Quote from: jhkimWhat's even more annoying is that you're trying to give the impression that the NYTimes article is citing a drop in scores.  I'm going to repeat this again for clarity -- the drop in scores mentioned in the article was for districts other than the one whose curriculum was being complained about!!  Again, here's the start of the article.

The article says that it's not the only district where the curriculum is being complained about.  "As school districts from affluent enclaves in Greenwich Village to poor minority neighborhoods like East New York have embraced constructivist math, parents have formed e-mail networks and turned out in force at school meetings to protest what they say is 'fuzzy math' and the systematic 'dumbing down' of mathematics teaching."  "Constructivist programs are being tried in more than half of New York City's 1,145 schools, Board of Education officials said."  The focus was on that district but it wasn't the only district to change things.  

Yes, it's true that District 2 held it's scores but consider the additional points made in the article.  "And tutoring services say that they are seeing an epidemic of children coming to them for basic math instruction."  "And other officials noted that the new test was closely aligned with the District 2 curriculum, and many parents attributed the good scores to tutoring by professionals and parents. And they noted that the district had been spending $800,000 a year on training math teachers."  "Parents said they were stunned as they talked to their friends and realized how many had hired tutors. Those who cannot afford tutoring tell of scouring educational bookstores for workbooks and textbooks to help them make sense of the new math."

So, sure, if you have affluent parents who can tutor their own kids, hire tutors, or buy their own books that can overcome all sorts of problems.  It also helps if a district spends nearly a million dollars (I'm rounding ) to make their teachers better teachers.  And it, of course, makes it maddeningly difficult to tell what works and what doesn't work.  Did your son learn multiplication tables as part of a pure curriculum or because he had good teachers that simply use what works?

As for Lucy West's claim that, ''There is a misconception that in the good old days everybody could add and subtract, multiply and divide really easily and efficiently.'' my family contains plenty of blue-collar people educated during the Depression in an urban school district in classing with as many as 30-40 students in them and they seem to do pretty well.  In fact, I had never heard of Casting Out Nines until an older person explained it to me.  As with the beautiful language found in those Civil War letters that Ken Burn used in his documentary, the reason why people had good language skills and decent mental arithmetic skills is that they couldn't waste their evening watching TV or fall back on using a calculator.  Engineers were using slide rules and log tables into the 1970s.  Accountants also had to do bookkeeping by hand or with simple adding machines.

Quote from: jhkimThat's the same district 2 that the article is focusing on from the start, and the same Ms. West who repudiated old-fashioned math teaching.  This is the same quote which you are trying to tell me shows a drop due to the "fuzzy math" teaching.

The article says that District 2 was the only district that didn't drop.  It then discusses why.  It talks about spending $800,000 a year to train teachers.  It talks about parents sending their kids to tutors, tutoring their kids themselves, and buying non-official books for them to learn from.  It also talks about the test being aligned with that particular district's curriculum.  In other words, the article is skeptical that the new math should be credited with the performance.  Perhaps that's bias or perhaps it's not.  My main reason for posting it was the anecdotal evidence from the parents who are not happy with the progress their children are making.

Quote from: jhkimOne of my complaints about John Gill, mentioned in the LJ post, was that it seemed to be excessively emphasizing rote material like computation and spelling, to improve performance on standardized tests -- which I felt short-changed other aspects of education.

What's important to note here is that's what NCLB is designed to do.  At it's heart, it's meant to tell the constructivist programs, "Put up or shut up."  In other words, if these teaching programs produce kids that can pass tests, then they'll be left alone.  If they can't, they'll be tossed under the truck and replaced by material that emphasizes more traditional computation and spelling so that they can pass the tests.  I think the valid question to ask here is whether the tests actually test kids for the skills they should be learning in school.  If they do, then I think that's a good thing.  If they don't, then I think the tests need to be changed.

What exactly is your problem with changing the way the school teaches so that kids can pass the tests?  Do you think that the tests don't test for skills that the kids should have?

Quote from: jhkimAs far as funding, I did note pretty clearly that money spent and quality of schools aren't the same thing.  It is most definitely possible to mismanage money.  However, funds and especially competitive teacher salaries and benefits are vital to maintaining a good system in the long term.  I've long supported moving schools off local funding to the state level, but keeping local control.

It's beyond simple mismanagement of money and tenure (something that disconnects teachers from incentives to do a good job).  There simply isn't a clear correlation between money spent per pupil and how well they are educated.  A much bigger factor involves parents and the prevailing culture of the area where the child lives.  If their parents and neighbors value education, the kids will overcome a great deal to get one.  If their parents and neighbors don't value education, then all of the money in the world may not help them learn.

Quote from: jhkimHonestly, I can't tell.  Most of the things that the parents are quoted complaining about in the articles don't seem relevant to me.  My son has done plenty of exercises that sound pretty similar to issues like working with tiles and fences.  The handshake problem cited at the start of the Time magazine article sounds great to me.

(POSTED TOO SOON - FIXING)

But what if your son didn't know his additional and times tables and had trouble coming up with correct answers?  Would you be as happy?  That's my point.  You've had a good experience so of course you are happy.  Other parents have had worse experiences and they aren't happy.  If your son knows his multiplication tables, it sounds like your school district has sensible teachers that mix and match.  I have no problem with that.  My complaint is with districts that embrace programs like whole language and constructivist math programs fully and don't teach the basics.  

Quote from: jhkimFor example, my son recently completed a project where he made a little diorama about a book he read.  (He chose "Me and Max and the Time Machine".)  I did not then feel that the school was failing to teach reading because he had an English project that involved no literacy -- it just seemed like a fun project that got kids involved.  In contrast, the NYTimes article cited parents outraged that their student had an amusing-sounding assignment to write about their favorite number.

