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Why is Math so special?


regentrude
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I am really puzzled about the acceleration debate because it seems to center exclusively on mathematics. No other subject seems to create as much debate and worry.

If a child is a gifted musician, it is generally accepted that this child will be able to progress through musical instruction much faster and will, for instance, at age 10 be able to perform pieces that average students do not master until age 20 (or never). I have not come across anybody who argued that this student should be slowed down because it could create problems if he was allowed to play Beethoven on his violin when other students are just playing Twinkle little star.

I have also not found anybody who argued that children should be slowed down in their language acquisition or reading.

 

Why do people single out math?

Is it because people are uncomfortable about math? If I talk to people who use higher math for a living on a daily basis, I encounter none of these fears.

Interested to hear your thoughts.

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Why do people single out math?

Is it because people are uncomfortable about math? If I talk to people who use higher math for a living on a daily basis, I encounter none of these fears.

Interested to hear your thoughts.

 

In the general population? I feel like it's a combination of people being uncomfortable with math, and specifically the relatively poor math instruction that too many US schools produce. (I feel awful saying that, because I know of at least two excellent HS math teachers IRL, & they or their spouses post here, but I'm generalizing.) Because in general many people never truly understand math, they become even more uncomfortable with the subject.

 

I would also argue that, in general, while there is much lip service paid to the value of math, most people would see a greater value in advanced reading skills. There seems to be an attitude of "what's the point?" (Variations of this include people asking "What if she runs out of math?" and "What does all that math let you do?").

 

Finally, there seems to be a difference perceived between those that are extremely advanced in math versus, say, reading or music, in terms of whether it can be taught or if it's just an advanced gift.

 

I don't have good answers, though. I have my own questions, like why a musically-talented child is assumed to have private instruction and opportunities, but doing the same for a mathematically-talented child will get you strange looks.

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I'm not uncomfortable with the level of reading my children possess... However, I may be uncomfortable about the content/subject material of books AT their reading ability may contain.

 

When it comes to math, for me, it becomes more of a question of what in the world are we going to do when pony girl or bionicle man is in the 8th grade doing Calculus... and we haven't hit high school yet.

 

The costs of on-line/college courses are more than we spend on all of our children combined right now, as the high school years approach, the cost would almost double our anticipated costs there as well. Our local public schools do not pay for high schoolers to attend college classes either... they take what is offered (through AP Statistics).

 

I am not comfortable teaching beyond Algebra II. I would be relying on programs like Chalkdust. My husband can dig out some college texts and throw in spherical trigonometry, and differential equations -- assuming he has the time to do so.

 

When it comes to humanities, there are plenty of ways I can enrich, deepen, broaden and meet them where they need to be without breaking the bank. Math is much more difficult to affordably obtain instruction/assistance.

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Math is much more difficult to affordably obtain instruction/assistance.

 

Not necessarily, with the right resources. There are wonderful math books that are written towards the student and are intended for use without a teacher. The AoPS books cost between $44 and $59 and can be reused for several children or sold - I don't consider that expensive.

I understand that in your personal situation, cost of instruction may be a financial hardship. But I was thinking more of societal values in general: there are plenty of people willing and able to pay a lot of money to have their children take private music lessons or play sports - and it is generally accepted that this is money well spent. OTOH, most people would think it nuts for somebody to spend the same amount of money on math. Why?

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It seems much easier to identify a "grade level" or otherwise identify where a person is achieving on a linear scale than it is with reading; upper elementary books often have reading levels that span 3 or 4 years or grade levels. If someone is "ahead" in math, it is much more obvious; starting algebra seems to be quite the milestone, for whatever reason.

 

(This from the mom who is freaking out about figuring out my dd9's math level more precisely :lol: so that I can begin homeschooling her in January). I've been pondering why I am so obsessed with math. There are other reasons I may homeschool dd9 starting in January, but they are minor compared to math - math would be THE reason. It's not hard for dd to read books at higher levels than her classmates - she's in a Montessori school after all, where instruction is relatively individualized - but we're finding that math instruction is a problem for the school at the moment; they're having difficulty combining more traditional curricula in the montessori setting and I'm not thrilled with how it's working out.

 

Writing is another angle, but not one in which she's as obviously ahead of peers. A lot of subjects can be learned once one is reading well, but math requires more direct instruction, either in the form of a curriculum or a person but mostly both, IMO.

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I think one concern is that some parents do push or rush their children before they're ready to move ahead. A child who has not really mastered elementary mathematics shouldn't be moved into algebra.

 

Another concern that usually others have is the mistaken belief that a child who is doing advanced work couldn't possibly have other interests or a social life. My son gets this all.the.time. from peers, teachers and even other parents who know little about his actual life outside of school. Usually it's said in a way that's not very nice. He's had to learn at a young age not to be proud of his academic accomplishments and to attribute them to luck and not hard work. Sports on the other hand, are treated in an entirely different manner.

 

In general, I think a lot of people are uncomfortable with children who are advanced or gifted regardless of the subject. We've come across it in the schools my youngest has attended. It's one of those darned if you do, darned if you don't situations. We just move ahead despite what others think.

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A lot of subjects can be learned once one is reading well, but math requires more direct instruction, either in the form of a curriculum or a person but mostly both, IMO.

 

I completely understand why somebody would be worried about providing or finding math instruction at a higher level, because that may seem difficult to a parent without the math background - so I have complete understanding and sympathy for these concerns. But that was not what I was getting at.

My question is: why do people worry that accelerating math may be detrimental for the kid - since similar concerns are not voiced in any other area?

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Totally guessing here... but could it be that people have been taught both directly and indirectly that acceleration means kids may be able to manipulate numbers but won't possibly understand the concepts, because they need to reach a certain age for their brain to develop in ways that allow this understanding?

 

The other aspect of it is just plain anti-intellectualism, I think, and it's aimed at math because that is the representative nerdy field. Kids who accelerate in math are not going to be "able to be kids," they'll be socially inept, etc. I think this incredible stereotype is alive and flourishing in our society.

 

One further thought: I don't think many people can imagine a child's joyous engagement with math or an intellectual pleasure in solving puzzles. Math is thought of as sheer drudgery, and perhaps the fear is that the only way a child will be advanced in math is if the parent is pushing more and more drudgery. Maybe this is what lies behind the "why don't you let that child just enjoy being a child" response.

