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.

And, for students pushed into Algebra I unprepared in eighth grade, the state policy has been a disaster, with very few students who repeat Algebra – some two or three times – ever passing the state exam.

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.

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 11^{th} 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 11^{th} 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.

Filed under: A to G Curriculum, Common Core, Reporting & Analysis, State and Federal Policies, STEM, Tests and Assessments

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John,

Your final paragraph’s reference to 7th grade math completion should have been paragraph one. Please use real calculations. The percentages get completely screwed up if you don’t include the kids who complete algebra proficiently in 7th grade. That’s a growing group that must be counted.

Bottom line for the future: no Algebra 1 proficiency means no Algebra 2 proficiency. And no Algebra 2 proficiency means no readiness for college mathematics.

And….no readiness for college mathematics leads to significantly reduced career opportunities in coming decades as well as huge increased remedial math costs for California’s Community Colleges.

Can a 21st century young adult survive, even thrive, without mathematics skills? Yes, but it will be trickier and trickier for coming generations. There are careers in entertainment, sports, law, education, construction, journalism, sales and service industries, etc that do not require advanced math. Kids will grow to adulthood whether they have math skills or not. But someone who is unproficient in Algebra 1 and Geometry will find narrowed career opportunities as the century progresses.

One can’t aim for degrees in engineering, architecture, sciences, etc., without solid mathematics skills. But such skills aren’t just taught in a classroom. They are built through many hundreds of hours of homework, tutoring and foundation building during the decade from kindergarten to ninth grade. If a student’s parents don’t personally have higher math skills, that student won’t have natural coaching at home and will have to work twice as hard to earn proficiency. An hour or two of daily math studies in a classroom alone cannot fill a child’s math proficiency. It’s the repetition and continued training outside the classroom that gets one up the math ladder.

Chris Stampolis

Governing Board Member, West Valley-Mission Community College District

State Board Member, California Community College Trustees

408-771-6858 * stampolis@aol.com

el: regarding your question whether we are correctly detecting algebra skills, the data actually seems to show that the STAR generally provides good guidance for placement — it is the teachers and administrators who place kids inappropriately despite what CST scores say that do more harm than good. That was also the conclusion of last year’s EdSource MS study.

That’s a good question el. The doorways site lets you check course listings by high school

https://doorways.ucop.edu/list/app/home;jsessionid=46EBDB8A3A588208CE4A7737D7B13947?execution=e1s1

But obviously that does not include corellating middle school curriculum nor provide data at the state level.

It would be great to see how many high schools dont offer calc (and which ones and why). Or even how many don’t offer a-g (which includes alg ii). I think some of these questions were a focus in Williams v Ca. but even if that data was presented at that point it would be old now and things have changed a lot since then.

I think this kind of data is all the more interesting now that so many districts and parents will be thinking in STEM terms..

When schools put 7th graders in Algebra 1, does the matching high school always offer a second year of calculus or some other post-calculus math class? Or is it assumed that those kids will drop math as seniors and/or take classes at a community college?

The LACES case is special since it is part of the magnet pipeline at LAUSD. During the last two years, I’ve been told, LACES recognized they had a problem with math and began a program to bring those who did not go into Algebra I at 7th grade up to speed to reduce the “leakage” down the line. I was told they were doing very well and the 2011 STAR results (which I did not include above) seem to bear that out. It would be interesting to see what happened in 2012.

Unfortunately, LAUSD took away Title I money from LACES and 22 other schools for the 2012-13 year. Because the math program (it was after school intensive tutoring of students who did not have strong math skills in elementary and 6th grade) received its funding from Title I, it was not going to be offered this year. I do not know if the school managed to get funding from elsewhere to continue it. The upshot is that even successful schools with naturally high-achieving populations can have problems teaching math and when they work to change that, their funding sources can, and will, be cut. So we get back to this being a policy not a teaching problem.

As far as schools offering a 12th grade advanced calculus class to those 7th graders who took Algebra I, I’ve never heard of any but this may be because I never needed to find out. Checking on LACES web site (http://www.lacesmagnetschool.org/apps/pages/index.jsp?uREC_ID=31877&type=d&pREC_ID=classes), the highest math they teach is AP Calculus BC, which, according to the College Board’s web site, “is designed to qualify the student for placement and credit in a course that is one course beyond that granted for Calculus AB.” Sounds impressive. However, a student must score a 5 on the AP exam in order, for example, to get credit for two quarters (Math 31A and 31B) at UCLA (http://www.math.ucla.edu/ugrad/new-apmed.shtml). Scoring a 4 gets you to skip only 31A plus get credit for four unit of Calculus (how that “credit” works, I have no idea; you still have to take the classes to get them to count for your major).

I’d love to know how many kids are enrolled in AP Calculus BC, not only at LACES, but at LAUSD and the state.

