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As school begins this fall, many students are returning with unfinished learning in mathematics due to COVID-19 school closures last spring. This makes it more important than ever to be thoughtful about student placement in and design of accelerated programs.
There are parallels between addressing learners with unfinished learning and addressing learners who are interested in moving at a faster pace and accelerating in math before high school. In both cases we have to ask: How can we ensure students don’t miss crucial concepts they’ll need for higher-level mathematics? How can we identify possible sources of bias and take concrete steps to eliminate them?
Here are six strategies to support middle schools (and districts) in making well-informed decisions about coursework and course placement policies with respect to accelerating students’ learning in mathematics.
Base acceleration policies on current standards
Mathematics standards tell the story of mathematics, following a progression of concepts and procedures across grade levels. The concepts addressed in K–8 mathematics today are extremely important, and all students need time to learn this content properly. Yet, it wasn’t always this way.
Prior to 2010, most U.S. math curricula were highly repetitive in grades K–8 and redundant in middle school. As a result, many schools (reasonably) accelerated students by skipping one or more middle school mathematics courses.
New standards implemented in 2010, however, shifted content previously addressed in high school to grade 8, and topics previously addressed in grade 8 cascaded into lower grades (see figure below). As a result, middle school math courses are now much less repetitive and much denser with critical content. This means that a key goal of old acceleration policies — access to algebra earlier in students’ schooling — is now achieved by students taking grade-level mathematics. Thus, much of the rationale for policies that allowed students to skip middle school mathematics courses has disappeared.
Commit to cultivating a strong mathematics foundation
Research shows that a sound command of middle school mathematics content is vital to students’ readiness for college and careers. An ACT National Curriculum Survey in 2012 found that students with a solid understanding of middle school mathematics were better prepared for an advanced course in high school, which improved their success rates in college-level courses. The survey also found that topics from grades 6-9 were more important to college faculty for college preparation than advanced topics.
Further, according to a 2013 report from the National Center on Education and the Economy, the mathematics that enables the vast majority of students to be successful in first-year college courses is not from high school courses, but rather middle school courses, especially arithmetic, ratio, proportion, expressions and simple equations.
These findings help demonstrate why moving too quickly through foundational content in grades K–8 can impede current learning and undermine future learning. Instead, before considering acceleration, it is often better to provide students who are ready for more of a challenge with extension and enrichment opportunities that aim for deeper understanding.
Compact, rather than skip, standards in grades 6-8
Even with the current standards-based model of mathematics education, many traditional accelerated programs advance students by skipping standards or entire grades. This approach can create significant knowledge gaps as students approach higher grade-level mathematics.
For learners who are ready to move at a faster pace, it is better to use a curricular approach that compacts (covers the same content in less time) rather than skips important foundational content. This type of accelerated program lets sixth- and seventh-grade students — who have displayed exceptional fluency and understanding of mathematics addressed in earlier grades — complete all of the standards for grades 6-8 over two years rather than three
No matter which curriculum a school or district uses for acceleration, the content should be sequenced based on grade-level standards progression to ensure that no standards are skipped. It should also include plenty of checkpoints to review comprehension and provide teachers with recommendations for extensions or extra supports to guide students as needed.
Address disproportionate racial and ethnic representation
Babies of all racial and ethnic groups have the same inherent likelihood of growing into adolescents who are interested in and able to study mathematics at an accelerated pace. Yet, in many schools, students from different racial and ethnic groups do not enroll in and complete accelerated coursework in math at the same rates as their representation in the population. This may be due to bias in the selection process or differences in opportunities to learn that build throughout schooling, as Karisma Morton and Catherine Riegle-Crumb reported in their 2019 research study.
Schools must take concrete steps to close opportunity gaps and challenge biases that result in historically underserved students being disproportionately denied opportunities to participate in accelerated mathematics courses. This is one reason why it is so important to use multiple metrics to place students in acceleration. In addition to prior math achievement and preparation, these metrics can include student and parent self-assessments, teacher recommendations, and assessment scores — as well as students’ academic and career goals. Use data from these metrics and interrogate historical data, too, to identify possible sources of bias in the selection process and then take action to eliminate them.
Support underrepresented populations and address opportunity gaps
Data collected by the U.S. Department of Education Office for Civil Rights show that, among grade 8 students who are enrolled in Algebra I, white students tend to be overrepresented and black and Latinx students tend to be underrepresented. If the group of students placed in accelerated courses is not representative of the school’s student population, then the district should consider how to address opportunity gaps in elementary schools. Both the district and middle school should also consider how to support students who have interest and aptitude but also have unfinished learning in mathematics. For example, providing accelerated pathways that start in middle school, or offering acceleration through extra math courses or summer options, will increase the likelihood that students with unfinished learning have access to the same opportunities going forward as their peers who had access to more opportunities from the beginning.
Support populations who are overrepresented and may be missing critical learning opportunities
Alternatively, for students from racial and ethnic groups who are overrepresented in accelerated pathways, it is important to inform students and families about the potential negative consequences of acceleration before high school. Ensure that they understand that grade-level mathematics is important and rigorous, and that it doesn’t need to be rushed. Highlight the availability of pathways that don’t require acceleration before high school but still enable students to accomplish their goals. It is also helpful to build in a checkpoint with families after the first semester or year of acceleration so students who might be better served by building a stronger foundation will have a well-defined opportunity to decide not to continue on an accelerated path.
All students come to the mathematics learning community as capable learners and deserve opportunities to engage in meaningful work that allows them to demonstrate their knowledge and meets their unique needs. By designing course pathways thoughtfully and creating an equitable evaluative process for identifying students for acceleration, we can provide all students with equal access to learning the crucial mathematics content represented in the middle grades standards, as well as course pathways that best serve their interests.
William G. McCallum, Ph.D, is a Distinguished University Professor Emeritus of Mathematics at the University of Arizona, one of the lead writers for the Common Core State Standards in Mathematics, and the co-founder and CEO of the nonprofit organization Illustrative Mathematics.
Kate Nowak is the Vice President of Product Strategy at IM, and was the instructional lead of the writing team for IM 6–8 Math and IM 9–12 Math. IM is the developer of IM Math, a problem-based core mathematics curriculum for grades K–12.
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