That's because you sound confident that your son has the basics.  I hated reading until high school (and didn't really start reading books until late in high school), which is yet another part of the irony of my having a BA in English.  How did I manage to stay in track 1 and 2 English classes?  Because I knew how to fake reading books.  Let's just say that dioramas and art book reports were a great way for me to avoid reading books.  They are harmless for a kid who likes to read.  They provide an easy out for a kid who doesn't want to read.

Quote from: jhkimIt's not like I inherently trust the government or anything, but it's not like one professor at an individual college giving the same test twice is necessarily a better measure of the nation's progress.  The National Assessment of Education Progress collects statistics by giving identical tests over time since 1969.  This is not the same as the the regular tests that regularly change, but rather a sampling measure that strives to remain constant.  If you want quick info, you can skip to the online executive summary from 1999.  The full article has more discussion of methodology.  For the even shorter summary:

I'll need to look into that in more detail.

Quote from: John MorrowThe article says that District 2 was the only district that didn't drop.  It then discusses why.  It talks about spending $800,000 a year to train teachers.  It talks about parents sending their kids to tutors, tutoring their kids themselves, and buying non-official books for them to learn from.  It also talks about the test being aligned with that particular district's curriculum.  In other words, the article is skeptical that the new math should be credited with the performance.  Perhaps that's bias or perhaps it's not.  My main reason for posting it was the anecdotal evidence from the parents who are not happy with the progress their children are making.

I'd be damn skeptical whether the new math was responsible for the improved performance relative to other districts as well.  

However, your claims that such curricula are "child abuse" are pretty extreme.  If constructivist math teaching really is completely insane child abuse where nothing is taught to the students, then as I said, I would expect a fucking drop in scores -- not staying the same while other schools dropped.

You attempted to dispute me by citing a drop in scores mentioned, but it was a drop in other schools.  Yes, some -- though not all -- of those other schools might have some constructivist material (to a lesser degree than District 2).  However, the article made no claim that the drop was at all correlated to this.  i.e. It doesn't claim that the schools where scores dropped were the ones where constructivist curricula were used.  Maybe the overall drop otherwise was in schools without the new curricula.  They don't cite any claims either way.

Quote from: jhkimHowever, your claims that such curricula are "child abuse" are pretty extreme.  If constructivist math teaching really is completely insane child abuse where nothing is taught to the students, then as I said, I would expect a fucking drop in scores -- not staying the same while other schools dropped.

I do think that experimenting on children and not teaching them the basics is a form of child abuse in that it leaves them unprepared for the world around them which should be the primary purpose of a public school education.  That said, I'm sure there are examples of these styles of teaching being used sensibly and/or combined with traditional methods and that's clearly not child abuse and probably isn't bad teaching.  From the New York Times article, we have this quote:

"Mrs. Kell said she loved the freedom and creativity of the new math. But on her desk was a secret weapon: a stack of worksheets -- the antithesis of constructivist math -- pages of classic problems in long division, the addition of fractions and reducing the sum of fractions to its simplest terms. "

In other words this teacher didn't follow a pure constructivist program and it sounds like your son hasn't been subjected to one either.

However, with respect to their scores staying the same, that doesn't surprise me if the use of outside tutoring is really as widespread as they said, and if the test was geared toward the lessons being taught in that school, which the article also says.  But most telling, I think, is the quote by Bruce Winokur, a math teacher at Stuyvesant High School who said that "he is seeing more students who are gifted in math but unable to keep up with high school work. They understand concepts, he said, but have not internalized the rules."  Given Stuyvesant's reputation and the children it attracts, I think that's significant.

Quote from: jhkimYou attempted to dispute me by citing a drop in scores mentioned, but it was a drop in other schools.  Yes, some -- though not all -- of those other schools might have some constructivist material (to a lesser degree than District 2).  However, the article made no claim that the drop was at all correlated to this.  i.e. It doesn't claim that the schools where scores dropped were the ones where constructivist curricula were used.  Maybe the overall drop otherwise was in schools without the new curricula.  They don't cite any claims either way.

I think we're both focusing on different details of the article.  I understand the point you are making and it's a fair one, but I think the article gives several reasons for why that happened.  In particular, parents sending their children to tutors or tutoring them themselves warps the ability to measure these programs and the article offers a few examples of that sort of thing.  I'm more interested in the parents' specific examples of what their children were being taught (why I posted the article), how it was effecting their children, and so on.  I also think that opinions about abilities and trends like those of Bruce Winokur are worth considering.

The error of this kind of "let them get it in the ballpark at first and then they'll figure out the specifics later" is glaringly obvious to anyone who's ever tried to learn a language or how to play a musical instrument: If you encourage people to to learn something in a way that is generally competent but ignores small mistakes, they will have those mistakes programmed into their thinking and will continue to repeat that "sloppy method" for the rest of their lives. It becomes much harder to unlearn than to learn it right in the first place.

Well, for everyone except the teachers, of course. For them its easier to teach the sloppy way, which is part of why they so love things like "friendly spelling" and "fuzzy math".

RPGPundit

Quote from: John MorrowI do think that experimenting on children and not teaching them the basics is a form of child abuse in that it leaves them unprepared for the world around them which should be the primary purpose of a public school education.  That said, I'm sure there are examples of these styles of teaching being used sensibly and/or combined with traditional methods and that's clearly not child abuse and probably isn't bad teaching.  From the New York Times article, we have this quote:

"Mrs. Kell said she loved the freedom and creativity of the new math. But on her desk was a secret weapon: a stack of worksheets -- the antithesis of constructivist math -- pages of classic problems in long division, the addition of fractions and reducing the sum of fractions to its simplest terms. "

In other words this teacher didn't follow a pure constructivist program and it sounds like your son hasn't been subjected to one either.

