Fuzzy future

The future of fuzzy math rests on a bureaucratic fight in Washington, writes David Klein, a math professor, on Gadfly.

“Fuzzy math,” a philosophical sibling of whole language learning, refers to textbooks and school programs that intentionally de-emphasize basic arithmetic and algebra skills. At the elementary school level, these programs encourage students to invent their own arithmetic procedures, while discouraging the use of the traditional and far superior methods for addition, subtraction, multiplication, and division. Calculator use is encouraged to excess — in some cases, they’re even included in kindergarten lesson plans, at precisely the age that students should be learning basic computational skills unaided. Student “discovery group work” is the preferred mode of learning, sometimes the only mode, and the discovery projects are almost invariably incoherent and aimless. Some of the elementary school fuzzy math programs do not even provide textbooks for students, as books might interfere with student discovery projects. Arithmetic and algebra are radically de-emphasized by these programs. In the higher grades, mathematical definitions and proofs are generally deficient, missing entirely, or even incorrect.

The administration wants to transfer math education from a pro-fuzzy agency in the National Science Foundation to a division in the Education Department, which is likely to be anti-fuzzy.

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Comments

  1. The NSF is PROfuzzy and Education is ANTI?!?! Scary!

  2. Am I the only one who finds in odd that the fuzzies are in a corner of the NSF and the antifuzzies in the DoEd?

  3. Why is that “odd” or “scary”?

    NSF *should* be studying the effects of new approaches to math and the effects on students cognition. Education reform should be grounded in science.

    On one hand, republicators want scientifically-sound practices, but on the other hand they’re quick to dismiss scientific studies of methods if they are not congruent with their conservative agenda. Ah well.

  4. The fuzziness correlations may not be surprising if:

    – the NSF people think in terms of science-as-discovery and have forgotten how they got the basics down in the first place

    – and if the Education Department people have had more hands-on teaching experience which led them to realize that fuzziness fails

    But I doubt that.

    I like how David Klein calls the EHR division of the NSF a “directorate.” Makes me think of the directorates of the KGB. Is American e-duh-cation a Commie plot? 🙂

  5. Nina,

    It’s “odd” and “scary” that the National *Science* Foundation should support (not just try out, but support for YEARS) approaches that are opposed by “many of the nation’s most accomplished scientists and mathematicians.” And I doubt that those “scientists and mathematicians” are all Republican drones. This isn’t about politics.

  6. Nina D. says:

    Amritas,
    “Many of the nation’s most accomplished scientists and mathematicians” do not support these appraoches, and many of the nation’s most accomplished scientists and mathematicians do support these approaches. Look at the grant authors and advisory committees of NSF – they are more well established in the field of science and mathematics than you or I.

    I have a lot of respect for the science and the peer review process. If NSF-funded studies have determined there are merits to a number of math curriculum, then I think they should have the right to publish that regardless of the concerns of parents and a small group of scientists who are politically motivated – If these scientists were really concerned about education they certainly had ample time to volunteer their feedback and concerns through offering to review the results of related NSF studies.

  7. Nina D wrote:
    “Education reform should be grounded in science.”

    Read David Klein’s article to understand why many believe that the Education and Human Resources (EHR) division of the National Science Foundation (NSF) is biased and failing on this very task.

    Nina D wrote:
    “On one hand, republicators want scientifically-sound practices, but on the other hand they’re quick to dismiss scientific studies of methods if they are not congruent with their conservative agenda. Ah well.”

    It is incorrect to think that those who oppose the the low content, low skill mastery and vague standards (fuzziness) of current math curricula have a political agenda. Many are practicing scientists, mathematicians, and engineers who know exactly what is needed to prepare students for the work they do every day. They are also parents who see the silly math come home each day with their kids. These math curricula do not get the job done. Is it conservative to demand strong and competent math curricula for ALL students?

  8. Nina D. says:

    Follow-up:
    http://www.csun.edu/~vcmth00m/
    It seems the author of this study, David Klein, has published extensively in peer-reviewed journals related to gravitation and relativity. However, none of his writings in education and mathematics have survived the process of peer review.

    Why?
    Because he is drawing on a specific ideaology regarding education, not facts or scientific evidence. In my opinion, it’s irrespionsible for him to use his position to slander NSF’s EHR division when he himself has contributed absolutely nothing to the understanding of how children best learn mathematics.

  9. Nina D. says:

    Steve wrote:
    It is incorrect to think that those who oppose the the low content, low skill mastery and vague standards (fuzziness) of current math curricula have a political agenda.

    Oh Steve, I know not everybody concerned about these programs solely has a political agenda. I’m concerned about these programs, but that doesn’t mean I approve of what Klein at al did.

    But David Klein and his cronies certainly do. His “open letter” and subsequent efforts are politically motivated and have little to do with scientific progress. Much to the chagrin of mathematicians and educational researchers, Klein hand-picked the readers and signatures of the letters and ignored the concerns of many pre-eminent mathematicians and education researchers.