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One further thought: I don't think many people can imagine a child's joyous engagement with math or an intellectual pleasure in solving puzzles. Math is thought of as sheer drudgery, and perhaps the fear is that the only way a child will be advanced in math is if the parent is pushing more and more drudgery. Maybe this is what lies behind the "why don't you let that child just enjoy being a child" response.

 

This is a great point. MIL recently asked my oldest dd what she did for fun. Dd mentioned math, trumpet, piano, reading new books, and at the last, almost as an aside, said that the past few days, she'd been doing some finger knitting. MIL paused, clearly out of her depth, and said, "So, finger knitting is your main leisure activity?" She just didn't get that the rest of it is *fun* for dd.

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I have not come across anybody who argued that this student should be slowed down because it could create problems if he was allowed to play Beethoven on his violin when other students are just playing Twinkle little star.

 

 

Well, I have, although indirectly.

I read Lang Lang's biography, a Chinese classical piano player. He was preparing a piece for a concert in Japan, and people were telling his teacher he was too young to play such a piece. I don't remember the exact details here, I never expected I'd ever discuss it :) The piece was about a woman being abandonned by her lover, and he was 10yo and quite sheltered. People were concerned he could not get the emotions through, even if he could do the techniques. Well the piano teacher changed the 'story' by emphasing how much Lang Lang missed his mom. He aced the contest (he either placed first or second, I'm not sure) and impressed everyone.

 

On another note (haha), my young cousin was gifted in violin, placing first in Canada a few years back. He found a teacher that would push him at his level, only to end up with Carpal Tunnel Syndrome at 15, when his body grew quite a bit. He can no longer play. The pieces he was playing were too hard on his body.

 

So, yes, you can push too far ahead in music.

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It isn't just math. The reasons you should not let your child read advanced books are out there too.

:iagree: I've had this reaction to different areas where my dc excel. Since my younger two really don't broadcast their abilities, it hasn't come up as much with them. I have no problem with dc going far ahead in any subject they are ready to. The only problem I have, and this is chiefly in music since I have taught it, is with prodigies doing a lot of performing at an early age since it frequently leads to burn out. I feel very strongly that a music prodigy should only dopublic performances if they are begging to do it on their own, not being offered it or told to do it. I also feel strongly about dc who are acting prodigies, too, and hate to see them become stars early, particularly in screen acting, which is not a kind business even to adults.

 

My personal rule of thumb is that if a child is pushing to learn more in a subject let them go as far as they like as long as there isn't content that could make a sensitive dc become worried, stressed, lose sleep, etc. No one in my extended family, where everyone is hg-pg reads early, either. Perhaps we don't have the close vision early or perhaps we're just not that interested when we have family reading to us so much.

Edited by Karin
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No one in my extended family, where everyone is hg-pg reads early, either. Perhaps we don't have the close vision early or perhaps we're just not that interested when we have family reading to us so much.

 

Completely off-topic, but I really needed to read that today. I do come from a family of early readers, so ds has been at best puzzling to me. (He *can* read, of a fashion, but not with the voracity and skill that I realize I have come to expect at an early age.)

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Having been a math tutor, I can attest that there are certain topics that just seem to "click" with many kids at about the same age. And when a school decides to have all their kids do Saxon a year ahead of grade level (for example), there are kids who are perfectly fine on the placement tests, but who hit that specific topic (multiplication and division of fractions, for example), and just plain don't get it. Go on to something else, and come back 6 months or 12 months later, and they do-and it's usually when they're right at the grade/age that the textbook writer expected them to be able to handle it. But meanwhile, the kid is sitting in class every day, convinced they're stupid, and struggling with the concept that math, which used to be easy, suddenly isn't.

 

I think many of the fears on accelerating in math come from these sort of experiences, and the expectation that math will be linear, so a child who hits a wall will be stuck waiting. I don't think this applies at home. Not only do not all kids hit walls, and it's going to be that sort of kid who demands acceleration, but math at home doesn't have to be linear, and in fact, shouldn't be. So if your child isn't quite ready to multiply fractions, you go do geometry, or logic, or something else for awhile. And then you come back and the wall isn't there anymore.

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I am really puzzled about the acceleration debate because it seems to center exclusively on mathematics. No other subject seems to create as much debate and worry.

If a child is a gifted musician, it is generally accepted that this child will be able to progress through musical instruction much faster and will, for instance, at age 10 be able to perform pieces that average students do not master until age 20 (or never). I have not come across anybody who argued that this student should be slowed down because it could create problems if he was allowed to play Beethoven on his violin when other students are just playing Twinkle little star.

I have also not found anybody who argued that children should be slowed down in their language acquisition or reading.

 

Why do people single out math?

Is it because people are uncomfortable about math? If I talk to people who use higher math for a living on a daily basis, I encounter none of these fears.

Interested to hear your thoughts.

 

I don't think it is just math. I think math is discussed on this forum often because there is a linear progression that is easily defined. It is not so easy to define the progression in other areas such as reading and writing once a child is able to do each skill fairly well. I often hear people in other "forums" discussing the "evils" of early reading or the "evils" of children doing anything at a high level very well...whether it be music, gymnastics, whatever.

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I am really puzzled about the acceleration debate because it seems to center exclusively on mathematics. No other subject seems to create as much debate and worry.

If a child is a gifted musician, it is generally accepted that this child will be able to progress through musical instruction much faster and will, for instance, at age 10 be able to perform pieces that average students do not master until age 20 (or never). I have not come across anybody who argued that this student should be slowed down because it could create problems if he was allowed to play Beethoven on his violin when other students are just playing Twinkle little star.

I have also not found anybody who argued that children should be slowed down in their language acquisition or reading.

 

Why do people single out math?

Is it because people are uncomfortable about math? If I talk to people who use higher math for a living on a daily basis, I encounter none of these fears.

Interested to hear your thoughts.

 

Can't post in depth at this moment, and will be back soon to comment more, but I wanted to say that for ME, I have concerns that if my child moves ahead at the pace he wants to (my thoughts are that he would easily be able to tackle SM5 right now) he might miss out on solidifying basic facts and gloss over in-depth conceptual comprehension. I really, really want my son to have a deep understanding of the math he is doing: we look at math from many different angles, use a few different workbooks, approaches, etc so that I am comfortable that he really knows his stuff before we move to the next level. Maybe I don't really "believe" that he understands the material? Maybe I don't have enough faith in his ability? Maybe there's something inherent in math (as opposed to say, literature analysis or science) that evokes this anxiety is me (us??)--I don't know. I do know that I am really trying to think this through right now, and do what's right for my son.

