This study explored whether and how teachers’ mathematical knowledge for teaching contributes to gains in students’ mathematics achievement. The authors used a linear mixed-model methodology in which first and third graders’ mathematical achievement gains over a year were nested within teachers, who in turn were nested within schools. They found that teachers’ mathematical knowledge was significantly related to student achievement gains in both first and third grades after controlling for key student- and teacher-level covariates. This result, while consonant with findings from the educational production function literature, was obtained via a measure focusing on the specialized mathematical knowledge and skills used in teaching mathematics. This finding provides support for policy initiatives designed to improve students’ mathematics achievement by improving teachers’ mathematical knowledge.

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.

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.

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. Our results suggest partial success in measuring this domain among practicing teachers but also identify key areas around which the field must achieve conceptual and empirical clarity. Although this is ongoing work, we believe that the lessons learned from our efforts shed light on teachers' knowledge in this domain and can inform future attempts to develop measures.

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.

Mixed evidence on the relationship between school closure and COVID-19 prevalence could reflect focus on large-scale levels of geography, limited ability to address endogeneity, and demographic variation. Using county-level Centers for Disease Control and Prevention (CDC) COVID-19 data through June 15, 2020, two matching strategies address potential heterogeneity: nearest geographic neighbor and propensity scores. Within nearest neighboring pairs in different states with different school closure timing, each additional day from a county’s first case until state-ordered school closure is related to 1.5 to 2.4 percent higher cumulative COVID-19 deaths per capita (1,227–1,972 deaths for a county with median population and deaths/capita). Results are consistent using propensity score matching, COVID-19 data from two alternative sources, and additional sensitivity analyses. School closure is more strongly related to COVID-19 deaths in counties with a high concentration of Black or poor residents, suggesting schools play an unequal role in transmission and earlier school closure is related to fewer lives lost in disadvantaged counties.

This article describes and evaluates a web-based coaching program designed to support teachers in implementing Common Core–aligned math instruction. Web-based coaching programs can be operated at relatively lower costs, are scalable, and make it more feasible to pair teachers with coaches who have expertise in their content area and grade level. Results from our randomized field trial document sizable and sustained effects on both teachers’ ability to analyze instruction and on their instructional practice, as measured by the Mathematical Quality of Instruction instrument and student surveys. However, these improvements in instruction did not result in corresponding increases in math test scores as measured by state standardized tests or interim assessments. We discuss several possible explanations for this pattern of results.

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.

BACKGROUND AND OBJECTIVES

Children entering kindergarten ready to learn are more likely to thrive. Inequitable access to high-quality, early educational settings creates early educational disparities. TipsByText, a text-message–based program for caregivers of young children, improves literacy of children in preschool, but efficacy for families without access to early childhood education was unknown.

METHODS

We conducted a randomized controlled trial with caregivers of 3- and 4-year-olds in 2 public pediatric clinics. Intervention caregivers received TipsByText 3 times a week for 7 months. At pre- and postintervention, we measured child literacy using the Phonological Awareness Literacy Screening Tool (PALS-PreK) and caregiver involvement using the Parent Child Interactivity Scale (PCI). We estimated effects on PALS-PreK and PCI using multivariable linear regression.

RESULTS

We enrolled 644 families, excluding 263 because of preschool participation. Compared with excluded children, those included in the study had parents with lower income and educational attainment and who were more likely to be Spanish speaking. Three-quarters of enrollees completed pre- and postintervention assessments. Postintervention PALS-PreK scores revealed an unadjusted treatment effect of 0.260 (P = .040); adjusting for preintervention score, child age, and caregiver language, treatment effect was 0.209 (P = .016), equating to ∼3 months of literacy gains. Effects were greater for firstborn children (0.282 vs 0.178), children in 2-parent families (0.262 vs 0.063), and 4-year-olds (0.436 vs 0.107). The overall effect on PCI was not significant (1.221, P = .124).

CONCLUSIONS

The health sector has unique access to difficult-to-reach young children. With this clinic-based texting intervention, we reached underresourced families and increased child literacy levels.

Many states use high-school exit examinations to assess students’ career and college readiness in core subjects. We find meaningful consequences of barely passing the mathematics examination in Massachusetts, as opposed to just failing it. However, these impacts operate at different educational attainment margins for low-income and higher-income students. As in previous work, we find that barely passing increases the probability of graduating from high school for low-income (particularly urban low-income) students, but not for higher-income students. However, this pattern is reversed for 4-year college graduation. For higher-income students only, just passing the examination increases the probability of completing a 4-year college degree by 2.1 percentage points, a sizable effect given that only 13% of these students near the cutoff graduate.