Algebra for all California 8th graders

In three years, all California eighth-graders will be tested on algebra. Pushed by the governor, the state board of education voted 8-1 to enforce the long-standing eighth-grade algebra standard with an algebra test. No Child Left Behind forced the state to end the practice of letting some eighth-graders take an easier math test covering sixth- and seventh-grade skills.

The decision means that an intense ramp-up period is about to begin, as the state scrambles to hire and train more algebra teachers, align curriculum and get young students ready for more rigorous course work.

In essence, remedial math will be pushed into sixth and seventh grade. That’s better than waiting for high school to get serious about getting students caught up in math skills. Those who learn algebra in middle school will be able to take advanced math and science in high school.

Currently, 52 percent of eighth-graders take algebra, though many do so poorly they have to take it again in ninth grade. Before eighth-grade algebra became a state standard, only 16 percent of students took the course in middle school.

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  1. ucladavid says:

    This is extremely stupid and idiotic. I teach at a really good middle school in Los Angeles Unified and I tutor middle school kids 2x a week after school in math. It is way too soon and way too early for about half of these kids. Kids fail 6th and 7th grade math and get no consequences for that fail from the school. Thus, they fail 8th grade regular math and now you are forcing them to take algebra. Give me a break. Why force so many of these kids on a college track when for many of these kids just graduating high school would be an achievement?

  2. Ragnarok says:

    We must equalise intelligence. Since the private sector hasn’t done a thing about it, it’s up to the State of California to do it.

    Perhaps Sally Lieber would care to introduce a bill that would equalise intelligence by fiat?

  3. Children need to reach a certain stage in their cognitive development before they are able to successfully learn algebra. The time frame for this varies from child to child, and not every one will be ready by age 13. Pushing the subject before it’s developmentally appropriate will simply lead to frustration.

    I personally ran into a similar issue with calculus. I enrolled in it my senior year of high school and even though I worked my tail off, I simply couldn’t understand it. I tried a number of different study guides, a couple of tutors, and so on. Nothing helped and I had to drop the class halfway through the year. The following year, I enrolled in a calculus class at college that used the exact same textbook that my high school one had used. But this time, it “clicked” for me and I went on to earn an A. I’m absolutely convinced that the difference was simple cognitive maturity. Something in my brain switched on between 17 and 18 that made the difference between confusion and comprehension.

  4. I agree with Crimson Wife. I was in a special program in which I took algebra in 7th grade – the other advanced students took in in 8th, and everybody else took it in high school. Although I was a good student, I really struggled with algebra. When, after taking geometry, I took Algebra II in 9th grade I thought it was a breeze. It’s really not hard to believe that some kids aren’t ready in 8th grade and that some may never be.

  5. BadaBing says:

    What do you suppose is the minimum IQ required to comprehend algebra, and what if some students just don’t have that cognitive prerequisite? I think there are a lot of those types at my school. You can find them repeating Algebra I two and three times without success. ¿Si que no tienes los cesos para aprenderlo? Que entonces?

  6. I’ll kindly disagree with the assertion that some kind of cognitive development continuum prevents access to algebra as a 13-year-old, as suggested by lu-lu and crimson wife. If there’s something in the standards and literature that suggests otherwise, something beyond reminiscence, I’d love to know about it.

    No, it’s poor teaching, and poor school practices that cause kids to be unable to access algebra in the 8th grade. Sadly, if you’re poor, Black, Latino, or some combination of the three, your chances of being on the receiving end of poor instruction or poorly functioning schools/ districts is dramatically higher than otherwise. As a result, your chances of even getting access to algebra in 8th grade, much less learning it, are correspondingly low.

    This is not small thing, and the effects are far reaching. White and Asian kids completed A-G requirements at nearly three times the rate of other groups, notably Blacks and Latinos. Algebra is again and again seen as the primary inhibitor of A-G completion. Mandating its instruction in 8th grade significantly increases the ability of poor, Black, and Latino kids to access the curriculum they need for future success. This is not about equalizing intelligence or attempting to smooth over the differences in individual human beings. It is about the repudiation of an implicitly tiered system that sets certain kids up for success, and tracks others toward increasingly limited outcomes, based on systematic, not individualistic, failings.

    Of course, sticking kids who can’t multiply into algebra and patting oneself on the back isn’t going to help either. This is why the plan calls for a multi-year phase in period, a period one can only hope will be marked by schools and districts altering their structures and practices to provide the foundational skills kids need to be successful in 8th grade algebra classes. The failure to do so is a failure of the adults that inhere the system to do right by kids, and not a failure of policy. Take a good look at 5th grade math standards, which are remarkably similar to 7th grade math standards, the presumed algebra pre-req: Are we really willing to say, as a matter of formal state policy, that we can’t hop over such a low bar?

  7. I’ve always heard that students learn best when pushed to the limits of their abilities, and no further. I’d love to see the regulations regarding testing be supportive of this approach to teaching. It seems like some of these ideas might help with that:

    1. Test for proficiency in subjects and not grade levels
    2. Have teachers set testing levels for students that guarantee students capabilities are exceeded
    3. Report subject proficiency levels by school and grade along with expected results
    4. Measure schools on how quickly the enrolled students are progressing toward proficiency

  8. I tutor algebra at a CA high school. If I give a student a problem like:

    5 + _ = 12

    and ask him to solve it, I almost always get the correct answer of 7. Which is mostly good but also somewhat sad, because a proficient first grader can solve this kind of problem. ( Some students have real life problems and totally overwhelm the capacity of the school to help )

    However, if I give a student a problem like:

    5 + x = 12, solve for x

    A significantly fewer percentage of students can come up with the identical correct answer of 7. When I translate the mathematical statement into the english sentence, “There is a number that when added to 5 equals 12, what is that number?”, it immediately becomes equivalent to the first problem.