 

My concern with moving ahead at the pace he wants is that we might, just might, gloss over something that will rear its ugly head down the road, when it will be less easy to remedy. That said, in our "spare time" we do play with topics well ahead of his stated level. We don't do formal work on these topics, however. Based on my previous post about accelerating math, I am wondering at this moment whether my approach is the right one for my son.

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I too have been surprised by people saying they are going to put the brakes on for math. I think part of the reason for this is the perception that there is one, and only, one path to higher math: pre-algebra, algebra I, geometry, algebra II then pre-calculus and finally calculus. Each of those is supposed to be a one year course and since most of us never explored math more deeply, we cannot imagine what else our kids could be exploring in math. It is hard to comprehend that there is a way to go more deeply into one of these topics. We simply don't know how and can't think outside that very regimented linear approach.

 

People seem to think of science in the same way -- year long courses that are finite in content. But literature and music and history don't quite get boxed up the same way -- there isn't that regimented linear progression that causes someone to say "whoa, slow down!" (Limiting reading selections is a separate issue.)

 

Which leads me into something I had wanted to share with Regentrude and anyone else interested in this.

 

My 15yo ds is taking Algebra II at the community college because, quite frankly, I am not a good math teacher for him. He likes math, and he would often find unique ways of tackling problems in Algebra I and I certainly couldn't assess what he was doing, make suggestions, show him where he went wrong. He'd have to explain his thought process to me, and would have arrived at the correct answer, but not in a way I would have ever considered. I've felt for a while he needed a math mentor. He is loving the CC class, doing well and is looking forward to the day when he finally has the calculus he needs to take real physics courses. (It's in his genes -- my dad was a prof of physics) (I have the conceptual part down, but had a lousy math education and a passion for the social sciences.) He'd like to major eventually in engineering or physics or math.

 

He could take pre-calculus next semester, but his professor urged him instead to take his time and instead take a semester of college algebra and a semester of trig before taking pre-calculus. Apparently, in the professor's experience, lots of kids get through the calculus sequence just by memorizing formulas, but they don't understand it deeply. He felt, considering my son's interests, that my ds should take time to get that deep understanding. He also strongly feels, as a dad of a kid who finished his math degree at age 20, that there is some benefit to taking some time, that there is much to be gained as the brain matures -- it isn't necessarily a great thing to finish early.

 

I thought it was interesting because I know SWB has commented on how even the brightest and most advanced kids are not necessarily ready for college at 16 or 17. This opinion was based on her own experience as a young college student and as a professor. And it isn't necessarily the level of work, but simply the maturity and life experience that comes with, well, coming of age. I had never considered this in terms of math or science and yet it makes sense. What do y'all think?

 

As far as my ds is concerned, he is perfectly happy taking college algebra next semester. I don't see it as putting the brakes on but as a chance to go deep with a trained mathematician guiding the way. I'm really happy to have finally found the right place for him.

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I'm not sure if I've put the brakes on in the sense being talked about here, but we are putting off moving into algebra for a bit. But:

 

  • math isn't DD the Elder's passion
  • we keep short days and aren't ready for the time commitment of the higher maths
  • we've been able to find engaging materials to fill the gap

There's not much left for her to do... finish Zaccaro and do LoF: Pre-Algebra 2 w/ Economics (if for no other reason than it's Fred). After that, I don't know if Algebra will be the first step, or if it will be in conjunction with another topic, but she'll have to move on. We'd have to do so soonish anyway because she's almost done her (admittedly superficial) middle school level science, and is hungering for something more substantial. I've picked up a conceptual biology text and am considering conceptual physics, but these will last a year and a half at most.

 

I'm not worried "running out" of math and have no intention of sending her in a straight line path to Calculus. When the math gets to be too much for me to facilitate (roughly anything theoretical after first year college level), there are always advanced courses available at EPGY and elsewhere. I simply don't see self-pacing in math as a problem and am frequently surprised at the handwringing that goes on over it around these boards.

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The other aspect of it is just plain anti-intellectualism, I think, and it's aimed at math because that is the representative nerdy field. Kids who accelerate in math are not going to be "able to be kids," they'll be socially inept, etc. I think this incredible stereotype is alive and flourishing in our society.

 

One further thought: I don't think many people can imagine a child's joyous engagement with math or an intellectual pleasure in solving puzzles. Math is thought of as sheer drudgery, and perhaps the fear is that the only way a child will be advanced in math is if the parent is pushing more and more drudgery. Maybe this is what lies behind the "why don't you let that child just enjoy being a child" response.

 

This is what I see around here. I'm surrounded by mostly unschoolers who keep telling each other that math isn't important, that the only math children need is 'supermarket math' (we need 5 oranges, I take 3, how many do you need to pick up?.....and no, they are *not* talking about 5yo's, sigh). And whatever I say, I cannot convince *anyone* that math can be fun, that there are lots of kids who *like* doing math. I'm no longer surprised that 'no homeschooled kid' likes math...of course not with parents who keep telling their kids that from birth :glare:. So the few parents who do use a math curriculum and who have a kid who is doing well, are not going to accelerate or spend time finding enrichment math, while they do spend lots of time reading advanced literature.

 

ETA: I forgot to say that in the Netherlands there is not the fear for starting Algebra that I see with Americans. Here, math is perceived as a subject where you just go from one step to the other, addition, subtraction, multiplication ..up to higher levels of math, but no new step/level is considered a huge step up.

Edited by Tress
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Apparently, in the professor's experience, lots of kids get through the calculus sequence just by memorizing formulas, but they don't understand it deeply. He felt, considering my son's interests, that my ds should take time to get that deep understanding. He also strongly feels, as a dad of a kid who finished his math degree at age 20, that there is some benefit to taking some time, that there is much to be gained as the brain matures -- it isn't necessarily a great thing to finish early.

