When are students “ready” for algebra?

It will not come as a surprise to any educator that students are diverse in what they know and can do. Take any classroom of 30 students and it will include those who have had dramatically different life experiences. It will also include students who are at very different levels in their math content mastery: what concepts they’ve already learned and what mathematical procedures they can apply.

A few years ago, Blaine Pedersen, now a psychometrician at NWEA, analyzed data from the Trends in International Mathematics and Science Study (TIMSS) to see how many of the four international benchmark proficiency levels were present in an average American eighth-grade classroom. These benchmarks span the continuum of students who do not yet have basic knowledge of whole numbers and graphs up through those who can solve linear equations, understand linear functions and algebraic expressions, and interpret a wide variety of data to draw inferences. What percentage of American classrooms include students at all four of these levels? 35%. That’s right: one in three American eighth-grade classrooms includes both students who need help understanding whole numbers and students who are already algebra proficient. Prior research using MAP® Growth™ data has generated similar findings. In a study of two large districts, we observed that the range of student math readiness in a typical classroom spanned three to seven grade levels.

Challenging all these students and helping them grow is a difficult task for even the most seasoned educator. While much of the focus, both historically and post-pandemic, has been on how to best help learners who would benefit from extra support, this work calls out the fact that many classrooms also include students who are ready to move on to more advanced content. Many of the eighth-grade TIMSS classrooms mentioned above included students who were already proficient in algebra. Many more would be ready to learn algebra in eighth grade, even if they are not already proficient (perhaps as many as 40%, according to one study). And students who complete Algebra 1 by eighth grade (as opposed to ninth) often benefit by going on to take more—and more advanced—math courses. But placing students in Algebra 1 before they are ready can have negative consequences on their achievement. So how are schools to know when students are ready and would benefit from enrolling in Algebra 1? This is the topic of new guidance released by NWEA.

New guidance on using MAP Growth for Algebra 1 placement decisions

To answer this question, we first had to define what “success” in an Algebra 1 course looks like. While by no means an exhaustive or definitive list, we settled on two definitions to guide parallel analyses. In one analysis, we defined success as a score of “proficient” or “meeting standards” on a state end-of-course (EoC) exam in Algebra 1. These tests, given in states such as Ohio, Texas, and Georgia, are administered to students at the end of an Algebra 1 course as a kind of summative accountability exam specific to algebra standards. For the second analysis, we partnered with three NWEA school districts to collect data on Algebra 1 course grades. Although each district handled grading differently, in each case, we identified a grade above which we coded students as “proficient” or “successful” in Algebra 1.

While we believe MAP Growth can help schools make decisions about Algebra 1 placement, such decisions are always best made with multiple data points and from a strengths-based perspective.

With both benchmarks of success in hand, we were able to work backward to identify the MAP Growth 6+ math score a student needed to have earned the prior spring, that is, in the spring of seventh grade, to have a greater than 50% chance of scoring proficient on an EoC exam or in a course grade. While the exact score was slightly different depending on the metric of success (we discuss this more in the guidance document), even we were surprised by the consistency. Students needed to score around a 235 to 238 on MAP Growth in the spring of seventh grade to be on track to score proficient at the end of an Algebra 1 course. According to NWEA norms, this is roughly one-third of students in the spring of seventh grade, or roughly one-fifth of students in the spring of sixth grade.

Unpacking the guidance

Of course, there is nuance to this seemingly simple answer.

First, it’s important to emphasize the relatively low or inclusive cut score we used for our analyses. By looking for students who have a greater than 50% chance of being successful, in an average school, up to 50% of students who are placed in Algebra 1 will go on to not be successful in the course. Some schools might be uncomfortable with this and want to set a higher probability for success. And that’s fine! Our guidance describes how partners could adjust their placement criteria accordingly. But higher cut scores also mean some students who would have gone on to do well will be missed. This is why districts should think carefully about how to balance these competing priorities.

Second, especially regarding EoC exams, these recommendations are based on average growth over the course of eighth grade. Some students will grow more than average, and some will grow less. Schools can review historical growth for their own students and modify placement criteria accordingly. If students tend to grow at atypically high levels, students can be placed with lower scores. Conversely, if students tend to require extra supports, the decision might be made to only place students with higher scores (ideally also using other data points to make such a decision). Again, schools need to balance inclusiveness (i.e., lower cut scores for placement) with the instructional implications of needing to provide additional supports to students who might have gaps in their pre-algebra knowledge.

Third, our analyses assume a certain amount of instruction, that is, 28 weeks between fall and spring testing. Schools that have 32 weeks between testing events could admit students with lower scores because their students have more time to learn the content before any EoC testing or final grading.

And finally, while we believe MAP Growth can help schools make decisions about Algebra 1 placement, such decisions are always best made with multiple data points and from a strengths-based perspective. Some students will score lower than the benchmarks we’ve identified and will do very well in an algebra course. MAP Growth can help with that decision, but only educators have the complete picture.

Why does it matter?

The NWEA mission is partnering to help all kids learn®. We see the new guidance as directly contributing to this mission by helping schools identify students who would learn best in an Algebra 1 course. The identification process has important equity implications. Absent a universal and proactive screener for which students might be ready for such a course, the default is often relying on parent requests or teacher referrals. The result ends up being differences in enrollment by race or gender that cannot be explained by differences in test scores. An effective and equitable placement system will flag all students who are ready and would benefit, regardless of their race, ethnicity, gender, socioeconomic status, or zip code.


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