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, Featured, K-12 Reform, Reporting & Analysis, Research and Reports, State and Federal Policies, STEM, Tests and Assessments · Tags: Bill Honig, Center for the Future of Teaching and Learning, Instructional Quality Committee, WestEd

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Dave,

I share many of your sentiments regarding “college for all” and the idea that any one-size-fits-all curriculum will ever be satisfactory for every kid. At the same time, much of your post is based on incorrect information and/or assumptions.

Specifically, the current policy is California is NOT to place all kids into Algebra 1 in grade 8. The current policy calls to place ONLY the kids who are ready for algebra into an algebra course (and, incidentally, this new report we are discussing clearly supports placing such kids in algebra). This has been documented in the Calif. Math Framework and in numerous other policy documents and directives. One cannot ignore the fact that many administrators do foolishly place unprepared students in algebra, but we should look for solutions to this harmful behavior rather than defer algebra for all through weakened curriculum to accommodate stupid administrators.

Further, the push to place as many (prepared!) kids in algebra by grade 8 does not “confuse … correlation with causation” as you write. Read pages 3-45 through 3-47 of this National Math Panel report: http://www2.ed.gov/about/bdscomm/list/mathpanel/report/conceptual-knowledge.pdf . This is what the high achieving nations across the world do.

But expecting a successful Algebra I course for HS graduation does not imply “college for all” — it implies a reasonable expectation that HS diploma is supposed to mean something. I am myself unsure whether a (serious) Algebra II course is a reasonable expectation for HS graduation, but I am sure that Algebra I is.

Ze’ev,

Thanks for your thoughtful response. From it, I sense we agree that students should have the opportunity to progress with more advanced material once they are ready, but not until.

For clarity, my comment, and philosophy, speaks to the unfortunate misapplication of CA state policy, or guidelines, by school and district policies, written or not, that place the vast majority of students into algebra 1 in grade 8, whether they are ready or not (as you refer to as well).

Many, if not most, schools misapply state recommendations regarding placing students into algebra 1 to maximize their API scores, or for beliefs that it is the right thing to do to improve access to advanced mathematics later in high school. The action is not malicious, but misguided, and does cause more harm than good. The bottom line is that what happens today is not in line with what is recommended. Hence, the mere existence of the state policy and framework, while necessary, is insufficient, which is the essence of my comment.

If you limit teaching students algebra 1 concepts in in any grade to when they are “prepared,”, then I neither have an issue with it as policy, nor will I state the act confuses correlation with causation; however, as implemented today, it absolutely confuses the two and is nearly irreparably harmful.

Lastly, much of the justification for algebra 1 centers on college readiness, hence, its association with the “college for all” mantra. Whether passing a course in algebra 1, or any of the existing math courses beyond it is a truly reasonable expectation for a high school diploma is debatable. What is the diploma intended to signal? Should there be varied levels of the diploma? All of these complicate the discussion as to whether algebra 1 or beyond is necessary. If we constrain our view of algebra 1′s necessity to whether it is critical for one to live a successful life, raise a family, contribute to society, and etcetera, I would say no.

Why would a school not try to maximize their API scores? There are some who clearly can afford not to, but for the vast majority of them, that number is almost life and death.

I am also interested in what you mean by ‘irreparably harmful’. While I understand what the subsequent ‘CST results’ seem to say, isnt claiming that that proves harm also assuming causation?

Personally, I think its impossible to discuss this issue without being more specific about the environment and policy implementation. Here is an anecdote that might give some idea why I believe that: in our district, we have a middle school in which 40% of their enrollment takes Algebra 1 in 7th grade. The proficiency rate is 100%. The same school even has 30% of their enrollment take the Geometry CST in 8th grade. Again, 100% proficiency. That same school has about 15% of its population take the CST General Math test in 8th grade (instead of Algebra 1), with an only 20% proficiency rate (clearly the decision as to whether to let kids take the Algebra 1 CST is based on some kind of evaluation of ‘readiness’).

In contrast, a middle school across town does not even offer Geometry and has 90% of its enrollment taking the Algebra 1 CST in 8th grade, with a proficiency rate of barely 20%. Essentially nobody even takes the CST General Math test in that school.

I’ll let people guess on the demographics of those schools.

I will also point out that a superficial analysis of this ‘problem’ would likely lead to some middle schools essentially not even offering Algebra (as some now dont offer Geometry). Would that makes sense? From a data analysis standpoint, perhaps; from a school and district environment standpoint and the impact on the kids, that would be a disaster, imho.