 

I thought it was interesting because I know SWB has commented on how even the brightest and most advanced kids are not necessarily ready for college at 16 or 17. This opinion was based on her own experience as a young college student and as a professor. And it isn't necessarily the level of work, but simply the maturity and life experience that comes with, well, coming of age. I had never considered this in terms of math or science and yet it makes sense. What do y'all think?

 

I think this is extremely dependent on the individual child. I have encountered younger (16/17 y/o) college students who possessed both the intellectual readiness and maturity to do extremely well. I see plenty of average age college students who have neither. And I observe that non-traditional students, who attend college later in life, are struggling in my physics classes and are usually never among the top students (even though some of them are among the most motivated ones).

 

There are several factors that play a role in college success.

One is obviously preparation - a lousy math and science background will be an obstacle, no matter how mature the student. It has, however, been my impression that the reason students are ill prepared for higher math is poor instruction - I have not seen any signs that it is due to them having been taught the math at too young an age.

The other crucial factor is work ethic, time management and prioritizing. These latter skills may be more related to maturity - but again, I think a lot of issues are inherited from a high school education that does not prepare students to take responsibility for their learning (and maybe, I am guessing here, a family upbringing that has not instilled work ethic into the child from a very young age on).

 

I absolutely agree that one should go as slowly in math as needed to thoroughly understand the material. Sadly, most students who have taken calculus have no idea what it really means - as you say, they plug and chug formulas, but have no real understanding that a derivative is the slope of a curve. I am, however, not sure that simply being older and more mature would cure this ill - it seems to me that only a more rigorous mathematical training, starting from an earlier age, would have an impact. (And a math teacher who really understands the material.. I am not so sure that is always the case in school.)

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There are several factors that play a role in college success.

One is obviously preparation - a lousy math and science background will be an obstacle, no matter how mature the student.

 

 

LOL -- you are talking straight to the hugely self doubting side of my homeschool self, the side that worries I've ruined my child's education by not being good enough!! And math is the one subject that is not a natural for me. Writing was never a worry, general science was a joy, music, literature, art -- well all of those subjects are as natural to me as breathing. But I don't have that same broad, deep understanding of higher math that gives me the big picture of what I should have been striving towards. The contrast in my knowledge and capabilities makes me worry so much more for my math inclined ds.

 

But back to the maturity issue. I think SWB's point was directed at another side of the homeschool parent mindset, that earlier is somehow better. For instance, it is completely nuts that I would even pause to consider for the briefest moment that my son is doomed because he isn't diving into Calculus by the age of 16. I don't believe that at all, but it flits across my mind. I think your distinction is an important one, and why you started this thread, that earlier, when a student is truly capable and ready, is not detrimental.

 

My dad passed away many years ago, so I've not been able to have these conversations with him since I was a teen. But I can remember him talking about how there is a wall for some people in physics. It wasn't the math he was talking about, but wrapping the mind around concepts -- some people hit that wall early, others in grad school. There was one grad student in particular who backed up and tried again and again, but kept slamming into the wall and couldn't not break the barrier. It really perplexed him as she had been so good at it, but wasn't ever going to get that PhD.

 

He was also, by the way, the last faculty member to give in and start offering multiple choice tests to those huge freshman physics classes. Writing, to him, was just as important as the math and the concepts, but grading a couple hundred short answer tests was a time-eating task.

 

All right. Enough of my cold-induced middle of the night ramblings. I'm supposed to be getting up in 2 hours to get my ds to his 7am math class!

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On another note (haha), my young cousin was gifted in violin, placing first in Canada a few years back. He found a teacher that would push him at his level, only to end up with Carpal Tunnel Syndrome at 15, when his body grew quite a bit. He can no longer play. The pieces he was playing were too hard on his body.

 

That is really interesting. My son is a precocious pianist who is on his 3rd teacher. Had we stayed with his 2nd teacher, I could easily have seen something like this happen. There are definitely teachers (or parents or even the kids themselves) who get highly invested in having a "child prodigy" on an instrument. Our current teacher recognizes my son's ability to learn quickly and be expressive in his music, but won't take his music to new levels until his technique at the current level is flawless and relaxed. Not to mention the teacher also teaches theory and values skills like sight reading. However, to keep my son happy he gets about 3 to 4X the repertoire of the average kid his age, and allows him to pick and choose what he'd like to learn. Which went from Scott Joplin, to Harry Potter theme music, to contemporary Russian composers. My son is playing a Beethoven Sonata in his next recital, so he's ahead of the average 4th grader taking piano. But his teacher has done a good job moderating forward momentum and likes to talk about when he's in high school he can play anything he wants!

 

Relating back to math, I think you could get through basic curriculum really fast with some of these GT kids. But I think there is much to be gained by really digging in at each level in some problem solving and coming at the concepts from many angles. I know my own kid, who's doing Singapore NEM 1 as a 4th grader, has understood algebra concepts for as long as I remember. But really just now is pulling together the patience, writing skills, and work ethic to really jump into it. And I think if I pulled out a more basic curriculum, he'd race through it. NEM 1 is hard and slow for us, but it is going well enough that we'll stay the course. I also have Lial's here that I considered (and other options), but going through that would make him pull his hair out. I pull additional practice problems from Lial's as necessary. I have a math degree, so I think long and hard about our math decisions. On the up side, higher level math is one thing I can teach! :001_smile: I'm fine if NEM takes us even 2 years to complete.

 

My first grader right now has had some sort of math light turned on the past few months and all of a sudden conceptually understands many, many math concepts like early multiplication and addition and subtraction of larger numbers and can put it down on paper. So I'm letting her race through for now without doing much extra. At some point, it will become a challenge again.

 

So my older kid looks accelerated in both these areas (and he is), but on many levels I feel like he's been held back to enrich the experience, deepen understanding, and just let him mature a bit. We just work on both piano and math for a finite length of time each day and see where that gets us. I do not have one of those GT kids that is clamoring to do math or practice piano all day! :D So count me as one that can see the value of deep conceptual understanding for a child and moving ahead only when you see that piece is there. I'm also not a parent who envisions sending my child to college very early. Maybe some community college classes to fill some holes, but both my kids are happiest with other bright kids in their own age range.

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Having been a math tutor, I can attest that there are certain topics that just seem to "click" with many kids at about the same age.

 

I think many of the fears on accelerating in math come from these sort of experiences, and the expectation that math will be linear, so a child who hits a wall will be stuck waiting. .

