Flunking 8th-grade algebra

California eighth graders are supposed to take algebra, according to standards adopted in 2003.  That’s boosted the number of eighth-grade algebra students by 80 percent, concludes a study by EdSource, working with Stanford and American Institutes for Research.  Expectations are high. But performance is just what you’d expect.

Low-scoring students placed in algebra have “almost no chance for success.” Nearly a third of students with “below basic” and “far below basic” scores were placed in eighth-grade algebra.

Not surprisingly, students who were proficient in seventh-grade math tended to be proficient in eighth-grade algebra. “Basic” students in seventh-grade math who were placed in eighth-grade algebra tended to score “basic” on the exam.

Not rocket science.

Low-scoring students should spend eighth grade learing the math skills that will give them a shot at passing algebra in ninth grade, researchers concluded.

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Comments

  1. As an “old” math teacher turned administrator, I cannot agree more.

    Several factors need to be considered. First, algebra is a develompmental concept. Some very capable eighth graders simply do not have the developmental skills to master algebra. That doesn’t make them poor students. To the contrary, we should celebrate individual differences in children and allow for them. Countless times I’ve seen 8th graders pushed into algebra, many times by well-meaning parents, only to watch them struggle and ultimately begin to believe they are dumb in math, or that math is hard. The only thing they needed was an additional year or two to mature, when algebra suddenly becomes easy.

    Second, experiements in other states such as Texas have show the truth behind the push for all high school students to master high-level algebra. Most schools there have courses such as Algebra 1A and Algebra IIA which simply track students according to math ability. But we can say that every student is taking Algebra I and II.

    I agree that we need to set high standards. No argument about that. But let’s be realistic about the individual differences and abilities in young people.

  2. For only half the money, *I* could have told them the same thing. No need to spend big money on those high-falutin’ researchers, especially if they’re going to tell us what most of us already know.

  3. I don’t really understand where this push to have everybody take Algebra comes from. I would think we’d be better off if people really understood basic math (including fractions, decimals, percentages, exponents, etc), even if it took all 12 years to get to that point. A lot of people don’t have to use algebra to get through their day – it might make solving some problems easier, but the arithmetic would be more helpful.

    I also wonder about the age – I was in a highly accelerated program and struggled with 7th grade algebra, but found it very simple in algebra II in 9th grade – it was all developmental. A student who isn’t ready from a developmental or a math perspective has almost no chance of success. Poor kids.

  4. They certainly can’t spend the elementary years with Everyday Math and then spring proper Algebra on the kids in the eighth grade. That’s just cruel. My homeschooled children have been very successful with Saxon Algebra I in eighth grade, but they were solid in arithmetic by the end of sixth grade.

  5. Lu-Lu, the push for Algebra in earlier grades is done by people with an incomplete understanding of mathematics (statistics). They see studies that people who took algebra earlier are more likely to have success in high school and college, and assume that correlation equals causation.

    They infer that early algebra classes are causing them to suceed in later years, instead of that another factor is why students are in algebra earlier, and why students suceed in later years.

    A lot of educational policy is caused by people with no idea of what real research is, how it is interpreted, or how to actually analyze data and the trends underneath of it. In some cases, ideology causes them to ignore underlying reasons.

  6. lu-lu; The 8th-grade algebra idea dates back to research done at least 20 years ago, which found that kids who took algebra in 8th grade did better (various measures) in HS and on SATs. The ed world, being unable to understand the difference between correlation and causation, immediately jumped to the conclusion that the algebra was the magic remedy. The fact that 8th-grade algebra was then honors-level only, for the top students, was conveniently ignored. The same conclusion was repeated with Latin, modern foreign languages and debate, and has now moved to pre-calc and calc; all of which factors essentially serve as proxy variables for the identification of the most able and most motivated students.

  7. If kids had proper math instruction K-7, most of them would be ready for 8th grade algebra. Plenty of other developed nations manage to do it. The problem is that kids get passed along from grade to grade without having mastered the necessary skills. Also, far too many students are stuck in schools using awful curricula like Every Day Math, TERC Investigations, and so on.