This is a empty rhetorical dodge.  Here you (and the article) are trying to claim that what is being done in District 2 isn't a "pure" constructivist program because it includes learning regular computation -- and therefore it isn't really what you're complaining about.  

When I talk about constructivist math, I'm not talking about a hypothetical "pure" form -- I'm talking about the real programs that follow the recommendations of the 1989 report of the National Council of Teachers of Mathematics or the subsequent reports.  The report does not say anything like "don't teach any long division or addition of fractions" -- thus claiming that such is the "antithesis" or that the District 2 program isn't "pure" for including it is straw man, plain and simple.  

As far as your hypothetical pure form where students are taught nothing by lazy teachers who don't want to bother teaching -- Well, hell yeah!  Damn those pure constructivist teachers!  They suck, and their lazy teaching abuses those poor hypothetical children!  

Quote from: John MorrowI think we're both focusing on different details of the article.  I understand the point you are making and it's a fair one, but I think the article gives several reasons for why that happened.  In particular, parents sending their children to tutors or tutoring them themselves warps the ability to measure these programs and the article offers a few examples of that sort of thing.  I'm more interested in the parents' specific examples of what their children were being taught (why I posted the article), how it was effecting their children, and so on.  I also think that opinions about abilities and trends like those of Bruce Winokur are worth considering.

I realize that -- but hypothesized reasons for a lack of evidence is not the same thing as evidence.  Unless you can show me evidence that the real programs are overall failing to teach effectively, I'm going to be extremely skeptical.  Regarding tutoring -- do you really think that the rich East Side parents only started hiring tutors three years ago because of the reformed math program?  I understand that some parents are irate, but my experience is that this is par for the course.  Most parents (especially rich yuppies) are convinced that their kid is smarter than average, and if they aren't doing well, then they are quick to blame anyone else.  I don't discount them, but I don't consider a handful of quoted opinions from them real evidence.

Quote from: jhkimThis is a empty rhetorical dodge.  Here you (and the article) are trying to claim that what is being done in District 2 isn't a "pure" constructivist program because it includes learning regular computation -- and therefore it isn't really what you're complaining about.

That quote wasn't about District 2.  It was about The Daniel Boone School, in West Ridge near Chicago.

Quote from: jhkimWhen I talk about constructivist math, I'm not talking about a hypothetical "pure" form -- I'm talking about the real programs that follow the recommendations of the 1989 report of the National Council of Teachers of Mathematics or the subsequent reports.  The report does not say anything like "don't teach any long division or addition of fractions" -- thus claiming that such is the "antithesis" or that the District 2 program isn't "pure" for including it is straw man, plain and simple.

And I'm not talking about the details of that 1989 report but about what teachers actually teach in classrooms.  I'm not even sure we are talking about the same thing here.  Go back to my original comments and the claims that I've made throughout this thread.  They were not a specific criticism of that report and never were.

Quote from: jhkimAs far as your hypothetical pure form where students are taught nothing by lazy teachers who don't want to bother teaching -- Well, hell yeah!  Damn those pure constructivist teachers!  They suck, and their lazy teaching abuses those poor hypothetical children!

If such children were only hypothetical, it wouldn't be a problem.  And it's not simply lazy teachers who drink the pure constructivist Kool Aid.  But if you go back to my original comments that triggered this discussion, I was talking about the pure form, not how it's filtered through good teachers who make it work.  The point of the quote from the West Ridge school is that the teacher isn't teaching a pure constructivist class and the complaints increase the more constructivist and less traditional the class gets.  Your defense of your son's education included the observation that he knows his times tables.  Other parents aren't so lucky.  You seem determined to think of them as hypothetical.

Quote from: jhkimI realize that -- but hypothesized reasons for a lack of evidence is not the same thing as evidence.  Unless you can show me evidence that the real programs are overall failing to teach effectively, I'm going to be extremely skeptical.

You don't find the widespread use of tutors and teachers not following the pure programs evidence?  You don't consider that Calculus test experiment evidence?  You don't consider the use of calculators on college entrance exams evidence?  You don't consider the anecdotal from parents, not just those in the article but plenty of parents around the country that have created local activist groups to fight their public school programs (including people from both ends of the political spectrum) evidence?  Given how easy it is to dismiss the results of testing, be it the SATs or NCLB, how could objective evidence be gathered?  

Quote from: jhkimRegarding tutoring -- do you really think that the rich East Side parents only started hiring tutors three years ago because of the reformed math program?

Of course not, but I do think it's become far more widespread and has trickled down to the middle class.  I also think that the reports I hear from parents I know about the amount of homework their children are given and the amount of time they need to spend teaching their children is a huge change from what I experienced.  I rarely had any sort of homework and never needed parental help to do it.  Yet I don't see a lot of evidence that kids are getting a better education than I did.

Quote from: jhkimI understand that some parents are irate, but my experience is that this is par for the course.  Most parents (especially rich yuppies) are convinced that their kid is smarter than average, and if they aren't doing well, then they are quick to blame anyone else.  I don't discount them, but I don't consider a handful of quoted opinions from them real evidence.

It's not difficult to find tons of websites by irate parents and local groups.  Do some Google searches if you are really interested.  I don't have the time to filter through all of the information out there to find something you'll consider credible.  Yes, I realize that parents are not always objective but I don't think that entirely explains the specific anecdotal evidence that many parents provide.  And I've asked you how you'd feel if your son didn't know his additional and times tables and had trouble coming up with correct answer and didn't get an answer.  How would you feel if your had reason to believe that your son's ability wasn't to blame but the teaching was?  What would you do about it?

Quote from: John MorrowTo be honest, I think the whole issue of state standards is irrelevant, which is why I'm not really talking about that at all.  What I care about is what schools actually teach.