Thanks for this post and reminding me of this, as I've been thinking about ds next year.

I too have been surprised by people saying they are going to put the brakes on for math. I think part of the reason for this is the perception that there is one, and only, one path to higher math: pre-algebra, algebra I, geometry, algebra II then pre-calculus and finally calculus. Each of those is supposed to be a one year course and since most of us never explored math more deeply, we cannot imagine what else our kids could be exploring in math..

Good points. I delayed one dd a year for Algebra and did just that--had her go deeper into what she new but at a harder level that challenged her in new ways. It also met her needs (the Russian math I mentioned somewhere.) I need to find some things to do with ds that will go deeper where, but haven't figured that all out yet.

 

This is what I see around here. I'm surrounded by mostly unschoolers who keep telling each other that math isn't important,

 

Wow, that's really something!

I think this is extremely dependent on the individual child. I have encountered younger (16/17 y/o) college students who possessed both the intellectual readiness and maturity to do extremely well.)

 

This is the point people are making :001_smile:. I had wanted my older two to graduate early, but there is no way that my eldest is mature enough for that, nor is she ready emotionally.

 

But back to the maturity issue. I think SWB's point was directed at another side of the homeschool parent mindset, that earlier is somehow better.

:iagree:

 

That is really interesting. My son is a precocious pianist who is on his 3rd teacher. Had we stayed with his 2nd teacher, I could easily have seen something like this happen. There are definitely teachers (or parents or even the kids themselves) who get highly invested in having a "child prodigy" on an instrument. Our current teacher recognizes my son's ability to learn quickly and be expressive in his music, but won't take his music to new levels until his technique at the current level is flawless and relaxed. Not to mention the teacher also teaches theory and values skills like sight reading. However, to keep my son happy he gets about 3 to 4X the repertoire of the average kid his age, and allows him to pick and choose what he'd like to learn. .

 

 

What a great teacher! It sounds like she has a great balance and she is absolutely correct about the technique. By doing this first it will help prevent phyical problems later, among other things.

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I get a little chuckle reading some of the recent threads on this topic, as I think what some of us might call "putting on the brakes" represents far greater math enrichment that is typical of math education in the USA.

 

For myself, I can see how I might causally say that I'm looking to "slow my son down" when that means not just marching through the Singapore Math series at the pace he might if I did not create "diversions." That does not actually mean I want to put "the brakes" on his learning (far from it) but my best guess is he gets more from sideways moves than were we to just blast through Primary Mathematics.

 

So I'm comfortable for him to be a year above grade level and I'm not attempting to "accelerate" beyond that. Children are different. If I had a "savant" (rather than a bright and teachable child) I might make other moves (in addition to being panic stricken :D) but for now all I can do is try to get a feel for what he needs. And to try to keep the challenge at the point where it inspires interest and doesn't lead to frustration. Mixing up programs has helped on on every level.

 

My hope is that building a really soild foundation now will give my son the tools to continue far beyond where old-dad will be able to follow.

 

Bill

Edited by Spy Car
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It isn't just math. The reasons you should not let your child read advanced books are out there too.

 

 

:iagree:

 

 

In both cases, it may be a reflection of either the person's distaste for the subject matter or uncertainty regarding the best approach to teaching it.

 

I'm comfortable with math, so I tend to be able to wing that particular subject with good results, but I really really dislike teaching literary analysis and composition, so this is my angst-ridden area (the boxes and boxes of writing curricula stuffed in the attic "just in case" speak for themselves). :tongue_smilie:

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I am really puzzled about the acceleration debate because it seems to center exclusively on mathematics. No other subject seems to create as much debate and worry.

If a child is a gifted musician, it is generally accepted that this child will be able to progress through musical instruction much faster and will, for instance, at age 10 be able to perform pieces that average students do not master until age 20 (or never). I have not come across anybody who argued that this student should be slowed down because it could create problems if he was allowed to play Beethoven on his violin when other students are just playing Twinkle little star.

 

The difference is that there is no particular cognitive milestone that needs to kick in for a student to progress in music the way there is for a student to be able to comprehend algebra. Students who are rushed into algebra before their brains have matured enough to handle the abstract reasoning often wind up frustrated and that can turn them off math for good. As mom to a daughter, I'm particularly concerned about the high percentage of girls who become math-haters in middle school. The last thing I want to happen is to rush through elementary math only to have her hit a brick wall & decide she s*cks at math and wants nothing to do with it from then on. :(

 

I loved algebra and calculus and want my DD to have a positive experience with those courses rather than a very negative one because she hit them prematurely.

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Students who are rushed into algebra before their brains have matured enough to handle the abstract reasoning often wind up frustrated and that can turn them off math for good.

 

I definitely agree that one should not rush math.

It would be interesting, however, to find out to what extent algebra failure is actually due to lack of brain maturity - or whether it is due to a lack of preparation. If a student has not thoroughly mastered arithmetic with fractions, he will fail at algebra, no matter what his maturity level. So I'd be interested to see whether there are any hard data separating the two effects. (Whatever it is, rushing is bad - for for different reasons)

 

I hear you about math and daughters - but from what I experienced with the middle school math curricula, they are boring enough to turn anybody off math. Spending three to four years, 5.-7th or 8th grade, on arithmetic with fractions,as it is done in this country's public schools, after having spent four years on arithmetic with integers in elementary school is overkill and could make any student hate math.

Another huge factor is societal pressure: it is considered uncool for girls to love math. My DD was bullied in middle school because she cared about academics (and math) -one reason we pulled her out of school. Girls who want to be popular better pretend to hate math... and they will eventually not do well. The whole culture is one of academic mediocrity where more value is put on a girl being pretty and wearing the right clothes...

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I definitely agree that one should not rush math.

It would be interesting, however, to find out to what extent algebra failure is actually due to lack of brain maturity - or whether it is due to a lack of preparation. If a student has not thoroughly mastered arithmetic with fractions, he will fail at algebra, no matter what his maturity level. So I'd be interested to see whether there are any hard data separating the two effects. (Whatever it is, rushing is bad - for for different reasons)

 

I hear you about math and daughters - but from what I experienced with the middle school math curricula, they are boring enough to turn anybody off math. Spending three to four years, 5.-7th or 8th grade, on arithmetic with fractions,as it is done in this country's public schools, after having spent four years on arithmetic with integers in elementary school is overkill and could make any student hate math.

