'Algebra for all' flunks the test

Pushing algebra for all students has failed to prepare low-achieving students for college,  reports Education Week.

• An analysis using longitudinal statewide data on students in Arkansas and Texas found that, for the lowest-scoring 8th graders, even making it one course past Algebra 2 might not be enough to help them become “college and career ready” by the end of high school.

• An evaluation of the Chicago public schools’ efforts to boost algebra coursetaking found that, although more students completed the course by 9th grade as a result of the policy, failure rates increased, grades dropped slightly, test scores did not improve, and students were no more likely to attend college when they left the system.

Students with very poor math skills are “misplaced” in algebra classes, concluded Tom Loveless in a 2008 Brookings Institution paper.

“No one has figured out how to teach algebra to kids who are seven or eight years behind before they get to algebra, and teach it all in one year,” said Mr. Loveless, who favors interventions for struggling students at even earlier ages.

Algebra-for-all policies were a reaction to research showing that remedial math is a dead end, especially for low-income and minority students, while algebra is a “gateway” to advanced math classes and then to college.

But putting all students in the same math class seems to have held back the high achievers without doing much for the low achievers, says Elaine M. Allensworth of the Consortium on Chicago School Research.

“Meanwhile, the kids who weren’t taking advanced classes before are taking them now,” she said, “but they’re not very engaged in them. They have high absence rates and low levels of learning.”

Some districts now are double-dosing, requiring low-scoring students to take a math “readiness” class at the same time they take algebra. In many schools, algebra teachers “spend a very large portion of that year on basic arithmetic,” said William Schmidt, a Michigan State education professor.

It seems obvious that schools should teach arithmetic in elementary school to give students a shot at learning algebra in eighth or ninth grade. Why isn’t this happening? And if detracking holds back the good students, frustrates the poor students and exhausts the teacher, why keep doing it?

Update: Students who worked in a computer lab on a pre-algebra and algebra learning program outscored similar students taught in a classroom, reports What Works Clearinghouse.

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  1. one reason to keep doing it is so that middle school and elementary school know where to aim.

    clipping students out of algebra effectively derails them out of college.

  2. I believe the answer is embedded in your post:

    “Algebra-for-all policies were a reaction to research showing that remedial math is a dead end, especially for low-income and minority students, while algebra is a “gateway” to advanced math classes and then to college.”

    Given the unfortunate history of discrimination in our country, fairness has come to mean that everyone gets the same education at the same time.

  3. Algebra only helps students get to college if they pass Algebra, and if the Algebra class they pass is really a standard Algebra class. FAR better to take an extra year for getting the K-8 curriculum down, then take Algebra, than to take it in 9th grade and flunk.

  4. Algebra is one subject that can give the students the assurance that they can go to college. They really have to pass this subject.

  5. Why don’t elementary teachers teach arithmetic? Because we’re forced to teach fuzzy math!

  6. “Why isn’t this happening?”

    Why don’t you think it is happening? You think they aren’t teaching it? Of course they are teaching it–or trying to. It’s just not easy to learn fractions, percentages, and proportional thinking.

    They’ve dumbed down math in the earlier grades quite a bit to give the illusion that all students are learning the same thing. All it’s doing is slowing the strong kids down a bit, hurting the mid-range kids more, as they’d be doing better wiht more direct instruction and rote, and not doing the low ability kids any good at all.

    But they are teaching it. That’s all fifth through seventh grade is, in most schools–proporational thinking, fractions, and math facts.

  7. Student of History says:

    Teach? said it well. Many districts or schools and occasionally states require discovery math, sometimes out of well-intentioned naivete and others because of the terms of accepted grants.

    That’s what the Seattle lawsuit was ultimately about-the ability to teach math content directly and sequentially using examples. Without that option for unknown information too many students are failing to master arithmetic.

    Authentic Algebra requires the foundation of arithmetic. Too many American students are not getting the instruction or textbooks they need despite great expense, initially and remedially.

