Reforms > Common Core

Many math students are flailing, repeating courses without success



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.

Students with a solid foundation for math in seventh grade tended to do well in subsequent years, as measured by proficiency on California Standards Tests, starting with Algebra I in eighth grade, moving on to Geometry in ninth and Algebra II in 10th. Proficiency rates lagged for other students. Source: College Bound in Middle School and High School? (click to enlarge)

Students with a solid foundation for math in seventh grade tended to do well in subsequent years, as measured by proficiency on California Standards Tests, starting with Algebra I in eighth grade, moving on to Geometry in ninth and Algebra II in tenth. Proficiency rates lagged for other students. Source: College Bound in Middle School and High School? (Click to enlarge)

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.

Proficiency rates were substantially less for low-income students on state standardized tests in Algebra and Geometry. Source: College Bound in Middle and High School? (click to enlarge)

Proficiency rates were substantially less for low-income students on state standardized tests in algebra and geometry. Source: College Bound in Middle and High School? (Click to enlarge)

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: Common Core, Reforms, State Education Policy, STEM, Testing and Accountability

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40 Responses to “Many math students are flailing, repeating courses without success”

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  1. Vivek Agarwal on November 2, 2014 at 7:27 pm11/2/2014 7:27 pm

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    While teaching Alg 1, Geo & Alg 2 in 3 consecutive academic years would have its own base in logic, to my mind introducing the easy concepts in Grade 8, both from Alg 1 as well as Geometry would serve to integrate well the two in students’ minds. Having said that, over the past two years I’ve been able to alleviate the Math-phobia during my one-to-one tutoring sessions with around 100 students. For instance if my 8th grade students would fumble on Percent or decimal equivalent for 1/10 , I’d straight away pull a 5th grade worksheet showing the ‘easiness’ of these concepts. As teachers our responsibility towards removing this Math phobia is at least as important as delivery of the course content. The course content is very student-friendly, it’s only up to us as teachers to deliver in a student-friendly manner. It’s like saying the same knife could be used by a doctor for healing his patient, while used very differently by a person with dubious intent.

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    • Tina Tots on December 8, 2014 at 3:16 pm12/8/2014 3:16 pm

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      You a good teacher that is why you care, but most of the teachers who are unions don’t give a care at all. Instead, my daughter’s math teacher (who she transferred out of), made sure that she does not succeed, she told him that she gets nervous in the test, what advise he can give? He just said “why you nervous?” that’s all, and on her next test, sat right in front of her and kept shaking his head as if she made any mistakes just to freak her out. He misgraded her paper on purpose every single time until she gets tired of going to him to get them corrected, and he gives 0 partial credit, and 0 to questions which he said there is no right or wrong answer…..My daughter now say , she hates “math”… she was a straight A math student until she met him!!!!

  2. George DeMarse on October 18, 2014 at 5:28 am10/18/2014 5:28 am

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    It’s much easier and less failure-ridden to stop forcing 7th and 8th graders to take Algebra, which inevitably results in about a 50% or more failure rate in the subject. We are not talking about a 50% ”C” passing rate, but a “failure” rate. We look to the stats on kids who repeat the course and see dismal failure again—no improvement.

    The dismal failure rates in math are because of the peculiar curve of exam grading in math. Math scores are rarely a Bell curve. As early as seventh grade we see the math kids bunched at the A grade, followed by the B kids and surprisingly, few kids bunched at the C level. The next big “bump” is in the D-F range. In other words, many kids are not capable of the C range and fail.

    I have not read any other papers or studies suggesting other subjects are like math in this manner. So that is the difference with math and why we should stop making it mandatory and start making it an elective from the middle school years on.

    George DeMarse
    The Sage of Wake Forest

    Replies

    • navigio on October 18, 2014 at 9:32 pm10/18/2014 9:32 pm

      • 000

      Nothing ‘forces’ students to take algebra in 7th grade (except maybe parents and peer pressure in a few cases). API incentives did coerce students to take it in 8th grade, though that coercion has gone away. However it’s useful to think about why that existed by looking at what removing the 8th grade requirement will likely achieve. In many, many middle schools algebra will not even be offered (ie where students will be deemed ‘unready’). In other middle schools, both algebra and geometry will be offered because there are still plenty of kids there who can do fine taking algebra in 7th grade and geometry in eighth (whether that’s necessary or even useful is a valid, but separate question). So firstly, this will create differential opportunity in the very classes offered at those schools and this difference will be dictated by the very students attending (ahem). Second, the teachers needed to teach in those two schools are very different so how they are distributed in districts where both kinds of schools exist will match that difference (ahem, ahem).
      It amazes me how much time we spend on this notion of ‘unequal’ teachers as somehow caused by ed code yet we seem just fine with explicitly segregating kids and opportunity as long based on ‘ability’.

