Algebra II mandate gains momentum

Algebra II is becoming a required course in a growing number of high schools, reports the  Washington Post.

Of all of the classes offered in high school, Algebra II is the leading predictor of college and work success, according to research that has launched a growing national movement to require it of graduates.

In recent years, 20 states and the District have moved to raise graduation requirements to include Algebra II, and its complexities are being demanded of more and more students.

In Arkansas, which now requires Algebra II for most graduates, only 13 percent of students passed a rigorous end-of-course exam.

“All those numbers and letters, it’s like another language, like hieroglyphics,” said Tiffany Woodle, a Conway High School student and an aspiring beauty salon owner. “It obviously says something. I’m just not sure what, sometimes.”

As part of its push for higher standards to prepare students for college, Achieve has promoted Algebra II. The skills learned in the course are needed for college and in the workplace, the group claims.

But Georgetown’s Anthony Carnevale, one of the researchers who reported the link between Algebra II and good jobs, says that just because taking the class correlates with success doesn’t mean that it causes success.

“The causal relationship is very, very weak,” he said. “Most people don’t use Algebra II in college, let alone in real life. The state governments need to be careful with this.”

The danger, he said, is leaving some kids behind by “getting locked into a one-size-fits-all curriculum.”

Does Tiffany really need advanced algebra to run a beauty salon?

Economist Russ Roberts, who’s married to a math teacher, warns of a one-fad-fits-all mandate on Cafe Hayek.

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Comments

  1. Richard Aubrey says:

    Some kids cannot, and some will not, learn A2. Do they graduate? You damn bet they will.
    Thus, A2 will be dumbed down. What would you do with the college-track, technically-oriented kids? AP math would be elitist.
    Same-same with foreign language requirements.
    Stupid idea.

  2. Elizabeth says:

    One may not “use” Algebra II, but mathematics teaches logic and analytical thought. Are we here to educate or babysit?

  3. My youngest daughter is not “mathy.” She was pushed through Algebra 2, but I could tell it wasn’t real Algebra 2. She would have benefited far more from taking the slower route with math; then she would have ended up better at fractions and decimals, which she actually does need to understand and use. And this is not a slow learner; she if great at reading, writing, history, etc. Just not math.

  4. As a HS teacher, I taught required Alg II to the weakest math students in the school. I am a big believer in the value of knowledge. I understand that you may not NEED some particular subject to get by, but if you have that knowledge, you will find a surprising number of places where you can use it. Still, the bottom line for me is that it is impossible to justify making non-college bound students take Alg II to graduate. I tried my best to point out the occurrence in the real world of conic sections. At best, it was of mild interest to my students, but there was no way to make the case that they needed to understand the underlying equations. I think everyone’s time could have been much better spent pursuing other subjects.

  5. I don’t agree with an algebra II mandate because of the one size fits all mentality; however, I don’t agree with the idea that because someone wants to own a beauty salon when she grows up she doesn’t “need” algebra II for several reasons.

    1. Many of us develop different aspirations later in life than the ones we had when we were in high school. The better educated you are the easier it can be to switch careers.

    2. Running a successful business isn’t a piece of cake. A salon is a business just like any other business owner she’ll need to deal with profit margins, taxes, employee benefits etc, – which all comes down to numbers and clear, analytical thinking.

    3. Tiffany, like most of us, needs very strong basic math skills including dealing with fractions, proportions, ratios and percentages. Her problem may be typical of many public school students – a combination of poor math teaching/curriculum combined with a lack of studying on her own so now she is struggling through a difficult course that she probably wasn’t prepared to take. So why does the conversation always turn to “Does Tiffany really need to take algebra to be a salon owner?” rather than to Why isn’t Tiffany better prepared to take this course?”

    I wish I had taken better advantage of the math education I was offered as a teenager and I wish the instruction had been better in some cases as well. Frustrated with how little I understood geometry (even though I sat through a year of it as a 10th grader) or understood the application of much of the math I studied I set out to study geometry, trig and advanced algebra on my own as an adult – all of which I studied in high school, but never quite understood. Thanks to the many books on the market today I was quite successful and have a lot of confidence in my math skills. The most beneficial of it all has been Euclidean geometry (which requires basic algebra). I am positive that it has incredibe cognitive benefits and It really makes me wonder why so much emphasis is put on advanced algebra and that no one ever seems to mention the importance of geometry.