    This strategy does nothing for real progress in the science of learning and teaching, and this is reflected in his less-than-impressive scholarly career.
    His efforts only serve to exaggerate and dichotomize views under some vague veil of science simply because he has a ‘Ph.D’ after his name.

  10. Jim Thomason says:

    “It seems the author of this study, David Klein, has published extensively in peer-reviewed journals related to gravitation and relativity. However, none of his writings in education and mathematics have survived the process of peer review.

    Why?
    Because he is drawing on a specific ideaology regarding education, not facts or scientific evidence. In my opinion, it’s irrespionsible for him to use his position to slander NSF’s EHR division when he himself has contributed absolutely nothing to the understanding of how children best learn mathematics.”

    I don’t see how the page that you referenced supports your contention in any respect.

    I would say that your apparently unfounded allegations regarding Professor Klein and your childish use of “Republicator” make it much more likely that YOU are the one more motivated by politics.

    I myself don’t have enough information to determine if Klein is correct or not, or if “fuzzy math” has any promise or not. His article seemed to assume that I knew much more on the subject than is the case, but then it was in the “Education Gadfly” column, so I suppose that makes sense.

    Your posts don’t add anything to my knowledge. What studies are you refering to? I have a vague memory of reading about a small study favorable to Everyday Math, but a number of the parents were interviewed who hated it. A number of them said that they were forced to teach math themselves and/or hire tutors, and attributed the favorable results to those efforts, not EM.

    Again, this is just a vague memory from a couple of years ago, and I may have some (or most) of the details wrong.

    PS Amritas – they call themselves the “Directorate”:

    http://www.ehr.nsf.gov/

  11. Let somebody who majored in math–and loves it–teach it any way he wants.

    Do that, and everything will turn out fine.

  12. ” I have a vague memory of reading about a small study favorable to Everyday Math, but a number of the parents were interviewed who hated it. A number of them said that they were forced to teach math themselves and/or hire tutors, and attributed the favorable results to those efforts, not EM.”

    Our school uses everyday mathematics. This week, at a gathering of five parents, it became clear that almost all were tutoring their children in math, or hiring math tutors. The one who did not tutor her child yet was taking notes. In affluent, educated settings, parents may complain about “fuzzy math”–and they take steps to protect _their_children.

  13. I think the NSF is another one of those organizations that have a name that contradicts their true intentions…

    I think that a scientist’s biggest complaint about fuzzy math, as well as most other education fads, is that they’re simply guesses at what would work… Rarely, if ever, are they introduced into a trial classroom or two, with the results carefully measured against a sample set, the results published for review, and after good results, then the new practice is implented in schools… (A.K.A. Controlled Experiment) Rather, someone come up with something that sounds good, and it gets rushed into schools…

    Granted, I don’t know the roots of fuzzy math or everyday math, so I can’t say with 100% certainty that this is true for these two fads… But I’d be willing to make a hefty wager on it…

  14. Sign me up as an upper middle class parent (and engineer) who is having both of his children (girls) tutored outside the fuzzy math curriculum. My 13 year old was having a very difficult time in math starting in 3rd grade. It’s really hard to understand concepts, averages for example, when your actual math capabilities will only allow you to do the simplest problems with confidence. BTW, after 1 1/2 years of external math instruction her confidence has soared along with her math abilities.

    Recently our 2nd grader had a parent teacher conference and she demonstrated an addition problem (i.e. 15 + 24 = ). She did it by drawing lines between the tens places and the one’s places. So the problem turned into 30 + 9 which she then summed to 39. What turned my stomach was when the teacher mentioned that in 3rd grade they would expect a detailed explanation of how she solved the problem. Two weeks later I (we) placed her in outside math program as well.

    Unfortunately, I expect to keep both my children in outside math programs until the fuzzy math program goes away. Initially I felt that in some grade “math would become math”. That appears not to be the case, as the fuzzy math curriculum goes through the HS grades. Now I have discovered there is Harvard Calculus to continue the fuzzy math tradition. Uugh

  15. It should be noted that the use of the term “fuzzy” in the post overloads the word. “Fuzzy logic” is a legitimate branch of mathematics, created by Lofti Zadeh, that deals with a probability-based variation of propositional logic. Instead of saying things such as “If a, then b,” fuzzy logic deals with things such as “If a, then there’s a c percent probability of b.” This means that the use of the word “fuzzy” in the context of the post stinks, in my opinion.

  16. george1 says:

    “Let somebody who majored in math–and loves it–teach it any way he wants.

    Do that, and everything will turn out fine.”

    I agree that ignorance is not a good prerequisite for teaching, but please check your history. Newton’s lectures on math were frequently attending by no one but Newton hinmself. Gauss’ lectures were poorly attended. Knowledge and accomplishment and enthusiasm are not automatic qualifiers for teaching. If the instructors cannot communicate to their students they are wasting their time.

