A big reason California students are pushed to take higher math in high school is to see that they satisfy the admission requirements to a state four-year university. And yet 68 percent of students who haven’t passed one of the required courses, Algebra II, by the end of 11th grade don’t even enroll in math as seniors, giving up on the possibility of applying to a UC or CSU school.
That puzzling statistic is among the data from an extensive research study by San Francisco-based research organization WestEd’s Center for the Future of Teaching and Learning of math courses that 24,000 students in two dozen districts took – or didn’t take – in middle and high school. Those findings point to great success for a minority of students – about one out of five – who take Algebra I by the end of eighth grade, geometry by the end of ninth and Algebra II by the end of tenth; many of those students then go on to complete pre-calculus in 11th grade and calculus as seniors.
But the findings underscore challenges and setbacks for the majority of students who, by seventh grade, already are showing they’re not ready for the math courses awaiting them in high school; half of all students will repeat a math course, most likely Algebra I (34 percent), and the vast majority of them will fare no better the second time around. For a state that is relying on a next generation of STEM majors and college graduates, that’s troubling.
About 44 percent of students covered by the study did get a C- or better in Algebra II by the time they graduated. The WestEd researchers didn’t speculate why more students didn’t try again to take Algebra II as seniors – whether it was poor grades or a lack of counseling or perhaps whether they just had had it with math. Instead, the researchers hope that the study’s extensive findings on students’ completion rates, proficiency levels and course-taking patterns will prompt superintendents and math administrators to reevaluate what courses students take, when they take them and what changes in content and teaching could better help students succeed.
“Our hope is to catalyze discussion at the district level,” said WestEd senior research scientist Neal Finkelstein, “and open up discussions over instruction.”
Now, with the transition to the Common Core standards in math emphasizing deeper learning and focusing on mastering core skills, is the time to do so, the study says. It’s also an opportunity to rethink interventions and refresher courses so that more students in middle school are better prepared for high school math.
Pivotal year: seventh grade
Seventh grade is not necessarily destiny, but the researchers found it is a crucial year, predictive of math outcomes in high school. Consider: For students who got an “A” or “B,” 27 percent took calculus and 13 percent took pre-calculus. Those students appear to have done well with all of the courses in between. For students who received between a “C” and “D” in seventh grade math, only 1 percent took calculus five years later as seniors and 8 percent took pre-calculus. Unless students fill in the gaps in knowledge in middle school, they’re destined to struggle throughout high school.
For a decade, the state, through accountability sanctions, pressured districts to push students to take Algebra I in eighth grade. In 2005-06, when students in the study were in eighth grade, 57 percent took Algebra I, with 63 percent passing it with a C- or better. The next year, 23 percent of the class repeated Algebra I in ninth grade, an inefficient use of resources and often a source of frustration for students. (Last year, 59 percent of eighth graders and 8 percent of seventh graders took Algebra I.)
By 11th grade, only 34 percent of students had tested proficient in Algebra I – nothing to brag about – and three-quarters of these students had been first-time takers in eighth grade. Of the remaining quarter, most were first-time takers in ninth grade. Repeat Algebra I takers showed little to no improvement. About one in five students who repeat Algebra I in ninth grade gain proficiency; that drops to one in 10 for tenth graders who repeat Algebra I.
Some districts with large concentrations of poor and minority students have funneled the majority of students into Algebra I, because they believe it is imperative to create equal opportunities. But previous reports by the Center for the Future of Teaching and Learning have documented that children in high-needs schools are more likely to be taught by novice and intern teachers. As the WestEd study found, achievement gaps continued among students who took higher math courses. The 24 percent proficiency rate for low-income students in Algebra I was nearly half that for other students; it was nearly a third of the 37 percent proficiency rate in geometry for non-indigent students (see graph).
Because math builds on prior knowledge, students who take Algebra I before they are fully prepared “never reach the level of Proficient on the Algebra 1 CST, an outcome that has direct consequences for their performance in higher-level high school math courses and, ultimately, for their placement in postsecondary math courses should they go on to higher education,” the study said.
The WestEd researchers tracked the courses that all 24,000 students took from seventh to 12th grade. The compilation showed surprising variations and combinations. Some students took pre-algebra in seventh grade, while others took basic math. Some repeated Algebra I in eighth grade, others in ninth, and 4 percent repeated the course in eighth, ninth and tenth grade.
The data showed that 30 percent of seniors took no math as seniors – a statistic that should alarm not only high schools but also public colleges. A gap year without math, especially for students who barely passed Geometry or Algebra II, ups the odds that they’ll be required to take a remedial math course at a CSU or community college. “For students who have had challenges in math in middle and high school, not taking math in senior year has the potential to make the journey to college that much more difficult,” the report said.
Early next year, the State Board of Education is expected to revise the state’s math standards to make Algebra I the default curriculum in ninth grade, in conformance with Common Core. The State Board is also promising that curriculum frameworks now under development will include guidelines for districts with students ready to take Algebra I in eighth grade. The WestEd data support preserving an accelerated path. But the report also notes, “When students take Algebra 1 (that is, in which grade) is less important than whether students are ready to take it.” Deciding when a student should take Algebra I should be based on multiple factors, the report said: whether the student has mastered pre-algebraic concepts, prior year CST scores, teacher recommendations, results from district tests, and discussions with students and their parents.
For students who do end up struggling in Algebra in eighth grade, the study suggests alternative approaches to a straight repetition of the course. Among the possibilities: focusing on particular content areas, using a tutor or other support services, assigning a teacher with different instructional approaches and mixing Algebra and geometry to avoid the stigma of retaking the subject. For seventh graders with a weak math foundation, the study suggests a two-year pre-algebra course, with an extended learning period, leading up to Algebra in ninth grade, the first of four years of high school math.
Filed under: Achievement Gap, Common Core standards, Featured, Reporting & Analysis, Research and Reports, Standardized tests, STEM, Tests & Assessments · Tags: Bill Honig, Center for the Future of Teaching and Learning, Instructional Quality Committee, WestEd