    My last beef is that I’m just so tired of the claims that certain students do need to take math or history because of what they say they want to be when they grow up. It’s such an elitist statement. Everyone benefits from a strong liberal arts education, whether they want it or not. I just can’t stomach the “blame the kid” mentality. It is the responsibility of adults to be providing a content-rich, rigorous liberal arts education and we, the adults, are failing miserably. Sure, some kids refuse to be educated and some schools are a chaotic mess – but who’s fault is that? The adults!

  6. Allison says:

    Before we ask questions like “Does Tiffany need Alg 2 to be a beautician?” let’s back up. Would YOU take career advice from a 17 yr old? Then why would you lock Tiffany into taking career advice from herself-at-17? Because who she is at 35 and what she likes, dislikes, and knows about life is probably as far from herself at 17 as you are from her at 17. Shouldn’t she be given the tools to make sense of algebra 2? If not, why do we have compulsory ed?

    People are pushing alg 2 because they believe that without a college degree you have very little path to success in an American life. That may not be entirely true, but we have moved well along a path of wage stagnation for the lower and lower middle class, and this recession has shown us that jobs lost aren’t coming back. Retraining someone later in life is a lot easier if they were given a decent education earlier–you aren’t going to successfully navigate alg 2 at 45 if no one taught you enough math to successfully navigate it at 17.

    Maybe not everyone is trainable or retrainable. Maybe not everyone can handle it. But until we deal with the fact that very many jobs are outsourceable, that technological efficiency will make there be fewer of non-outsourceable jobs in the first place, and that we don’t know what the future will hold, we should take seriously the concern that not being able to master algebra 2 probably means lacking the skills for financially prosperous work for most people in our nation in the coming years.

  7. It’s not a matter of desire, but of cognitive ability. This is insane.

  8. Sean Mays says:

    Why is it that we expect students to read Shakespeare, compose haikus, argue the merits of U.S. foreign policy and primary documents of the republic, maybe learn a little foreign language and some science, but requiring math beyond algebra I is problematic (even algebra I can be too I suppose)? I never heard a science or engineering student say they just couldn’t understand how to write a 10 page paper, but ask an algebra two class to find a quadratic that fits 3 points of data and instant fireworks.

    I don’t doubt that there are issues of cognitive ability blocking some people, but it’s less than the people who claim the issue.

    Math is one of the great bodies of knowledge. If we make any pretense to instilling a liberal arts education or turning children into educated human beings, math has a place.

    And yes, the whole correlation/causality problem rears its head. Requiring algrbra II to graduate won’t success in college. Especially if it gets watered down.

  9. LSquared says:

    Right now Alg II isn’t required (in most places), so the correlation might not be the obvious one: Alg II and college success, it might be “taking a math course beyond what’s required” and college success. If that’s the case, requiring Alg II would result only in Alg II and college success no longer being correlated. I think there’s an argument to be made here that this (the decision to require Alg II) is an example of why we need better statistics education (for our politicians).

  10. Michael E. Lopez says:

    I’ll say it: Algebra II (at least the course I took) is practically useless.

    Quite literally 90% of people never, ever need anything butl algebra, geometry, and an occasional dash of combinatorics.

    And most of them will never study combinatorics.

    Don’t mandate Algebra II. Mandate getting a B or higher in Geometry to graduate from high school. Mandate getting a B or higher in Algebra to graduate. Mandate a course in formal logic, maybe with a dash of set theory, if you’re worried about logical thinking. That at least has cross-application value.

    Don’t get me wrong: I think we should still offer it. I think it’s valuable. It’s just useless to most people and it’s a silly thing to mandate in high school. Even the GRE’s don’t have Algebra II on them.

  11. Stacy in NJ says:

    Yeah, it really does represent a lost opportunity. Is it better to push kids through A2 with poor understanding and no retention just so we say that we provide a “liberal arts” education? Or, is it better for them to firm up those basic math, algebra and geometry skills? Or, is it better to focus on a subject/topic that offers more value to them as individuals?