  17. Mad Scientist says:

    The basic problem with the so-called “scientific” studies on teaching methods are twofold.

    First, there is no rigorous control, where one group of students is not taught anything except “concept X”, and another group is allowed to have their parents supplement “concept X” with any means at their disposal. It simply cannot be done, because what are you going to do, penalize the parents who refuse to NOT supplement their kids supposed education?

    Second, (and I KNOW this will offend some people here) it is widely recognized that the Ed.D. degree is largely regarded as a joke outside the education establishment. Generally these people have not had to do rigorous, independent research that has had to stand up to the basics of scientific scrutiny (see above re: control groups).

    What passes as “peer reviewed research” makes my stomach turn when I can pick out the flaws in the methodology without digging very hard. Unfortunately, the popular press also lacks the critical thinking skills to scrutinize the reports, and basically passes on the author’s conclusions as presented in a news conference (which is generally favorable to the the author).

    Also, not all “scientific” orginizations are unbiased. It helps to know which ones they are and how their bias runs.

  18. Wacky Hermit says:

    I can’t help but wonder what the NSF would think of teaching students in Kindergarten to make up their own numerals. If they’re going to make up their own addition algorithms in first grade, why stop there? Let them invent math from scratch, like our distant ancestors did. Let them independently invent the concept of number, then make up their own symbols to describe different numbers. Let’s hope that some of them may develop a base-five system, others a base-seven system. All will be equally good.

    No? Why not?

    The truth is, we need a consistent set of mathematical symbols and procedures in order to communicate mathematics effectively. If we don’t teach them to our students, we will end up with a mathematical Tower of Babel. No one will be able to understand anyone else’s mathematics.

    And then there’s also the issue of progress in the field. Sir Isaac Newton’s quote about standing on the shoulders of giants is apropos here. If our kids spend all their time constructing their own giant’s feet, they will never get to the shoulders in their lifetimes.

  19. Wacky Hermit- You hit the nail on the head with the best post yet on this subject. I took a math methods course a few years ago while getting my master’s in education, and the insistence on the use group learning and alternative methods of computation for elementary students was a triumph of wishful thinking over common sense, in my opinion.

  20. Walter Wallis says:

    Fuzzy math – a branch of the fuzzy history department in the fuzzy thinking university.

  21. Sandy P. says:

    I’m a product of new math. My parents are in their 60s and STILL laugh at over how stupid it was.

    When I get HS and older who can’t make change w/o a calculator, we’ve got a serious problem.

  22. Nina D. says:

    Mad Scientist,
    You oviously have no experience in NSF-funded research – Ed.D’s are only useful for practioners. Every NSF-funded scientist I know studying education has a Ph.D in an area such as psychology, where rigorous independent research is expected.

    Also, you’ll be happy to know that there were control groups in NSF-funded longitudinal studies of everyday math dating back to 1993 and in a recent (2000 i think?) study of achievement in several states. In most cases, students engaged in “Everyday Math” curriculum outperformed students in the ‘control group’ using traditional curriculum. These tests were state-mandated achievement tests and the groups of students were fairly well-matched in terms of popular variables such as socioeconomic status.

    Granted, I don’t think the methodologies are perfect and I personally do not support everday math in particular based on other evidence. But we have to acknowledge that there was *some rationale* for NSF showing support for so-called fuzzy math programs.

    People like Klein are motivated by particular ideaologies and contribute nothing to our understanding of how children learn math. It is particularly furstrating because he is a scientist and should know better – he would be more helpful to improving education if he participated in the peer-review process, contributed research findings of his own, or otherwise supported dialogue around these important issues rather than organization-slandering.

  23. Anonymous says:

    “Let somebody who majored in math–and loves it–teach it any way he wants.

    Do that, and everything will turn out fine.”

    Here’s the problem: This person will be a good teacher for kids who love math too, and to whom it comes easily. He’s going to hit a brick wall with the average kid who has to struggle to understand that year’s lessons. (And let me say, it should be a struggle – otherwise you’re wasting time.)

    I’ve reached this conclusion from talking to people my age (40’s) and older who swear that they just could not do math; from 7th grade on they just couldn’t get it at all. And these were extremely intelligent people. I suspect that they didn’t intuitively grasp what the teacher was trying to tell them, and that they had questions that the teacher didn’t understand and so couldn’t answer, because it was so intuitive to the teacher. I remember in 7th grade there were kids, and they weren’t the dumbest ones in the class, who had trouble with the concept of using variables. We had a pretty good teacher. I remember him telling them, “You’re making it harder than it is!” and working with them until they got it. Being a mathmatician or even just a person who loves math isn’t the same as being a math teacher.