    This all goes back to that 1989 idea that “no student will be denied access to the study of mathematics in grades 9-12 because of a lack of computational facility”.

    No denial doesn’t mean it will work out well.

  8. Unfortunately, what is too often taught in 5-8 is not authentic pre-agebra anymore. Look at many of the popular texts in use. You will understand exactly why students are not prepared for algebra. High classroom grades and scores on fuzzy math tests cannot indicate a students’ readiness for authentic algebra.

    We’ve got to get the junk math out of our schools and stop MISLEADING parents and students that it can prepare them for college. It’s not possible – JUST LOOK AT THE LACK OF REAL CONTENT.

  9. I remember when it was reported, decades ago, that kids who took algebra I in 8th grade did better on several measures. Of course they did; that was the honors track, so the kids in that group were at the top of the academic pyramid and had the prerequisite knowledge and skills. It was correlation, not causation, with 8th-grade algebra serving as a proxy variable for identifying the top students. That was also true of the relationship between taking Latin and other positive outcomes because only the top students took Latin. It is the same for various other factors, such as number of books in the home.

    Absolutely, we should have more kids taking the top math route, but they must be ready for it. That means the prerequisite knowledge and skills must be fully mastered, starting in kindergarten and progressing in a sequential, integrated manner each year.

  10. It’s also true of foreign language study. The correlation between foreign language study and college attendance is very high, not because studying foreign language increases intelligence, but because most colleges require 2-3 years of language study in their applicants.

  11. I may be wrong, but I seem to remember that, back in the 1960’s when I was doing it, everyone had to take Algebra I. Algebra II was optional (although I think few opted out), but Algebra I was required.

    When did that change?

  12. I think we just don’t move kids fast enough through math in the lowest grades. We homeschool, and I started my kids on multiplication in grade 1. My grade 7 daughter is currently working on a grade 11 textbook. Sure she’s smart, but most of it is just because we gave her good grounding early. In Asia and Africa, kids are typically 2 years ahead in terms of what concepts you learn when than here in North America.

    But the problem with remedying it by requiring that all kids take algebra is that you start teaching to the lowest common denominator, and then the kids who understand it lose out. It’s not fair to the bright kids, and yet it’s the bright kids who usually get overlooked, because people figure they’ll succeed anyway.

  13. My grade 7 daughter is currently working on a grade 11 textbook.

    There’s no such thing as a “grade 11” math textbook.

    In Asia and Africa, kids are typically 2 years ahead in terms of what concepts you learn when than here in North America.

    Parts of Asia, yes. Africa? Come on.

  14. The BIGGER question is WHY do SO MANY kids NOT learn????????? and what can be done about it???

    The focus is always on the curriculum, the textbooks, fuzzy math, non-fuzzy math, teachers, standards, etc. etc. BUT NEVER on the students themselves.

    Dr. Sharon Griffin http://www.clarku.edu/academiccatalog/facultybio.cfm?id=39 has translated her research findings into a curriculum – Number Worlds: http://www.sranumberworlds.com/ to get kids from disadvantaged backgrounds (not necessarily just social but a lack of intellectual stimuli for proper brain and cognitive development) up to speed or close to on par with kids whose parents surround them with such a richness = board games to help development of the NUMBER LINE CONCEPT, puzzles, investigations, etc. that are CRITICAL for proper cognitive development. The GOAL of elementary education should be for EVERY student to be NUMERATE, to have automaticity and fluency in the Basic Facts, and understand PLACE VALUE!!! EVERY student who has these attribute WILL PASS – a BETTER word is MASTER Algebra 1 without fail. They will even be able to MASTER Algebra 2, trigonometry, Pre-Calculus, and Calculus. Those who do NOT have these attributes by the time they reach 9th grade in high school (this is like the auto assembly line = just keep moving the faulty product down the assembly line) WILL FAIL and they do so as this discussion board is showing and EVERY high school teacher of mathematics knows.