  3. Paul Amos on April 8, 2014 at 12:31 pm04/8/2014 12:31 pm

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    Dear Mr. Fensterwald,

    Your article was very well written and I enjoyed reading it. However, I cannot find in your article how one can get a copy of the Research Study that you are summarizing and reviewing. You only describe it as a Research Study by WestEd’s Center for the Future of Teaching and Learning. I don’t see a formal bibliography citation, or a website location, relating to the Study.

    Would you kindly let me know where I can find a copy of the Study itself? I am working on a Master’s Thesis and certainly need to see it.

    Thanks very much.

    Paul Amos

    Replies

      • Floyd Thursby on April 8, 2014 at 2:35 pm04/8/2014 2:35 pm

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        Children need tutors at this age and they aren’t getting them. It’s hard to get it in a group setting. Some do, but those that don’t need tutors at least 2 hours a week. Often a bridge will help, not forever, but as long as they need it. We should pay for this.

  4. Tamara on March 26, 2014 at 2:44 pm03/26/2014 2:44 pm

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    Can you provide the correct hyperlink for the second article listed at the bottom of this article? The link for “Another study questions state’s push for 8th grade Algebra” goes to the same place as “California to adopt Common Core’s view of Algebra in 8th grade”.

    Replies

  5. Excelonz on December 12, 2013 at 9:17 pm12/12/2013 9:17 pm

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    Math is the only one subject where it was possible to score hundred percent. Even today this holds true for the well-prepared.
    http://www.excelonz.com/

  6. Luz E Virgen on December 10, 2012 at 10:07 am12/10/2012 10:07 am

    • 000

    Professionald should step in and tutor those 7 and 8 graders to ensure the build the fundamentals of math to ensure success doen the road. Many teachers that teach math in elementary are not math teachers , many don’t know how to teach. Let me [know] how I can help

  7. Manuel on December 9, 2012 at 11:26 pm12/9/2012 11:26 pm

    • 000

    As I’ve stated before, any analysis based on the CST needs to take into consideration what the actual distribution of scores is before pontificating on the “conclusions.”

    Some time ago, I pointed out that the distributions of CST scores in ELA for all grades and for all administrations to date are roughly Bell Curves with averages at around 350. The same can be said of math for grades 1 through 7. For Algebra I and above, that’s no longer the case because the students can take them “out of sequence” or even repeatedly. (All this can be confirmed by examining the CST score distributions given in the Technical Reports. If you want copies of the graphs I have made from these numbers, let me know.)

    Since 2007, the CDE has released the distributions for students taking the Algebra I test and makes them available as “all students”, “8th graders only”, and “not 8th graders.” All of them show a distribution skewed to the left, proof that students taking the test are not even getting close to the prediction of the vendor of meeting the Bell Curve. It is also indirect proof that not all the 8th graders are “ready” to take the test. If they were, then the distribution would look like all the distributions for grades 2 through 7th: a reasonable Bell Curve.

    I am not familiar with the policies of school districts as far as meeting the requirement of “passing Algebra I” to be eligible for high school graduation, but I would not be surprised if such policies are a mixture of passing the class and/or attaining a proficient score in the CST. This could account for the large number of not-8th-grade students retaking the CST.

    To give you an idea of the numbers, here they are:

    8th graders not 8th 8th-graders ELA
    2007 238,426 499,805 479,717
    2008 247,372 494,991 480,891
    2009 261,565 491,628 462,898
    2010 273,857 472,385 450,321

    As you can see from the table, roughly half of 8th graders who took the ELA took the Algebra I CST, bu an equally large population retook the test or took it while on 9th grade (and this also includes the 5-7% of 7th graders who take it early). (One of these days I’ll process the more recent years as well as get the proficient-and-above percentages, which are readily at the STAR web site.) By the time each cohort gets to 11th grade, only around 25% of students is taking the CST in Summative Math (with roughly half being proficient). Clearly, Algebra I is the gatekeeper for meeting the A-G requirement mandated by the “college for all” frenzy.

