Quote from: jhkimIt's not clear to me what you're saying here.  Are you saying that there should never be any real curriculum that covers estimation?  In other words, there should never be any math homework or test question that doesn't insist on an exact numerical answer?  For example, that would mean that my graduate course in physical estimates would be completely worthless, since it never had that.  If so, then I disagree with you.  

Or are you simply saying that there needs to be coverage of both estimation and exact answers -- to which I would say, "Duh".

First: Let me make sure I understand: There is actually a collegiate course in 'estimating'.

Like, I use 29 miles to the gallon in my car, I have a 10 gallon tank and I"m driving 1000 miles, so I'll use a bit over 3 tanks of gas, and at three dollars a gallon, that works out to 90-100 dollars for gas, not counting what's in the tank when I start.

They actually have to teach that to people? Or is this something a bit more complex that I'm missing?  Seriously: I've taken some college courses, but compared to all the professors and and whatnot here I might as well be Gomer Pile.

That said:  Provided I understand what you are talking about with 'estimation' at all, basically, I feel that its a valuable skill, sure, but it does not replace the need to teach MATH as math.  I mean what I said before: If the student doesn't grasp that 2+2 always equals 4, then the fact that he can 'ball park it' to 3 or 5 is unimportant.  

Hell, I learned to estimate when I realized i was too fucking lazy to sort out multi-digit/step computations to exact numbers when all I needed was 'close enough'.  But I had to know how to get those exact numbers first before I could be too lazy to get them.

In short: Estimation is something to teach AFTER they grasp the basics, the fundaments.

Quote from: jhkimOut of curiousity, where are you at?  I've got one son in 3rd grade, living in northern California.

San Jose.

Quote from: jhkimNote that there is a huge difference between the actual recommendations of the 1989 report and the hysterical claims of the "child abuse" of "fuzzy math".  What you describe isn't inconsistent with the report's advice, though I can't really tell.  California has supposedly split from the NCTM recommendations in recent years.  Notably, my son was taught some about fractions in 2nd grade, which is a practice the 1989 report recommends against.  On that, I think the report was on-target.  It seemed to me that none of the 2nd graders really grasped fractions, and it was a waste introducing it that early.

The California content standard for mathematics (adopted in 1997) is here. The curriculum framework (adopted in 2005) is here.

I don't remember to what extent fractions were covered in 2nd grade, but going by the state standards above, it was likely at a very introductory 'number sense' level, i.e., if you divide something into equal-sized pieces, each piece is a fraction of the whole (2 pieces = two 1/2s, three pieces = three 1/3s, etc.); the more equal-sized pieces you divide something up into, the smaller each piece must be (1/3 < 1/2, etc.); if you have all the pieces, you have the whole (2/2 = 3/3 = 1). According to the state standards, addition and subtraction of simple fractions comes in 3rd grade.

Quote from: SpikeIn short: Estimation is something to teach AFTER they grasp the basics, the fundaments.

That's been my experience as to how it's taught. Obviously, you cannot estimate by performing arithmetic on rounded numbers unless you already know how to perform the basic arithmetic operations on any numbers.

The method to use (estimation vs. exact calculation) depends on how the question is framed. For example, the problem might suppose someone with a $20 bill and a bunch of things to buy with exact prices given in dollars and cents. If the question is: does the buyer have enough money, then estimation may be sufficient to correctly answer yes or no; if the question is: how much change will the buyer get back, then calculation comes into play. Often both questions will be asked (i.e., does he have enough, and if so, how much change).

In short: I've not seen estimation taught as a precursor or complete substitute for calculation, but as a sometimes appropriate shortcut for students who already understand calculation.

  -- Matthew Gabbert

Quote from: SpikeFirst: Let me make sure I understand: There is actually a collegiate course in 'estimating'.

Like, I use 29 miles to the gallon in my car, I have a 10 gallon tank and I"m driving 1000 miles, so I'll use a bit over 3 tanks of gas, and at three dollars a gallon, that works out to 90-100 dollars for gas, not counting what's in the tank when I start.