To be honest, facts are more relevant than what you think schools actually teach, which is determined by the current state standards I've posted, not old magazine articles or flimsy Wikipedia entries. You made a claim that children in California were being abused by being force fed "fuzzy math." I replied that my experience with my children in actual California public schools following the actual California public school math curriculum showed no evidence whatsoever of this. Another California parent, jhkim, agreed.

Quote from: John MorrowIf you look at those school performance figures, something becomes fairly clear -- the "inadequacies of school funding" are largely meaningless.

First, you were the one who tried to discount my experience (and jhkim's) by suggesting that because our kids were in relatively better funded schools, that this somehow spared our kids from fuzzy math child abuse. I'm not sure why you think the poor kids in Oakland are somehow being taught something other than the state-mandated curriculum.

Second, if you look at the complete school performance figures rather than your 'Best of' list, you'll see that the inequities (not inadequacies) of school funding statewide are a pretty accurate predictor of how well schools perform. But again, this is irrelevant to your initial charge.

Quote from: John MorrowThe mother who complained that her son was being discouraged from calculating the correct answer was certainly making that claim.

"One parent, Anna Huang, said her son, Mack, a fourth grader, 'felt a lack of clarity' when his teacher insisted that he estimate answers, rather than compute them precisely."

I think you're misreading it. She wasn't concerned that her son was being taught estimation instead of calculation, but that he was being told to use estimation instead of calculation when the method being taught that day was estimation. In other words, she was worried about his "fragile self-esteem."

It's kind of like when my daughter was learning how to solve systems of linear equations in algebra using the addition/subtraction method. When I checked her answers, I sometimes used the substitution method instead because it was easier for the particular problem, but she had to use whichever specific method the problem called for to demonstrate that she knew both methods.

Anyway, I'm sure Mrs. Huang's reaction was genuine. I had a similar, albeit milder, experience during the initial period that estimation was covered in my kids' classes because I could add the real numbers in my head, and like you, it surprised me that estimation was a skill that had to be taught. But then, I'm constantly surprised at the things I can do that I assume kids can do because I don't remember learning them 30+ years ago.

The fact remains that estimation was the skill being taught that day even thought it was being introduced with easy numbers that most kids could already calculate. That was the point. Over the next couple of days, the estimation problems used much bigger numbers and other arithmetic operations where the method made sense, and as I watched my kids do their homework, it became clear why it was taught the way it was.

BTW, with regard to multiplication tables, kids here are expected to memorize their 2s, 5s, and 10s by the end of 2nd grade, and all the rest in 3rd grade. Is that too fuzzy?

  -- Matthew Gabbert

Quote from: Matthew GabbertTo be honest, facts are more relevant than what you think schools actually teach, which is determined by the current state standards I've posted, not old magazine articles or flimsy Wikipedia entries.

Do you think that standards automatically translate into what children actually get taught in classrooms?  

Quote from: Matthew GabbertYou made a claim that children in California were being abused by being force fed "fuzzy math." I replied that my experience with my children in actual California public schools following the actual California public school math curriculum showed no evidence whatsoever of this. Another California parent, jhkim, agreed.

Please provide me the quote where I made the claim that "children in California were being abused by being force fed 'fuzzy math.'"  I posted a link to a Wikipedia article that mentioned that it was widely used in California.  Since neither your nor John disputed that, I assume that was true.  So I finally went and looked at the actual standards since this has turned into a debate on the specifics of California (which I still think are entirely irrelevant to the point I was making) and while they have a few constructivist elements, they look fairly traditional to me and include, for example, "Memorize to automaticity the multiplication table for numbers between 1 and 10," in third grade.  So if many or even all California schools are simply using elements of constructivist math and otherwise use traditional teaching methods with or instead of constructivist approaches, your gripe is with the author of the Wikipedia article who made a claim that is largely irrelevant to the point I was making.  I didn't post it as a dig on California, even though that's how you've chosen to interpret it.  

Quote from: Matthew GabbertFirst, you were the one who tried to discount my experience (and jhkim's) by suggesting that because our kids were in relatively better funded schools, that this somehow spared our kids from fuzzy math child abuse. I'm not sure why you think the poor kids in Oakland are somehow being taught something other than the state-mandated curriculum.

Having looked over the "state-mandated curriculum" you keep mentioning, the math requirements for each grade can fit on a page or two.  How that gets expanded out into a full school year and actually gets taught should vary quite a bit from school to school but perhaps California is far more regimented than my own state in that regard.  But if the "state-mandated curriculum" is so rigidly followed, why does the education that students get in different schools, even different schools in the same district, vary so significantly?

Quote from: Matthew GabbertSecond, if you look at the complete school performance figures rather than your 'Best of' list, you'll see that the inequities (not inadequacies) of school funding statewide are a pretty accurate predictor of how well schools perform. But again, this is irrelevant to your initial charge.

If school funding is an accurate predictor of how well schools perform, then why is there such a disparity of performance between students in schools in the same district which draws funding from a common pool?  In other words, the schools in San Jose have a single budget yet even looking only at the best schools, their performance varies substantially.  Why is that?

And please bear in mind that I live in a state that is #1 (or sometimes #2) in school spending per pupil.

Quote from: Matthew GabbertI think you're misreading it. She wasn't concerned that her son was being taught estimation instead of calculation, but that he was being told to use estimation instead of calculation when the method being taught that day was estimation. In other words, she was worried about his "fragile self-esteem."

I think we are both reading what we want to read into an admittedly vague quote.  I find it difficult to imagine the mother complaining so loudly about a one-time or brief situation but I suppose that's possible.  And I do wonder what the value is of forcing students to estimate is.  Then again, I was always terribly frustrated by having to show my work because that's not how my brain thinks through problems.  