  8. Roger Sweeny says:

    The idea of algebra for all owes a lot to Bob Moses and his book Radical Equations: Math LIteracy and Civil Rights(2001) Moses argued that anyone who didn’t take algebra was shut out of most STEM jobs and a lot else, besides. Moses is affiliated with a group, the Algebra Project, that has actually done algebra teaching to people who wouldn’t have taken it years ago. That has given the idea credibility. Of course, like so much in education, there is tremendous difficulty transferring something from a small group of committed people to everyday practice with everyday people.

  9. I’m with CW on the curriculum issue – and I gather that VERY few public schools use Singapore or Saxon math, which could make a huge difference IF there was enough math expertise among ES teachers to enable them to teach it well. By the time kids arrive in MS, far too many are hopelessly behind. The disdain for solid mastery of math facts and the related far-too-early use of calculators are also part of the problem.

  10. I have to agree with CW and Momof4 as well. A student (regardless of age, race, income, whatever) is not going to succeed in Algebra (at any grade level) unless they have the necessary skills in grades 1 through 7 is a documented fact.

    Being shut out of a STEM job (I work in this field, information technology/security) isn’t the end all to everything, but a person who struggles with basic math concepts (add, subtract, multiply, divide, fractions, percentages) and more advanced concepts like graphing, exponents, base notation (which I use a lot of in my field), and so on is going to have nothing but trouble in algebra (forget trig if you haven’t mastered fractions).

    I was watching some old school house rock video clips on youtube yesterday, and was amazed at how well the math segments were presented (Naughty Number Nine, Four-legged Zoo, Lucky Number 7, Zero my Hero), and educated an entire generation of students (math, science, government, grammar, etc). A student who has mastered the basics can be taught more advanced math (at the correct pace), but a student who doesn’t know the basics will have the door closed to them in many fields, not just STEM careers.

    An example of this, there was a job fair held last month by employers looking for employees who work with money (cashiers, waiters, etc), but several managers present lamented that approximately 80 percent of the applicants could not do basic math (even with pencil and paper), and these aren’t STEM type jobs.

    I don’t think I want a whole society of Einsteins, but I do want high school graduates who can perform the basics without having to struggle. I also agree that the way math is taught to elementary and middle school kids is atrocious and must be completely overhauled (get rid of the calculators in elementary and middle school, start using them when a student reaches algebra II/Trig).

  11. Three recent examples of the math ability of some people who have full-time jobs:
    (1) a salesman at a mall kiosk who couldn’t figure 5% sales tax on a item costing $10.00 when his computer died, either with a calculator or on paper

    (2) a deli clerk and his manager both assured me that they were unable to measure 2/3 of a pound on a digital scale, even when I supplied the decimal version (they finally condescended to keep loading until I said “stop”) .

    (3) a bakery clerk who not only couldn’t make change when given $3.05 for a purchase of $2.85 but couldn’t figure out how to plug the problem into her calculator.

    The brightest spot? Farmers’ markets; both kids and adults. However, a number of the most fluent kids are homeschooled.

  12. I’ve had experience #1 and #2 personally, haven’t run into number 3 (yet). A pretty sad commentary on the lack of knowledge in our society today (in the case of #2, the deli clerk told me she didn’t know what 2/3rds of a pound was on the scale, just having barely passed college algebra).

    How she managed to do that and not know how to convert a fraction to a decimal and back simply boggles the mind.

  13. Bill, “college algebra” probably was (1) neither of those or (2) test answers were essentially provided or (3) the grading was a farce, and possibly all three.. The same game is played with k-12 algebra. Years ago, I remember reading that the Montgomery County, MD Board of Education was shocked! shocked! to discover that each school had their own pass rate for the countywide algebra I exam, even though it had been an open secret for years and even though it was also well-known that only certain high schools’ coursework actually matched the countywide course descriptions (those schools required real passing grades).

  14. Cardinal Fang says:

    If a class’ name starts with “College,” it’s not a college-level class at all, but a remedial class. “College Algebra” is high school algebra. “College Writing”? Ninth grade English. “College Math”? Seventh grade math.