They actually have to teach that to people? Or is this something a bit more complex that I'm missing?

The course was called "Physical Phenomena" -- it was a graduate physics course, but quite distinct from any other.  The first question the professor asked in class (this was at Columbia University in New York) was "How many piano tuners are there in Manhattan?"  Working through that was our introduction to estimations.  

We went on to focus on more physics-oriented questions, but a lot of the course was learning how to estimate with no hard numbers available.  These were problems that are usually called "back of the envelope calculations", and really I've done this a lot more than in real life than any formal computational problem.  We would encounter problems like about how much power it takes to drive a submarine, and on through considering novas, nebula, superfluids, and more.  

In the course, test and homework questions never gave any numbers or equations.  All tests were open-book.  As I said, it was a real eye-opener, and it contributed a lot to my understanding of physical phenomenon.  I think I had been indoctrinated for a while on physics problems consisting of weightless ropes on frictionless planes and such, with exact answers.  It was very interesting moving more into the realm of real-world problems where there was no exact answer but we were trying to get close.  

Quote from: SpikeThat said:  Provided I understand what you are talking about with 'estimation' at all, basically, I feel that its a valuable skill, sure, but it does not replace the need to teach MATH as math.  I mean what I said before: If the student doesn't grasp that 2+2 always equals 4, then the fact that he can 'ball park it' to 3 or 5 is unimportant.

This is the sort of overblown hyperbole which isn't helpful.  No one is suggesting that 2+2 not be taught.  The actual issue is more like this:  Suppose you're teaching multi-digit multiplication in 3rd grade, and some students aren't doing well as well as others.  This always happens.  Some students simply aren't as good as others.  

So suppose there are two math tracks in 4th grade.  (There aren't in my school system, but it isn't inconceivable.)  Should those who didn't do as well in multi-digit multiplication and division repeat it without being taught other  topics, on the principle that mastery of those should be prerequisite for any other math topics?  Or should they simultaneously review multiplication and division, while also covering topics like estimation and other topics covered by the more advanced students.

Quote from: Matthew GabbertSan Jose.

Cool.  I'm up in Redwood City.  

Quote from: Matthew GabbertIn short: I've not seen estimation taught as a precursor or complete substitute for calculation, but as a sometimes appropriate shortcut for students who already understand calculation.

Obviously no one has suggested estimation as a substitution for calculation.  However, I don't agree that mastery of calculation is a necessary precursor.  I think that the two can complement each other.  

For example, a student is learning to do multi-digit multiplication like 19 times 58.  The correct answer is 580 + 522 = 1102.  However, a typical mistake might be to forget to add the zero on the right and come up with 58 + 522 = 580.  I think it's appropriate for them to learn to estimate it at the same time as they are learning to perform the calculation.  A quick estimate would be that it's a little less than 20 times 60 which is 1200 -- this requires less mastery and can be done quickly.  

I think it is reasonable to teach students to recognize that the answer of 19 times 58 = 580 is wrong by clashing with the estimate, and conversely to recognize the error of their estimates by the process of working out the full operation.  

I'm not even sure that this specific example is the best teaching method, but the main issue is that there is ridiculous outcry over the idea of doing approaches like this.  The choice of which is best should depend on study of results.  Neither is a priori insanity or child abuse.

Quote from: jhkimObviously no one has suggested estimation as a substitution for calculation.  However, I don't agree that mastery of calculation is a necessary precursor.  I think that the two can complement each other.  
.

Quote from: post 2One 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. Another parent, Anne Cattaneo Santore, said she was troubled because her son, William, a second grader at P.S. 124 in Chinatown, spent months counting with coins and solving equations using ''friendly numbers,'' for instance, converting 71 + 19 into the easier 70 + 20.

It seems that in at least one case, posted by the polar opposite John, would directly contradict your assertion that no one is complaining that Estimations is being taught over Calculation.