    Why is this happening? In my opinion, there are many reasons, some of which have been mentioned in other posts. But I’ll stick with the data and conclude that this has been a disaster if we want STEM for all. However, I don’t believe that this was what California had in place prior to the PSAA of 1999. Because of the PSAA demands, the bar has been pushed rather high without a clear plan on how to get there.

    As for where is Algebra used in real life, well, it is necessary for having basic numeracy skills (like calculating tips, discounts, compound interest, etc). I believe, however, that trying to teach statistics without Algebra II is a mistake. For that matter, geometry, which usually includes trigonometry, teaches many spatial concepts and should come in handy in many trades. For instance, I doubt that you can get anywhere in a modern machine shop unless you’ve got a good understanding of Algebra I and II, trigonometry, and geometry. And all trades where anything is built (housing, design, tailoring, etc.) require them too. Granted, a clerical worker will probably never have to use these concepts, but why should we reduce the opportunities for future retraining simply because we let high schoolers bail out on these classes?

    Replies

    • Manuel on December 9, 2012 at 11:29 pm12/9/2012 11:29 pm

      • 000

      oops. White space was not preserved on the table above. Please note that the first column is the year, the second the number of 8th graders taking the Algebra I CST, the third the number of non-8th graders, and the fourth the number of 8th graders taking the ELA CST.

      (It would be nice if there was a preview button as well as a short tutorial on the use of HTML-like commands, if any.)

      • Gary Ravani on April 8, 2014 at 5:22 pm04/8/2014 5:22 pm

        • 000

        Manuel:

        First, I fail to see any magic in the demands for a 4th year of math for all students and/or STEM for all either.

        One of the key problems for education in the state and nation has been the narrowing of curriculum due to the emphasis on those courses, the testing in math and ELA, and the consequent loss in classes for a well rounded education; e.g., social sciences, art, music, and industrial arts, agriculture, even actual science, etc. The obsession on A-G has also contributed.

        Some industrial arts teachers have worked to make their courses more academic to qualify for A-G status. Who would object to this? Many of the same trade unions who run the training programs for the trades you mention. Many students who are trade oriented will happily learn the applied applications of higher math, geometry, etc., when they are just that: applied. To make them overly theoretical, as often required by the A-G process, makes the courses unattractive to those oriented toward the trades. And remember, no one is going to send plumbing jobs to a call center in Bangalore.

        This gets us to the whole question of “A-G for all” and “college for all,” as much as it has become a fetish in some circles. Today the US has 30+ percent of the population with a BA at minimum. That is a historical high. Where is the comprehensive discussion about what that % ought to be? It is known that many with BAs are working at jobs that don’t require a BA. There are reports that in STEM occupations there is a current surplus of qualified workers and flooding the employment market with more is simply lowering the comparative advantage of those currently qualified, thereby lowering salaries.

        And then there is the question of international competitiveness. There was a report that China turns out thousands more “engineers” than the US. Then it was found that those “engineers” had the equivalent of an AA in the US.

        When it comes to A-G, math, or college, just “more” is too simple an answer.

        • Manuel on April 8, 2014 at 11:08 pm04/8/2014 11:08 pm

          • 000

          Gary, it’s been a long time since I wrote that comment so forgive me for perhaps not understanding the gist of your comment. The demand for a 4th year was not my idea. Someone in the UC Office of the President must have pulled that out of some committee. In fact, it makes no sense, at least to me, for UC to ask for students to take calculus since very few are allowed to skip the first year of calculus at UC, not even those with 5s in their AP (oh, sure, you might be able to do it with a petition, but good luck with that).

          Since I am not, nor have I ever been, a high-school math teacher, I couldn’t tell you how “theoretical” the approach to the teaching of algebra, geometry and trig is. I do know that none of those courses teaches higher math (and, trust me, I know what higher math is). I also do know that when CNC lathes were introduced at our local machine shop, some of the operators there bemoaned not having paid enough attention when taking trig and geometry back in high school.