  24. Laura (southernxyl) says:

    Sorry, that was me.

    And Nina, keep poking at us. We all need to have our assumptions questioned from time to time.

  25. “..had trouble with the concept of using variables”…I think this problem is a fairly common one, and might be a case where the use of computers or calculators could actually help. Seeing variables “in action,” so to speak, might help in grasping the concept.

  26. Mad Scientist says:

    Nina:

    You are incorrect in your assessment. I have written proposals for NSF grants way back in grad school. But never for the SOFT sciences (like psychology) where there are no real rigorous controls.

    Unless you can show me a study where the EM students were kept from other outside influences (i.e., their parents paying for tutors who actually KNEW what they were doing), then the study is BOGUS.

    A true controlled experiment would look at students RANDOMLY chosen from a school district to participate in EM or not, have teachers who were experts both methods randomly chosen to teach EM or traditional curricula, and manage to keep all the students and teachers from outside influences. You would NEVER get approval for that.

    Yes there was some rationale for NSF studies: try something new, and prove it is somehow better. We are a nation of math illiterates in this country, and by giving up and moving to EM, we are solving the problem by acknowledging it exists and trying to make it easy. It is never going to work.

    All I know is that I have to make hiring decisions in a field where math skills are necessary, and most of today’s students don’t know squat. Campare that with 20 years ago, and things have gotten WORSE.

    And as for the NSF not having a political agenda, I would expect you should know better. These so-called “scientists” are doing a disservice to this country.

  27. Nina D. says:

    Unless you can show me a study where the EM students were kept from other outside influences then the study is BOGUS.

    The real world is a complicated place, and the study you propose above is impossible as you probably know. But that should not stop us from trying to understand the effects of teaching practices on our children.

    I know at least one of those studies i mentioned above queried parenting practices, and presumably they found balanced approaches in all populations of students (regardless of math curriculum).

    Again, I feel like we share concerns about so-called fuzzy math, particularly everday math. I just don’t think we should support Klein’s approach to the problem. He does nothing to add to our understanding of how children learn math, but adopts the kind of polarizing position that i find stifles scientific progress.

  28. Laura (southernxyl) says:

    David, I don’t think computers or calculators would help 7th graders understand what variables are.

    Teacher: Suppose we are buying a candy bar with a five-dollar bill and we want to calculate how much change we get back. Let “x” = the price of the candy bar.

    Kid: But what does that MEAN?

  29. Laura…my thought is that you write a simple program with the expression C=A-X*N, where

    C=change you get back
    A=amount of money you paid
    X=price of the candy bar(s), each
    N=number of candy bars purchsed

    ..and then let them watch how C changes as you change the other variables. The idea is that they would get used to the idea that you can have a relationship among variables independent of what the values of the variable are.

    Might or might not work…just an idea.

  30. Laura (southernxyl) says:

    David, I think that would give rise to about forty more questions.

    I think I remember our math teacher telling us that an equation is just a sentence that you write using mathematical symbols instead of words. He got the kids to tell him how the $5, the cost of the candy bar, and the amount of change were related, then wrote out the equation. Which is kind of backwards from your computer example.

    My guess is that there is no one way to get this concept across, that will reach every kid. An educator would have to be able to understand what a particular kid’s roadblock is, and not think he’s stupid for not getting it from the same explanation everybody else got it from, and that’s going to take patience and imagination. That’s why I think that somebody who wasn’t the class math whiz might turn out to be the most effective teacher.

  31. Mad Scientist says:

    Nina:

    Why do we NEDD to understand how kids learn math? Math has been taught well for many years, why mess with something if it is not broke?

    In the kind of work I do, chemists are coming up with all sorts of formulations; it is my job to take their ingredients and make them into a viable product. I am limited in the tools (process) I can use. I do not need to understand how they go together to make a superior product.

    What about cooking? Some people are better at it than others. I very much doubt they either know or care to find a better way to make a tastier cake. Sometimes tried and true methods are superior. Experience counts for something.

    Take learning to read as an example. A whole industry is built around selling a phonics course because the schools have supposedly found a “better” way.

    The point is that if you refuse to teach some basic skills, then the product you end up with is garbage.

    You are the one putting a “political” agneda on this issue.

    And, for your edification, none of these studies is “scientific” in even the loosest definition of the word. Just because you can correlate something with something else, does NOT infer that you have a causative relationship. Psychology and psychological studies are all a load of crap driven by one persons questionable interpretation of sketchy so-called “facts”.

    But if you want to call a process where the person who convinces the most people of his pet theory science, that is your right.

    It would be wrong, but it is your right.