But then, I don't blame you too much for failing to read what at one time was the only rebuttal to your original post. Morrow wears me out too, and I tend to agree with him more than disagree. Further, only by handwaving away all of his linky posts could you continue to claim that this Fuzzy Math thing is at all bad. I'll debate wether or not it is being used... I'm rather curious if its at all real, but given what I've heard of it, I'll stalwartly oppose you if you try to claim it's good.

And on the topic of your blithe dismissal earlier: I'll trust the Time Magazine article long before I trust some random gob I've never met on the internet (or, really, any random Gob...). I'd like more verification and cross referencing outside a singular source, it's true, but I haven't heard that many people treat time magazine like a gossip rag about bat boys and big foot.  Thus, I am forced to conclude that they have at least SOME journalistic integrity.

Quote from: SpikeIt seems that in at least one case, posted by the polar opposite John, would directly contradict your assertion that no one is complaining that Estimations is being taught over Calculation.

Obviously, I don't know the particular teacher and student in question, so I can't give a definitive answer here.  However, there are two possible interpretations the first quote:  

1) The first teacher was not teaching any calculation whatsoever, and always insists that kids estimate for every problem in the class.  

2) That at one point in the curriculum, the first teacher was teaching estimation, and thus wanted the kids to... y'know... estimate.  

Either of these match the expressed facts in the quote.  I happen to think that assuming #1 is true is unwarranted.  Still, it is possible.  However, even if some teacher, somewhere, is doing something outrageously stupid involving estimations, though -- that doesn't invalidate the principles I expressed.

Quote from: jhkimObviously no one has suggested estimation as a substitution for calculation.  However, I don't agree that mastery of calculation is a necessary precursor.  I think that the two can complement each other.

I completely agree that they go well together. I thought someone above was making claims that estimation was being taught instead of calculation. And I didn't mean mastery of calculation, only that you still need a basic understanding of calculation (e.g., times tables) before you can multiply rounded numbers instead of precise numbers. It seemed to me that some of the folks concerned about estimation were confusing it with 'guessing.'

Quote from: jhkimFor example, a student is learning to do multi-digit multiplication like 19 times 58.  The correct answer is 580 + 522 = 1102.  However, a typical mistake might be to forget to add the zero on the right and come up with 58 + 522 = 580.  I think it's appropriate for them to learn to estimate it at the same time as they are learning to perform the calculation.  A quick estimate would be that it's a little less than 20 times 60 which is 1200 -- this requires less mastery and can be done quickly.

Again, I agree and I think I mentioned in an earlier post that estimation was also useful as a quick sanity check. In addition to using it to check multi-digit multiplication, it's also useful when multiplying/dividing decimal numbers as IME it's pretty common for students to put the decimal in the wrong place after making a lot of otherwise correct numeric calculations.  

Quote from: jhkimI think it is reasonable to teach students to recognize that the answer of 19 times 58 = 580 is wrong by clashing with the estimate, and conversely to recognize the error of their estimates by the process of working out the full operation.  

I'm not even sure that this specific example is the best teaching method, but the main issue is that there is ridiculous outcry over the idea of doing approaches like this.  The choice of which is best should depend on study of results.  Neither is a priori insanity or child abuse.

Well, we're 3-for-3 in agreement here.

  -- Matthew Gabbert

Quote from: jhkimCool.  I'm up in Redwood City.

In the Wikipedia article on the highest income places in the United States, Redwood City ranks #50 in the 100 highest-income places with a population of at least 50,000 with respect to Per Capita Income and #62 with repect to Median Household Income while San Jose ranks #46 in the Highest-income places with a population of at least 50,000 with respect to Median Household Income.  It's just possible that these two towns are not typical, right?  How do the kids over in Oakland fare?  

You might also find this article interesting:

'Surprisingly, local educators say class size really has little bearing on the quality of a child’s education; rather, responsibility falls on the teacher and his or her ability to individualize instruction. “Much has been made of the advantages of smaller class sizes,” Wilcox says, “but most research shows that unless the size is limited to about a dozen students, it doesn’t make a significant difference if there are as many as 30 students in the room.”'