So I am going to circle back to the firestorm issue: I will contend that we know by the end of 3rd grade which kids will not be ready for Algebra 1 in 8th grade. I would also content that if that is true, then we are clearly not doing what needs to be done in those early grades. Shoot me for CST or other assessment bluntness and for pushing the SSC as something other than a joke, but if we do know this at 3rd grade (or earlier) and are not doing anything about it, please provide me the alternative as you pull the trigger.

Therein lies the problem…maximizing API sacrifices student learning on the altar of some artificial metric, which distorts the entire purpose of an educational system: students learning.

Irreparable harm occurs when you take students who might have a chance of learning material if it were at their level (and thereby building some self-confidence regarding their math skills) and force them to attempt to learn multiple levels above their skill level, at which, said learning minimally occurs. Try taking someone who cannot swim and toss them into water well over their head. Its not a pretty sight.

I might be oversimplifying this dilemma. But the current approach sure seems nonsensical to me. And all of the hullabaloo about “what might happen if” is too difficult to follow since just about anything might happen sometime. Let’s focus on truly helping these students learn rather than some nice sounding approach that yields minimal success.

And this is not a data analysis perspective. This is based on watching hundreds of students struggle. As skilled as I might be in the topic, pedagogy, and other items in my control, it is nigh impossible to help students who are in way over their head. The lifeguard drowns in that scenario.

As this report notes whether a student takes Algebra 1 in 8th grade (or not)is a predictor of whether they complete Pre-Calculus or Calculus in high school. Additionally, whether they complete Pre-Calculus or Calculus in high school is a predictor of whether they major in a STEM field in college.

The question that I have is what the exact criteria are for recommending students for Algebra 1 in 8th grade. At my former district students had to earn a 4 (advanced) on the 7th grade state exam and earn A’s on their report cards throughout the year in 7th grade. However, exceptions were made in some cases. Perhaps uniform standards (throughout the country) need to be established for recommending students for Algebra 1 in 8th grade.

With regards to the high failure rates of students taking Algebra 1 in 9th and/or 10th grade I agree that these students failure can be attributed to their lack the necessary pre-requisite skills (fractions, multiplication/division). However, it seems puzzling how they have not obtained these skills after being exposed to them for 5 or more years of schooling. I believe that these students are capable of being successful in mathematics, but they have poor math attitudes (interest, efficacy, utility, and identity). Perhaps if educators work on improving students’ math attitudes, then improvements in their achievement will follow. I also believe that these students could benefit from online educational resources, a more applied curriculum, and peer 1 on 1 tutoring.

An article in the December edition of AERJ sheds new light on the predictors of declaring a STEM major in college for males and females. Findings suggest that high school course takings, math and science report card grades, and test scores do predict whether students’ declare a STEM major. The unique finding was that the COMPARATIVE performance of students explained more of the variance in declaring a STEM major for males versus females than any of the previously mentioned predictors. Comparative performance was operationalized as the difference between their English grades (on report cards and test) and their math grades. This suggests that within student differences are more significant than between student differences. It seems that students’ decisions and performance are dependent on a mix of their relative strengths and weaknesses (which is reciprically correlated with their preferences).

I also think that 4 years of math should be a national graduation requirement. Many 16 or 17 year olds are not going to take 4 years of math if it it not required. These students do not realize that not taking Math as a senior could cause them to not be admitted to a college or lead to the necessity for them to take remedial math in college.

Furthermore, I agree that Probability & Statistics as well as a variety of Math elective courses (i.e. Computer Science, Consumer Math) should be offered in high schools. Probability & Statistics may be more useful for students not pursuing a career in the physical sciences or engineering (i.e. business/finance, social science, or biological science majors).

Rather than debate minutia, I believe it is important to step back and question the logic behind the policies that herd students into an algebra 1 course, irrespective of their readiness, whether as the first time in 6th grade, or the last time in 12th grade. While I am new to education as a profession, it is readily apparent to me, and anyone skilled in scientific inquiry, as tempered by common sense, that those policies are deeply flawed in multiple ways. First and foremost, the rationale that algebra 1 is a gateway course, hence all must take it in middle school confuses correlation with causation. The continued misinterpretation and subsequent misapplication of statistical analysis twists policies to suit agendas, rather than reality as they fly beneath slogans of “College for All” or “No Child Left Behind,” which anyone would wish for all children; yet simply wishing it were so has never worked in any repeatable, sustainable fashion. Pushing beliefs that all students must go to college since we need more STEM graduates, or for social justice / equity reasons, places wishful thinking ahead of reasoned approaches, and logic itself.

Routing all students into algebra, whether in middle school, or high school presumes all are prepared; yet as this report shows, the well-intended policy repeatedly, and in increasingly large numbers, forces a student, parent, teacher and school into stressful situations where success is elusive, no matter how intensely we support a student. Worse, the end result has been a generation of students disgorged from public education ill equipped to support themselves, much less a family.