  32. Laura, et al., It seems to me that the difference between the teacher who likes so-called “fuzzy math” methods and the more traditional teacher is that the first thinks it’s GREAT when a lesson leads to more questions, while the second one says, “Here, memorize this method. No questions? Fantastic.” I’ve overstated this slightly, as I personally think there is a time and a place for both in the math classroom at any grade level. Ask most adults how to divide one fraction by another, and they know the method. Ask them WHY the method works, and very few can tell (show) you, and those who can take several minutes (or hours) to figure it out. I would be curious to know how many posters on this board were “good” math students who learned things quickly through traditional methods. I suspect many of us! But for every one like that out there, there’s another adult bemoaning how they never really GOT math, even if they learned how to DO it. Hmmm. I wish this issue were not so polarized – kids need a little of EACH, I would say.

    I understand people’s problems with the studies of whether fuzzy math works. Nevertheless, it seems inconsistent to turn around and in the next breath claim that traditional methods ARE supported by rigorous, fully-controlled studies – the same problems that plague the studies of fuzzy math would seem likely to plague studies of ANY classroom curriculum or method.

  33. Nina D. says:

    …none of these studies is “scientific” in even the loosest definition of the word. Just because you can correlate something with something else, does NOT infer that you have a causative relationship. Psychology and psychological studies are all a load of crap driven by one persons questionable interpretation of sketchy so-called “facts”.

    Glad you placed your ignorance on display for all to see.

    Do yourself a favor and actually read the reports. This isn’t simply a case of correlation rather than causation or “one persons interpretation”.

  34. Mike McKeown says:

    A number of comments, mostly by one person, refer to David Klein’s political agenda, which is inferred to be notably conservative. I know David and can state with confidence that David’s politics are of the far left persuasion.

    David’s views on education reflect, but were not necessarily formed by, the educational philosophy of Antonio Gramsci, an early 1900s Italian Communist. In part, Gramsci argued that the purpose of a state education was to give the unempowered access to all the intellectual tools of power that would otherwise be limited to the advantaged ruling class. The fastest, most effective way to do this involves quite a bit of direct instruction.

    David’s non-conservative views are not unusual among opponents of constructivist/discovery learning math, although the major attack on those of us who oppose such programs is that we are “right-wing Christian fanatics.” To raise this objection, or imply that that is the case, about the people who signed the Letter to Secretary Riley is patent nonsense. Almost all of the signatories are university mathematicians. Many of the signatories that I know are decidedly neither right wing nor Christian. On the other hand, there are Nobel Prize and Fields Medal winners, members of the National Academy of Sciences, and professors at respected universities.

    WRT to the claims that the NSF has been doing research on what works in math ed, it should be noted that Luther Williams, former NSF EHR director, shifted the entire emphasis of EHR instructional and Urban Systemic Initiatives to constructivist/discovery learning models in both math and science. He did this with little or no supporting evidence. From that point on, the grant money went to the development of such programs, or the implementation of such programs, not to finding out what really works best. What measures of effectiveness were done were almost exclusively run by those devising the programs that EHR wanted. Remember, the research on effective reading instruction was not funded by NSF, it was funded by the National Institutes of Health.

  35. Mad Scientist says:

    Nina:

    I see you are quite adept at gratituitous ad hominem attacks. Congratulations!

    The fact remains is that “Psychological Science” is an oxymoron. Anything that relies solely on statistics to prove a point one way or another is pure crap.

    So tell me, were there “teaching method neutral examinations” graded by disinterested third parties? Didn’t think so.

    You see, when there are no objective measures, anything can be whatever you want it to be.

    I, and others here, would be quite interested in knowing your credentials and special interest in this bogus method.

  36. Nina D. says:

    Mike – it’s possible you were referring to me. I used the word “conservative” in my first post to describe the administration, which is trying to move funding from NSF at the same time claiming to support a science-based approach to education policy.

    My major concern with David is that he has a particular agenda and ideaology that is informing his “work” rather than actual evidence beyond anecdotes. His views end up being quite polarizing and therefore unhelpful to progress in reforming education.

  37. Nina D. says:

    The fact remains is that “Psychological Science” is an oxymoron. Anything that relies solely on statistics to prove a point one way or another is pure crap.

    Psycholgy “relies soley on statistics”?

    This is enlightening and humorous at the same time.

  38. Mad Scientist says:

    Nina:

    Afraid to take up the challenge?

    Thought so.

  39. Nina D. says:

    What challenge?

  40. Mad Scientist says:

    Nina:

    Apparrently you read just as far as you want to and emotionally respond. Here was the challenge:

    “I, and others here, would be quite interested in knowing your credentials and special interest in this bogus method.”

    Capice?

  41. …”Ask most adults how to divide one fraction by another, and they know the method. Ask them WHY the method works, and very few can tell (show) you, and those who can take several minutes (or hours) to figure it out.”

    Well, two of the fuzzy programs I am familiar with (TERC and Trailblazers) don’t teach division of fractions AT ALL. It’s not in the curriculum anywhere. While understanding the concept is certainly optimal, being able to do the algorithm is better than nothing. These kids will get to algebra without ever having heard of division of fractions.

