**Regional need and study purpose**

As the use of online courses continues to grow nationwide, more information is needed about the effectiveness of using online courses to expand schools' course offerings and student access to key gateway courses—introductory courses that are the foundation for further study in a field. This study investigates the use of an online course to expand access to algebra I to students in grade 8 who are ready to take the course but unable to do so because their schools do not offer a full algebra I course to eighth graders (often because the schools are small or in rural areas).

Eighth graders who take algebra I—a well documented gateway course (Atanda 1999; Kilpatrick, Swoffard, and Findell 2001)—are more likely to participate in advanced mathematics courses in high school (Stevensen, Schiller, and Schneider 1994). Yet more than 10 years after the U.S. Department of Education recommended expanding access to algebra I in middle schools, schools throughout the Northeast and Islands Region and the rest of the country are delivering algebra courses to only a small proportion of their eighth graders (U.S. Department of Education 1997). According to the 2007 National Assessment of Educational Progress (NAEP), 32 percent of eighth graders nationwide were enrolled in algebra I (U.S. Department of Education, National Center for Education Statistics 2007b^{1}). In the Northeast and Islands Region states, less than 25 percent of eighth graders take algebra I.

Online algebra courses offer a means for broadening access to algebra I in middle schools, especially where recruiting and retaining highly qualified teachers is difficult, such as in Maine and Vermont, which have many schools in rural areas. According to a 2007 report by the Rural School and Community Trust Policy Program, Maine has the highest percentage of students attending rural schools nationwide, at 52.9 percent, and Vermont has the second highest, at 51.3 percent (Johnson and Strange 2007). Rural schools face special challenges in offering a full range of courses due to limited resources, difficulties attracting and retaining qualified teachers, and small student bodies (Hannum et al. 2009). In Vermont only 22 percent of eighth graders take algebra I, and in Maine only 23 percent do. Virtual courses offer a promising solution: ensuring that students in small schools and isolated communities have access to critical courses, especially in science, technology, engineering, and mathematics (Tucker 2007).

The goal of this randomized controlled trial is to ascertain the effects of online algebra I on the achievement and subsequent course-taking patterns of eighth graders in schools that do not typically offer algebra I. In particular, this study addresses the following policy question: In schools that do not typically offer algebra I to eighth graders, is it beneficial to offer it as an online course, in terms of student achievement in mathematics and subsequent high school mathematics course-taking? This broad policy question is addressed through two primary and four secondary research questions.

Two primary research questions focus on the direct effects of the intervention on algebra-ready students, asking: What is the impact of offering algebra I online to algebra-ready students on

- Algebra-ready students' end of grade 8 algebra achievement?
- Algebra-ready students' subsequent high school course-taking patterns?

The direct effects of this intervention on such outcomes are key to determining whether this intervention is an effective way for schools to broaden access to algebra I.

Four secondary research questions focus on possible indirect effects of this intervention on algebra-ready students and their peers who were not considered ready for algebra. These questions are designed to test whether implementing online algebra for algebra-ready students has significant side effects (or unintended consequences). Implementation of the online course requires removing algebra-ready students from their general grade 8 mathematics class. This may affect algebra-ready students' general mathematics scores—an effect that is important to teachers and administrators concerned with student achievement on end of grade 8 accountability assessments. Removing algebra-ready students may also indirectly affect other students who are not considered ready for algebra I. Although these other students do not take the online algebra course, their mathematics instruction may be affected by the presence of the online course in their schools. For example, removing the algebra-ready students from the regular class may yield smaller grade 8 mathematics classes that are more tracked by ability than usual.

Four secondary research questions examine these indirect effects, asking: What is the impact of offering algebra I online to algebra-ready students on

- Algebra-ready student's end of grade 8 general mathematics achievement?
- Other students' end of grade 8 algebra achievement?
- Other students' end of grade 8 general mathematics achievement?
- Other students' planned grade 9 mathematics courses?

Answering these primary and secondary research questions will generate useful information about what happens to the entire population of eighth graders—including potential benefits and detriments—when a school uses an online course to give algebra-ready students access to algebra I. The observed impacts on the outcomes of algebra-ready and other students will help to determine whether the intervention is an effective choice for schools that do not typically offer algebra I to eighth graders.

This study is designed to produce policy-relevant, foundational information about the effectiveness of using an online course to provide access to a gateway algebra course that is not otherwise available. It will not provide information about the relative effectiveness of online algebra I courses compared with traditional face-to-face algebra I courses. The generalizability of the findings to different contexts will be presented with caution. In particular, the findings here will be interpreted by carefully considering the many aspects of the intervention tested, including the content of the course and the provision of highly qualified mathematics instructors.

^{1}Percentages are for grade 8 students enrolled in public schools who took the 2007 National Assessment of Educational Progress student survey. Students were considered enrolled in algebra I if they were enrolled in either a one-year algebra I course or the second year of a two-year algebra I course.