    While I agree that challenging kids and maintaining high expectations is worthy, I wonder how many capable kids are turned off because of these kinds of requirements. Better to do something really well and squeeze out all value from it then slog through a bunch of meaningless requirements. A bit of slogging has value, a couse load full of it is a real turn-off.

  12. –It’s not a matter of desire, but of cognitive ability. This is insane.

    Cal, I grant you that there are many kids who may lack the cognitive ability to handle it.

    But are you sure that 100% of the kids who don’t succeed at it now do so because they lack the cognitive ability?

    How many of them are failing at it because they were poorly taught fractions, decimals, negative numbers, and algebra 1? Can you tell the difference? Are you willing to bet a kid’s future that you can tell the difference?

  13. –. Mandate a course in formal logic, maybe with a dash of set theory, if you’re worried about logical thinking. That at least has cross-application value.

    We lack the structure in place to start teaching set theory and logic at a high school level. We don’t lack the structure to teach algebra 2. For over 100 years, we’ve come to general conclusions about what that material is, what needs to be conveyed, and we have a poor-but-better-than-nothing method for finding competent high school teachers to teach it. We lack all of that for set theory, logic, combinatorics, probability and statistics.

  14. “But are you sure that 100% of the kids who don’t succeed at it now do so because they lack the cognitive ability?”

    Pretty close, yes. I’d say around 95%. And yes, given the vast swaths of students who are currently forced into algebra I because of requirements they take it despite a complete ignorance of the prerequisites, I would bet the kid’s future on it. Because right now, in your dewy-eyed and idiotic idealism, you’re forcing kids to fail in huge numbers.

    “How many of them are failing at it because they were poorly taught fractions, decimals, negative numbers, and algebra 1?”

    Many of them are failing it because they don’t understand decimals, negative numbers, fractions, and algebra 1. In most cases, it’s not because they were poorly taught, but because they didn’t have the cognitive ability to learn the subject properly. They should have been taught these subjects much later, and much differently than you teach them to kids who do have the cognitive ability to learn them.

    And of course, why not ask why kids are taking algebra II (or, for that matter, algebra I) when they don’t know negatives, fractions, etc? Because teachers do’t like to fail kids who have taken algebra for the umpteenth time, despite having no ability to master the material. It’s cruel. So they will pass. Just as the hundreds of thousands of kids who don’t get algebra II will pass despite having no clue what’s going on. Teachers aren’t cruel. And so, the kids will pass, have algebra II on their transcript, and go to college–where they will end up in remedial arithmetic for as many years as they are willing to borrow taxpayer money for wasting their time.

    We are doing cruel things to kids because we don’t want to accept that cognitive ability predicts academic success. We are also ignoring the kids’ wants and interests, and forcing them into subjects that they don’t care about, and wasting huge amounts of time–and setting kids up for failure–all because people like you are determined to ignore reality. It’s tragic–as well as insane.

  15. Roger Sweeny says:

    Retraining someone later in life is a lot easier if they were given a decent education earlier–you aren’t going to successfully navigate alg 2 at 45 if no one taught you enough math to successfully navigate it at 17.

    I guarantee that if you pass algebra 2 at 17 and don’t use it for the next 28 years, you will remember less than 5% of what was in the class (most people will be within epsilon of zero).

    There is a ridiculous assumption that people often make when they talk about education: that passing a course means you will know the subject matter the next year and the next year and … But most people retain very little of what they supposedly learned. Deep down everyone knows this. You probably can’t even remember all the courses you took in college, let alone what was in them.

    Knowledge that isn’t used quickly decays, especially if it wasn’t well understood in the first place.

  16. Allison says:

    –They should have been taught these subjects much later, and much differently than you teach them to kids who do have the cognitive ability to learn them.

    So how does that support your claim that these kids can’t learn these subjects? Seems to argue against it. Now you’re saying they could have been, but didn’t, so we should give up. How about trying something else–teaching them well in the first place, and then seeing who can handle what going forward?