Quote from: Matthew GabbertIt's kind of like when my daughter was learning how to solve systems of linear equations in algebra using the addition/subtraction method. When I checked her answers, I sometimes used the substitution method instead because it was easier for the particular problem, but she had to use whichever specific method the problem called for to demonstrate that she knew both methods.

I understand your point and it's a fair one.  I'm not convinced that's what triggered Mrs. Huang's complaints and, in this particular instance, I'm not sure how it benefited her son to frustrate him.

Quote from: Matthew GabbertAnyway, I'm sure Mrs. Huang's reaction was genuine. I had a similar, albeit milder, experience during the initial period that estimation was covered in my kids' classes because I could add the real numbers in my head, and like you, it surprised me that estimation was a skill that had to be taught. But then, I'm constantly surprised at the things I can do that I assume kids can do because I don't remember learning them 30+ years ago.

Well, that raises an important but tangental question.  Why do kids need to be taught things that people weren't formally taught years ago?  And, no, I don't think it's just a product of not remembering being taught.  I have an excellent long-term memory (I can remember standing in my crib, learning about what the crickets chirping outside were, where we purchased my first real bed, and I can go on and on).  For example, I know that I never did homework or, more accurately, didn't do homework until I had a morning study hall with other kids who did their homework during that study hall.  

Quote from: Matthew GabbertThe fact remains that estimation was the skill being taught that day even thought it was being introduced with easy numbers that most kids could already calculate. That was the point. Over the next couple of days, the estimation problems used much bigger numbers and other arithmetic operations where the method made sense, and as I watched my kids do their homework, it became clear why it was taught the way it was.

I don't see evidence in the quote that the estimation complaint was due to a one day or one lesson experience, though it could have been.  The complaint immediately after that, by Anne Cattaneo Santore, complained that her son "spent months" solving equations that way in the second grade.  Does it really take months to teach estimation?  At the very least, it would have made sense for the teacher to explain why the student was being forced to estimate, perhaps letting the student get a preview of a challenging problem so that they'd understand that.  

Quote from: Matthew GabbertBTW, with regard to multiplication tables, kids here are expected to memorize their 2s, 5s, and 10s by the end of 2nd grade, and all the rest in 3rd grade. Is that too fuzzy?

Of course not.  Looking over the standards, it looks like a hybrid of constructivist and traditional ideas.  I have no problem with that and I'm not advocating a mindless adherence to memorization, drills, and tests.  But I am against programs that never seem to get to accurate answers, correct spelling, and so on.  And while I understand why teachers want to see the work, I'm not convinced that it's more important than getting the right answer.

Quote from: John MorrowAnd I'm not talking about the details of that 1989 report but about what teachers actually teach in classrooms.  I'm not even sure we are talking about the same thing here.  Go back to my original comments and the claims that I've made throughout this thread.  They were not a specific criticism of that report and never were.

OK, here's your original comment:

Quote from: John MorrowThen there is Whole Math a form of child abuse (along with its equally evil twin, Whole Language):

   It emphasizes word problems and understanding the concepts behind mathematical operations, rather than necessarily getting the right arithmetic answers for these operations. It has been widely used in the United States - particularly in California - since 1989, when the National Council of Teachers of Mathematics released standards that recommended children be taught the ideas behind math, versus focusing on calculation.

"In a typical fuzzy math class, children are placed in small groups, and encouraged to develop their own methods of solving arithmetical problems, presented in sentence format."  And, remember, that it's not important that they get the right answer, just that they invent their own methods to solve the problem.  Yeah, I want to fly in an airplane designed by one of these kids when they grow up.  :rolleyes:

So you quoted the "Fuzzy Math" Wikipedia article specifically citing the NCTM 1989 report.  The NYTimes article you linked to similarly named the NCTM report as a basis for reformed curricula.  If you are not in fact criticizing the NCTM report, but rather a different thing that is "pure constructivism" -- then how do you define it?  How can I tell if a particular curriculum or class is pure constructivist by your definition?

Quote from: jhkimSo you quoted the "Fuzzy Math" Wikipedia article specifically citing the NCTM 1989 report.  The NYTimes article you linked to similarly named the NCTM report as a basis for reformed curricula.  If you are not in fact criticizing the NCTM report, but rather a different thing that is "pure constructivism" -- then how do you define it?  How can I tell if a particular curriculum or class is pure constructivist by your definition?

I haven't read the NCTM report so it's difficult for me to criticize it.  Frankly, I'm not particularly interested in reading a several hundred page document (the 2000 version is 402) directed at teachers, but it's not difficult to find detailed critiques of it out there.  One of the most common critiques was that the report encourages access to calculators at all grade levels and it's a critique I agree with.  Other critiques are based on how the recommendations are interpreted by people implementing it.

As with any large lengthy document put together by a committee, I suspect that there would be things I agree with in there and things that I don't but the main reason why it gets a mention in both places is that the report encouraged the reforms, not that the reforms were perfect reflections of the report.  Taken in moderation by sensible teachers, the report might be useful and even sensible.  In the hands of reformers with an axe to grind about rules and memorization looking to throw traditional education out or who would rather hand kids a calculator rather than actually teaching them to do arithmetic, it seemed to give them justification to do so.  If constructivist mathematics weren't replacing or eliminating traditional approaches, I doubt they'd be as controversial.

But the bottom line point that I was making is that there are schools that actually are handing kids calculators at all grade levels for everything and allow or use approximation for a great deal.  Apparently the 1989 report says, "Students should be able to decide when they need to calculate and whether they require an exact or approximate answer. They should be able to select and use the most appropriate tool."  Do you agree with that?

Quote from: John MorrowDo you think that standards automatically translate into what children actually get taught in classrooms?

Automatically, no. In practice, yes.

Quote from: John MorrowPlease provide me the quote where I made the claim that "children in California were being abused by being force fed 'fuzzy math.'"