Advocating to continue the policy simply since the aggregate number of students taking more advanced levels of math has increased over the years, or some other myopic metric, seems equally illogical. Yes, a student is neither a percentage, nor a statistic; they are cognitive and emotive beings with specific knowledge, understanding, and skill at specific moments in time, which may or may not be adequate for them to succeed in a specific course of study, or sequence according to a one-size-fits-all master plan. That is the essence of this study, which any secondary mathematics teacher could have readily explained after a few months teaching a heterogeneous set of students, especially one whose demographics includes a high concentration of students from low-income families.

Nonetheless, my limited time running an algebra intervention class, two algebra 1 classes, and two AP Calculus AB classes in a Title I school provides me with a glimmer of hope that finding ways to elevate students from their existing level of understanding and skill, wherever that might be, yields more benefit to the student, and potentially society, than any ongoing debate about specific standards a la common core, pacing calendars, benchmark exams, CST scores, district mandated pedagogy, or other well-meant but often ineffective solutions. I’m seeing traction teaching students where they are in the moment; albeit, it consumes a tremendous amount of time and energy to do so.

See my latest post related to this topic. http://mathequality.wordpress.com/2012/12/02/the-big-lie-college-for-all/

I would not go as far as John Mockler does and call the study “flawed,” — much of its data and its analyses seem generally OK.

But the study is wrong-headed in that it focuses only on how students in these districts “don’t make it,” while completely ignoring how many more students — in the same districts — made it in 2010 versus 2003. In other words, the study highlights the failures and ignores the successes. No system is perfect and such one-sided focus incorrectly frames its overall conclusions.

Further, the study cohort seems not representative. For example, in 2010 we’ve had 32% proficient and advanced in Algebra 1 by grade 8 across the state, while this cohort shows only 25% (fig. 3). Quite a large difference.

Intriguing, Ze’ev: so you would say that individuals and groups who ONLY focus on the negative when it comes to math education, who deny, ignore, explain away, etc., any positives, are perhaps, oh, biased in some way and should not be taken too seriously? That their viewpoint might just be, ahem, “wrong-headed”?

I fully concur. And suggest that you are a member of such a cohort of narrow-minded, wrong-headed, biased people, and closely affiliated with other such groups: HOLD, NYC-HOLD, Mathematically Correct, to name three.

Students are not percentages. The question is what is the increase in the number of students who take these high pathways. % proficient masks the fact that we have 1million more kids in secondary schools taking high end math and science than we did in 2003.

It is almost always true that students who start strong end strong. And it is true that we need much better math instruction especially in grades 3 though 7 but this study is just flawed.

I am not surprised by the study in the least. I worked with teens at church and I found the same problem pointed out by the study,that many students who are struggling with Algebra still have problems when retaking the course. The solution is not to take it again, find out what was not mastered in the lower mathematics courses and help them master those concepts first.

I found that the teens had not conquered what we previously called “times tables”. How can you factor if you do not understand muliplication/division tables? I went and bought them simple flash cards at the dollar store. Next, I noticed they did not understand how to work with fractions. We worked on adding, subtracting, multiplying and dividing fractions.

After helping them to master these two areas of deficiency they were able to do much better in Algebra.

The point is to actually learn, not just to be able to pass a test.

Not being a numbers person myself, I even had a hard time following all the data in this article! But I am concerned because my son is one of the 23% who repeated Algebra I in 9th grade and barely passed. I worry that he won’t be able to attend a CSU – I’m realistic about UC – he’s not going! But he is interested in the Maritime Academy….what chance will he have with ok grades in Geometry but poor grades in Algebra?

The Maritime Academy in Vallejo is extremely cool. I had the opportunity to tour the campus and their ship earlier this year (even got to drive the simulator!) and really enjoyed learning about their program. I had no idea CSU had integrated it into their system; I’m glad they did.

Best of luck to your son, Leslie. I don’t know what the admissions are like, but I suspect they are going to want to see evidence of fluency in algebra for most of their programs. A good grade in Algebra II might do that. There’s also the option of trying a community college Algebra course or even something like Coursera.org (which is the free project being built by several universities) to get a different approach. He could practice and review through the free Khan Academy also.

I noticed that UC Irvine has a free coursera Algebra 1 course offered for the spring semester. You don’t get any credit from coursera, but you get a certificate and presumably the knowledge which is supposed to be the point of all this.