          Anyway, I once took a look at the CST scores of this high-performing magnet that shall remain nameless. What I found is that about 30% of students were able to take Algebra I in 7th grade but the rest followed the typical path of most high school students. By the time this cohort made it to 11th grade, their CST distribution looked like any other school: a good number of them could barely pass algebra II. And all these kids had ELA CST scores putting 70% of them above proficient. Math is a tricky thing to teach in California. I’m sure they could improve those numbers, but it takes, I think, effort.

          And you are rigth, “more” is not the answer so I don’t see why so many insist on 100% of students must take A-G. That’s insane.

          • navigio on April 9, 2014 at 5:21 am04/9/2014 5:21 am

            • 000

            I think ‘x for all’ policies are a response to the market forces that have created an ‘x for none’ reality in some/many of our schools. in other words, its more about access than about what eventually happens. its too bad we have to ‘force’ ourselves to make fair policy.

          • anon on June 14, 2014 at 8:28 am06/14/2014 8:28 am

            • 000

            AP calculus is an unofficial prerequisite to UC calculus. Most students who come in without high school calculus fail UC calculus.

        • Don on April 9, 2014 at 8:41 am04/9/2014 8:41 am

          • 000

          I couldn’t believe I was reading this. You’re seriously advocating that we produce fewer college-educated people in this country? I wonder how many of your fellow teachers would agree to dumb down your profession to produce candidates for apprenticeships that don’t exist. We certainly wouldn’t want to flood the market with highly qualified personnel and lower the bargaining power of those already employed, especially when you can still throw in a line of a pier in a pinch.

          It won’t be long before your job is taken over by a call center in Bangalore. And you know why? Because they have plenty of college educated people.

  8. Tracey on December 8, 2012 at 10:47 pm12/8/2012 10:47 pm

    • 000

    I’m an educator in Australia so I’m not sure I follow all the data in this article. But, as I say to my Middle School students, Algebra is the arithmetic of High School. Just like we need basic arithmetic (addition, subtraction, multiplication and division) in all the strands we study in Elementary School (Geometry, Measurement, Chance and Data), we need Algebra to solve all problems, in all Math strands, in High School.

  9. Ze'ev Wurman on December 7, 2012 at 9:29 pm12/7/2012 9:29 pm

    • 000

    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.

    Replies

    • Dave on December 8, 2012 at 11:36 am12/8/2012 11:36 am

      • 000

      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.

      • navigio on December 9, 2012 at 1:30 pm12/9/2012 1:30 pm

        • 000

        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.

        • Dave on December 9, 2012 at 10:34 pm12/9/2012 10:34 pm

          • 000

          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.

  10. LC on December 7, 2012 at 1:57 pm12/7/2012 1:57 pm

    • 000

    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).

  11. Dave on December 7, 2012 at 1:39 pm12/7/2012 1:39 pm

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    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/

  12. Ze'ev Wurman on December 6, 2012 at 7:46 pm12/6/2012 7:46 pm

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    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.

    Replies

    • Michael Paul Goldenberg on December 7, 2012 at 3:15 pm12/7/2012 3:15 pm

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      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.

  13. john mockler on December 6, 2012 at 2:36 pm12/6/2012 2:36 pm

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    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.

  14. VR on December 6, 2012 at 2:08 pm12/6/2012 2:08 pm

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    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.

  15. Leslie Parker on December 6, 2012 at 1:02 pm12/6/2012 1:02 pm

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    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?

    Replies

    • el on December 6, 2012 at 1:32 pm12/6/2012 1:32 pm

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      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.

  16. navigio on December 6, 2012 at 12:41 pm12/6/2012 12:41 pm

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    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

  17. John Fensterwald on December 6, 2012 at 12:31 pm12/6/2012 12:31 pm

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    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.

    Replies

    • el on December 6, 2012 at 1:23 pm12/6/2012 1:23 pm

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      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.

    • Gary Ravani on December 7, 2012 at 3:44 pm12/7/2012 3:44 pm

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      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.

    • Derek on December 7, 2012 at 7:31 pm12/7/2012 7:31 pm

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      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.

      • George DeMarse on August 30, 2013 at 11:34 am08/30/2013 11:34 am

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        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

  18. el on December 6, 2012 at 10:41 am12/6/2012 10:41 am

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

    Replies

    • navigio on December 6, 2012 at 11:42 am12/6/2012 11:42 am

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      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)

    • George DeMarse on July 1, 2013 at 10:02 am07/1/2013 10:02 am

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      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.

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