Originally Posted by John Morrow
Then there is Whole Math a form of child abuse (along with its equally evil twin, Whole Language):

    It emphasizes word problems and understanding the concepts behind mathematical operations, rather than necessarily getting the right arithmetic answers for these operations. It has been widely used in the United States - particularly in California - since 1989, when the National Council of Teachers of Mathematics released standards that recommended children be taught the ideas behind math, versus focusing on calculation.

"In a typical fuzzy math class, children are placed in small groups, and encouraged to develop their own methods of solving arithmetical problems, presented in sentence format." And, remember, that it's not important that they get the right answer, just that they invent their own methods to solve the problem.Yeah, I want to fly in an airplane designed by one of these kids when they grow up.:rolleyes:

Quote from: John MorrowI posted a link to a Wikipedia article that mentioned that it was widely used in California.  Since neither your nor John disputed that, I assume that was true.

You not only posted a link to it, you quoted the text, as well, presumably because you agreed with it. I immediately disputed it, as did jhkim. In fact, that dispute is what lead to the spinning off of this thread.

Quote from: John MorrowSo I finally went and looked at the actual standards since this has turned into a debate on the specifics of California (which I still think are entirely irrelevant to the point I was making)

What was the point you were making? As I recall, in a gaming thread about games that get a lot of hate/criticism, in response to complaints vis a vis 'too much math' you went off on a strange and somewhat curmudgeonly tangent about 'little darlings' using calculators to protect their 'fragile self-esteem' and fast food cashiers who can't make change properly and blaming it all, as every generation seems to do, on how things aren't being done how they were in your day. Then you tried to support this view with a bunch of Wikipedia nonsense, got called on it, and here we are.

Quote from: John Morrowand while they have a few constructivist elements, they look fairly traditional to me and include, for example, "Memorize to automaticity the multiplication table for numbers between 1 and 10," in third grade.  So if many or even all California schools are simply using elements of constructivist math and otherwise use traditional teaching methods with or instead of constructivist approaches, your gripe is with the author of the Wikipedia article who made a claim that is largely irrelevant to the point I was making.  I didn't post it as a dig on California, even though that's how you've chosen to interpret it.

Fair enough. [Colbert]Apology accepted.[/Colbert]  

Quote from: John MorrowHaving looked over the "state-mandated curriculum" you keep mentioning, the math requirements for each grade can fit on a page or two.  How that gets expanded out into a full school year and actually gets taught should vary quite a bit from school to school but perhaps California is far more regimented than my own state in that regard.  But if the "state-mandated curriculum" is so rigidly followed, why does the education that students get in different schools, even different schools in the same district, vary so significantly?

If you're measuring "the education that students get" by annual test scores, then I suspect the differences mostly come down to local demographics and funding.

Quote from: John MorrowIf school funding is an accurate predictor of how well schools perform, then why is there such a disparity of performance between students in schools in the same district which draws funding from a common pool?  In other words, the schools in San Jose have a single budget yet even looking only at the best schools, their performance varies substantially.  Why is that?

Because your premise is incorrect. San Jose alone is represented by 14 school districts and the 'Best of' list you were looking at covered a much wider area than just the city of San Jose. Even within a single school district like the inaccurately named San Jose Unified, the schools in the wealthy enclave of Almaden Valley have far more resources available than those in working class East San Jose.

Quote from: John MorrowAnd I do wonder what the value is of forcing students to estimate is.  Then again, I was always terribly frustrated by having to show my work because that's not how my brain thinks through problems.

The value of forcing students to estimate is to make sure they understand how to do it. Same thing for showing your work. Also, in the case of the latter, if the student gets an incorrect answer, it's much easier show them where they went wrong if they write down all the steps they did. And it's a sliding requirement of sorts. Once the student moves on to more advanced topics, steps based on earlier subjects typically get streamlined and the focus is on breaking down the steps of the new material.

Quote from: John MorrowWell, that raises an important but tangental question.  Why do kids need to be taught things that people weren't formally taught years ago?  And, no, I don't think it's just a product of not remembering being taught.  I have an excellent long-term memory (I can remember standing in my crib, learning about what the crickets chirping outside were, where we purchased my first real bed, and I can go on and on).

I suspect that you don't consider yourself to be of merely average intelligence, so why would you expect yourself to be used as the baseline when developing educational methodologies for millions of children?

Quote from: John MorrowBut I am against programs that never seem to get to accurate answers, correct spelling, and so on.  And while I understand why teachers want to see the work, I'm not convinced that it's more important than getting the right answer.

Based on what I've seen in my kids' schoolwork, they're both important and ultimately, you can't separate the two. Mistakes in either deserve points taken off. Better understanding of a process leads to making fewer errors, and it makes it easier to adapt the process to new conditions and still get correct answers.

  -- Matthew Gabbert

Quote from: John MorrowWell, that raises an important but tangental question.  Why do kids need to be taught things that people weren't formally taught years ago?  And, no, I don't think it's just a product of not remembering being taught.  I have an excellent long-term memory (I can remember standing in my crib, learning about what the crickets chirping outside were, where we purchased my first real bed, and I can go on and on).  For example, I know that I never did homework or, more accurately, didn't do homework until I had a morning study hall with other kids who did their homework during that study hall.

What is taught can and should change because the world changes.  The necessary skills of people today are notably different than what they were years ago.  In the 1960s, the skills of working out multi-digit computations on pencil and paper were vital to the workforce.  Those were core skills used by people at their jobs every day for critical tasks, and a slide rule was a key instrument.  It was good sense for this to be emphasized in schools at the time, and it prepared students well for the world they would enter.  

