This report addresses a renewed interest in individualized instruction, driven in part by advances in technology and assessment as well as a persistent desire to increase the access, efficiency, and cost effectiveness of training and education. Using computer-based instruction we delivered extremely efficient instruction targeted to low knowledge…

Taking algebra by eighth grade is considered an important milestone on the pathway to college readiness. We highlight a collaboration to investigate one district's effort to increase middle school algebra course-taking. In 2010, the Wake County Public Schools began assigning middle school students to accelerated math and eighth-grade algebra based…

Middle-school students are expected to understand key components of graphs, such as slope and y-intercept. However, constructing graphs is a skill that has received relatively little research attention. This study examined students' construction of graphs of linear functions, focusing specifically on the relative difficulties of graphing slope and…

In 2008, the California State Board of Education voted to require all students to enroll in algebra by 8th grade. This policy initiative, yet to be actually implemented, represents the culmination of a decades-long movement toward offering algebra instruction before the traditional high school years. Nationally, the proportion of 8th grade…

Background: High school and college students demonstrate a verbal, or textual, advantage whereby beginning algebra problems in story format are easier to solve than matched equations (Koedinger & Nathan, 2004). Adding diagrams to the stories may further facilitate solution (Hembree, 1992; Koedinger & Terao, 2002). However, diagrams may not…

This report discusses the second year of Austin Independent School District's (AISD) High Dosage Tutoring Program: students' progress, program summaries, and participant survey results.

"It's All Connected" provides teachers of mathematics the support they need to improve their instruction. This in-demand collection of lessons for grades 6-8 explores proportionality, proportional relationships, and proportional reasoning, acknowledging that the ability to reason proportionally is crucial in the middle school mathematics…

Objectives: Group-randomized designs are well suited for studies of professional development because they can accommodate programs that are delivered to intact groups (e.g., schools), the collaborative nature of professional development, and extant teacher/school assignments. Though group designs may be theoretically favorable, prior evidence has…

We conducted an evaluation study of the Middle School Algebra Readiness Initiative, a middle school mathematics intervention that was implemented in two West Virginia school districts during the 2011-2012 school year. In participating middle schools, the Carnegie Learning MATHia® software intervention and accompanying classroom curriculum were…

"Saxon Math" is a textbook series covering grades K-12 based on incremental development and continual review of mathematical concepts to give students time to learn and practice concepts throughout the year. The series is aligned with standards of the National Council of Teachers of Mathematics (NCTM) and various states, and can be…

Despite widespread agreement that the activity of "reasoning-and-proving" should be central to all students' mathematical experiences, many students face serious difficulties with this activity. Mathematics textbooks can play an important role in students' opportunities to engage in reasoning-and-proving: research suggests that many decisions that…

In 2006-07, seven Wake County Public School System (WCPSS) middle schools piloted Algebraic Thinking as an alternate approach to teaching middle school mathematics. Algebraic Thinking was developed to help students in grade 6 reach higher mathematics courses by combining the regular and advanced middle school mathematics courses into one…

This report makes recommendations for the development of middle-school assessment in mathematics, based on a synthesis of scientific findings in cognitive psychology and mathematics education. The focus is on background research, rather than test specifications or example tasks. Readers interested in early development and pilot efforts associated…

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…

Interviews 53 sixth grade students individually in an attempt to discover whether wrong interpretations of the algebraic structure found in an algebraic context occurs in a purely numerical context. Concludes that students' difficulties with the algebraic structure were also found in purely numerical contexts. (Contains 27 references.) (Author/ASK)