Another huge factor is societal pressure: it is considered uncool for girls to love math. My DD was bullied in middle school because she cared about academics (and math) -one reason we pulled her out of school. Girls who want to be popular better pretend to hate math... and they will eventually not do well. The whole culture is one of academic mediocrity where more value is put on a girl being pretty and wearing the right clothes...

 

Wickelgren (Math Coach) is a big advocate of algebra in middle school and believes the brain maturation argument is a myth. He makes a few points relevant here, some of which are very similar to your points. From p. 23:

 

MYTH #2: The brains of seventh and eighth graders are too immature to learn algebra, and elementary school students have a limited ability to solve story problems because they have trouble understandign the meaning of addition and subtraction.

 

FACT: As discussed earlier, over age three there are no known biological barriers to learning math. Age is not an important factor; knowledge is.

 

From p. 7:

(Research supporting maturational limits done by a famous developmental psychologist, Jean Piaget, has been contradicted by later studies in the field.)

 

Of course, your child may have temporary trouble learning certain math concepts, but the reason for that is unlikely to be a maturation issue. It could be a lack of verbal skills. Indeed, Huttenlocher and Levine conclude that it is the verbal encoding of addition and subtraction that is often lacking in young children and not the nonverbal understanding of these concepts.... An even likelier reaon: Your child hasn't adequately learned some important background ideas in math.....None of the children I have taught had any persisting difficulty comprehending any math concept. When they forgot some concepts more quickly than I expected, this signaled a need for more practice and instruction with these concepts, rather than a maturational limit.

 

From pp. 3-5:

 

What most American educators, and parents, consider a "normal" rate of progress through the math curriculum is actually too slow for the vast majority of children.... In a regular middle school two of my children attended, all of the children took algebra in or before eighth grade and over 80 percent mastered it, putting them one or more years ahead in math.

 

Entire countries of students accomplish this routinely....

.....

Why do I frame the goal with algebra? It is the math prior to algebra that is taught especially slow in the U.S. Thus, the pre-algebra years are the ones in which you can most easily speed your child ahead, or help him or her catch up in math, giving the child to learn as much math as possible.

....

...The more math your child knows by the end of high school, the more math he or she will be able to use all of his or her professional life...

 

In addition, it is during the slow, pre-algebra years that your child is most at risk of becoming bored with math and unmotivated to study it. Worse, if your child earns high grades with little effort, he or she might well conclude that studying hard in math is unnecessary, becoming lazy and failing to develop good work habits...

 

He doesn't really go into detail on why the U.S. tends to teach math more slowly, unless I missed that someplace.

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I didn't hear anyone argue 7th-8th grade being too early to learn algebra. The question was about algebra in the late elementary/early middle school years.

 

Do I think some kids are perfectly capable of learning algebra prior to late middle school? Sure.

 

Do I think most students, even most gifted ones, are? No, I don't.

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I was downgraded in a piano competition in 3rd or 4th grade because one of the judges felt the selection was 'too mature for a child of my age'. It was some gypsy piece? Anyhow...so it does happen in music.

 

I definitely agree that one should not rush math.

It would be interesting, however, to find out to what extent algebra failure is actually due to lack of brain maturity - or whether it is due to a lack of preparation.

 

 

Well, there's algebra and then there's algebra, as has been discussed at length in at least one other thread here. There is at least one algebra program designed for younger learners, Hands on Equations, although we haven't tried it. Algebra was introduced younger than it is now back when I was in school and prior to that; it was common here to see it started in grades 7 & 8, depending on when and where. I really think that the person

to discuss this with is Jann in TX who may know of research you are looking for. She herself is pg, she is a math major & has been a math teacher for years; she does online math courses.

 

No one has answered my question yet about whether or not the schools in Europe that start Algebra so early are teaching it to all students or if it's after they've streamed them. It is common practice in at least some countries in Europe to do this. If this is the case, then we aren't making a reasonable comparison.

 

One never sees child prodigies in certain fields, but there are definitely child prodigies in math!!! In fact, most big math breakthroughs are done by the time the mathematician is in their early 20s.

 

 

I didn't hear anyone argue 7th-8th grade being too early to learn algebra. The question was about algebra in the late elementary/early middle school years.

 

Do I think some kids are perfectly capable of learning algebra prior to late middle school? Sure.

 

Do I think most students, even most gifted ones, are? No, I don't.

:iagree:It's easy to have skewed perspectives if you are from families where giftedness is the norm. When my eldest was tiny, I had no idea at first just how early she was learning certain things compared to most dc, and I wasn't doing anything special, drilling her, etc. I followed her interests for the most part. For a while I had a skewed idea of what dc should be doing at certain ages.

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No one has answered my question yet about whether or not the schools in Europe that start Algebra so early are teaching it to all students or if it's after they've streamed them. It is common practice in at least some countries in Europe to do this. If this is the case, then we aren't making a reasonable comparison.

 

One difficulty in answering this question is that math is not as compartmentalized in Europe as it is in the US. I am only familiar with Germany. There, students just do "math". Even in high school. There is no "algebra" or "geometry" or "calculus" class - the topics are taught intermixed, and algebraic concepts introduced among other things. So, it is difficult to pinpoint when "algebra" is taught because it is not isolated as a special milestone. (One advantage of this method is, of course, that review is built in because algebra concepts are reviewed, expanded and built on continuously after they had been introduced. So it is impossible for a student to "forget" algebra during the "geometry year".)

 

I have just looked at the different standards for the different kinds of schools in my home state. Students are streamed into two different kinds of schools, starting from 5th grade. About 50% attend a school whose highschool degree qualifies them for university entrance .

I have specifically looked at the math schedule for the OTHER schools, those attended by students who do not shoot for a college education. There, congruency theorems for triangles are taught in 6th grade (something that would belong in a geometry course), linear equations and functions are taught in 8th grade (which would be algebra 1 - something my local US ps teaches in 8th grade only to gifted students).

