Abstract
Research suggests that students who take and successfully complete Algebra I in middle school go on to have greater success in mathematics than students who do not take the course until high school. However, not all middle schools offer Algebra I to eighth graders and the opportunity to take Algebra I in middle school is particularly limited in rural schools. This chapter describes a study that examined the effects of using an online course to broaden eighth-graders’ access to Algebra I. The study was conducted in nearly 70 schools, across two northeastern states, which did not typically offer a formal Algebra I course. In schools randomly assigned to the treatment condition, the online course was offered to eighth graders who were considered academically ready for Algebra I. In control schools, eighth graders considered “algebra-ready” took the typical mathematics course available to them. The study examined whether using an online course to broaden access to Algebra I in eighth grade could improve students’ knowledge of algebra in the short term, open doors to more advanced course sequences in the longer term, or both. Findings showed that students who took online Algebra I had greater algebraic knowledge at the end of the eighth grade and were more likely to take an advanced mathematics course sequence in high school than their counterparts in control schools. The chapter also describes the mathematics content taught in treatment and control schools, as well as the implementation of the online course in treatment schools.
This chapter is based on a report prepared for the National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, under contract ED-06C0-0025 with Regional Educational Laboratory Northeast and Islands administered by the Education Development Center, Inc. The citation for the full report is Heppen, J.B., Walters, K., Clements, M., Faria, A., Tobey, C., Sorensen, N., and Culp, K. (2011). Access to Algebra I: The Effects of Online Mathematics for Grade 8 Students (NCEE 2011-4021). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.
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Notes
- 1.
The Algebra I → Geometry → Algebra II sequence is known as the traditional mathematics coursetaking pathway (Common Core Standards Initiative, 2010; National Mathematics Advisory Panel, 2008). Some schools reverse the order of Algebra II and Geometry, yielding an Algebra I → Algebra II → Geometry sequence; this ordering is less common than the traditional sequence. Other schools offer an integrated course pathway that combines the content of Algebra I, Geometry, and Algebra II into integrated courses, which typically have generic names, such as Mathematics 1, Mathematics 2, and Mathematics 3 (National Governors Association Center for Best Practices, Council of Chief State School Officers, 2010; National Mathematics Advisory Panel, 2008).
- 2.
Studies that qualified for inclusion in the meta-analysis used an experimental or quasi-experimental design (if quasi-experimental, the study must have included statistical controls for prior achievement). They also reported data sufficient for calculating effect sizes per the What Works Clearinghouse (2008) guidelines.
- 3.
The p-value associated with the coefficient representing the difference in posttest scores between students in online and face-to-face classes was 0.093.
- 4.
Schools in the control group received the online course for the 2009–2010 school year. All schools (treatment and control) were provided the online course for 2 consecutive years.
- 5.
We did not follow non-algebra-ready students into high school because of cost constraints (there were approximately three times as many non-algebra-ready students as eligible students) and because assessing the impact of the online Algebra I course on algebra-ready students’ subsequent high-school coursetaking was most critical and relevant for the study.
- 6.
For the secondary questions, the study was not designed to determine whether the groups are statistically equivalent. A lack of statistical significance for an impact estimate does not mean that the impact being estimated equals zero. Rather, it means that the estimate cannot reliably be distinguished from zero, an outcome that may reflect the small magnitude of the impact estimate, the limited statistical power of the study, or both. For the secondary questions, lack of statistical significance was defined as a difference with a p-value greater than 0.05, at 80 % power.
- 7.
A stand-alone class was defined as one full section of Algebra I taken by at least 20–25 % of grade 8 students in the school, with a dedicated teacher. This proportion was derived from the percentage of grade 8 students in the northeast US who took Algebra I as of 2007, which was 25 % (U.S. Department of Education, 2007).
- 8.
Technology requirements and system specifications were provided to all schools during recruitment and again to the schools in the treatment group before the beginning of the 2008–2009 school year.