And looking the school ratings chart provided with that article, does your son attend North Star Academy (Elementary) in Redwood City where 93% of student tested at or above the 50th percentile in English and 98% tested at or above the 50th percentile in Math in 2005 (in other words, there are almost no below-average kids in that school) or Clifford Elementary where where only 58% of the kids score at or above the 50th percentile in English and 65% score at or above the 50th percentile in Math?  (Cloud (Roy) Elementary is in the middle, but closer to Clifford with 70% and 72% above the 50th percentile.)  In fact, according to that school chart, no school district in San Mateo has students performing at or below the average.  In Santa Clara county, there is a similar above average profile, except that a few schools have just below 50% of their students scoring at or above the 50th percentile on English and one below 50% on Math.  But nearly all of the schools are above average.  

Color me unsurprised that you are both happy with your school districts.  Yes, a median income listed in that report as $102,094 in Redwood City and $99,007 in San Jose Unified will do that for you.

Quote from: jhkimObviously no one has suggested estimation as a substitution for calculation.  However, I don't agree that mastery of calculation is a necessary precursor.  I think that the two can complement each other.

In the examples given in those articles, the students were being taught estimation as a substitution for calculation.  Of course the two can compliment each other but I'm also surprised that children need to be taught estimation.  

Quote from: jhkimFor example, a student is learning to do multi-digit multiplication like 19 times 58.  The correct answer is 580 + 522 = 1102.  However, a typical mistake might be to forget to add the zero on the right and come up with 58 + 522 = 580.  I think it's appropriate for them to learn to estimate it at the same time as they are learning to perform the calculation.  A quick estimate would be that it's a little less than 20 times 60 which is 1200 -- this requires less mastery and can be done quickly.

Correct.  But if you really know your arithmatic, you can get the actual answer by doing 20 times 60 = 1200 and then subtract away the 60 and 2 times 19 (1200 - 60 = 1140 - 19 = 1121 - 19 = 1102).  I often do this when I need to to long multiplication without anything to write on.  Basically, I correct the estimation.

Quote from: jhkimI think it is reasonable to teach students to recognize that the answer of 19 times 58 = 580 is wrong by clashing with the estimate, and conversely to recognize the error of their estimates by the process of working out the full operation.

But that's not what those parents were describing.  They were describing doing only the estimation and actually discouraging students from working out the real answer.  Are you saying that they are liars because even the brief descriptions of their complaints in those articles were fairly detailed and specific.

Quote from: jhkimI'm not even sure that this specific example is the best teaching method, but the main issue is that there is ridiculous outcry over the idea of doing approaches like this.  The choice of which is best should depend on study of results.  Neither is a priori insanity or child abuse.

Yes, they should study results but how do you determine what works?  You'll notice that the biggest critics of standardized testing are those pushing whole math and whole language.  Why do you think that is?  And if schools don't use standardized testing to determine what works, what should they use?

Quote from: John MorrowColor me unsurprised that you are both happy with your school districts.  Yes, a median income listed in that report as $102,094 in Redwood City and $99,007 in San Jose Unified will do that for you.

And this relates to your criticism of state standards how? I think I already raised the issue of the inequities in school funding upthread. It is definitely a real problem and has nothing to do with your fuzzy math child abuse spiel.

Quote from: John MorrowIn fact, according to that school chart, no school district in San Mateo has students performing at or below the average. In Santa Clara county, there is a similar above average profile, except that a few schools have just below 50% of their students scoring at or above the 50th percentile on English and one below 50% on Math. But nearly all of the schools are above average.

That's because it is not a complete list of San Mateo and Santa Clara County schools; as the article plainly states, it is a list of the best (i.e., highest scoring) schools. The latest test scores statewide can be found here, but as all of these schools follow the same California standards, how does this support your contention that children are suffering the child abuse of fuzzy math?

