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Conventional methods for mediation analysis generate biased results when the mediator-outcome relationship depends on the treatment condition. This article shows how the ratio-of-mediator-probability weighting (RMPW) method can be used to decompose total effects into natural direct and indirect effects in the presence of treatment-by-mediator interactions. The indirect effect can be further decomposed into a pure indirect effect and a natural treatment-by-mediator interaction effect. Similar to other techniques for causal mediation analysis, RMPW generates causally valid results when the sequential ignorability assumptions hold. Yet unlike the model-based alternatives including path analysis, structural equation modeling, and their latest extensions, RMPW requires relatively few assumptions about the distribution of the outcome, the distribution of the mediator, and the functional form of the outcome model. Correct specification of the propensity score models for the mediator remains crucial when parametric RMPW is applied. The paper gives an intuitive explanation of the RMPW rationale, a mathematical proof, and simulation results for the parametric and non-parametric RMPW procedures. We apply the technique to identifying whether employment mediated the relationship between an experimental welfare-to-work program and maternal depression. A detailed delineation of the analytic procedures is accompanied by online Stata code as well as a stand-alone RMPW software program to facilitate users' analytic decision-making. [This article was published in "Journal of Educational and Behavioral Statistics," v40 n3 p307-340 Jun 2015 (see: EJ1063649).]

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 paper provides a summary of the authors' attempts to uncover links between their measures, classroom mathematics instruction, and student learning. This paper also provides evidence regarding one central critique of their measures: that multiple-choice assessments cannot validly represent the knowledge, skills, and judgment involved in actual teaching practice. To the extent that there is a relationship between the test domain and practice domain, it strengthens their claim that they can measure knowledge for teaching in this format. In this article the authors describe the aims, methods, and preliminary findings from a large-scale statistical study of teacher knowledge and student achievement and a videotape study of teachers' classroom mathematics instruction. If a teacher knowledge/student achievement relationship is found in the former, the latter will help identify the mechanisms through which this relationship is realized. Finally, as a means for informing the debate about why test validation is often better conceptualized than practiced, they consider the cost and obstacles to this type of work. (Contains 2 tables, 1 figure and 1 footnote.)

Widespread agreement exists that U.S. teachers need improved mathematics knowledge for teaching. Over the past decade, policymakers have funded a range of professional development efforts designed to address this need. However, there has been little success in determining whether and when teachers develop mathematical knowledge from professional development, and if so, what features of professional development contribute to such teacher learning. This was due, in part, to a lack of measures of teachers' content knowledge for teaching mathematics. This article attempts to fill these gaps. In it we describe an effort to evaluate California's Mathematics Professional Development Institutes (MPDIs) using novel measures of knowledge for teaching mathematics. Our analyses showed that teachers participating in the MPDIs improved their performance on these measures during the extended summer workshop portion of their experience. This analysis also suggests that program length as measured in days in the summer workshop and workshop focus on mathematical analysis, reasoning, and communication predicted teachers' learning. (Contains 2 tables and 6 footnotes.)

Two papers examine the positive impact of professional development on student achievement. One discusses experiences in California which show that standards, assessment, and accountability are more likely to succeed when accompanied by extended opportunities for professional learning grounded in teachers' practice. The second explains that the content of professional development makes a significant difference in regard to student learning. (SM)

The article contends that professional development programs have been most effective when they are closely linked with actual classroom concerns such as curriculum and academic content, student learning problems and assessment tools. It was noted that workshops in California that encouraged teachers to explore creative approaches to learning resulted in voluntary enhancements in teaching techniques.