  15. I’ve lost track. Do we believe, for the purposes of this discussion, that students are proficient in 7th grade math due to instruction or due to intelligence? If we think that schooling makes a difference, why would we think that a system which can’t produce proficient 7th grade math students would produce proficient algebra students?

    “Low-scoring students should spend eighth grade learing the math skills that will give them a shot at passing algebra in ninth grade, researchers concluded.”

    This assumes that the reason the students aren’t learning algebra lies with the students, and only the students (and their families). Our schools in this country are wildly uneven in quality. It might be true that a student who hasn’t learned the necessary math skills in Greenwich, CT, has had the benefit of good instruction. Is that true in every school in California? What if the instruction in a particular school is incompetent in every class? It’s hard to find good math teachers. Many parents can’t support their students at home, because they themselves never mastered math.

  16. Cardinal, unfortunately, many colleges keep admitting students who have absolutely no business being there (and lets call college what it is, a BUSINESS), racking up piles of debt for a piece of paper which guarantees nothing.

    As a nation, approximately one of every three students (coming directly from high school) needs remediation. Approximately 2/5ths of the group need two or more remedial courses. Studies are showing that if a student needs three or more remedial courses, there is a very good chance they will never finish a degree of any type (associate’s or bachelors).

    Approximately 57 percent of all college students have not finished a degree within 6 years, and the percentage of individuals holding degrees in the United States is between 25 and 35 percent (which is what it has been for the last 30 to 40 years).

    There was a time in this nation’s history (through most of the 80′s) where a high school dropout could earn a decent living, but this is no longer the case. A person who leaves school (either by graduating or dropping out) with a lack of basic skills is going to find their employment choices very limited in our society.

    Some students think of joining the military after dropping out of high school and getting a GED, but what the students fail to understand is that a GED holder requires a minimum score of 65 on the ASVAB in order to qualify for enlistment (or 30 credit hours of college level coursework, per military standards). A diploma holder only requires a score of 29 to 43 depending on which branch of the service they want to enlist in (Air Force requires the highest ASVAB scores for enlistment, the Army the lowest).

    We’ve watered down standards in high school, and now we’re starting to do so in college (where will it all end, I wonder)…

  17. Cranberry, to this day I still remember a statement which my 9th grade algebra teacher told me (1977-78):

    You guys and gals have no problem with algebra, you just can’t add, subtract, multiply, and divide.

    Amazing how it always comes back to basic concepts.

  18. If kids had proper math instruction K-7, most of them would be ready for 8th grade algebra.

    This is absurd. It assumes that all kids are of equal ability.

    Do we believe, for the purposes of this discussion, that students are proficient in 7th grade math due to instruction or due to intelligence?

    There is no “we”. You and Cranberry want to argue it’s instruction. Most sane people know that cognitive ability is the best predictor, with some line blurring near the middle.

  19. Mark Roulo says:

    Cal: “This [If kids had proper math instruction K-7, most of them would be ready for 8th grade algebra] is absurd. It assumes that all kids are of equal ability.”

    A question I’ve never found a good answer to is: Why does the rest of the 1st world (Europe, China, much of Asia) seem to get their kids to algebra by 8th grade (or, as nearly as *I* can tell, 7th grade), when it takes the US until 9th grade?

    I don’t think it is “tracking” … these countries don’t track that early.

    I don’t think the US kids are that different in cognitive ability (on average). Yes, some kids here won’t be ready and some kids there won’t be ready, but I don’t think that lots of non-US kids are crashing and burning when they hit algebra in 7th or 8th grade.

    What is so different about the US?

  20. When do schools test for IQ? SPED kids are tested in the course of qualifying for IEPs, and kids trying to get into gifted programs are tested, but unlike the good old (bad old?) days, as far as I know, no one administers cognitive tests to all students in any public school.