  42. Nina D. says:

    MD,
    I saw that inquiry, but i’m in a position where i should reamin anonymous, at least publicly. I do have an email address.

    We can also continue to debate the merits of specific disciplines that claim to be scientific. Your position seems to be that scientific research in the classroom is impossible due to the complexities. My concern is that the administration wants “science-based” policy, so there should at least be some semblance of scientific process and gathering of data rather than politically-motivated educational policies and educational ideaologies informed by anecdotes (Klein’s alternative to science).

  43. “Do yourself a favor and actually read the reports. ”
    Nina,
    Where exactly can they be found? They don’t appear to be on the NSF site. The Everyday Math publisher doesn’t have a link, and it’s not in the ERIC database. In the many times I’ve seen this Everyday Math “study” cited, I’ve never once seen a citation. I’d appreciate suggestions on how to find it.

  44. Mad Scientist says:

    Nina:

    Not even willing to post a degree level in a specific subject? Wow.

    Your “concern” is that you want a new fad that will leave children ill-prepared for college and later, the workforce. You have a political agenda, and rely on largely anecdotal evidence to “substantiate” your claims.

    I see the effects of these watered down programs every day. You are partially responsible for educating a generation of children that have limited critical thinking and reasoning abilities.

    Stick with the basics of what works. What you so vigorously defend is destroying the ability of this country to compete in a global marketplace.

    Besides, show me the “Informed Consent” documentation where the parents have agreed to use their kids as guniea pigs in those experiments.

  45. Nina D. says:

    KPM,
    I know the ARC center has a 13-page executive summary available online:
    http://www.comap.com/elementary/projects/arc/tri-state%20achievement%20full%20report.htm
    It’s an all-too-concise summary of the three-state comparative study I referenced above.

    MD,
    I’m a little confused – you think i support everyday math? To be explicit;
    1) I do not support most so-called reform curriculum, particularly everyday math
    2) But i still think Klein’s polarizing tactics are unproductive at best and at worst harmful to real progress in education

    To answer your other question, I doubt “informed consent” existed for these studeis. IRB generally does not require active consent in situations where normal practices are occurring. These schools already chose their curriculum, so the *studies* did not force the teachers to do anything unusal or put the children at further risk (though the curriculum might have!).

  46. Mad Scientist says:

    Nina:

    As opposed to your polarizing language?

    What I could see of the study that ARC put on the website, the study is inherently flawed for two reasons:

    1) It is well known that as population size increases, it is easier to see a significant difference (since the t-test result is scaled by the inverse of the square root of the number of samples). As the sample size approaches infinity, a small difference can easily yield a false positive.

    2) More importantly, the study is looking for differences in percentile score on a test that is supposed to have a gaussian distribution of scores. The two groups did not appear to have a bimodal or higher distribution of performance and all still fell well within the normal distribution for the exam.

    To summarize, while it may be possible to distinguish statistically between performance at the 50th and 55th percentile, in reality both of these scores are well within the “normal” range.

    Until you can demonstrate the difference between populations is TRULY significant (i.e., one group of scores changed from the 50th percentile to say the 75th percentile while the other held constant), the analysis is flawed. This study does not make that demonstration, and therefore proves NOTHING.

    This is known as the classic Type II error (finding a significant difference when, in fact, once does not exist).

    So, I’ll put my PhD in Engineering (with enough graduate level Math credits to have a Masters in Applied Math) up against the analysis of that study any day.

    Only a true Math Illiterate would buy what they say in that executive study.

  47. Nina D. says:

    lol, you’re too funny…
    Where in that document did you see anything about t tests or distributions?

    This isn’t freshman statistics, you know!

  48. You still have to go from point A (counting numbers) in Kindergarten to point B (algebra) by eighth or ninth grade. This argument over “fuzzy” math is not just about how you teach. It’s about what you teach. compare any of these math programs grade by grade with Saxon math or Singapore math and you will see a very large difference beginning in first or second grade.

    I remember four or five years ago when I first started looking at educational methods when my son was about 3. I was thinking about what I would improve about the (traditional) math that I was taught when I was growing up. Then I read a glowing article about TERC and was dumbfounded! Anyone can make math easier by covering less material and expecting less from students. Talking about problem solving or critical thinking just covers up the fact that less material is covered and fewer basic skills are mastered.

    Compare these programs with Singapore or Saxon math for exactly what is taught. You don’t need any scientific study for this. My son moved from a school still using MathLand ( which still works on adds and subtracts to 20 in third grade!!!) to one using EM (supplemented, of course). However, I use Singapore math with my son at home and the differences in difficulty level are very clear even in second grade.