There is something fishy about this data. The report claims that of students who took algebra in 8th then repeated it in 9th, their 9th grade algebra CST proficiency rate was ‘only 21%’. And for those who took it in 9th then repeated it in 10th, their 10th grade algebra CST proficiency rate was ‘only 9%’. But the overall 9th grade 2010 algebra CST proficiency rate was only 22% and the 10th grade rate was 12% (both higher, but only slightly). And that is only for the 2010 CST data (last year of data used in the report). If you go back further, 9th and 10th grade overall rates are actually lower than those cited in the study for repeating students. It would be helpful to understand whether those numbers were for the entire set of years as well as why the repeater rate was mentioned, but the overall rate was not. If it was for all years, it would appear that repeating algebra did benefit some students, though not many.

It should also be noted that since this analysis is based on CST data, the assumption is that every child who took algebra 1 in school also took the algebra 1 CST that year (and if one was repeated, both were). It would be useful to know whether that was true for essentially all students analyzed. I expect so but didnt notice it mentioned in the study.

It should also be noted that not many kids are ever ‘ready’ for Algebra if you use the Algebra 1 CST results as a metric (admittedly may not be the best metric). Only 10% of 7th graders took Algebra 1, but their proficiency rate was almost 90%. So thats about 9% of all students who clearly were ‘ready’. I expect none of those repeated in 8th grade, so based on 8th CST results about 20% of students were ‘ready’ for algebra in 8th grade (50% prof rate on about 40% test takers). The numbers drop from there. The EOC rate is about 34%.

I do agree outright with one point made in the study:

“While this research focuses exclusively on middle- and high-school math course-taking, the large variation in students’ grade-7 math performance suggests that more work must be done at the elementary level to prepare students for success in middle-grade math.”

Algebra readiness goes way back to the lower grades. Although I dont want to start another CST firestorm, I will point out that if this analysis is based on CST data, then I expect looking at those same kids’ results in elementary, even as far back as 2nd grade might be enlightening. As many problems as I have with CSTs, I have seen exactly such correlations. Of course, that could just mean that CSTs are just really good at being inaccurate for certain kids in a very consistent manner. :-) If that’s the case, then we dont need to bother discussing this report anyway. :-D

I’ve heard arguments on both sides whether requiring Algebra II as part of the courses for UC-CSU admission is an unnecessary hurdle or a useful requirement. I can see where a basic statistics course could serve as a substitute with more practical applications for non-STEM majors.

I welcome readers to provide their insights.

I would like to see all kids get a good statistics course in high school. I’m not sure you can introduce it before Algebra II.

My point about 4 years is not necessarily that kids need to progress to precalculus or calculus per se, but that math fluency is important and that I think it would be valuable for all seniors to be taking some kind of math or math-based class. It could be a sideways step rather than a vertical step, perhaps applying math techniques already learned integrated with a practical CTE bent. I just think the practice of letting kids skip a year of math before going to college and then having to take math again is educationally unsound, and I don’t think that math fluency is any more arcane than say Shakespearean plays. I suspect it relates to the fact that people who make those decisions are more comfortable personally with Shakespeare than algebra.

Well, let me tell you John, I took Algebra II back in high school (coming up on my 50th reunion) and I have found quadratic equations to be exceptionally important in everyday life. Why, I’ve used them for…ummm..let’s see…there was the time….no, not that….but wait….no, I guess not then either. Well, had to be something I’m sure. A great series of intellectual exercises at any rate.

No offence intended to the Math folks out there.

Algebra II should absolutely be a requirement for UC-CSU admissions. Admissions are already impacted, and this could be a basic math requirement. In order to pass algebra II by graduation, you only have to pass algebra 1 by tenth grade. I think upping the math requirements may also encourage science/math/engineering enrollment. We have enough people with generic BA degrees filling up employment at Starbucks and Trader Joe’s.

Ya. We have enough STEM majors filling up Starbucks and Trader Joe’s to boot. The competition for minimum wage jobs is fierce!

I seriously doubt “upping” the math requirements for poor math students will enourage STEM enrollment any time soon.

The Sage of Wake Forest

Why is it that the state requires 4 years of english to graduate from high school but only 3 years of math?

I expect one reason is that historically, the vast majority of high school graduates never used anything but arithmetic in their real lives. Knowing how to speak coherently and read with some level of understanding is a lot more important, at least for the general person. For a while this seemed to be changing, but now it appears with technology, ‘normal’ people actually ‘need’ to know less math now than before. Going into a STEM career is obviously an exception, but so far the rates of STEM directed kids seems to be a small portion of the overall enrollment. (not saying whether this is right or wrong, just an observation)

El–

Because with an averge failure rate of about 40% in algebra 1, and about 40% in geometry–why would schools want to inflict more pain and waste more resources on this subject?

English has no where near the failure rate of math.