  -- Matthew Gabbert

Quote from: jhkimI don't feel that a Time magazine article quoting a handful parents who complain is any more of an authoritative source about the larger picture than a Wikipedia article.  The articles don't actually look at the state curriculum to see whether what of the counter claims are representative -- nor do they critically examine the parents complaints against, say, the relative test scores for the students.

And if I find other articles, are you going to focus on the problems with them, too?  You provided anecdotal evidence of how great your son's school is.  I gave you anecdotal quotes from other parents who are far less happy with how their children are being taught.  Would you be happy if your son's education matched those described by those parents?

I notice you didn't comment on the fact that Newark, NJ spends about $1 million for every student that graduates academically qualified.  Exactly how much are public schools supposed to spend, if you think spending is the answer, and would you support California, for example, taking money from your son's school district to give to Oakland or perhaps bussing kids in from Oakland to benefit from the nice schools in Silicon Valley?

Quote from: jhkimThe 2001 Time magazine article is terrible -- it gives a bare IP address for MathLand (invalid, of course).  It describes the term "whole math" as a derisive term made by critics, but then uses that term for the subject throughout.  It also doesn't bother to actually examine the actual results.

There is evidence that it doesn't work so well if you look for it.  You might find this one interesting, for example:

'For my fall 2006 Calculus I for the Biological and Social Sciences course I administered the same final exam used for the course in the fall of 1989. The SAT mathematics (SATM) scores of the two classes were nearly identical and the classes were approximately the same percentage of the Arts and Sciences freshmen. The 2006 class had significantly lower exam scores.'

'Since 1994 the College Board has allowed the use of calculators on the test. The College Board's calculator policy, [Cal07b], states: "Every question on the SAT Reasoning Test [SATM] can be solved without a calculator; but you will gain an advantage by using a calculator with which you are familiar." I conjecture that it is precisely this gained "advantage" that causes the SATM to fail universities in the admissions process. This conjecture is consistent with the 2002 JHU study, [WN04], that found that students for whom "in K-12, calculator usage was emphasized and encouraged" had lower mathematics grades in the large service courses. As it stands, universities have no way of rejecting applicants who do not know arithmetic adequately for college-level mathematics."'

Please note that I am not advocating a drill-only approach to mathematics.  But there are programs that go to the other extreme, and don't focus on the basics at all.

Quote from: jhkimOK, so according to the article, scores are up in a whole state, and drop off in two cities.

Is that really what it says?

Quote from: jhkimThe NYTimes article never cited any drop in math scores -- it instead argued that improvements in math scores weren't necessarily proof of success because of other factors.

Uh, the NY Times article states:

"District 2, which has a high percentage of affluent students, has long ranked near the top of the city school system. Last year, when a new math test was introduced, scores across the city declined, and District 2 was the only district to remain stable."

As far as my old fashioned education taught me, "declined" indicates a drop in scores.  Only one district remained stable (i.e., didn't drop) and that was the one with the high percentage of affluent students.

Quote from: jhkimAnd I'll admit that improved standardized test scores aren't proof of anything, and there are lots of things that aren't tested by them.  However, if the claim is that the new curricula are insanity which teaches kids nothing, then I would damn well expect a drop in scores.

The problem is that they change the tests and renorm the scores so that they don't drop.  See the article above about the professor who gave his 2006 students the same test that he gave in 1989.  And look at how American students perform on international tests against students from other countries, year after year.  Here is another interesting article that goes even further back for minority students.

Quote from: jhkimI've looked at the U.S. and California performance on standardized math tests over time.  I didn't review them specifically for this, but there hasn't been a noticeable drop-off since 1989 when the maligned report was issued.  Scores have generally been getting better. (I'll have to see about a link later -- I seem to have misplaced it.)

Do they allow students to use calculators for the tests?

