Unteachable

If California adopts common core standards in math with an algebra supplemnt, the result will be unteachable, argue Bill Evers and Ze’ev Wurman, both dissenting members of the standards commission, in the Sacramento Bee.

Because of the distortions the proposed standards will cause, the Algebra I course in eighth grade will be burdened with an unteachable and unlearnable number of topics (about 70 standards in one year). Topics like the Pythagorean theorem and scientific notation (how scientists write large numbers in a simplified form using exponents) will now be taught in Algebra I. Yet these and many other algebra-prep topics have been part of pre-algebra courses both in California traditionally and in high-performing countries.

Currently 60 percent of California students take algebra in eighth grade.  Under the new stndards, only the best students will be prepared to pass eighth-grade algebra, they write.

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Comments

  1. Wow, only those students who understand math should pass algebra in eighth grade! Shocking.

  2. Deirdre Mundy says:

    Cal– did you actually bother to read their article? They’re upset because the new standards discourage teaching these concepts in earlier grades and try to cram too much into one year. (Even though Scientific Notation is helpful from at least 6th grade on… and so is pythagorus…)

    Also, they’re complaining about methodology–that the standards impose unproven methodologies (for similar and congruent triangles? I’m kind of confused– we were taught them by 1. Learning the Definitions. 2. Doing examples. 3. Learning the proofs once we got to geometry….)

    Any way, the complaint seems to be that instead of cramming everything into 8th grade, some things can be taught earlier….

  3. Currently 60 percent of California students take algebra in eighth grade. Under the new stndards, only the best students will be prepared to pass eighth-grade algebra, they write.

    This is what I was responding to.

    As it is, 32% of 8th graders don’t score at “basic”, much less proficient or higher in Algebra. So if it drops from 32 to 50%, oh well. We should only put the top students in algebra in 8th grade, anyway.

    In other words, the standards debate is not the real problem. The real problem is that kids are taking math they aren’t prepared for and failing at it–yet being moved on.

  4. As someone who’s taught Algebra 1 under the current state standards for over a decade now, I can say that they are “ambitious”. To add even more material is crazy. Covering all the required topics is like drinking from a fire hydrant already.

  5. I agree with that. But if you note, the actual standards test is considerably less broad. If you focus on the “big ideas” of algebra, you’ve covered most of what the kids need.

  6. Miller Smith says:

    Sad to see that the reason for scientific notation is not understood. It is not just a way to write very big numbers, but rather a method of doing calucaltions with very big numbers from a time when there were no calculators or computers.

    By reducing the very large number to digits of less than the number ten times the power of ten, one can do math with very big numbers very easily. What is a million times a billion? Well, that is ten to the 6th times ten to the 9th for the answer of ten to the 15th (add the exponents). Easy.

    Problem is that my honors chemistry students have to use their calulators to do the very problem above. Something is not right.

  7. If people have a problem with Math standards, just imagine all the problems Social Studies or English standards will generate. The problems become obvious with Math standards for the same reason that scholars use Math performamce to assess school performance: Math is the simplest curriculum.
    A loving homeschooling parent can teach counting, whole number operations, very basic Geometry (the meaning of “between”), rational number operations, and the notation of set theory and logic, by third grade if s/he starts early enough. At this point, a student is ready for the material we call Alg. I (linear equations in one and two variables, basic Analytic Geometry), after which the student can read Math independently, with just the occasional pat on the back.
    The State cannot subsidize education without a definition of “education”. State (government, generally)-imposed curriculum standards bind students, parents, real classroom teachers, and taxpayers to the State’s definition. The fundamental problem with curriculum standards is that humans are not standard.

  8. “The State cannot subsidize education without a definition of “education”. State (government, generally)-imposed curriculum standards bind students, parents, real classroom teachers, and taxpayers to the State’s definition.”

    The State (federal government) should not be funding or subsidizing education nor should The State have a definition of education. The State (federal government)should follow the Constitution with regard to education.

    “The fundamental problem with curriculum standards is that humans are not standard.”

    Most ed schools do not teach their young (or old) charges that there are individual differences in intelligence, achievement, aptitudes, motivation, etc. If one does try to do so,s/he is “outed” and called terrible names by the other professors. Of course, the other professors do teach their charges nonsense like there are differences in learning styles and if you can just “find that style” all students will learn information at the same level.

  9. (Anon): “The State (federal government) should not be funding or subsidizing education nor should The State have a definition of education. The State (federal government)should follow the Constitution with regard to education.”