    Only when these issues, not just FREE breakfast and FREE lunch – which are important to get the right food for proper brain and physical development – are addressed will there ever be any improvement in the Achievement Gap by bringing the LOW achieving students UP rather than decreasing this gap artificially by bringing the HIGH achievers down.

    Entry to high school should require a PLACEMENT TEST for Mathematics and English just like they do in the run of the mill colleges where upwards of 40% of incoming freshman MUST take REMEDIAL classes in these subjects. The same should be done in high schools!!!!!!

    The Emperor/Empress is NAKED, everyone knows it, BUT is any district REALLY doing anything about getting him/her some clothes???

  15. There is a fair amount of nuance in the reports that is missed. Dr. Schmidt has a fair amount of research that goes into exactly what is happening inside of classrooms, as compared to what is stated in the curriculum, required by the state or presented in the textbook. The reality is that there is no standard set of anything associated with even such a concrete sounding thing as “Algebra I.” Further, the people who teach “Algebra I” have a very wide range of qualifications–from actual college majors in mathematics to those who have only take “math education” courses, not to mention those who have no related qualifications at all but were needed to fill a slot in mathematics (and through NCLB HQT reqs have been granted the opportunity to be declared Highly Qualified by summarizing a patchwork of experience and summer workshops).

    What does appear to be the case–based on research over time–is that the kids who are assigned to the non-achievement tracks (by whatever mechanism this takes place and whatever they are called) do not achieve. They don’t catch up. They are never exposed to the same curriculum as the kids who are identified as either regular or top of the heap. A kid doesn’t get to be seven or eight years behind overnight. They get there through a systematic process of being cycled through the same ineffective methodology for a decade.

    I believe that there was noted in the research that while passage rates in Algebra I did not show success, actual knowledge of Algebra increased.

    There simply are no simple answers. Declaring that all children will take Algebra I in 8th grade is insufficient if there are not concurrent efforts to ensure that all teachers who teach Algebra are competent, all children arrive at the 8th grade adequately prepared to handle Algebra, and that those who require additional assistance at that point (as well as all earlier points) actually receive meaningful additional assistance.

  16. I teach Algebra, and last year taught Algebra Support–one of the classes that helps at risk students get an extra hour of teaching. I’m teaching at the high school level, which means that the students have already had from 1-3 years of algebra, depending on their grade, and have failed it at least once. I’m also teaching at suburban high schools, teaching kids who range from low to high income, but who have all had teachers with either a math degree or (as I have) passed the math single subject CSET, which is probably a better indicator than a math degree.

    I teach algebra in a fairly “squishy” fashion (algebra tiles for the weak students, not too much discovery). It’s not hours of boring lectures, I spend tons of hands on time with all my students. Currently I have a very small class–just 14 students.

    Algebra is incredibly difficult for some kids to learn, and it’s not exclusively linked to incoming math knowledge. Over the years, I’ve worked with several kids with excellent basic math facts, who know multiplication tables quickly and easily, who have struggled for months to learn how to solve for a single variable. I’ve known kids who have to reach for a calculator to divide 48 by 6 who are otherwise exceptionally strong at algebra. And, of course, I’ve worked with kids who lack both math facts and who, after six months, can’t solve a single variable equation.

    I’m a pretty good teacher, as teachers go. It’s not about the teachers. It may be about the method of teaching, but if it is, then we haven’t discovered the right method yet–and that method is one that we will have to admit can only be used for students who can’t learn algebra the “normal” way. I actually think that mental development has something to do with it. I’ve seen more than one 17 year old finally “get it”, after four years of failure.

    But this whole problem begins because we can’t admit that kids have a wide cognitive range that requires different educational metrics and schedules, and that these ranges aren’t evenly distributed by race and, to a certain extent, income.

    A kid doesn’t get to be seven or eight years behind overnight.