    After 30 years of writing CAD/CAM, engineering and 3D computer graphics software (and teaching college math and computer science for many years), I think I have a pretty good idea of what content and skills are needed for a technical career. The comparative content analysis is very easy. Look at the problems that the students can solve at the end of each grade. From their answers you can tell how much math they know and what kind of problems they can solve. I am not talking about state or national standardized tests, since they test only for minimal competence.

    While you are comparing curricula, get sample questions from standardized tests (NAEP, NSRE, etc) and compare them too. Improving standardized test scores may be nice, but these questions are so easy that they have no meaning for parents who want their kids properly prepared for technical careers. Your school could be rated very highly on state or national tests, but your kids might not be properly prepared for a technical career.

  49. Nina D. says:

    Oh, you made a point worth revisiting – the type II error.
    Social scientists (or pseudo-scientists, if you prefer) claim that exploratory studies should be more vulnerable to the type II error than type I. The reason is that it’s better to err on the side of caution and then follow-up with confirmatory evaluations that have low risk for type II error. This same logic applies to, say, exploratory medical diagnostics such as a pregnancy test (it’s better to be erroneously told you are pregnant than erroneously told you are not pregnant). In these cases, a test susceptible to a type II error is first used and then a follow up with a doctor will confirm with more rigid tests that lower the risk of type II error.

    So personally i would agree that this one study “PROVES” nothing – it only suggests there’s something going that should be examined through better-designed studies (such as the longitudinal strategy you seem to suggest, where real *change* is observed).
    But again, this all assumes it’s worth trying to gather and evaluate evidence responsibly in response to the administrations desire for “science-based” policy. And you seem to be against that because social sicence is not possible, statistics are “crap”, etc.

  50. Mad Scientist says:

    Nina:

    This is what I mean about INFERING methodology. When you do a test and state that something is significant at a given level of confidence, you do a t-test or and F-test. It just so happens that the F statistic is simply the t statistic squared.

    So the psuedo-scientists are saying they would rather err on the side of finding a real effect when one does not exist? THAT is totally bogus. No self respecting Scientist would agree to that, unless, of course they just want to be gainfully employed writing grants and conducting research that is meaningless.

    And you example of a pregnancy test is spurious. How would you like to get a flase positive for, say, breast cancer and go ahead and have surgery?

    The problem is that the FIRST study that says X, if later refuted by a more rigorous study, is ALWAYS cited as gospel, and later studies are flawed.

    If you really wnat to prove something in this arena, you would have to conduct a study that shows the SHAPE of the distribution of test scores significantly changes. It the method is effective, then one should get a demonstrably positively skewed distribution to higher scores; no chance should not alter the shape of the distribution; and poor performenace should show up as a negatively skewed distribution.

    I never said statistics was crap. Please reread my statement. I said that anything proved by statistics alone was crap. There is a big difference.

    It does remain that the methodology of the study is indeed crap.

  51. Nina D. says:

    haha.. confidence levels always invole t or f distributions? Again, move beyond you univariate introductory text and then get back to me with your methodological concerns.

    Your breast cancer example is an insulting and intentional misreading of my point. The idea is that a false positive will be followed up with confirmatory testing, *not* surgery. This is the model practiced in medicine and should be the model followed in studying children’s learning. I do agree with your second point that when an exploratory study yields a finding, too many people are quick to accept the results “as gospel” when they should be further scrutinizing the results and developing better measures.

  52. Pouncer says:

    “Your breast cancer example is an insulting and intentional misreading of my point. The idea is that a false positive will be followed up with confirmatory testing, *not* surgery”

    If educational methods were subject to the same scrutiny that medical methods are, we’d have a better school system.

    Anecdote. I took my daughter into our new neighborhood’s public school and asked, “what class should we start her in? She can read well, her math is limited to single digit addition and subtraction, she can’t read music or play any instruments, yet, but she can mimic a tune vocally in the correct key. Is there a placement test to help us find the best fit?”

    I was, in turn, asked: “How old is she? Oh, well that means — (grade). The next opening in (grade) is for Ms (name’s) class. ”

    No testing at all. It’d be like having heart surgery or liposuction because a patient just turned 50, or 40, or something. Worse. It’d be like having ACCUPUNCTURE and LEECHES because you’d reached a certain age. Then, after 3 years of treatment, THEN we’d do tests to see how well the leech thing had worked out. If the test results were, in general, poor, we’d blame the home environment …

  53. Mad Scientist says:

    Nina:

    Damn, girl, you are real good with the gratituitous ad hominem attacks. Try to put the sarcasm on hold. I never said I was a professional statistician; I do, however, use statistics on a regular basis.

    Unfortunately, all of the data presented looks like univariate results. And if it’s not, why not dazzle us with YOUR understanding of the techniques used. That crap would not hold up to real scrutiny.

    I am surprised that the comparison of scores on a standardized test was not checked against statistical significance against the distribution of the test.

    Let me assure you I am well versed in mulitvariate statistics, design of experiments, Partial Linear Regression and Partial Least Squares methods.

