Questioning is recognised as a well-established aspect of good mathematics teaching, and this study draws on this instructional practice to provide multilingual learners high-level mathematics, discourse, and cognitively demanding mathematics. Three seventh grade mathematics teachers engaged in professional learning to develop their questioning…

Research on teacher professional learning has shown that formative assessment can improve student learning more than most instructional practices. Empirical evidence indicates that thoughtfully implemented formative assessment practices improve students' learning, increase students' scores, and narrow achievement gaps between low-achieving…

This study used the Eccles et al. expectancy-value (E-V) theory to test the influence of motivation on mathematics achievement and enrollment using data from a cohort of 926 seventh-grade prealgebra students (49% male, 76% Hispanic, 76% low income, and 55% English learner). E-V beliefs were assessed in seventh grade along with achievement, and…

To raise math success rates in middle school, many schools and districts have implemented summer math programs designed to improve student preparation for algebra content in grade 8. However, little is known about the effectiveness of these programs. While students who participate typically experience learning gains, there is little rigorous…

Schools use an array of strategies to match curricula and instruction to students' heterogeneous skills. Although generations of scholars have debated ''tracking'' and its consequences, the literature fails to account for diversity of school-level sorting practices. In this article, we draw on the work of Sørensen and others to articulate and…

The Effects of the Elevate Math summer program on math achievement and algebra readiness: This randomized trial examined the effects of the Elevate Math summer program on math achievement and algebra readiness, as well as math interest and self-efficacy, among rising 8th grade students in California's Silicon Valley. The Elevate Math summer math…

Questions about how best to place students into appropriate middle grade math courses have been central to ongoing education policy and practice discussions in California and across the United States. Recent studies have shown that enrolling in algebra I in grade 8 works well for some students but backfires for others. This REL West report…

Commercial video games undergo usability studies to determine the degree to which the player is able to learn, control, and understand the game. Usability studies allow game designers to improve their games before they are released to the public. If usability studies could be expanded to include information about the presentation of the…

We interviewed 40 students in Grade 7 to investigate their integer reasoning. In one task, children were asked to write and interpret equations related to a story problem about borrowing money from a friend. Their responses reflect different perspectives concerning the relationship between this real-world situation and various numerical…

This mixed design study investigated the predictive and instructional uses of two different types of interim mathematics assessments given in two different districts. One district administered the same summative type of assessment three times a year, while the other district administered a different interim assessment after six-week intervals of…

California's Academic Performance Index (API) is the state's main accountability metric. Authorized by the Legislature in 1999, around the time California was implementing rigorous new standards in math, science, social studies, and English language arts, the API relies heavily on the results of standardized tests designed to align with those…

In spring 2010, Houghton Mifflin Harcourt (HMH) began planning a pilot of an application for the Apple iPad, "HMH Fuse: Algebra 1," which was then in development. The application was to be piloted in four California school districts during the 2010-2011 school year. HMH contracted with Empirical Education Inc. to conduct a one-year…

In spring 2010, Houghton Mifflin Harcourt (HMH) began planning a pilot of an application for the Apple iPad, "HMH Fuse: Algebra 1," which was then in development. The application was to be piloted in four California school districts during the 2010-2011 school year. HMH contracted with Empirical Education Inc. to conduct a one-year…

This report is a follow-up to "Gaining Ground in the Middle Grades" (Williams, Kirst, Haertel, et al., 2010). That study specified a comprehensive set of actionable practices that differentiated higher academic achievement among 303 middle grades schools in California. In doing so, the study provided a compelling and coherent account of…

This appendix focuses on the descriptive statistics of the middle study schools that participated in the "Gaining Ground in the Middle Grades: Why Some Schools Do Better. A Large-Scale Study of Middle Grades Practices and Student Outcomes. Initial Research." This appendix contains the following figures: (1) Student…