At the state’s prodding, the proportion of students taking Algebra in eighth grade increased 60 percent over the past decade – a significant achievement. But there has not been a parallel success in encouraging students to continue on to become proficient in more advanced math courses. The pipeline to higher math has grown, but so has the leakage: the percentage of students who fall by the wayside.
These are the highlights of a study conducted by a researcher with the California Department of Education and two education professors from the University of California, Davis. The results have led them to suggest that “other mathematics focuses (beside Algebra in middle school) might, instead, provide students with greater future success in mathematics.”
“What Do the California Standards Test Results Reveal About the Movement Toward Eighth-Grade Algebra for All?”– published this summer in Education Evaluation and Policy Analysis but made available by the authors – certainly isn’t the first to question an algebra-for-all approach. But the study’s extensive data analysis offers new insights.
The study followed three cohorts of eighth graders (2003, 2005, 2008) from Algebra I through Summative Math in 11th grade, examining results on standardized tests each year. (Click to enlarge.)
Authors Jian-Hua Liang, a research consultant with the state Department of Education; Paul Heckman, associate dean of UC Davis’ School of Education; and Jamal Abedi, a professor of education at UC Davis, examined math test results for three cohorts of eighth graders, in 2003, 2005, and 2008, and then tracked the courses they took and scores they got through 11th grade (see table).
It showed that the percentage of eighth graders taking Algebra I increased from 32 percent in 2003 to 51 percent in 2008. Despite the increased numbers, the proficiency rate on the Algebra CST rose as well, from 39 percent to 42 percent. Bottom line: About 45,000 more eighth grade students were proficient in Algebra in 2008 than in 2003. One reason was that, as leverage to encourage Algebra enrollment, the state started docking points from schools’ API scores if their students continued to take General Math instead of Algebra.
Goal versus reality
California requires only Algebra I to graduate from high school, but the hope, in promoting Algebra early, was that more students would continue on to complete Calculus by high school graduation. The University of California and California State University require a minimum of three years of high school math, through Algebra II, although pre-calculus is encouraged.
There’s always been a leak in the math pipeline; however, by 2009 the drop in students taking Geometry and beyond was huge. In 2004, about 90,000 students took Geometry in ninth grade, compared with 152,000 in Algebra in eighth the year before. In 2009, 128,000 students took Geometry, compared with 248,000 in Algebra the year before, a difference of 120,000 students.
Put another way, 45,000 more eighth graders tested proficient in Algebra I in 2008, compared with five years earlier. By the time they were 11th graders, taking summative math, that impressive number had shrunk in half: In 2011, 22,000 more high school juniors were proficient in summative math than five years earlier.
“It appears that simply encouraging more students to take eighth-grade algebra does not by itself lead to significantly more students taking advanced mathematics in high school, nor does it lead to substantial increases in performances in higher mathematics CSTs,” the authors concluded. “Such encouragement for students to take courses is certainly necessary, but it is not sufficient for realizing students’ understanding and encouraging their motivation to continue to learn higher mathematics.”
Second, third time’s no charm
The study also compared the ninth grade math results for two subgroups of 2006 eighth graders. One group consisted of a minority of students who had been assigned General Math in eighth grade and tested proficient or advanced on that CST. The other group were eighth grade students who had tested below proficient on the Algebra CST.
About 37 percent of the eighth grade General Math students taking Algebra I for the first time in ninth grade scored proficient on the CST. No great shakes for sure, but more than twice the rate of repeat Algebra students. Only 15 percent of ninth graders taking Algebra I for the second time scored proficient.
The CST results don’t reveal whether the General Math students got an extra year of good preparation for Algebra I or whether they should have been assigned Algebra I as eighth graders. But what is clear is that eighth graders who aren’t ready for Algebra I rarely succeed the second and third time around. And they continue to be the majority: 58 percent of eighth graders tested below proficient on the Algebra CST in 2008.
That soon may change. Under the Common Core standards, which California adopted two years ago and is beginning to implement now, Algebra is recommended for ninth grade, and pre-Algebra is taught in eighth grade.
Students who are ready for Algebra in eighth grade will continue to take it, and computer adaptive tests that are being designed to roll out in 2015 will, in theory, be better able to identify students who are algebra-ready. The philosophy behind Common Core math is to spend more time in-depth on math basics, like fractions, leading up to algebra, so that students are conceptually ready for Algebra and Geometry, starting in ninth grade.
The authors of the study don’t mention Common Core, but they do suggest that students may lack both the interest and the conceptual framework to excel in higher math. “Among the students in our study, the algebra-for-all policy did not appear to have encouraged a more compelling set of classroom and school-wide learning conditions that enhanced student understanding and learning of critical knowledge and skills of algebra,” they wrote, adding, “Educators may have to challenge and move away from the weak or absent classroom learning conditions that now appear to characterize students’ school learning in mathematics, namely the extreme focus on procedural knowledge.”
Paul Heckman said that there will be a follow-up study to examine in more detail what’s needed for preparation for Algebra, along with the underlying factors that motivate students to learn math.
Ze’ev Wurman, an opponent of Common Core and the move away from teaching algebra in eighth grade, dismissed implicit criticism of the missing conceptual framework of the California standards in the study as speculation unsubstantiated by the data. He said that he authors should have included the numbers of seventh graders who take algebra – about 7 percent – and then go on to higher math courses; had they done so, the completion rate would have been higher. But Wurman, who helped create the sate math standards, praised the study in an email as well-done and interesting.
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