    Now, if your argument is that it isn’t cost effective to teach these kids these subjects later and/or differently, that’s a different issue. I think it’s unsubstantiated, too, and likely true that better teaching is cheaper as well, but at least that’s a different argument about where our money should be spent, and what’s deriving a good bang for a buck.

  17. So how does that support your claim that these kids can’t learn these subjects?

    Where did I say they can’t learn it at all?

    They could learn a much easier, much less challenging form of algebra 1 at a much later age, with much of the difficulty filtered out. I’m not sure that they could ever learn a lot of algebra II.

    How about trying something else–teaching them well in the first place, and then seeing who can handle what going forward?

    You’re back to asserting that they were taught badly, and that’s not what I said.

    Teachers are tasked with teaching algebra to those who are cognitively ready to learn it. Not all teachers are able to teach simpler, less challenging forms of algebra to kids who aren’t cognitively able to learn algebra as it’s supposed to be taught.

    You also missed the fact that the different teaching would have to be taught at a much later age.

    And then, you completely miss the fact that any kid who is incapable of learning algebra by eighth or ninth grade, because it will take them that long just to learn proportional thinking and fractions (taught differently and in a simpler manner, in view of their cognitive limitations), and will take two years at least to learn first year algebra, another year or two to truly master geometry and who knows if they’ll ever master algebra II completely–that this kind of student will never be able to handle the cognitive demands of a genuine college degree.

    It’s not that the kids aren’t “taught properly”. It’s that they don’t have the mental aptitude for the subject, and the teacher has to teach them far more slowly and in a very different way.

    If they were ever “taught properly”, in recognition of their limitations, they would be taught separately from kids who didn’t have these limitations, taught far more slowly, and would possibly be truly competent in first year algebra by the age of 18.

    It always amuses me to see how idealistic nincompoops can convince themselves that there’s no such thing as intelligence.

  18. CarolineSF says:

    All education reporters, commentators and bloggers should chant “Correlation does not equal causation” for five minutes first thing in the morning.

    If anyone here doesn’t understand this concept, please request an explanation.

  19. tim-10-ber says:

    Excuse me…but how many school districts are this far behind the curve? Four years of high school math is the requirement…this is either pre-cal or calculus if you have algebra i in 8th grade…we had to have algrebra II when I was in high school more years ago than i care to admit…it isn’t hard

    then they go to college and take college algebra and calculus…don’t you know?

    said seriously but with tongue in cheek…

    I am serious…how many school districts are this far behind the curve? The better private schools in my city require four years of high school math and the government schools started this requirement for incoming freshman in 2009…

    the government schools have all but taken algebra out of 8th grade — i don’t agree with that…I am not saying I agree with 4 years of high school math either…just saying countless districts haven’t gotten the message LOL!!! Enjoy! 🙂

  20. Sean Mays says:

    Cal:

    In your opinion, what percentage of the population is cognitively incapable of learning Algebra II? What percentage of the population do you believe has been poorly taught, but would be capable given better teaching and scaffolding? I’m trying to get a quantitative grasp on how you see this problem.

    (Cal sayeth): It always amuses me to see how idealistic nincompoops can convince themselves that there’s no such thing as intelligence.

    I respectfully disagree. The nincompoops know there is such a thing as intellegence, the problem is they think Harrison Bergeron is a how to and not a warning.

    (Allison): We don’t lack the structure to teach algebra 2…

    But we DO lack the structure, the state standards that existed before the Common Core State Standards initiative were all over the place for algebra II; even if we get 100% buy in, I’ll be amazed if we see a common definition in practice.

    Set theory and logic might be nice, a good statistics class would rock! I’d settle for a strong personal finance class as a math requirement beyond geometry. Something where the kids have to make a portfolio, calculate a beta, know about the efficient frontier and saving for retirement? Teaching a basic financial math class would be as dangerous as teaching sex ed though. Your parents took out a mortgage with a 50% D/I ratio? That’s bad,mmmm’k?

  21. Michael E. Lopez says:

    Allison saith:

    For over 100 years, we’ve come to general conclusions about what that material is, what needs to be conveyed, and we have a poor-but-better-than-nothing method for finding competent high school teachers to teach it. We lack all of that for set theory, logic, combinatorics, probability and statistics.

