and instrumental variables (IV) estimation to examine the effects of maternal job loss on child classroom behavior. Random assignment to the treatment at one of three program sites is an exogenous predictor of employment patterns. Cross-site variation in treatment-control differences is used to identify the effects of employment levels and transitions. Under certain assumptions, this method controls for unobserved correlates of job loss and child well-being, as well as measurement error and simultaneity. IV estimates suggest that maternal job loss sharply increases problem behavior but has neutral effects on positive social behavior. Current employment programs concentrate primarily on job entry, but these findings point to the importance of promoting job stability for workers and their children. (Contains 7 tables, 2 figures and 9 footnotes.)

Background/Context: Teachers' mathematical knowledge has been the subject of recent federal policy, public programs, and scholarly attention. Numerous reports identify a need for improving this knowledge, and total federal spending on content-focused math and science professional development during the period 2002-2007 is estimated to be above $1.2 billion. Purpose/Objective/Research Question/Focus of Study: In this study, we investigated the patterns in and the effect of professional development in the area of middle school mathematics. We focus in particular on professional development thought to influence teachers' mathematical knowledge, and use a measure of such knowledge to gauge potential growth in a sample of teachers included in a national survey. Research Design: We surveyed a nationally representative sample of roughly 1000 teachers in both 2005 and 2006 and obtained responses from 461 middle school teachers at both time points. The survey measured their mathematical knowledge for teaching at both time points and also inquired about their professional learning opportunities during the intervening year. Data Collection and Analysis: We used survey data both to describe the nature of teachers' learning opportunities during 2005-2006 and to associate participation in these learning opportunities with teachers' 2005 knowledge scores as well as other characteristics. We also linked these learning opportunities to observed growth in teacher knowledge. Findings/Results: Results indicate that extensive effort and expenditures have not dramatically transformed teacher professional development practices as compared to past descriptions, in that learning opportunities reported by teachers are still typically short and fragmented. However, there are indications that teachers' mathematical knowledge might have improved somewhat during this time period. Conclusions/Recommendations: Results from this study suggest a very mixed picture of the middle school mathematics professional development system. Effects on teacher knowledge are modest, and critics might claim that money would be better spent in hiring or induction programs.

This article explores elementary school teachers' mathematical knowledge for teaching and the relationship between such knowledge and teacher characteristics. The Learning Mathematics for Teaching project administered a multiple-choice assessment covering topics in number and operation to a nationally representative sample of teachers (n = 625) and at the same time collected information on teacher and student characteristics. Performance did not vary according to mathematical topic (e.g., whole numbers or rational numbers), and items categorized as requiring specialized knowledge of mathematics proved more difficult for this sample of teachers. There were few substantively significant relationships between mathematical knowledge for teaching and teacher characteristics, including leadership activities and self-reported college-level mathematics preparation. Implications for current policies aimed at improving teacher quality are addressed. (Contains 5 footnotes and 8 tables.)

The need for postpositivist or antipositivist methods in the social sciences, including library and information science, is well documented. A promising alternative synthesizes critical realism and phenomenology. This method embraces ontological reality in all things, including human and social action. The ontology underlying the realist phenomenological approach recognizes, following Bhaskar, intransitive and transitive objects of knowledge (mind-independent reality and individual and social perceptions of that reality). The synthesis encompasses some particular elements, including perceptions of parts and wholes, the reconciliation of presence and absence, and the essential character of intentionality. Withholding judgment (exercising a particular kind of skepticism) enables inquirers to delve into the historicity and background of action. Potential uses of the method are manifold; some specifics are examined here.

Mathematics teachers need specialized math knowledge that is different from the knowledge needed by mathematicians, including the mathematical understanding involved in posing questions, interpreting students' answers, providing explanations, and using representations. Based on the authors' work involving over 300 teachers, they have found that teachers' Mathematical Knowledge for Teaching (MKT) is strongly related to the mathematical quality of their instruction, including their use of mathematical explanation and representations, responsiveness to students' mathematical ideas, and ability to avoid mathematical imprecision and error. In this article, the authors discuss how teachers develop and use MKT. In order for teachers to have opportunities to learn MKT, the authors stress that those who prepare teachers and provide professional development will themselves need to have adequate support. Better materials, more specific guidance focused on the teaching of MKT, and better design of opportunities to learn from practice are essential.

This "Research Commentary" addresses the quality of statistical research in mathematics education. To do so, 10 years of Journal for Research in Mathematics Education (JRME) articles were analyzed on the basis of criteria suggested by the American Educational Research Association, American Psychological Association, and National Council for Measurement in Education, and the American Statistical Association. (Contains 5 footnotes.)

The professional development "system" for teachers is, by all accounts, broken. Despite evidence that specific programs can improve teacher knowledge and practice and student outcomes, these programs seldom reach real teachers on a large scale. Typically, reformers address such perceptions of failure by discovering and celebrating new formats and content for teacher professional learning. However, without a hard look at the actors in the system and the incentives facing those actors, these fads will prove the educational equivalent of pouring new wine into old bottles. Instead, policy makers must invest in fixing the system writ large in order to have a discernible impact on teaching and learning. This article presents several recommendations on how state and district policy makers can restructure the professional development system.

The authors examined the effects of welfare programs that increased maternal employment and family income on the development of very young children using data from 5 random-assignment experiments. The children were 6 months to 3 years old when their mothers entered the programs; cognitive and behavioral outcomes were measured 2-5 years later. While there were no overall program impacts, positive or negative, on the development of children in this age group, there was a pair of domain- and age-specific effects: The programs decreased positive social behavior among 1-year-olds and increased school achievement among 2-year-olds. After exploring several explanations for these results, the authors suggest that the contextual changes engendered by the programs, including children's exposure to center-based child care, interacted differentially with specific developmental transitions.

This study illuminates claims that teachers' mathematical knowledge plays an important role in their teaching of this subject matter. In particular, we focus on teachers' mathematical knowledge for teaching (MKT), which includes both the mathematical knowledge that is common to individuals working in diverse professions and the mathematical knowledge that is specialized to teaching. We use a series of five case studies and associated quantitative data to detail how MKT is associated with the mathematical quality of instruction. Although there is a significant, strong, and positive association between levels of MKT and the mathematical quality of instruction, we also find that there are a number of important factors that mediate this relationship, either supporting or hindering teachers' use of knowledge in practice. (Contains 5 tables, 9 figures and 3 footnotes.)

There is widespread agreement that effective teachers have unique knowledge of students' mathematical ideas and thinking. However, few scholars have focused on conceptualizing this domain, and even fewer have focused on measuring this knowledge. In this article, we describe an effort to conceptualize and develop measures of teachers' combined knowledge of content and students by writing, piloting, and analyzing results from multiple-choice items. (Contains 3 footnotes, 4 tables, and 2 figures.)

This article describes a study in which measures of mathematical knowledge for teaching developed in the United States were adapted to measure mathematical knowledge for teaching in Ireland. When adapting the measures it was not assumed that the mathematical knowledge used by Irish and U.S. teachers is the same. Instead psychometric and interview-based methods were used to determine a correspondence between the constructs being measured, and ensure the integrity of item performance in the Irish context. The study found overlap between the knowledge that is used to teach in both Ireland and the United States, and that the items tapped into this knowledge. However, specific findings confirm the usefulness of conducting extensive checks on the validity of items used in cross-national contexts. The process of adaptation is described to provide guidance for others interested in using the items to measure mathematical knowledge for teaching outside the United States. The process also enabled the authors to raise questions about the assumptions that lie behind the practice-based construct of mathematical knowledge for teaching.