Quote from: jhkimOn a more personal note: I feel that an emphasis on estimation is great.  I never had a class that emphasized estimation until graduate school, and when I did it was a huge eye-opener.  It is an extremely useful real-world skill that is sorely lacking in most people.  I remember being shocked when grading a physics test where a sophmore college student gave an answer for the mass of Mars that was around a ton due to a miscalculation, and he wrote down that answer on his test with no comment.  He went through the rote procedure and made a mistake -- which happens often.  However, when he got an answer like that, he should immediately realize it and go back.  However, he was apparently locked into doing mechanical procedures rather than looking at the whole problem and relating it back to the world.

I have no problem with estimation or hands on exercises or explaining the meaning behind the math (e.g., calculus makes a whole lot more sense when you understand that it can be used to calculate the area under a curve, logorhythms make a whole lot more sense when you understand they are an exponent, and so on).  I have a big problem with students not learning the basics because they are too busy playing games and discovering things on their own.

Quote from: jhkimAlso, my personal experience is in physics education, which is a field where the traditional teaching methods -- when exposed to real research on the students -- sucked.  U of Wisconsin had a team who were actually looking at teaching methodology, and when they conducted follow-up research on how well students retains knowledge of basic concepts from a physics course, the answers were pretty damn depressing.  It's pretty common in most higher education fields, sadly, for there to be little research on teaching methods.  Real education research is usually reserved for younger ages.

That's because most of the things that students are taught have no bearing on their daily life.  I'm all for making math relevant to students.  But at the end of the day, the right answers are important and students who can't come up with the right answers are having a great disservice done to them.

Quote from: Matthew GabbertAnd this relates to your criticism of state standards how? I think I already raised the issue of the inequities in school funding upthread. It is definitely a real problem and has nothing to do with your fuzzy math child abuse spiel.

To 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.  If you look at those school performance figures, something becomes fairly clear -- the "inadequacies of school funding" are largely meaningless.  Redwood City spends toward the low-end per-pupil of the districts in those two counties, yet has one of the top-performing elementary schools.  According to the article I quoted from earlier, Newark, NJ spends about $1 million for each student that can pass the rigorous state exam to graduate and Newark and Camden spend about a billion dollars between them on education.  Exactly how much money would be needed to correct those "inadequacies of school funding"?

Quote from: Matthew GabbertThat's because it is not a complete list of San Mateo and Santa Clara County schools; as the article plainly states, it is a list of the best (i.e., highest scoring) schools. The latest test scores statewide can be found here, but as all of these schools follow the same California standards, how does this support your contention that children are suffering the child abuse of fuzzy math?

Fair enough.  Somehow I've been dragged into researching schools in a state on the other side of the country from me, so you'll have to forgive my carelessness.  But I'm curious.  Do your children attend one of those top schools because that's certainly relevant to your happiness with their education.

Quote from: Matthew GabbertI completely agree that they go well together. I thought someone above was making claims that estimation was being taught instead of calculation.

The mother who complained that her son was being discouraged from calculating the correct answer was certainly making that claim.

Quote from: Matthew GabbertAgain, I agree and I think I mentioned in an earlier post that estimation was also useful as a quick sanity check. In addition to using it to check multi-digit multiplication, it's also useful when multiplying/dividing decimal numbers as IME it's pretty common for students to put the decimal in the wrong place after making a lot of otherwise correct numeric calculations.

Have you ever heard of Casting Out Nines?  This is something that children were once apparently quite commonly taught in schools before the first wave of New Math.  Of course you need to know your basics to do it.

Quote from: jhkimObviously, I don't know the particular teacher and student in question, so I can't give a definitive answer here.  However, there are two possible interpretations the first quote:  

1) The first teacher was not teaching any calculation whatsoever, and always insists that kids estimate for every problem in the class.  

2) That at one point in the curriculum, the first teacher was teaching estimation, and thus wanted the kids to... y'know... estimate.  

Either of these match the expressed facts in the quote.  I happen to think that assuming #1 is true is unwarranted.  Still, it is possible.  However, even if some teacher, somewhere, is doing something outrageously stupid involving estimations, though -- that doesn't invalidate the principles I expressed.