    No offense intended, but it’s clear that you have absolutely no idea what you’re talking about. We don’t lack “general conclusions about what that material is” or “what needs to be conveyed” when it comes to set theory and logic. There are plenty of logic primers out there even for elementary students and frankly the human race has been at work at propositional logic since at least the Stoics. Algebra II calculations are a relatively recent invention, comparatively.

    The material’s there. The syllabi are there, whether you want to do Sentential, Quantificational, or even second-order logic. (I wouldn’t recommend second order for high schoolers, at least not unless they were an honors class.)

    It’s true that we don’t have secondary school level teacher-credential programs in place for logic or set theory, but that’s only part of what you said.

  22. Really, people have to get over the bizarre notion you have that kids do poorly in math because math teachers are terrible. High school and middle school math teachers have to pass fairly rigorous competency tests, and have for years.

    Kids aren’t learning math in large part because they aren’t capable of doing so. A push for heterogeneous classes has also compromised the depth and difficulty of math classes for many students, and so some of the middle level students who are more than capable of learning probably aren’t learning as much if they go to schools that refuse to track.

    I’m not saying all teachers are perfect, but math teachers are, for the most part, teaching the subject adequately. Kids aren’t learning because they aren’t capable, for the most part.

    the problem is they think Harrison Bergeron is a how to and not a warning..

    They are correct. Vonnegut saw Glampers as the hero of Bergeron, not the title character. In short, he wanted everyone equalized. He certainly wasn’t warning against the evils of affirmative action; he wrote the story in 1961. Vonnegut was jealous of excellence.

  23. Michael E. Lopez says:

    Cal…

    I’ve had some really objectively terrible math teachers in my time.

    I’m not incapable by any standards save those of graduate and post-graduate mathematics professionals (who would probably laugh at me as a talented amateur), and I flat-out quit math in high school and taught myself because the teachers were so bad.

    I’m not saying that my school was representative of schools in general, but really bad math teachers exist, certifications or no.

    Now you might think that the people on this blog’s comments are, typically, somewhat above-average, and that their evaluations of their substandard math teachers are going to be accordingly biased. Perhaps that’s the case, and what you say about math teachers is true.

    But there’s probably some truth behind what people are saying. We only have our own experiences from which to base our opinions, after all.

  24. Charles R. Williams says:

    Innate cognitive skill is more important in mathematics than in any other subject. That said, effective instruction and student effort still counts for a lot.

    Students in the US have such difficulty with algebra because they have not mastered middle school math. Achieving this mastery is more important than getting students through a watered-down Algebra 2 course. It is also much more important for students’ future careers.

  25. J. D. Salinger says:

    What Charles R. Williams says.

    I know someone who teaches high school math and who has students who have been passed on with very weak skills in fractions and general arithmetic concepts. She reports that the middle and elementary schools that feed the high schools use very poor math programs, such as Investigations, and Connected Math. The “different method of teaching” that Cal talks about often amounts to a direct and explicit form of instruction that has been lacking in the so-called normal classes.

  26. their evaluations of their substandard math teachers are going to be accordingly biased

    dingdingdingding.

    No one here gets to talk about their terrible math teachers in an “objective” way as terrible.

    Around 40% of the students who take Algebra II currently get below or far below basic on the CST. A huge number of those students are Hispanic or African American. When people talk about “terrible teachers” they are discussing it in the context of why these students are so far behind, as if “great” teachers will close the achievement gap. And that’s absurd. (which is not to say that only Hispanic and black students are failing; only that no one would care if all races were failing proportionately.)

    That said, effective instruction and student effort still counts for a lot.

    Sure. But again, we’re talking about “effective instruction” as something that teaches students who can’t “get” normal instruction, and “student effort” as something that goes above and beyond what the average cognitively able student is able to pull off. So *if* teachers of students with low cognitive ability are able to “scaffold” math instruction adequately to insure that these students don’t get lost, and *if* these same students are willing to work incredibly hard, then results will be better. Better, not equal to those kids who have average cognitive ability.