    No. They get to be seven or eight years behind after seven or eight years. If you keep teaching a group of kids the same thing, with no recognition of their different cognitive abilities, then some of the kids won’t learn at all. Until we recognize, however, that even the most perfect outcome will result in some kids being two years ahead and others being three years behind, we’re not going to have much success at cutting the gap.

  17. Hobson’s choice: either assign a student who is a few years behind in math skills to Algebra in 9th grade, or assign her to a pre-Algebra class that will work on bringing those skills up to Algebra-readiness level. In the first instance, the student will be “exposed” to higher level math, but doens’t have a very good chance of mastering the material, passing the class, and moving on to other college-prep math classes. Maybe a few of the unprepared will catch up on their basic arithmentic skills thanks to a simultaneous Algebra Support class, but others would (pedagogically speaking) benefit more from an extra year before taking on Algebra. However, all of these struggling students in 9th grade Algebra will be in a class that also has students who are at grade level and maybe above grade level; they’ll be in an atmosphere where at least some students are moving along, and that tamosphere surely does count for something. In the second instance, no matter what the content of the pre-Algebra class, the struggling students will see only other struggling students around them, and it is this reality more than the actual content of the class that makes for the “dead end” designation of the class. So, which is worse, giving students a set of classmates that includes high achievers, but no instruction that meets them where they are, OR giving them instruction that builds on where they are but no higher-achieving classmates? Actually, both of these are bad options, but of the two I’ll take the second any day. At least it doesn’t decieve students and parents into thinking that Algebra is being learned when it is not. And I speak as the mother of a student who was passed along and passed along until she crashed into the wall in Algebra 2, where she had no idea what was going on at all. That experience didn’t do wonders for her confidence, let me tell you.

  18. Lets break it down to exactly where the problem is, and that is the lack of ability to perform the following functions (which should be learned in grades 1-5):


    Without a SOLID mastery of the above items (without the USE of a calculator) no student will be able to succeed in algebra I or higher math.

    Math teaches critical thinking, problem solving, and analysis. I would have to say that math doesn’t care how you feel about yourself, it doesn’t care about your parents feel about math, and given what passes for math textbooks these days, it is no wonder why programs like Sylvan, Kumon, and Singapore math are in such demand by parents of school age kids who want to ensure their kids get a proper education.

  19. IMO,

    A student who hasn’t mastered the six basics I stated in my previous post has ABSOLUTELY no business taking Algebra I (or higher math beyond that) due to the fact that they will simply fail the course outright.

  20. Bill, I’d add decimals and the relationship of decimals, fractons and percentages.

  21. andrei radulescu-banu says:

    Bill, I would place percentages after fractions, and I would also take them off the algebra prerequisites list. I would add to the list operations with units of measurements, which are badly neglected in the K-5 sequence.

    The reason some students just can’t ‘get’ algebra by the time they reach Cal’s high school class is simple – variables and simple equations need to be introduced gradually from 1st grade, and not back loaded after 9th grade. Start with those X+1=2 problems in 1st grade, and with things like 2x+3=x+4 in fourth grade.

    It’s not the children’s fault that they are not getting it. They are not born some smarter than others. Algebra is simple, you don’t need to be Mozart to learn it, although I’ll be quick to point out that he had a pretty insistent father that taught him a lot.

    As ‘teach?’ points out, the problem is the fuzzy math forced onto the elementary grades that does all the damage. It’s the TERC Investigations, the Math Trailblazers and the Everyday Math curricula, heavily sponsored with federal dollars from the Education and Human Resources Division of the National Science Foundation. Barry Garelick summarizes the entire scandal here:


  22. PS: foreign language instruction as conducted by the US military is a good example of how to align instructional level with readiness. They don’t let you proceed to the next level until you master the current level, thus demonstrating readiness to move on. If you are having a hard time mastering the current level, they don’t pass you on, they expect you to study outside of class time in order to keep up.