How else would you interpret:

"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. Another parent, Anne Cattaneo Santore, said she was troubled because her son, William, a second grader at P.S. 124 in Chinatown, spent months counting with coins and solving equations using 'friendly numbers,' for instance, converting 71 + 19 into the easier 70 + 20."

Are you actually reading these articles?  You seem to be missing a lot.

I live in Redwood City.  To fill in some of your questions: My son used to go to John Gill school, but this year he is going to North Star Academy.  Redwood City does have some excellent schools, including North Star.  However, compared to neighboring Atherton or Palo Alto to the south, it is more of an integrated community.  I had a post on my personal LJ last year, No Child Left Behind in Redwood City that talks about some of the statistics.  

One 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.  

As 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.  

Quote from: John MorrowAnd if I find other articles, are you going to focus on the problems with them, too?  You provided anecdotal evidence of how great your son's school is.  I gave you anecdotal quotes from other parents who are far less happy with how their children are being taught.  Would you be happy if your son's education matched those described by those parents?

Honestly, 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.  

For 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.  

Regarding the articles not citing any drop due to the new math curricula:

Quote from: John MorrowUh, the NY Times article states:

"District 2, which has a high percentage of affluent students, has long ranked near the top of the city school system. Last year, when a new math test was introduced, scores across the city declined, and District 2 was the only district to remain stable."

As far as my old fashioned education taught me, "declined" indicates a drop in scores.  Only one district remained stable (i.e., didn't drop) and that was the one with the high percentage of affluent students.

Well, yes, but District 2 -- the one whose scores didn't drop -- was also the one that aggressively adopted the new "reformed" math curricula that the article is criticizing.  i.e. The one district whose scores didn't drop was the one with the supposedly broken new curriculum that the article is complaining about.  It might be an affluent district, but logically that would have an effect both before and after the curriculum change and shouldn't affect the recent change in scores.  

Quote from: John MorrowThe problem is that they change the tests and renorm the scores so that they don't drop.  See the article above about the professor who gave his 2006 students the same test that he gave in 1989.  And look at how American students perform on international tests against students from other countries, year after year.  Here is another interesting article that goes even further back for minority students.

It'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:

QuoteGenerally, the trends in mathematics and science are characterized by declines in the 1970s, followed by increases during the 1980s and early 1990s, and mostly stable performance since then. Some gains are also evident in reading, but they are modest. Overall improvement across the assessment years is most evident in mathematics. National trends in average reading, mathematics, and science scores are depicted in Figure 1.

Quote from: John MorrowHow else would you interpret:

"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. Another parent, Anne Cattaneo Santore, said she was troubled because her son, William, a second grader at P.S. 124 in Chinatown, spent months counting with coins and solving equations using 'friendly numbers,' for instance, converting 71 + 19 into the easier 70 + 20."

Are you actually reading these articles?  You seem to be missing a lot.

Look, John, I appreciate the discussion and I'm interested in the topic -- but your attitude is getting pretty annoying.  I already replied regarding that quote -- do you bother reading my posts?  

What'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.  

QuoteThree years ago, one of New York City's most adventurous school districts set out to tackle a nagging problem: the math phobia that afflicts many students, and the disparity between the test scores of white middle-class students and their poorer black and Hispanic counterparts.

That's District 2 there.  Here's a quote from the director in the article.  

QuoteAnd Lucy West, the director of mathematics at Manhattan's District 2, where the new math has been most aggressively adopted, said that old-fashioned math had been oversold. ''There is a misconception that in the good old days everybody could add and subtract, multiply and divide really easily and efficiently,'' she said.

And now here's the quote which you claim shows a drop due to this "fuzzy math"

QuoteDistrict 2, which has a high percentage of affluent students, has long ranked near the top of the city school system. Last year, when a new math test was introduced, scores across the city declined, and District 2 was the only district to remain stable.

Ms. West, the math coordinator, said that was evidence the program was working.

That'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.