    It would be more fair if IQ tests were administered, rather than assuming that failing to learn basic math by the end of 7th grade equates to low intelligence. It might, of course. On the other hand, it might be a consequence of having 4 bad teachers in a row–or moving too frequently to keep track of math instruction–or frequent absences due to parental dysfunction.

  21. The reason why US students do so badly at math in grade and middle school is that the over-reliance on technology has caused students today to lose their computational skills which were routine in nature 30+ years ago in this country.

    I learned math at a time where scientific calculators (which were affordable) were just becoming available in the late 1970′s. I owned a TI-55 which cost around 100-120 dollars back then (a considerable sum of money for a teenager at that time). However, I learned my basic skills in math the old fashioned way, through repeated exercises using pencil and paper, memorization of basic mathematical facts, and quite a bit from school house rock during Saturday morning cartoons.

    The parents of students today are probably as weak in math as their children (in many cases), and the instruction children receive in math in elementary and middle school doesn’t help (I’ve seen Singapore Math and Kumon, and the concepts are like the math I learned in elementary, middle, and high school some 30+ years ago).

    The over-reliance on technology has ruined the basic ability of an entire generation of persons, and the US will only continue to worse, until we can get back to old school methods of learning math (I’ve seen the lattice method for multiplying numbers, would drive me completely crazy if I even attempted it). I ask you, what is so hard about teaching the concept of borrow and carry, etc in a classroom these days?

    I fear that math phobia has gripped this nation, and it will take many years of concerted effort to reverse that trend.

  22. Why does the rest of the 1st world (Europe, China, much of Asia) seem to get their kids to algebra by 8th grade (or, as nearly as *I* can tell, 7th grade), when it takes the US until 9th grade?

    This is so completely not true that one has to wonder how much else you don’t know.

    When do schools test for IQ?

    I didn’t say IQ, and you shouldn’t immediately jump to IQ as synonymous with cognitive ability.

    That said, yes, the best and most reliable predictor of academic success is cognitive ability.

    The reason why US students do so badly at math in grade and middle school is that the over-reliance on technology has caused students today to lose their computational skills which were routine in nature 30+ years ago in this country.

    Technology had nothing to do with that de-emphasis, and success in algebra is only slightly correlated with computational skills.

  23. tim-10-ber says:

    So…reading through the comments the problems caused by public school consultants, administrators and educators for kids taking math are: teachers in elementary school do not have (in general) true math skills to lay a solid foundation (same for countless middle school teachers). Then there is a generally weak curriculum and not tracking kids based on their on individual abilties and readiness to move to the next level regardless of the subject being taught. Does this cover it? So…isn’t this all the more reason to have academically qualified teachers by subject beginning with kindergarden or first grade. (The teacher candidates can take education courses appropriate to the grades they will be teaching but I keep hearing from teachers how education classes are a waste of time and money.) We need teachers that understand what it takes to read and comprehend what was read and how to teach it . We need teachers that understand math and how to teach it beginning the day kids set foot in school…I would say the same for science and in middle school the same for history. This is my wish list to help improve government schools.

  24. We need teachers that understand math and how to teach it beginning the day kids set foot in school…I would say the same for science and in middle school the same for history. This is my wish list to help improve government schools.

    This is exactly correct…go back to teaching students basic math by the time tested method of using pencil and paper (no student should be touching a calculator for math until they reach at least the 8th grade and have mastered the basics)

  25. My most “mathy” son, with a math master’s (not ed), says that calculators are both unnecessary and undesirable until pre-calc, although that’s no longer reasonable because kids must know how to use them well for the SAT.

    In addition to Tim-10-ber’s summary, there’s the issue of motivation/work ethic. Kids, families and communities need to put in the effort to do well in school. Some communities ridicule/insult good students. Dysfunctional families do not enforce the habits and behaviors necessary for learning. Education is an active process; kids need to work at it. I have issues with the ed world, but education starts with the families and far too many are falling down on the job.

  26. j.d. salinger says:

    I didn’t say IQ, and you shouldn’t immediately jump to IQ as synonymous with cognitive ability.