The 1st tier schools (gymnasium) have a similar schedule; a lot of geometry is taught in 6th grade already; the main difference is that they progress faster and further, with mandatory differential calculus in 11th and integral calculus in 12th grade (these are not the students who choose extra hard math courses, but this is the math requirement to get a highschool degree that allows university entrance)

 

One big problem I have with American schools is that they do not have a sufficient differentiation between the students who need to go slowly and the students who could progress much faster. In our school district, absolutely no differentiation exists till 7th grade when the gifted students are "allowed" to study pre-algebra (which is still not challenging for gifted students; it's what the German streamed school teaches to the 7th graders who do not want to go to college.)

I do not think every child is able to accelerate in math - but those who are should be given the chance.

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One difficulty in answering this question is that math is not as compartmentalized in Europe as it is in the US. I am only familiar with Germany. There, students just do "math".

 

I have no idea what math education in the UK looks like today, but when dh went to school there some years back math was as regentrude describes. Dh often expresses shock when he looks at the math standards or pieces of the algebra textbook, because he was exposed to those things so much earlier.

 

In the book The Teaching Gap, there is a sample lesson from a general, non-tracked 5th grade math class in Japan, and the kids are designing their own problems using what they have learned about angles; the pictures show the ways they designed multiple bends in lines crossing two parallel lines, and the problem was to figure out how many angle measurements they'd have to know to solve every angle measurement on the page. In the US, this is 10th grade geometry.

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One difficulty in answering this question is that math is not as compartmentalized in Europe as it is in the US. I am only familiar with Germany. There, students just do "math". Even in high school. There is no "algebra" or "geometry" or "calculus" class - the topics are taught intermixed, and algebraic concepts introduced among other things.
This is the way we did math when I was in high school in Ontario Canada. It wasn't broken up until Gr. 13 (now OAC) maths, which are essentially college prep courses.
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One difficulty in answering this question is that math is not as compartmentalized in Europe as it is in the US. I am only familiar with Germany. There, students just do "math". One big problem I have with American schools is that they do not have a sufficient differentiation between the students who need to go slowly and the students who could progress much faster. In our school district, absolutely no differentiation exists till 7th grade when the gifted students are "allowed" to study pre-algebra (which is still not challenging for gifted students; it's what the German streamed school teaches to the 7th graders who do not want to go to college.)

I do not think every child is able to accelerate in math - but those who are should be given the chance.

 

:iagree: and this does answer my question--there is streaming and not all dc take Algebra in early middle school. Can anyone who wants to go to university opt to stream that way, or is it dependent on academic ability?

 

There isn't enough streaming in math here, IMO. There is a bit here where I live, but all it means is that honours math students can be a grade ahead. Not all high school Algebra courses use the same text, but the only difference between the honours & Academic A classes are the theory that the teacher adds in class (same textbook) and that the do more of the problems.

 

This is the way we did math when I was in high school in Ontario Canada. It wasn't broken up until Gr. 13 (now OAC) maths, which are essentially college prep courses.

 

In BC, way back when I was in high school, there was a choice at some point in high school where you could choose business math or regular math. Geometry was a separate class in grade 10, but other math was all together. However, there was no option of getting as far as Calculus in high school because it simply wasn't offered until later. I think it is still the same, but don't live there and haven't checked lately.

 

My elementary school (K-7) tried some streaming even though there were only 2 classes in our grade. However, those of us in the more advanced class weren't allowed to progress to the next level in grade 7 because the high school didn't want us ahead. In fact, one of the greatest points of frustration for me in high school was not being able to progress in math at my own speed.

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Can anyone who wants to go to university opt to stream that way, or is it dependent on academic ability?

 

Depends on the state. In some state, it is dependent on student ability and decided by the school. In other states, it is parental choice.

To make things clear: not attending gymnasium does not mean that the student never gets a chance to go to university. A student can, after completing the 2nd tier school with a 10 year degree, do a three year program that gives him the necessary degree (which my niece is currently doing), or take the exam independently.

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My elementary school (K-7) tried some streaming even though there were only 2 classes in our grade.

 

Our middle school here has TWELVE 5th grade classes and SIX 5th grade math teachers. The math teachers I spoke to would have preferred to have streaming (or whatever you want to call it: splitting classes according to student level)- and it would not have cost the school district a single penny because they HAVE classroom space and teachers already, and it would make things easier for teachers and students, both high and low performing ones alike. Alas, political correctness...

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I think the problem with higher level math for younger students is the lack of textbooks geared for younger students, not brain maturity. I don't think that younger students are incapable of understanding higher level math simply because they are young. I think that they might need to be taught using different methods from those used with older students.

 

My daughter is in 2nd grade and she is weak in math. She still hasn't finished the 1st grade math book. However, she has surprised me by understanding more advanced math concepts, like negative numbers, "x" as an unknown in written equations, solving for an unknown, etc, when given manipulatives and age-appropriate explainations.

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I have been enjoying this discussion and didn't want to see it die, so I'm bumping :)

 

I have nothing of interest to add, however, except I agree with Kuovonne's statement that there simply aren't enough "high level" math books geared towards younger students. We are playing with a wonderful book called Let's Investigate Number Patterns (part of a series of books) and exploring complex concepts such as triangular numbers, the Fibonacci sequence, and Pascal's Triangle and my son is getting it because of the approachable way the text is written. It would be wonderful if such a text were available for algebra, but as it stands, we'll be investigating their geometry texts next.

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One difficulty in answering this question is that math is not as compartmentalized in Europe as it is in the US. I am only familiar with Germany. There, students just do "math". Even in high school. There is no "algebra" or "geometry" or "calculus" class - the topics are taught intermixed, and algebraic concepts introduced among other things. So, it is difficult to pinpoint when "algebra" is taught because it is not isolated as a special milestone. (One advantage of this method is, of course, that review is built in because algebra concepts are reviewed, expanded and built on continuously after they had been introduced. So it is impossible for a student to "forget" algebra during the "geometry year".)

 

:iagree: This is how maths is taught in the UK. Calculus is taught after 16 & only for those who choose to carry on with maths. Algebra & geometry are taught over several years, alongside other areas.

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It would be wonderful if such a text were available for algebra, but as it stands, we'll be investigating their geometry texts next.

Somewhat related to your other thread, but Simon Singh's code book is also interesting. I always thought codes were a fun thing for kids to study. But then, I was a huge Sherlock Holmes buff at around age 12.

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I think the problem with higher level math for younger students is the lack of textbooks geared for younger students, not brain maturity. .