    And since we can’t acknowledge cognitive ability because of the racial imbalances, we can’t actually instruct kids with low cognitive ability that way. And of course, no one knows what the actual specific cognitive load is for AII, and to what degree scaffolding and instruction method can compensate for the lack of cognitive ability.

    The “different method of teaching” that Cal talks about often amounts to a direct and explicit form of instruction that has been lacking in the so-called normal classes.

    Direct instruction can help with fractions and the like. But while not knowing fractions and negatives is a huge problem, there’s no evidence that this is the root problem. Somehow, whites and Asians come out of these same math programs and master higher math.

  27. A student who cannot handle the addition, subtraction, multiplication, and division of fractions will not succeed in taking algebra II (and by definition trigonometry) as both of these math disciplines require a solid foundation in this area of math.

    If you take students who have no basic knowledge of mathematical operations, operator precedence, and how to handle addition, subtraction, multiplication, and division, along with decimals, fractions, and exponents, they’ll never be able to get through a ‘regular’ algebra course (much less any higher mathematics).

    What will happen here is that Algebra II will get watered down so that it’s no longer algebra II.

    Sad indeed…

  28. The kids at the top of the cognitive ability curve are far more likely to learn (math or anything else), even with flawed curricula and ineffective instruction than are the kids further down the curve. Schools point to those kids, largely white and Asian, as evidence that their curricula and instruction “work.” The 800-pound gorilla is tutoring (parents, private tutors, Kumon, Sylvan etc) and exposure to rich content across the disciplines; the highly successful kids are likely to have had LOTS of it. Advantaged kids have parents who know what they need to learn and make sure they get it. Schools don’t want to know about this, even in highly affluent districts where over 50% of the first-graders are tutored. Admittedly, some of this is the “getting ahead of the Jonses” variety, but some is compensation for poor curriculum.

  29. Michael E. Lopez says:

    Yeah but Cal, if the smartest people in the room are saying that a math teacher is a failure, there might be something to that. Yes, they are saying it because they’re the smartest people in the room and from their perspective the math teacher in question is a failure.

    But you have to make value judgments like that from some perspective.

    In other words, their evaluations of substandard math teachers are biased, yes. But that doesn’t mean the math teachers aren’t substandard.

  30. “In most cases, it’s not because they were poorly taught, but because they didn’t have the cognitive ability to learn the subject properly.”

    Evidence?

    “High school and middle school math teachers have to pass fairly rigorous competency tests, and have for years.”

    Ah, but not elementary school math teachers. They get minimal training in math. As for their mathematical aptitudes, what I witnessed when I audited a math methods class at the local ed school (part of the local Ivy League university) was a majority of students who were extremely weak in math. Many, for example, confessed to getting help from their fathers, husbands, and boy friends on the weekly problems (which were at about the level of 4th-6th grade Singapore Math).

    *It is essential to remember that it’s in elementary school the problems begin!*

    Take, for example, the local elementary school in my neighborhood. It is a joint collaboration with the above ed school and the city school district. Its existence has caused real estate prices in its catchment area nearly to double. Because it’s perceived as a great place to teach (among other perks, class size is capped well below the city-wide class size limits), many teachers apply. *And* the school has site selection privileges, so the principal, a former high school math teacher, can hand-pick the teachers. So you’d might think that every elementary school teacher who gets a job at this school would, in particular, have a good grasp of mathematics.

    Not so. Indeed, some teachers have been hired after confessing during their interviews (which parents who sign up are allowed to attend) that they hate math and aren’t good at it.

    The school has also picked a terrible math curriculum: Investigations.

    The result of this is that only those children who are getting outside tutoring in math are mastering the fundamentals of arithmetic that, in turn, are prerequisites for success in algebra.

    And guess what? These children are disproportionately white, Asian, and middle to upper class.

    So, again, where is the evidence that “In most cases, it’s not because they were poorly taught, but because they didn’t have the cognitive ability to learn the subject properly”?

    Given how terrible things are at the elementary level even in some of our better schools, how can we even begin to know what the mathematical capacities are of those children who don’t have access to outside tutoring?