    Of course, children are not adult language specialists-in-training. They need someone else to figure out whether they’re catching on and mastering content, and to provide the extra practice, re-teach the missed material in a different way, OR provide the same material at a slower pace.

    The high school and college drop-out rates in our country come partly from the fact that being exposed to a topic is not the same as mastering it, and there are many subjects where mastery is required.

  23. Start with those X+1=2 problems in 1st grade, and with things like 2x+3=x+4 in fourth grade.

    Right now, very few children are being taught variable manipulation by fourth or fifth grade. Yet around 40% of kids get variable manipulation immediately in 8th grade, so clearly, it is not necessary to introduce variable manipulation early in order to master algebra.

    And the idea that a kid who hasn’t mastered basic addition and multiplication facts by 8th grade is going to have grasped variable manipulation in fourth is not really a credible proposition.

    They are not born some smarter than others.

    Yeah, actually, they are. Cognitive differences are real, and our failure to accept them and work within them has caused us to waste a lot of money.

  24. Algebra is a “gateway” course because it sifts out those who are capable of abstract thinking and those who are not.

    Let me tell you something: my AP English students are not taking Integrated Math — kids who are smart and college ready are smart and college ready. They may not be taking Calc II (our highest course), but they have sailed through algebra. My remedial English kids are not taking Alebra II Trig, either. (And all these kids went through the same system together with no tracking in math until 8th grade.)

    The emphasis should not be on Algebra for All, but Algebra for All who are Ready. Correlation, not causation.

    FWIW, my kid is the one who uses a calculator all the time (and we did multiplication tables for YEARS…) but is a genius in algebra. Reduce a fraction? Dicey. Calculate slope — doesn’t even have to think about it.

  25. It seems that a lack of grounding in the basics (covered in previous posts) appears to close the doors on many careers which students might be good at, but never get the chance to experience due to lack of preparation in reading, writing, math, and science. I learned all of these concepts before the common use of calculators (which were just becoming affordable in the late 70’s).

    Without the basics, students will never have the skills to succeed in higher level courses in middle/high school, or college and/or CTE (career & technical education).

  26. “Without the basics, students will never have the skills to succeed in higher level courses in middle/high school, or college and/or CTE (career & technical education).”

    But how can students learn these skills when their elementary teachers don’t have the skills and certainly have no idea how to teach them?

  27. andrei radulescu-banu says:

    Cal, the way math is structured, concepts are learned then revisited multiple times in a different light. One reason to sneak Algebra into elementary grades is precisely because it will help the understanding of the multiplication and division algorithms.

    The PISA international tests for 15 years old show us in the bottom half for performance among countries with advanced economies; at the same time, TIMSS tests show our 4th graders doing quite well. It is apparent from these statistics that the math learned in our elementary schools serves as a very poor basis for the math that shows up in high school.

    And you don’t need to rely on these statistics to make the judgment – it is readily apparent that our elementary school math text books are full of games, fun facts, maps of the world and pictures of the rain forest – and are pretty thin on actual mathematics content that can serve as a basis for later learning.

    On the subject of cognitive differences, Richard Nisbett has a nice summary of the state of the art in “Intelligence and How to Get It: Why Schools and Cultures Count”. He explains that the only experiments to prove to what extent intelligence is innate consist of IQ tests on identical twins separated at birth through adoption. These tests do indeed show correlation of intelligence between twins; however it is uncertain to what extent they give a correct picture – it is very likely that tiny differences in intelligence at birth get exacerbated as children grow by societal and cultural attitudes around them.

    On the other hand, Nisbett describes how IQ scores have been rising over generations – this is the so-called Flynn effect – in correlation to increase in school attendance and to the rise in sophistication of the school curriculum. This historic rise in IQ scores is too great to have a genetic, natural selection explanation. In other words, we are historically becoming smarter because we learn more.