However, that is no longer the case in the world today.  Conversely, there are a lot of key mathematical skills used every day by people now that were rare or non-existent in 1970.  Someone who goes to work in an office will not be asked to add up columns in a book, but rather to do tasks like sorting accounts in a spreadsheet and making a graph of projected growth.  

This may sound obvious, but it is important to establish the basics.  

Now, I'm sure you will say: "Well, it's OK to teach new skills, but we shouldn't cut back on anything else."  That's simply not realistic.  If they're taught something new, that's time that wasn't spent teaching them older topics.  You can't teach them everything that was critical in 1970 and everything that is critical in 2008 to equal degrees.  Something is going to give.  The NCTM document was clear that students should still be taught paper and pencil computation, but it should be emphasized less than it was previously, and mental computation and problem-solving should be emphasized more.  

Quote from: John MorrowI haven't read the NCTM report so it's difficult for me to criticize it.  Frankly, I'm not particularly interested in reading a several hundred page document (the 2000 version is 402) directed at teachers, but it's not difficult to find detailed critiques of it out there.  One of the most common critiques was that the report encourages access to calculators at all grade levels and it's a critique I agree with.  Other critiques are based on how the recommendations are interpreted by people implementing it.

The 1989 report is just 17 pages.  I linked to a PDF version in the original post of this thread.  Specifically, it's posted on the Department of Education website here: Curriculum and Evaluation Standards for School Mathematics[/b].

The main section on calculators is on page 8.  As far as I can tell, the quote that you gave is false.  

Quote from: John MorrowAs with any large lengthy document put together by a committee, I suspect that there would be things I agree with in there and things that I don't but the main reason why it gets a mention in both places is that the report encouraged the reforms, not that the reforms were perfect reflections of the report.  Taken in moderation by sensible teachers, the report might be useful and even sensible.  In the hands of reformers with an axe to grind about rules and memorization looking to throw traditional education out or who would rather hand kids a calculator rather than actually teaching them to do arithmetic, it seemed to give them justification to do so.  If constructivist mathematics weren't replacing or eliminating traditional approaches, I doubt they'd be as controversial.

How can there be any change at all without some replacing or eliminating of traditional approaches?  Unless you constantly keep lengthening the hours of the school day, then new material is going to have to come at the expense of some old material.

Quote from: jhkimWhat is taught can and should change because the world changes.  The necessary skills of people today are notably different than what they were years ago.

I'm not convinced that's true.  Somehow I managed to adapt to computers despite the fact that I learned to type on a manual typewriter and learned mathematics before even calculators became widely available.  In fact, I'm glad I was told how slide-rules worked even though I never had to use one because it gives me an understanding of what a "slide-rule calculator" is doing internally.  If the new mathematics teaching was improving students overall, I might buy it but I think the comments of people like Bruce Winokur at Stuyvesant and W. Stephen Wilson at Johns Hopkins University suggest that the education that they are getting isn't better.

Quote from: jhkimNow, I'm sure you will say: "Well, it's OK to teach new skills, but we shouldn't cut back on anything else."  That's simply not realistic.  If they're taught something new, that's time that wasn't spent teaching them older topics.  You can't teach them everything that was critical in 1970 and everything that is critical in 2008 to equal degrees.  Something is going to give.

The problem I have is that at least some of the stuff that they are cutting lose from 1970 is still critical in 2008 and the values of techniques like drills and memorization have value beyond simply learning basic mathematics.  Who is deciding what children don't need from 1970 and do need for 2008 and by what criteria are they choosing to cut stuff loose?

Quote from: jhkimThe NCTM document was clear that students should still be taught paper and pencil computation, but it should be emphasized less than it was previously, and mental computation and problem-solving should be emphasized more.

How can you solve a problem without the fundamentals to understand it and the tools that can be used to solve it?  That's what some of the anecdotal examples in those articles point out.  If you let students go off to figure out how many green gates fit into how many sections of red fence and the students lack the basics to answer the question, they tap away at their calculators, guess, and 20 minutes later, they'll be no closer to figuring out the right answer.  

Quote from: jhkimThe 1989 report is just 17 pages.  I linked to a PDF version in the original post of this thread.

No, it isn't.  That's not it.  The full version requires registration if you are really interested.  The paperback version on Amazon runs 258 pages.  

Quote from: jhkimHow can there be any change at all without some replacing or eliminating of traditional approaches?  Unless you constantly keep lengthening the hours of the school day, then new material is going to have to come at the expense of some old material.

One way to change is to replace.  Another way to change is to adapt.  I think they are throwing the baby out with the bath water in at least some cases.

Based on what I saw but without reviewing them too closely, the California standards looked decent.  The purpose of NCLB is to test to see what kids are really learning to make sure that they have the basics.  Do you think that's useful and, if not, how do you suggest assessing whether students are getting a good education or not?

Quote from: Matthew GabbertAutomatically, no. In practice, yes.

   Originally Posted by John Morrow
Then there is Whole Math a form of child abuse (along with its equally evil twin, Whole Language):

That's my words.  The bit about California was what Wikipedia says.  That should teach me a lesson about posting from Wikipedia, since that was not the intended focus of the bit I quoted.  

   Originally Posted by John Morrow
"In a typical fuzzy math class, children are placed in small groups, and encouraged to develop their own methods of solving arithmetical problems, presented in sentence format." And, remember, that it's not important that they get the right answer, just that they invent their own methods to solve the problem.Yeah, I want to fly in an airplane designed by one of these kids when they grow up.:rolleyes:

Yes, that again indicates the point I was trying to emphasize.  Whether or not Wikipedia is correct about how widely it's used in California in particular, that sort of mathematics instruction is actually used in schools and when children don't learn the basics because of it (or the basics of reading and spelling in whole language classes), I think that essentially abuses children.

Quote from: Matthew GabbertYou not only posted a link to it, you quoted the text, as well, presumably because you agreed with it. I immediately disputed it, as did jhkim. In fact, that dispute is what lead to the spinning off of this thread.

