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On December 02 2014 04:35 Symplectos wrote:
so why not teach them the algebraic rules to work with multiplication and division, then they will see that such expressions are easy to work with and they don't need to use "cheap" tricks.
The did this in the 60's and 70's in Germany actually and started mathematical education in university like fashion, starting out with set theory and such in an attempt to "build up" mathematics. Like a toned down version of how it's done in university basically. Turned out to be pretty bad as the kids actually didn't really understand what and more importantly why they're learning the stuff. It's just hugely impractical to start out that way. Obviously most parents didn't get the purpose of it, too.
From my experience children like to learn in a more holistic way. Stuff they learn should be easily applicable and practical rather than formal. Music is another example, too. If you try to teach young kids formal music theory you'll find yourself in an empty classroom rather quickly.
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On December 02 2014 00:53 Liquid`Drone wrote:Show nested quote +On December 02 2014 00:42 Danglars wrote:Firstly, not everything a student learns in school is measurable, or even supposed to be measurable. This varies a bit depending on subject, but school is supposed to be an arena to help children become wholesome people, not just capable workers. I think this is a fundamental battle to be had, where I feel the current political climate is too obsessed with school as a way of creating more engineers rather than as an arena for personal growth in every arena. In Norway, this educational change started after the first PISA-tests a little more than a decade ago, where it was showcased that Norwegian students were much worse at math, reading and sciences than students from Finland and South Korea, and not any better than the OECD average (so among comparable countries. ) USA performed disappointingly as well, and I can see how you would be drawing some of the same conclusions. You don't have to strawman your opposition by suggesting that all of them think only of good workers and think nothing of wholesome people. It's just as much hyperbole by coloring the debate that way. Can your 8th graders read and write at an 8th grade level? Not so they can be merry little capable workers (eerily reminiscent of old Communist propaganda), but so they can continue to have academic success in English in high school and know that they're not slipping behind. This applies to purely informational standardized testing administrated periodically. Are the minimums being met? Are you graduating people with the basics of what used to be known in the US as the 3 R's? These are useful questions particularly in my interest area of the circa 1-4% of teachers that get the label "grossly ineffective," but are essentially unable to be fired. Fair enough with the strawman, it's not my intention to portray my opposition as completely one-dimensional and I don't actually think they are. Still, we do have to prioritize - and it is a fact that favoring STEM over liberal arts/bildung goes hand in hand with wanting more accountability (which goes hand in hand with more measurability, which goes hand in hand with favoring STEM, not necessarily because it is more measurable, but there's some relation there). I actually highlight the importance of basic skills at the end of my post though, because yes, basic skills are the foundation of more advanced skills in every subject. And if 1-4% of teachers are the problem, then it's somewhere between insignificant and not all that significant of a problem. I agree that it should be possible to fire completely incompetent teachers, but wanting to introduce policies that I think would hurt the other 96-99% just to get it done makes no sense from my perspective. Edit: Funny tidbit, I actually oppose mandatory camera for police for the same reason. Seems like a kneejerk reaction to a few bad apples, one that steals autonomy and creates suspicion in a way that to me would be bound to make any workplace environment, and thus workplace performance, worse. I don't want to get too far afield here, because we're mostly in agreement. The policies that went so far to shield the obvious bad apples were opposed by teachers that didn't appreciate them forever in their ranks. That's more a state thing, and not representative of the U.S. as a whole.
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On December 02 2014 04:00 GreenHorizons wrote:Show nested quote +On December 02 2014 03:53 Introvert wrote:
This whole pursuit is useless. I know that teachers write the questions. Lordy. You used a math problem as an example then got unhappy when I displayed a little concern over the exact same problem. I don't have to satisfy the strange demand for lots of specifics when you fail to provide them yourself. I have seen no reason to think anything new is actually superior. And I don't need a list of examples because such a demand is unreasonable considering the topic and forum. You introduced a new criteria, as is normal. Is it useless because you don't know what standards, if any, are 'crappy' and you just said it without thinking? It's not strange to ask for at least 1 specific problem you have with the 'crappy standards' or 1 example of what the federal governments involvement influenced or changed to your dismay. Or to ask XDaunt who's main concern is defeating common core to prevent school from getting worse, what specifically about it (like an example or 2) is troublesome. You called the standards 'crappy' and have no identifiable reason as to why you believe they are 'crappy', your position here is quite telling. @Edit: Show nested quote + Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. SourceYour turn 0.0........... Still waiting...
I'm not sure where this came from. I don't really have a position on common core.
My oldest child is 3 1/2, so we're starting to look at schools. We visited a charter school last month that teaches a "core knowledge" curriculum as opposed to common core. I'm not entirely sure what the difference is, other than that core knowledge is more rigorous (which is certainly appropriate for my children). I was fairly impressed by what I saw. Alegebraic concepts are introduced far earlier than I remember learning them.
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the charter school is teaching algebra to 3 1/2 year olds?
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On December 02 2014 06:17 Sub40APM wrote:
the charter school is teaching algebra to 3 1/2 year olds?
Hah, no. To sixth (and maybe fifth) graders. I don't remember seeing any algebra until eighth grade.