    Abundant evidence supports the following generalizations:
    1. As institutions take from individual parents the power to determine for their own children the choice of curriculum and the pace and method of instruction, overall system performance falls.
    2. Political control of school harms most the children of the least politically adept parents.

    As a general rule…Homeschoolers outperform independent schools. Independent schools outperform government schools. Small school districts outperform large school districts.

    National standards will degrade the performance of the entire government-operated school industry.

    (Anon): “Most ed schools do not teach their young (or old) charges that there are individual differences in intelligence, achievement, aptitudes, motivation, etc. If one does try to do so,s/he is “outed” and called terrible names by the other professors. Of course, the other professors do teach their charges nonsense like there are differences in learning styles and if you can just “find that style” all students will learn information at the same level.”

    If children vary in their interests and aptitudes (and they do, enormously), then one might reasonably suppose that differences in learning styles would appear. Consider the extreme case of teaching, say, Math, to a blind or deaf kid. The real problem with the “learning style” hypothesis is that it does not work as applied in a conventional classroom. Seems to me, anyway.

  10. The Bee’s article focuses on the weirdly overloaded Algebra-in-grade-8 option, and its probable effect on early Algebra taking in California. Strangely, Cal chooses to ignore this and instead focuses on current Algebra achievement, claiming that:

    “As it is, 32% of 8th graders don’t score at “basic”, much less proficient or higher in Algebra. So if it drops from 32 to 50%, oh well. We should only put the top students in algebra in 8th grade, anyway.”

    There are many issues with this simplistic and misleading statement. Let us examine them.

    First, Algebra is taken by 60% of students in grades 7&8. When summing the total performance of this group, only 29% (rather then 32%) didn’t score at “basic” in 2009.

    Second, this number was 35% just 4 years ago, in 2005, when the fraction taking Algebra by 8 was only 45%. In other words, between 2005 and 2009 Calif. increased its number of Algebra 1 takers by 33% (45% to 60%) while at the same time reducing the number of failing students by 1/6, from 35% to 29%. I would quickly buy shares in any company producing similar productivity improvements.

    Thirdly, if Cal truly thinks that unless 100% of kids are ready to successfully pass a subject we should not place them in it, what does she make of our grade 6 cohort? Last year 25% of 6th graders didn’t score at least “basic” in math (incidentally, a nice reduction from 33% in 2005) — should have we retained 25% of the 6th grade cohort in grade 5?

    California has had an incredible success in increasing both Algebra 1 enrollment by grade 8 — from 16% in 1999 to 60% last year, and in increasing student’s success taking that class — from 34% proficient and advanced in 2005 to 48 last year. Even more importantly, the success of minority and disadvantaged students in Algebra increased much faster than the average cohort success. Translation: if 10 years ago mostly affluent white and Asian students took early Algebra, now many disadvantaged students do. Number of black students *successfully* taking Algebra (proficient or above) more than tripled from less than 1,700 to 5,400 between 2003 and 2009. Hispanics jumped from 10,000 to over 45,000. Successful low-SES students more than quadrupled from less than 12,000 to almost 50,000. And, by the way, similar albeit somewhat less spectacular results can be seen with Algebra 2 taking and success in high school.

    The proposed overloaded Algebra 1 will kill this hard-earned progress, and its worst impact will be felt among disadvantaged students. I guess Cal is OK with that.

  11. Don’t pout, Ze’ev. You got published! Deal with the fallout.

    I’m a math teacher. I see what happens to the kids who don’t score at the proficient level, yet move onto geometry and the like. It’s not pretty.

    I’m not in favor of overloading Algebra, and never said I was. But yes, I would rather we introduce algebra later for all but the strongest kids. The push for Algebra earlier is political, not pedagogical.

  12. Cal is right — I shouldn’t pout. And if that is how I came across, I am sorry.

    At the same time the facts need to be kept straight. They should guide us rather than musings and speculations. In that spirit, let me respond.

    I agree that unprepared kids should not be pushed into classes they are not ready for. In fact, so does the California Math Framework that goes on record multiple times to advise against placing unprepared students in Algebra. The increasing success of students taking early Algebra shows this is not a growing practice. Does it mean nobody does it? Tony Alvarado tried it in San Diego earlier this decade, and the results were disastrous. And I have heard of other school districts toying with similar foolishness.