    Most of the “studies” so not involve the use of PLS methods because the methods are not widely used outside of chemometrics. So when you can give me a good basis for your understanding of the right techniques to use, you can get back to ME.

    I still haven’t learned what degree you have, or in what field you work, or YOUR vested interest in this topic.

  54. Jim Thomason says:

    This site looks to have a lot of information on Everyday Math, in case anyone is actually interested:

    http://www.math.nyu.edu/mfdd/braams/links/em.html

    It doesn’t look good for EM, but maybe there is a bias in what was included on that professor’s site.

  55. Jim Thomason says:

    WRT math instruction in general, while the text and teacher can have a large effect, I think that the actual problem is the school system itself, at least as presently conceived.
    The problem is in every subject, but Math, by it’s very nature, accentuates it.

    The problem is that you have 20, 30 or more kids learning at their own rate, but the class has to move at the “average” student’s pace. The quicker students are bored, while the slower ones are lost. Advanced and remedial classes address this to some extent, but it’s not enough.

    The problem with math is that it, more than any other subject, continually builds on earlier knowledge. A kid who can’t diagram sentences can still understand and benefit from reading Shakespeare, but a kid who can’t multiply is going to be completely lost in algebra.

    This is why people complain about never really “getting” math: the class moved on without them. That’s also why so many people say that they “hate math”. How else would you feel it your teacher is droning on and on about something you have no chance of understanding (without the necessary knowledge base)? It would constantly make you feel stupid, and so you would hate it.

    PS And problems with math can have little to do with intelligence. Ben Franklin, one of the most brilliant men in history, not to mention perhaps the pre-eminent scientist of his day, reported of his year or so of formal math instruction that he “failed in the arithmetic, and made no progress in it”. It wasn’t until much later that he more or less taught himself mathematics.

    PPS If anyone is intersted, here is a site with Ben Franklin’s Autobiography, an American classic, online:

    http://www.ushistory.org/franklin/autobiography/page03.htm

  56. Edison, also, was apparently pretty bad at math. I’ve heard it suggested that one of the reasons he favored DC power is opposed to AC is that the math required for AC engineering is much more esoteric….

  57. Walter Wallis says:

    This would be even more fun if it were taking place in a vat full of Jello.

  58. Anonymous says:

    I agree with Jim. How many people out in the world say that they just aren’t good at math as if it is some sort of genetic defect? How many of these people could be good at math but had just one bad year or one bad teacher? This applies to whatever curriculum you use. (It is also true that math can be very difficult and many people just don’t like it.)

    However, many modern “reform” math curricula (like EM) use a spiraling approach that lets kids go from year to year without ensuring mastery of the material. The idea is that they will eventually master the material if they see it enough times. Unfortunately, this doesn’t guarantee mastery of the basics and it increases the ability differences between students in later grades.

    Add to this what our public schools refer to as “full inclusion” where borderline autistic kids are included in the same classroom as the exceptional kids. Then, add to this the philosophy of child-centered group discovery learning using mixed ability groupings. Our superintendent says that she will not do “pull out”, which means that she will not separate the better students using any sort of TAG or GATE grouping or program. This is a philosophical (not pragmatic) decision. They feel that all students can learn at their own level using some sort of group-centered differentiated learning approach. If you get past all of the happy talk, you realize that the better (even average) students are not allowed to move on to advanced material. They are forced to just do more depth or variation of the same material. For example, instead of moving on to learning the multiplication tables in second grade, they have to revisit simple adds and subtracts from one more angle.

    Full inclusion and spiraling are shown by the fact that our public school is still trying to get the kids to master their adds and subtracts to 20 half way through 3rd grade. Wider ability groupings require lower and/or fuzzier expectations. Their curriculum guide explicitly states that about 20 percent of the students are allowed to move on to the next grade without showing mastery of the material. I have never been able to figure out how this 20 percent finally masters the material? What are the better (80 percent) students doing when this happens? And, this is done in a mixed ability group setting? Educational philosophy runs smack dab into the brick wall of reality.

    Many people assume that the 20 percent plus of our students go to private school because the parents want an exclusive or elite education. Talk to the parents, most of whom went to public schools, and you will find them struggling to give their kids the challenge they need.

  59. Steve LaBonne says:

    Having been through brief but trying experiences with my kid with Everyday in 3rd grade(bad)and Investigations in 4th and 5th (worse), I say that Klein’s complaints are 100% on the mark, and I don’t give a damn about his political motives if any. See the Mathematically Correct website for a lot more information on what’s lacking in these unsuccessful experiments.

  60. Mad Scientist says:

    You know, I find it QUITE interesting that the so-called “study” Nina D. references does NOT list the authors.

    And I refuse to pay $15 to get the entire article.

    Something does not smell right.

  61. Walter Wallis says:

    …,with whipped cream.

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