  31. Chartermom says:

    Sean Mays said:

    “Set theory and logic might be nice, a good statistics class would rock! I’d settle for a strong personal finance class as a math requirement beyond geometry. Something where the kids have to make a portfolio, calculate a beta, know about the efficient frontier and saving for retirement? ”

    Yes! Although I’d substitute understanding credit for the higher level portfolio management skills. Portfolio management doesn’t help if you can’t get out of debt. And a class that incorporated logic, basic statistics and personal finance should be required of all students even if it supplanted a “higher level” math course. And there could be an honors version of this course to challenge brighter students. This is information that provides a foundation for understanding (and calling BS on) a whole lot of different things that students will need to deal with as an adult. It also helps to develop those critical thinking skills that everyone is always talking about.

    I know there are those who would argue against replacing the “higher level” math but those students who do go on to college will get the chance to learn it. However they may not ever learn the skills listed above and those that don’t go on to college won’t either.

    By the way, while we are on the subject (somewhat) whatever happened to the proofs in Geometry? I remember my geometry class being almost all proofs but when I ask my high schoolers about proofs, they look at me funny and then say something like “yeah, we did those one week”.

  32. Barry Garelick says:

    Proofs in geometry have been out of fashion for some time, probably since around the time that National Council of Teachers of Mathematics (NCTM) came out with their first set of standards in 1989 in which the importance of teaching geometric proofs was de-emphasized. See http://educationnext.org/anamazeingapproachtomath/

  33. The 800-pound gorilla is tutoring (parents, private tutors, Kumon, Sylvan etc) and exposure to rich content across the disciplines; the highly successful kids are likely to have had LOTS of it.

    You often make comments that betray your lack of understanding of how wide the achievement gap is. Yes, white and Asian kids are more likely to have tutors. Say maybe 10%. In no way does that explain the achievement gap. The vast majority of white kids do not have tutors of any sort, and effortlessly outperform black and Asian kids. Poor white kids outscore middle class and higher African American kids and tie with middle class and higher Hispanic kids.

    Tutoring does not explain it. Certainly not Sylvan, Kumon, and the like.

    Evidence?

    The cognitive gaps between whites, Asians, blacks, and Hispanics are reflected in the test scores. That is, we know that the average IQ of blacks is 1.5 SD below that of whites. The average test scores of blacks are roughly the same. The gap is almost certainly cognitive.

    Ah, but not elementary school math teachers.

    And yet, elementary math scores are much higher than high school math scores. The performance gap is smaller. That’s for two reasons. First, the tests are easier. Second, the math is easier.

    Ergo, we don’t need math teachers to be rocket scientists in the early years, and the kids are learning what they need to know. They run into trouble as math gets more abstract. And again, white and Asian kids are doing fine in high school math with those same “terrible” elementary school teachers.

    (Note: I am using race groups as proxies. the issue is cognitive ability. Race is the best predictor–but not the cause–of cognitive ability. Being black or Hispanic doesn’t automatically equate to low cognitive ability, being white and Asian doesn’t automatically bestow higher ability. But in groups, the frequencies are very clear.)

  34. What Barry says is true. Proofs are utterly irrelevant on the path to calculus (as is construction). In fact, from a utility standpoint, teaching two years of algebra back to back with needed geometry tucked in (formulas, triangle and circle facts, right triangle trig) would probably be a better way to teach math with the current curriculum priorities.

  35. Sean Mays says:

    Chartermom:

    Proofs have been out since NCTM and the 90’s math wars. They’re great if you’re planning on being a math major, maybe even a CS or physics person. For everybody else the utility is seen as low. I personally like them because building a proof is a nice integrative exercise, you see how the stuff hangs together, and you learn something about planning.

    Construction is out. Although actually doing a construction like bisecting an angle probably helps you “get it” when you talk about a bisector, it’s not just some abstract word.

    On a side note, the first time I tried to teach geometry with construction, other teachers looked at me like I was nuts. Turns out they like to break the points off compasses when you’re not looking and poke each other with the points. Great fun apparently.

