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Ready or Not: Using Existing Data as Clues for Algebra I Readiness

July 12, 2021

SRI International
   Mary Klute, REL Appalachia

Many middle schools are now offering Algebra I, a course that used to be taught primarily in high school. Educators and parents alike may wonder how to determine whether their students are ready for Algebra I in middle school. Taking Algebra I in middle school can increase students' opportunities to take more advanced math classes in high school, which opens doors to the widest possible variety of college and career options. But research suggests that if students enroll in Algebra I before they are ready, this option could have the opposite effect. Students who take Algebra I before they are ready may end up struggling with coursework, which may decrease the likelihood that they take higher level math ¹, ², ³

So how can educators know who is ready for Algebra I in middle school? Assessment vendors have developed tests that are specifically designed to assess Algebra I readiness. However, using these tests to determine which students are ready for Algebra I requires that students take an additional standardized assessment. Are other data already available that educators could examine? A recent REL Central study presented at the 2021 annual meeting of the American Educational Research Association explored using data from a state mathematics assessment that all students already take to inform Algebra I placement decisions.⁴

Although the REL Central study used data from assessments administered in Missouri, the results may be useful for educators elsewhere who are interested in supporting the success of students in algebra. For example, REL Appalachia's Student Success in Mathematics partnership members, comprising city school divisions in central Virginia, have identified a long-term goal of ensuring that all students master key skills, practices, and understanding of critical concepts of Algebra I to enable them to take higher-level mathematics courses in high school. The REL Central study demonstrates how they might use domain scores from existing assessments when considering which students are ready to take Algebra I in middle school. This blog highlights findings from the study and provides concrete recommendations for how educators across the country could use the results.

Study overview

The study in Missouri addressed three research questions to provide information that might help educators distinguish students who are ready for Algebra I in middle school from those who might need more time and support before enrolling:

• To what extent are scores in five math domains (ratios and proportional relationships, the number system, expressions and equations, geometry, and statistics and probability) associated with Algebra I achievement?
• How do the associations vary by English learner status?
• How do the associations vary by special education status?

Study findings

Prior to examining data to address the study's research questions, researchers examined the data to describe the students who were included in the study. The study included all students in Missouri who had taken Algebra I in grade 8 during the 2017/18 school year and had taken the grade 7 math assessment the previous year. In this statewide sample, the average score on the Algebra I end-of-course assessment was quite high, falling in the point range for advanced proficiency. This result was likely due to some districts and schools placing only the most advanced students in Algebra I in grade 8.

Next, to answer their research questions, researchers examined the associations between the five math domain scores in grade 7 and Algebra I achievement in grade 8, as measured by the end-of-course assessment. The researchers found:

• All five grade 7 math domain scores were strongly associated with Algebra I achievement in grade 8, and the association was strongest for the expressions and equations domain. These findings suggest that educators might consider adding math domain scores in grade 7, particularly the expressions and equations domain, to the factors they use to determine whether students are ready to take Algebra I in grade 8.
• The number system domain was more strongly associated with Algebra I achievement for English learner students than for students without this designation. This suggests that educators might want to pay particular attention to this domain when determining whether English learner students are ready to take Algebra I in grade 8.
• No clear differences among these associations were found between students who were receiving special education services and those who were not. This suggests that, when determining whether students who are receiving special education services are ready to take Algebra I in grade 8, educators might consider factoring in domain scores in grade 7 in a manner similar to how they consider domain scores for students not receiving special education services.

When interpreting these results, it is important to keep in mind that the students in the study were quite advanced in their math skills. The results of the study may have differed if students representing a wider range of achievement had been included.

What can you do with these results?