I'm sorry for not finding a better source and for not more rigorously editing the quote, which I provided largely as background.  You'll notice that I underlined two parts of the quote I intended to emphasize and were my purpose for posting it.  The bit about California wasn't central to my point and I opted not to replace it with an ellipsis.  My bigger mistake was using Wikipedia as a source, but I was trying to avoid something that would trigger an even lengthier debate on partisan sources.

To make it clear, the parts I underlined were the parts o the quote I endorsed and meant to emphasize.  That's why I underlined them.

Quote from: Matthew GabbertWhat was the point you were making? As I recall, in a gaming thread about games that get a lot of hate/criticism, in response to complaints vis a vis 'too much math' you went off on a strange and somewhat curmudgeonly tangent about 'little darlings' using calculators to protect their 'fragile self-esteem' and fast food cashiers who can't make change properly and blaming it all, as every generation seems to do, on how things aren't being done how they were in your day. Then you tried to support this view with a bunch of Wikipedia nonsense, got called on it, and here we are.

I wasn't trying to support my view with "a bunch of Wikipedia nonsense".  I was trying to explain what I meant by "whole math" with a weak Wikipedia quote because I didn't have time to sort through the enormous amount if material that was turning up on Google to find something suitable.  What I got called on was tangental to my point but, hey, the stuff that isn't tangental to my point is getting largely ignored or nit-picked (e.g., going after Anna Huang but ignoring Anne Cattaneo Santore who is harder to dismiss, ignoring the comments by math teachers and professors, etc.).

Quote from: Matthew GabbertIf you're measuring "the education that students get" by annual test scores, then I suspect the differences mostly come down to local demographics and funding.

What role do you think demographics play in education and why?

Quote from: Matthew GabbertBecause your premise is incorrect. San Jose alone is represented by 14 school districts and the 'Best of' list you were looking at covered a much wider area than just the city of San Jose. Even within a single school district like the inaccurately named San Jose Unified, the schools in the wealthy enclave of Almaden Valley have far more resources available than those in working class East San Jose.

And what would you do correct it?  I do think that this report about your area probably does a decent job of describing at least part of the problem but I'm skeptical that money, alone, will attract the best teachers to harder schools.  Why?  Because in New Jersey (the state where I live), the New Jersey Supreme Court rules that the state is constitutionally required to provide an adequate education and the state has been taking over and funding failing school districts to try to fix the problem.  You can find a good critical overview of New Jersey's solution here.  Conceptually I support the idea of state funding and even given more money to poor and troubled districts to help them attract better teachers, but I'm skeptical of simply tossing money at the problem without other reforms which are unpopular with teachers' unions including revising or eliminating tenure and vouchers.

Quote from: Matthew GabbertThe value of forcing students to estimate is to make sure they understand how to do it. Same thing for showing your work. Also, in the case of the latter, if the student gets an incorrect answer, it's much easier show them where they went wrong if they write down all the steps they did. And it's a sliding requirement of sorts. Once the student moves on to more advanced topics, steps based on earlier subjects typically get streamlined and the focus is on breaking down the steps of the new material.

And if the way that they get the answer isn't easily reflected by showing the work?  (I once had the person behind me in my high school physics class ask me where I found the equation to solve a problem and I honestly told him that I just made it up -- and I had the top scaled grade across all of the physics classes in my high school.)

Quote from: Matthew GabbertI suspect that you don't consider yourself to be of merely average intelligence, so why would you expect yourself to be used as the baseline when developing educational methodologies for millions of children?

For some things, I'm average and for others I'm not.  I was never in the top track English classes until my senior year, when I felt terribly outclassed by the top kids in my school, while I was had the top scaled grade in Physics.  Yet when I reached college, I couldn't hack physics because certain types of mathematics are difficult for me if I can't visualize what's going on.  I'm horrible at languages and music.  And so on.  My nine years in a college computer lab helping students suggests to me that no methodology will ever fit all children because children and adults learn things differently, which is part of why I think a focus on results is superior than a focus on teaching specific ways to get to a result.

I'm not advocating myself as the baseline for developing educational methodologies for millions of children.  The reason why I was talking about my memory is I actually remember sitting in class in elementary school struggling to remember my times tables and struggling to memorize a list of 50 or so prepositions.  I remember learning to write my letters and having trouble with left and right for numbers like 5.  I remember learning to read in the first grade, with books about Tip (the dog) and Mittens (the cat) and Jack and Janet and the books starting out with pictures of the characters and then switching to the "said" structure for dialog.  I remember learning Greatest Common Factor and Least Common Denominator and prime numbers in elementary school, too.  Heck, I can still remember the teacher writing the examples on the blackboard, though the details are fuzzy (because of how my memory works -- it's spatial but not photographic).  My point is that this isn't some sort of vague recollection for me but pretty clear memories of exactly what and how my teachers were teaching so I remember how I was taught.  And there are things that seem difficult for children today that I didn't have to be formally taught, and that's despite the fact that my education before I entered elementary school (I never went to preschool) would probably not qualify me for entry into many local kindergarten programs today.

Some of what I'm advocating wasn't easy for me (e.g., memorizing multiplication tables) but I think they were critically important for students to do.  So I'm not simply advocating what was easy for me or what worked for me.  I'm advocating what's necessary to get results.

Quote from: Matthew GabbertBased on what I've seen in my kids' schoolwork, they're both important and ultimately, you can't separate the two. Mistakes in either deserve points taken off. Better understanding of a process leads to making fewer errors, and it makes it easier to adapt the process to new conditions and still get correct answers.

Fair enough.  Does that mean you'd be as unhappy if their teachers de-emphasized the correct answers as you would be if they didn't care about how they got them?