    Cal has a good point on doing two years of algebra back to back and tucking in the geometry. I believe that’s how Saxon Math used to do it before they wrote a dedicated geometry book and moved to a more traditional sequence. There’s nothing wrong with two algebras except that you can run afoul of state high stakes tests; if that’s a concern to you. Heck, you LOSE alot of algebra I because geometry as taught doesn’t use alot of algebra

  36. Chartermom says:

    Well guess I was really showing my age when i asked about the proofs in geometry. 🙂

    I agree they aren’t much help with most other math but I actually was one of those very strange individuals who really enjoyed them (but then again I was also someone who never bothered to memorize a formula that I could derive on the fly). However I thought my older one would enjoy proofs too since he’s generally a pretty logical thinker. And I do think they carry benefits in helping to develop thinking skills. (and I admit those skills could be developed in other ways but typically are not.).

  37. Barry Garelick says:

    Clarification: My statement that proofs in geometry have been out of fashion for some time was not a statement that I believe they are unnecessary. I think learning how to do proofs is useful as an introduction to mathematical proofs in general. Geometry lends itself to proofs because the propositions can be illustrated in geometric diagrams, whereas in other areas such as algebra–and later in calculus and still later in real analysis–they are very abstract. Can you learn calculus without geometric proofs? Yes. But the proof concept in geometry also helps build the relationships between postulates, definitions and theorems and how one builds a heirarchy of mathematical propositions.

  38. Barry Garelick says:

    Sorry, I wasn’t finished, and I hit “post comment”.

    I agree with Cal that two years of algebra back to back is beneficial. That’s what I had, and then had geometry (with proofs) afterward. Two years of algebra builds a lot of confidence and mathematical maturity. No harm though in tucking in some aspects of geometry in the algebra courses. B

  39. Cal; I am well-aware of the cognitive differences across racial/ethnic groups and their impact on achievement, hence my comment that the most cognitively able kid s (lyes, disproportionately white and Asian) are the most likely to succeed despite poor curriculum and instruction. They are also likely to have parents of similar ability, who are likely to be educated and affluent enough to ensure that the kids start out ahead of the pack and

  40. Richard Aubrey says:

    Sort of OT. I liked plane geometry. The proofs, step by step, were frequently an enjoyable puzzle.
    The highest math I used after college was plane geometry, in the Army. “What do you do without an aiming circle?” “Draw this line, make a ninety, and back to each pit.” That sort of thing. No, don’t ask.
    After that, lower and middle arithmetic.

  41. 80%+ of students should not be taking and will never need Algebra I. Taking Algebra II is just more of the nonsensical advice that we get from educators.

  42. Understanding that the plural of anecdote is not data, I nonetheless offer my own anecdote, In 1973, I was in 7th grade, and they put me in an honors math class. The teacher used an 8th grade math book, and that included a section on algebra.

    I. WAS. LOST.

    I could not for the life of me figure out how one could add letters together. When the teacher asked me for the answer to a+b, my answer was “c” and I got in trouble for being a smart-alec, but I was truly clueless.

    Consequently, I was afraid of higher level math for years. Took General Math in 8th and 9th grade, and only took Alg 1 in 10th grade because I had to.

    Happily, I had an excellent teacher who used very methodical, logical progressions in her teaching, and my brain was ready for the more abstract concepts. I aced the class, and confident in my newfound ability, registered for Alg II the next year.

    Totally different teacher – fresh out of college, mathematical genius with no ability to communicate what came so easily to him. I was failing within six weeks, and dropped the class.

    Senior year, I took Geometry. Had another teacher who was able to explain concepts in ways that I could understand, and again aced the class.

    Was it me? Was it the teachers? Or a little bit of both? (also, someone told me after it was too late that I should never have tried to take Alg2 without having Geometry first. Is that true? If so, it was also a lack of guidance on the part of those who were supposed to vett my proposed schedule).

    And at age 50, I have never yet needed to know the answer to my Alg2 question about if 2 freight trains are traveling towards each other on the same track at different speeds, when will they crash.

    I have, however, needed to know how much square footage I just dug up in my yard, to calculate seed/sod/fertilizer requirements, etc. IIRC, I learned that in Geometry.