Here are some ways educators might apply the results of this study in practice:

• Consider students' skills with expressions and equations as one factor when determining who is ready to take Algebra I in middle school. The study findings suggest that while skills in all the assessed domains were important, understanding expressions and equations may be particularly important for student success in Algebra I.
• Consider whether you can conduct similar analyses in your school or district. Does your school, district, or state regularly administer student assessments that provide data on math skills at the domain level? For example, the grade 7 mathematics assessment in Virginia includes three domain scores, which the Virginia Department of Education calls reporting categories: (1) number, number sense, computation, and estimation, (2) measurement and geometry, and (3) probability, statistics, patterns, functions, and algebra.⁵ You might examine how scores on those domains are related to Algebra I success in middle school for your students. You could use the results from your own analyses in a couple of ways.
  • If you identify particular domain scores that are strongly associated with success in Algebra I, you might add those scores to the list of factors you consider when identifying students who are ready for Algebra I in middle school For example, if you find that one of the reporting categories from the Virginia grade 7 mathematics assessment is more strongly associated with Algebra I success, you might pay special attention to that score when identifying students who are ready to take Algebra I.
  • You can use the findings of your analyses to identify students in need of targeted support prior to enrolling in Algebra I. Continuing with the previous example, once you have identified which of the three reporting categories are most strongly associated with Algebra I success, you might identify students who score particularly low in those reporting categories and provide those students additional targeted instruction to boost their understanding of that domain prior to enrolling in Algebra I.

Resources for further learning

The resources below provide information on instructional practices and policies that can support Algebra I readiness, and research findings related to math course placement.

• Algebra for All: Focus on Visual Representations. This recorded REL Appalachia webinar presents research-based strategies that help prepare all learners for Algebra I, including English learner students and students who are struggling with math. Presenters focus on using visual representations to support math content learning, such as understanding algebraic relationships, and highlight recommendations from IES practice guides.
• What Works Clearinghouse (WWC) Practice Guide: Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students. This practice guide, designed for teachers and school leaders, provides three evidence-based recommendations with accompanying implementation steps and solutions (such as using solved problems to help students process large amounts of abstract information).
• Shining a Light on Algebra I Access and Success: Embracing Equity at All Levels. This blog describes a REL Appalachia study examining students' Algebra I course-taking pathways and how educators can use the findings.
• Algebra I and College Preparatory Diploma Outcomes among Virginia Students Who Completed Algebra I in Grades 7–9. This REL Appalachia study examined Algebra I outcomes and attainment of college preparatory diplomas among different student groups by their grade 5 math proficiency level and when they completed Algebra I (grade 7, 8, or 9). The report can help policymakers review and refine Algebra I placement policies and practices that may unintentionally contribute to differences in student access to Algebra I and their later outcomes.
• Using Assessment Data to Guide Math Course Placement of California Middle School Students. This REL West study used scores from a state assessment and an Algebra I readiness assessment to predict which students are ready for Algebra I in grade 8.
• Math Course Sequences in Grade 6–11 and Math Achievement in Mississippi. This REL Southeast study examined mathematics course-taking pathways in Mississippi, including whether students in different demographic groups were more likely to follow particular pathways.

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Footnotes:

¹ C. T. Clotfelter, H. F. Ladd, & J. L. Vigdor, (2012), The aftermath of accelerating algebra: Evidence from a district policy initiative (CALDER Working Paper No. 69), National Center for Analysis of Longitudinal Data in Education Research. https://eric.ed.gov/?id=ED529166

² T. Loveless, (2008), How well are American students learning? With sections on international assessments, the misplaced math student, and urban schools, Brown Center on Education Policy, Brookings Institution. https://eric.ed.gov/?id=ED506869

³ National Mathematics Advisory Panel, (2008), Foundations for success: The final report of the National Mathematics Advisory Panel, U.S. Department of Education. https://files. eric.ed.gov/fulltext/ED500486.pdf

⁴ M. Klute, B. Dougherty, & D. Van Dine, (2020), What grade 7 foundational knowledge and skills are associated with Missouri students' Algebra I achievement in grade 8? (REL 2020–023), U.S. Department of Education, Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, Regional Educational Laboratory Central. http://ies.ed.gov/ncee/edlabs

⁵ See https://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/index.shtml