 

I am hoping to find a "mathy" chapter book series along the lines of The Magic School Bus. About that reading level with chapters and some pictures but about math stuff. We have the Penrose book and even though my big girl likes me to read it to her, she's just too young for it.

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Depends on the state. In some state, it is dependent on student ability and decided by the school. In other states, it is parental choice.

To make things clear: not attending gymnasium does not mean that the student never gets a chance to go to university. A student can, after completing the 2nd tier school with a 10 year degree, do a three year program that gives him the necessary degree (which my niece is currently doing), or take the exam independently.

 

Thanks for the clarification on this! The university part makes sense, too. Is Germany one of the countries where you can get a baccalaureate after high school if you stream into the gymnasium?

 

Our middle school here has TWELVE 5th grade classes and SIX 5th grade math teachers. The math teachers I spoke to would have preferred to have streaming (or whatever you want to call it: splitting classes according to student level)- and it would not have cost the school district a single penny because they HAVE classroom space and teachers already, and it would make things easier for teachers and students, both high and low performing ones alike. Alas, political correctness...

 

Yes, PC causes a lot of problems in education. There's a middle ground between PC and calling a group of dc stupid, etc.

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I think the problem with higher level math for younger students is the lack of textbooks geared for younger students, not brain maturity. I don't think that younger students are incapable of understanding higher level math simply because they are young. I think that they might need to be taught using different methods from those used with older students.

 

My daughter is in 2nd grade and she is weak in math. She still hasn't finished the 1st grade math book. However, she has surprised me by understanding more advanced math concepts, like negative numbers, "x" as an unknown in written equations, solving for an unknown, etc, when given manipulatives and age-appropriate explainations.

 

 

This is a good point. There are fun books, such as Murderous Maths, but they only go so far (I can't remember if Calculus is one of them or not). Life of Fred is quite fun and the math is not dumbed down despite the story. In fact, there may be young dc who enjoy it simply because Fred is 6 (but younger in the Calculus book.) Then there is the Hands on Equations, which we haven't bought yet, but I would like to get for ds. I wish I'd heard of it and had it when my eldest was 9 because she hated arithmetic but likes Algebra, loves Geometry and can hardly wait for Calculus since the little taste she's had looked fun for her, but now she's stuck in ps (her choice). In fact, I may just get the LOF Calculus book because I know she'll read it for fun.

 

LOF can also be used as a read aloud if your dc is an auditory learner, and I had some fun with a friend's dc because I divided up different characters to different dc.

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Our middle school here has TWELVE 5th grade classes and SIX 5th grade math teachers. The math teachers I spoke to would have preferred to have streaming (or whatever you want to call it: splitting classes according to student level)- and it would not have cost the school district a single penny because they HAVE classroom space and teachers already, and it would make things easier for teachers and students, both high and low performing ones alike. Alas, political correctness...

Except that haven't studies shown that even average students perform miraculously well when the teachers are told they are gifted?

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Except that haven't studies shown that even average students perform miraculously well when the teachers are told they are gifted?

 

Do you HAVE studies which show this, for subjects where performance can be measured objectively (such as math), completely independent from a teacher's personal preferences (such as writing)?

 

I am very sceptical because I am an instructor myself. I encounter new students every semester without any previous knowledge of their abilities, and I have absolute grading criteria which are applied to every student's performance and leave no room for personal opinion. So I do not see how it could possibly make a difference that *I* know which student is gifted and which is not - unless I were using flawed evaluation criteria.

At the most extreme on the objectivity scale would be multiple choice exams (which I dislike for other reasons), where it is not even possible to have teacher bias. I prefer to use full problems for most exams, and if my rubric means taking off two points if the student switches sine and cosine, that is applied to everybody, period.

 

I can see how it could make a difference in subjects where there is always some subjective component to evaluation (writing comes to my mind; even the most objective teacher will like one student's writing style better than another's). But this was about math.

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I have always wondered about this study that is quoted so much, too. First, I have never seen the study. Second, my guess is that it was done in a general ed elementary school classroom.

 

 

Do you HAVE studies which show this, for subjects where performance can be measured objectively (such as math), completely independent from a teacher's personal preferences (such as writing)?

 

I am very sceptical because I am an instructor myself. I encounter new students every semester without any previous knowledge of their abilities, and I have absolute grading criteria which are applied to every student's performance and leave no room for personal opinion. So I do not see how it could possibly make a difference that *I* know which student is gifted and which is not - unless I were using flawed evaluation criteria.

At the most extreme on the objectivity scale would be multiple choice exams (which I dislike for other reasons), where it is not even possible to have teacher bias. I prefer to use full problems for most exams, and if my rubric means taking off two points if the student switches sine and cosine, that is applied to everybody, period.

 

I can see how it could make a difference in subjects where there is always some subjective component to evaluation (writing comes to my mind; even the most objective teacher will like one student's writing style better than another's). But this was about math.

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I definitely agree that one should not rush math.

It would be interesting, however, to find out to what extent algebra failure is actually due to lack of brain maturity - or whether it is due to a lack of preparation. If a student has not thoroughly mastered arithmetic with fractions, he will fail at algebra, no matter what his maturity level. So I'd be interested to see whether there are any hard data separating the two effects. (Whatever it is, rushing is bad - for for different reasons)

 

I hear you about math and daughters - but from what I experienced with the middle school math curricula, they are boring enough to turn anybody off math. Spending three to four years, 5.-7th or 8th grade, on arithmetic with fractions,as it is done in this country's public schools, after having spent four years on arithmetic with integers in elementary school is overkill and could make any student hate math.

Another huge factor is societal pressure: it is considered uncool for girls to love math. My DD was bullied in middle school because she cared about academics (and math) -one reason we pulled her out of school. Girls who want to be popular better pretend to hate math... and they will eventually not do well. The whole culture is one of academic mediocrity where more value is put on a girl being pretty and wearing the right clothes...

 

I agree particularly with the bolded parts. Individual experience is highly variable, but my daughter was growing to hate math until I allowed her to progress at her rate. I don't know what the norm is, as though that matters in the homeschooling environment anyway, but she had no trouble whatsoever with Algebra in fifth grade. I tend to think the standards here are way too low, and the notion about lack of brain maturity in matters of Algebra and Logic has not been true for us at all.

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