    You don’t say a lot of things, Cal, and you’re frequently wrong, though bristling with confidence and able to shut down whole conversations in a single bound. Bravo. Before you start condemning Mark Roulo and others who comment here, how much do you know about how math is taught in Asian countries? Are you familiar with the Singapore math series?

  27. To read/downloand the full Edsource report, go to
    http://www.edsource.org/iss-mgg-middle-math.html

    Since 2003, the chart available here

    http://concernedabouteducation.posterous.com/naep-performance-vs-authentic-preparation

    shows that California’s authentic Algebra prep is working!

  28. I don’t think that the cognitive ability of children of European descent in the U.S. is significantly different than the cognitive ability of European children. Yet the U.S. falls far behind European and other predominantly white countries in the percent of our white kids who reach the “advanced” proficiency level on 8th grade math tests. Are you really suggesting that white kids here in the U.S. have significantly lower cognitive ability than kids in Finland, Switzerland, Belgium, the Netherlands, Canada, New Zealand, the Czech Republic, Australia, Germany, Austria, Slovenia, Denmark, Iceland, France, Estonia, Sweden, the UK, Hungary, Poland, Norway, Ireland, and Lithuania?

    Of course, there is a range of math abilities. But I have a hard time believing that the U.S. has a disproportionately high share of dumb white kids compared to other developed countries.

  29. “What is so different about the US?”

    The US labors in the misconception that it’s everything but the curriculum: whether the teachers, the students, their families, and/or the broader culture. These things matter, but since so few people subject the curricula to the level of scrutiny they so readily apply to these other factors, an atrocious set of curricula has snuck into our classrooms–one that differs drastically from the various curricula used throughout continental Europe and Asia.

    Eradicating Everyday Math, Investigations, Trailblazers, Connected Math, IMP, etc., should be our utmost priority. Only after we accomplish this can we even begin to draw conclusions about how much these other factors contribute to our children’s mathematical shortcomings.

  30. Yet the U.S. falls far behind European and other predominantly white countries in the percent of our white kids who reach the “advanced” proficiency level on 8th grade math tests.

    Since when? We aren’t “far behind”.

  31. What is wrong with Singapore Math and Kumon that schools won’t adopt it? (one must wonder)…

  32. We aren’t “far behind”.

    That’s not what Hanushek found. See here. Notice how far down even the highest-ranking U.S. states are, not to mention the dismal U.S. average.

  33. Am I misreading that graph? You said “Yet the U.S. falls far behind European and other predominantly white countries in the percent of our white kids who reach the “advanced” proficiency level on 8th grade math tests”

    But the graph you cite isn’t broken down by race. The ones I know that are broken down by race has the US doing very well.

  34. From the study (emphasis added): “Without denying that the paucity of high-achieving students within minority populations is a serious issue, let us consider the performance of white students for whom the case of discrimination cannot easily be made. Twenty-four countries have a larger percentage of highly accomplished students than the 8 percent achieving at that level among the U.S. white student population in the Class of 2009.”

    Differences in cognitive ability is unlikely to be the reason why white U.S. kids lag students in other predominantly white countries when it comes to math achievement.

  35. It’s all about the “achievement gap”. The easiest way to narrow it is to prevent the top from moving further. Mainstreaming/full inclusion (meaning very heterogeneous classes, especially as kids age) and differentiated instruction work to prevent the most capable from being challenged and moving ahead.

    I remember a poster from my college days: “It’s hard to soar like an eagle when you’re surrounded by turkeys”, with suitable picture. It’s not PC, but NCLB really amounts to “let no child get ahead”.

  36. Engineer Dad says:

    Crimson Wife said:
    “Yet the U.S. falls far behind European and other predominantly white countries in the percent of our white kids who reach the “advanced” proficiency level on 8th grade math tests.”

    What 8th grade math test are you referring to? Please give references that indicate the percentages of American white and European kids who reach the “advanced” proficiency level.

    When broken down by ethnicity, American students do reasonably well compared to the countries from which their ancestors came. For example, the 2009 PISA Mathematics average results for American white and European 15 year olds are available on-line at the ‘IES National Center for Education Statistics’ and American white kids do very well.