- 9.
Schools made decisions about which students were ready for algebra on the basis of teacher perceptions of preparedness; grades in mathematics classes through grade 7; scores on state assessments; and scores on other assessments, such as algebra readiness tests. The research team did not impose a definition or set of criteria for algebra readiness on the participating schools for two main reasons. First, there were no common instruments across all schools that were administered prior to random assignment that were specifically measures of algebra readiness. Second, the study aimed to test the effectiveness of offering an online Algebra I course in a real-world context, where local decision-making about student eligibility for the course would be the norm. We found that the students identified as algebra-ready had, as expected, significantly higher prior math achievement scores than those who were not.
- 10.
However, scores based on less than 5 min of testing were determined to be invalid by the test developer and thus were dropped and treated as missing. For the algebra posttest, there were fewer than four such cases in the algebra-ready student sample and 118 in the non-algebra-ready sample (73 in treatment and 45 in control).
- 11.
Data on high-school mathematics coursetaking were not collected for the non-algebra-ready students because of cost constraints and the determination that assessing the impact of online Algebra I in grade 8 on subsequent coursetaking was most critical and relevant for the already-ready students.
- 12.
The examples are drawn from the Slope-Intercept topic of the Other Forms of Linear Equations lesson in the Linear Equations unit.
- 13.
We were not able to compare this to attendance in control schools, because we did not have mathematics class-specific attendance data for students in control schools.
- 14.
As described above, 20 % of algebra-ready students in control schools took a formal Algebra I course; some of these students took a traditional face-to-face version of the course and others took an alternate online version of the course. The study was not designed to compare the outcomes of algebra-ready students in treatment schools with those of subgroups of students in control schools and it would be inappropriate to conduct significance tests for these comparisons. However, to address questions regarding how the algebra scores of algebra-ready students in treatment schools compared to those of algebra-ready students in control schools who took a formal Algebra I course in grade 8 and algebra-ready students in control schools who did not take a formal Algebra I course in grade 8, we report the observed means for these three groups below. It is important to note that the study was not designed to test for the statistical significance of these differences and that the means reported below are based on the original and not imputed data, are not model-adjusted, and should be interpreted with caution. The observed Promise Assessment posttest mean scores were 447.91 (SD = 15.12) for algebra-ready students in treatment schools, 444.00 (SD = 11.16) for algebra-ready students in control schools who took a formal Algebra I course, and 440.98 (SD = 12.56) for algebra-ready students in control schools who took their schools’ eighth-grade general mathematics course.
- 15.
If students took more than one mathematics course in grade 9, they had to have earned a grade of C or better on the more advanced grade 9 course to meet this criterion.
- 16.
To address questions regarding how the percentage of algebra-ready students in treatment schools participating in an advanced mathematics course sequence compared to the percentage of algebra-ready students in control schools who took a formal Algebra I course in grade 8 and the percentage of students in control schools who did not take a formal Algebra I course in grade 8, we report the observed percentages for these three groups below. Again, it is important to note that the study was not designed to test for the statistical significance of these differences and that the percentages reported are based on the original and not imputed data, are not model-adjusted, and should be interpreted with caution. The observed percentage of students participating in an advanced mathematics course sequence was 54 % for algebra-ready students in treatment schools, 42 % for algebra-ready students in control schools who took a formal Algebra I course, and 24 % for algebra-ready students in control schools who took their schools’ eighth-grade general mathematics course.
- 17.
The lack of a significant difference does not definitively show that general math scores for algebra-ready students in treatment and control schools were equivalent. It simply implies that the difference was not large enough to be distinguished from chance, given the size of the sample.
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Heppen, J.B., Clements, M., Walters, K. (2015). Turning to Online Courses to Expand Access: A Rigorous Study of the Impact of Online Algebra I for Eighth Graders. In: Middleton, J., Cai, J., Hwang, S. (eds) Large-Scale Studies in Mathematics Education. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-07716-1_6
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