    Yet should the fact that there are fools around hide the soundness of the basic idea? The National Math Panel researched the question of the importance of early Algebra taking and it wrote:

    The consistency of their findings is striking. The studies by Ma and others provide some evidence that there are long-term benefits for Grade 7 or 8 students with the requisite mathematical background for algebra if they can take an authentic Algebra course in Grade 7 or 8: higher mathematics achievement in high school and the opportunity to take advanced mathematics course work in Grade 11 or 12. (http://www2.ed.gov/about/bdscomm/list/mathpanel/report/conceptual-knowledge.pdf p. 3-47)

    I think it is foolish to stop promoting excellence in the name of equitable mediocrity.

  13. Mark Roulo says:

    …But yes, I would rather we introduce algebra later for all but the strongest kids. The push for Algebra earlier is political, not pedagogical.

    Okay, why? As nearly as I can tell, the rest of the world gets their typical (not advanced) students up to algebra by 7th grader. Our accelerated (8th grade) would be their remedial track. What is so different about US students that being two years behind the rest of the world in math seems reasonable?

    -Mark Roulo

  14. Cynical says:

    What is so different about US students that being two years behind the rest of the world in math seems reasonable?

    Large minorities descended from Central American indians and ex-slaves.

  15. Cynical says:

    … and an insistence that all students can achieve at the same rate, so tracking = racism.

  16. Mark Roulo says:

    The US was treating algebra in 9th grade as typical back in the 1930s. The Central American Indian population in the US at that time wasn’t very large. Additionally, the non-white population tended to get their own schools. Asking the *white* students to run at European rates in the 1930s, while letting/forcing the non-whites to run several years behind would have been easy.

    But as a country we didn’t do that.

    -Mark Roulo

  17. Ze’ev writes: “I agree that unprepared kids should not be pushed into classes they are not ready for.”

    the answer seems clear: prepare them. why is this such a mystery? If additional grounding is needed in 7th grade for 8th grade success, then do so.

  18. Ze’ev,

    Why not restrict Algebra to the kids who passed Pre-Algebra or the equivalent with proficient or higher? That would still pick up the Hispanic and African American kids with ability, and lower the failure rate (which is disproportionately Hispanic and African American).

    The difference between 32 and 35 isn’t anything to write home about (and actually, it’s 34% this year if I’m reading this right: http://star.cde.ca.gov/star2009/ViewReport.asp?ps=true&lstTestYear=2009&lstTestType=C&lstCounty=&lstDistrict=&lstSchool=&lstGroup=1&lstSubGroup=1). The failure goes up from there. There just aren’t that many kids who can manage algebra, period, and we should be spending more time preparing them for algebra–even if it’s several years–than having them retake it, or worse, move onto geometry.

    To me, that’s a much bigger issue than the standards debate.

    The US was treating algebra in 9th grade as typical back in the 1930s.

    And we were doing pretty well for a lot of years, while Europe wasn’t. Suggests the age of entry ain’t all that.

  19. Cal,

    Let’s dispose of the numerical misunderstanding first. 35% were below basic in 2005, 29% (not 32%) were below basic in 2009. The 32% is only for grade 8 algebra takers. If you consolidate it with the much smaller fraction of below basic of the 7th graders who took algebra, you get 29% below basic of the algebra takers *by* grade 8. But even at 32% it would have been 10% reduction while increasing enrollment by 1/3, showing that more students are getting better prepared, and that fewer unprepared students are pushed into algebra.

    Now to the real question — why not have them pass pre-algebra to qualify for algebra.

    In principle, why not indeed? That is what many schools are effectively doing anyway. But without some push for Algebra, there will be little interest in making sure that even disadvantaged kids are pushed along, and most might end up in slower classes. That is what disproportionally happened before 1998. We have changed it, and now we will go back.

    So the incentive to push kids into algebra is important. That is what made the fraction of algebra takers grow from 16% in 1999 to 60% today, and among disadvantaged kids even faster. Not the better standards since 1999 — they only enabled it, but didn’t cause it to happen.

  20. That is what disproportionally happened before 1998. We have changed it, and now we will go back.

    Tests would allow us to identify the kids who are ready. The number of kids who are passed along without any idea of what’s going on is not worth the very small number of kids who are getting caught in the net.

    Let’s face it–the politics are why people oppose it. We would rather push along kids who aren’t ready than admit that tests show that the vast majority of black and Hispnic kids, as well as low income kids, simply aren’t ready.

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