It’s always seemed to me that the 8th grade algebra requirement was driven by a misguided desire to allow high school students to progress to Algebra II within the context of a “two years of high school math” requirement. If you’re serious about graduating students who will be able to take math classes in college which build on Algebra II, you don’t do it by having them take only two years of high school math.

The current system seems to be designed to rush students through high school math, leaving many of them needing to review it by the time they get to college.

El, if you are curious about what happens when a self-selected population of high-achievers is confronted with the Algebra-I-at-8th dilemma, take a look at the STAR scores in math for the Los Angeles Center for Enriched Studies, one of LAUSD’s 7-12 magnet schools and one of its highest API schools. Given their scores in the ELA CSTs, I’d be willing to bet that those kids do not space-cadet on the math portion.

What I found when I looked at them about nearly two years ago mirrors somewhat the general population: There is a continuous erosion on the size of the cohort advancing to higher math for the non-accelerated population, which remains somewhat stable. With minimum details and following one cohort:

2007: 7th graders: 64% took General Math, 36% took Algebra I

2008: 8th graders: 63% took Algebra I, 37% took Algebra II

2009: 9th graders: 24% took Algebra I, 45% took Algebra II, 28% took Geometry

2010: 10th graders: 5% took Algebra I, 18% took Algebra II, 41% took Geometry, 35% took Summative Math.

Do you see the pattern? (BTW, LACES changed the order of the classes: students take Algebra II before Geometry.) The surprise (or maybe not) is when the CST scores are checked: the number of proficient and above in 2010 is only 18% of 10th graders who took Algebra I, 7% of of those who took Algebra II, 56% of those who took Geometry, and 68% of those who took Summative Math. Guess which one is the accelerated group. (BTW, 87% of 10th graders were proficent-and-above in the 2010 ELA so these kids are driven to succeed.)

So, yeah, I’d say there is a problem with the implementation of the policy, even in an unofficial highly gifted magnet. I am more inclined to believe that demanding that Algebra I be a condition for graduation was a bone-headed move. This can only succeed if the fundamentals of math are emphasized before students are moved (forced?) into Algebra I, as you comment. But what do I know? I am only a physicist, not a math teacher.

I’m not convinced that including the 7th grade Algebra group is essential; it’s clear those kids are tracked into a math/accelerated track.. and likely would have been regardless of the state policy. Those are the kids who already have a clear affinity for math. The question is, is a policy that defaults kids into algebra when the placement is questionable helpful or harmful, and does the curriculum set up with that in mind meet the real goal, which isn’t algebra in 8th but precalculus in 11th and ideally, calculus in 12th.

I think the goal to get those kids into and through advanced math is a laudable one. However, I think sending kids into Algebra before their math foundation is strong is always going to be counterproductive.

I am curious too to know if this is all being measured solely by the STAR test. An alternate hypothesis that explains the data is that some percentage of the kids who are not scoring proficient are actually able to do the homework and regular tests competently, but then space-cadet on the bubble tests. IE, has anyone checked to see that we’re actually correctly detecting algebra skill rather than just kids who seize up on a bubble test regardless of the subject or questions tested? Would be interesting to compare their scores on some other material as a secondary control.

John: If that is a University study, then the University is in trouble. Of course you must include the 7th grade Algebra group; it is the highest scoring group. And of course you must adjust for the fact that more than 1/3 of students take Algebra twice and decide which STAR score to use. But UC did neither and thus their study while interesting is well below basic. John

The Liang paper is indeed interesting, but it is not a compelling argument that CA’s 1997 goal of increasing algebra by grade 8 was wrong headed policy. Rather, the study’s conclusions can point the finger at flawed implementation of the policy goal, particularly for students not yet ready for algebra by grade 8. The study shows that not-yet-ready students are not well served by premature placement in algebra, but it also shows there are students who may be ready but were not placed in algebra by grade 8. In other words, the results may be interpreted as flawed implementation of the policy goal, with improper placement decisions a major flaw, rather than a flawed policy in itself.

One line in your post, John, drew an eyebrow . . . “computer adaptive tests that are being designed to roll out in 2015 will, in theory, be better able to identify student who are algebra-ready.” The consortium tests, including the Smarter Balanced computer-adaptive tests, are being designed primarily as end-of-year summative tests to measure the results of previous year instruction, not as readiness tests or predictive tests designed for course placement decisions. It is beyond the current state of large scale assessment art to expect both functions to be served by a single test. Computer adaptive tests have a lot of promise, but we have to be very careful and willing to heed former Stanford Professor Lee Cronbach’s caution to be wary of “the gap between the demands of assessments and the state of our technical art.”

“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…” This issue will characterize the entire transition to Common Core. We have long known that mathematics instruction is as much a problem as student (whatever fault you want to place here – interest, ability, background, maturity). Educators must know more and teach better which is not part of the discussion but is the Achilles heel of higher levels of student learning.