    So to some extent first graders are already learning Algebra, we just don’t call it that.

    The tutors I work with are unanimous in thinking that the teaching of Algebra has become too mechanical. This overly mechanical approach motivates students to stop thinking. The tutors I work with are also unanimous in thinking that students would benefit greatly from being able to translate mathematical statements into english and vice versa ( those dreaded word problems ). It sure seems like one of the major culprits is the textbooks that are used. World problems are almost non-existent in the textbooks I’ve seen and seemed to be assigned even less.

    So at least some anecdotal evidence that california schools can do better.

  9. ucladavid says:


    I remember tutoring kids in very very basic geometry problems. The kids ranged from honors down to sheltered and kids only come in if they need help not if they already know it. They were doing area and circumference of a circle. They had the equations right in front of them, but the students could not put the number into the equation. For example, the equation said that the diameter is 2, what is the area and circumference? They could not do pi x (d/2 squared) for area and pi times d for circumference. Getting them to do things like the area of a donut, forget about it.

  10. In many countries children are ready for algebra when they are 13 and like TMAO says, there is literature that shows this has to do with academic preparation.

    I’m laughing at the idea that adults are not “cognitively” mature enough to handle Calculus. One might argue that some 50% of all adults haven’t matured enough to pass college algebra

  11. One could argue that many adults aren’t “cognitively mature” enough to pass remedial math in college even when they are in their 30s and 40s.

    Like TMAO says, there is literature out there that shows that this maturity is related to prior academic preparation. In Singapore all the children take algebra in the seventh grade, many of them just 12 and they do just fine.

    Prior to 1960 you would have been considered as crazy to attempt to teach Calculus to a high school student as you would be today to consider teaching full-blown algebra to a sixth grade, and yet, teaching practices improved and made Calculus for high school students possible.

  12. Bada Bing asks: “What do you suppose is the minimum IQ required to comprehend algebra, and what if some students just don’t have that cognitive prerequisite? I think there are a lot of those types at my school. You can find them repeating Algebra I two and three times without success. ¿Si que no tienes los cesos para aprenderlo? Que entonces?”

    Perhaps they could become teachers?

  13. Well, they called it “pre-algebra” when I was in Middle School in the 1960’s and no one seemed to think it was advanced or anything. We didn’t get into matrices or quadratics, as I recall, just simple first-order equations.

    I agree with TMAO and pm above. The right teacher can lead an average classroom of kids through the beginnings of algebra in 8th grade. The problem is that the teacher has to really know the math themselves – and not just the mechanics, but the underlying theory and meaning.

  14. If you’re going to teach Algebra to 8th graders, which in general I believe is a good idea, students need to learn their arithmetic in elementary schools. That includes math facts, long division, etc.

    Middle schools should test students math abilities upon entry and start remedial efforts immediately.

  15. “The right teacher can lead an average classroom of kids through the beginnings of algebra in 8th grade.”

    I would make that plural–“teachers”

    Not just the right teacher in the 8th grade, but the students need to have had the right teachers in the 5,6,7th grades, the right curriculum, and pushy parents.

  16. Independent George says:

    The issue here isn’t algebra in 8th grade; it’s adequate arithmetic in 1st, 2nd, 3rd, 4th, 5th, and 6th grade. I don’t object to the requirement itself, but it seems like a passive-aggressive way of telling the schools to continually track their students’ progress, and remediate as needed.

  17. Algebra requires abstract thinking, what Jean Piaget called the “formal operational” stage. This usually kicks in around puberty and probably has something to do with the myelinisation of neurons. It’s neurology, folks, not bad teaching. A child who has not reached the proper stage of cognitive development won’t be able to understand it regardless of the quality of instruction he/she receives. Many children will reach the proper stage by age 13 but not all will.

    And Myrtle, I graduated salutatorian of my high school class, scored 1450 on my SAT’s (prior to the recentering of the mid-’90’s), and earned a 3.8 in science at Stanford. So the difficulty I had with calculus at age 17 had nothing to do with being dumb, lazy, or unprepared. I simply wasn’t ready for it. One year later, I was.

  18. Ragnarok says:

    “So the difficulty I had with calculus at age 17 had nothing to do with being dumb, lazy, or unprepared.”

    Of course not, but that doesn’t mean that everyone will be ready for abstract thought at some point.

  19. Piaget makes no sense to me.

    Children are capable of abstract thought when they use words to represent concepts. The digits that kindergartners use are abstractions of concepts that are in and of themselves abstractions. The symbols representing the operations of arithmetic are abstract and so is reading for that matter.

    The question is what exactly is the principled difference between the abstraction in algebra and the abstraction the child is already capable of? (In fact, much that passes as algebra these days, rather than requiring high degrees of abstraction, requires almost no sentience at all–computers can be programed to solve the equations.)

    What does “developmentaly appropriate” mean in the context of a task which a nonsentient calculator or computer can do?

  20. Famous education “pioneers” like Piaget have no influence outside of college Education departments. He studied neurology? I don’t recall him ever going to medical school, or studying any brains from the inside out to see how they worked.

    Like most modern educrats, he was a believer in his own propoganda.

  21. Are you seriously claiming that a kindergartener’s brain is capable of the same level of thinking as an eighth grader’s given the “proper” instruction? Anybody who’s spent time around kids of different ages knows that’s nonsense…