    See here: http://nces.ed.gov/surveys/pisa/idepisa/dataset.aspx

    American white teens scored an average of 515, while German teens scored 513, France 497, Sweden 494, Britain 492, Portugal 487, and Spain 483. Its interesting to note that Belgium teens tied the US with 515, and Switzerland and Finland outdistanced the US with scores of 534 and 541, respectively.

    So as far as America’s attraction to Europe’s talented:

    “Toute personne ayant assez de motivation est déjà partie vers l’Ouest ou à l’étranger.”

  37. Well, I can remember when students in middle and high school were grouped by ability (based on testing done in middle schools, with stanines 1-3 meaning low, 4-6 meaning average, and 7-9 was high).

    Students grouped together by ability makes a lot more sense than we way we do it now, but I’m fortunate to have graduated before all the PC and self-esteem nonsense contaminated public education.

    NCLB is exactly that, let no child get ahead of any other child…

  38. Twenty-four countries have a larger percentage of highly accomplished students than the 8 percent achieving at that level among the U.S. white student population in the Class of 2009.”

    That’s an awfully complicated way of saying something he could have put in a graph, and there’s a number of ways of interpreting that sentence. So give me actual data. As has been mentioned several times, all data shows that US students do fine once you control for race.

    So to finish up: I said that the most accurate predictor of algebra success is cognitive ability. You are trying to break this argument by arguing that American whites do worse than European whites and thus are (by my reasoning) less cognitively able.

    I mean, do you ever really think this stuff through? Obviously, I’m not arguing that. Just as obviously, no data has ever shown major differences in European white vs. American white ability.

  39. What 8th grade math test are you referring to? Please give references that indicate the percentages of American white and European kids who reach the “advanced” proficiency level.

    Hanushek used the 2009 PISA results as basis for his study.

    American white teens scored an average of 515, while German teens scored 513, France 497, Sweden 494, Britain 492, Portugal 487, and Spain 483. Its interesting to note that Belgium teens tied the US with 515, and Switzerland and Finland outdistanced the US with scores of 534 and 541, respectively.

    Those are the overall averages, whereas Hanushek looked at how many of the students reached the “advanced” level. Are you okay with settling for mediocrity? I sure as heck am not sanguine about the performance of U.S. white students.

  40. CW,

    Given that the United States spends at all levels on K-12 education, some 550 Billion annually, we shouldn’t be settling for mediocrity. We out spend every other OCED nation in the world on Education (per capital) except for two I believe.

    If we want to see how badly we’re doing as a nation in education, one need look no farther than the percentage of students who need remediation in college who are admitted directly from high school (not an older student brushing up on their skillset), which is 33 percent.

    The fact that 33% of all students need one or more remedial classes is proof positive that our K-12 system failed to do the job when it comes to giving students a proper education in math and english.

    I remember what counselors said about classes needed for college (we had two tracks when I went to high school). It strongly suggested taking math (through algebra II/Trig), Science (including two lab sciences, chem/biology/physics/earth science), english (including literature (euro, american, etc)), and of course government.

    That level of preparation today (assuming students truly mastered the concepts) would give any high school graduate a skill set to be able to move on in life (voc-ed or college).

  41. Low scoring math students should be checked for a learning dysabiliy called dyscalculia. And then if found to hae it taught appropriately

  42. I feel some students are pushed through a math topic too fast when an extra week really digesting the material would have really helped cement the topic. I did not take accelerated math but had really good solid math teachers. I had no problem moving on to calculus in college without having already had a year of it in high school as many seem to do today. Good solid fundamentals are more important than racing through lots of material just to expose the kids to it. My kids would have done better with more repetition before moving on to the next topic. That would be boring for the kids that get it but not for the kids just on the edge.

    My younger son has a difficult time remembering math facts – he has to recount multiples on his fingers or use a calculator. This is a learning disability, not due to not enough studying. He has learned strategies to deal with this. It slows him down but it does not get in the way of his understanding the bigger math concepts.