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On December 02 2014 06:14 xDaunt wrote:Show nested quote +On December 02 2014 04:00 GreenHorizons wrote:On December 02 2014 03:53 Introvert wrote:
This whole pursuit is useless. I know that teachers write the questions. Lordy. You used a math problem as an example then got unhappy when I displayed a little concern over the exact same problem. I don't have to satisfy the strange demand for lots of specifics when you fail to provide them yourself. I have seen no reason to think anything new is actually superior. And I don't need a list of examples because such a demand is unreasonable considering the topic and forum. You introduced a new criteria, as is normal. Is it useless because you don't know what standards, if any, are 'crappy' and you just said it without thinking? It's not strange to ask for at least 1 specific problem you have with the 'crappy standards' or 1 example of what the federal governments involvement influenced or changed to your dismay. Or to ask XDaunt who's main concern is defeating common core to prevent school from getting worse, what specifically about it (like an example or 2) is troublesome. You called the standards 'crappy' and have no identifiable reason as to why you believe they are 'crappy', your position here is quite telling. @Edit: Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. SourceYour turn 0.0........... Still waiting... I'm not sure where this came from. I don't really have a position on common core. My oldest child is 3 1/2, so we're starting to look at schools. We visited a charter school last month that teaches a "core knowledge" curriculum as opposed to common core. I'm not entirely sure what the difference is, other than that core knowledge is more rigorous (which is certainly appropriate for my children). I was fairly impressed by what I saw. Alegebraic concepts are introduced far earlier than I remember learning them.
You're right, I'm sorry, it was Danglers. I'll make sure to correct it where I find the mistake.
I don't think most people would be opposed to hearing what the differences in rigor is between the two and if it's a gap that can be bridged. The concept that Common Core is a lower standard is prevalent, but it's virtually impossible to tell what it's specifically being based off. As in, what do "more rigorous" curriculum like "Common Knowledge" have that "Common Core" doesn't? I can believe it is, I am just not sure how others are so sure?
For clarity do you mean rigorous like "extremely thorough, exhaustive, or accurate" or more as in "a rule strictly applied or adhered to"?
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On December 02 2014 05:22 Nyxisto wrote:Show nested quote +On December 02 2014 04:35 Symplectos wrote:
so why not teach them the algebraic rules to work with multiplication and division, then they will see that such expressions are easy to work with and they don't need to use "cheap" tricks.
The did this in the 60's and 70's in Germany actually and started mathematical education in university like fashion, starting out with set theory and such in an attempt to "build up" mathematics. Like a toned down version of how it's done in university basically. Turned out to be pretty bad as the kids actually didn't really understand what and more importantly why they're learning the stuff. It's just hugely impractical to start out that way. Obviously most parents didn't get the purpose of it, too. From my experience children like to learn in a more holistic way. Stuff they learn should be easily applicable and practical rather than formal. Music is another example, too. If you try to teach young kids formal music theory you'll find yourself in an empty classroom rather quickly.
I did learn Mathematics like that, set theory, an introduction to groups, rings and fields at the age of 12. It was the best that has ever happened to me, it helped me immensely to see the true beauty of Mathematics. I don't see why it is impractical and I definitely do not see why everything must be based on applications, especially seeing how bad those "applications" are in most modern high-school text books. We did never do any "applied examples", we learned how to write rigorous proofs and simply how to do Mathematics. The examples come in other classes anyway (Physics, Chemistry ...)
As for the parents not getting the purpose of abstract Mathematics, well, that isn't too surprising, since most people don't get the purpose of Mathematics anyway, but that doesn't mean that we can't teach it to our children. Mathematics is not ancillary science.
We could ask the "why do we have to learn this" question for every single subject in school. The problem with Mathematics is though, that you need it, even though you don't realize that as a kid (the same goes for many other classes). Giving our children a bad mathematical education at a young age, hinders them going after many different subjects later on (Mathematics, Physics, "modern" Biology...).
When designing a "common core", you can't listen to politicians or parents, because parents will not be able to make rational decisions when it comes to their children. If I am not mistaken, Germany tried to find a "common core" as well, or at least something similar, and the many changes in the German school system has lead to first semester students that don't even know the very basics of Mathematics. The last three years, as a test, we had them solve the same written exam as ten years ago, and 98% of the students failed, while ten years ago, only 60% failed.
Visualization and applications might be seen as important to the "modern society", but it can't be done after we teach our children to work with numbers and to not be afraid of the underlying basics of Mathematics. If not, in my opinion, the result will be a disaster, as is currently seen in German Universities (and each time I tutor high school students). Thus the most important thing for a "common core", is to set a high level - no matter how much politicians and parents will cry. I had a look at what is proposed for the "common core" at the moment, in my opinion that is simply not enough, it is difficult to compare, but I would say that we (in Luxembourg) had surpassed the proposed level by the age of 15 or 16 - I guess the same goes for most other European countries as well, including Russia.
I do not want to derail the topic any further, thus in conclusion I strongly believe that a "common core" is a good thing, because it makes sure everyone gets a similar education, but one must make sure that the level is high enough and that one is not happy with some sham solution. (I so often hear proud parents - and politicians - say that so many more people get a good high school diploma now, but the reality is that they are not fit to enter an University.)
@GreenHorizons: I "know" TeamLiquid since the unfortunate WCG Qualifcation Tournament in Almere, a long long time ago (Greetings to Nazgul from the guy with the dad with grey hair.) - I prefer to just read, but this particular topic always gets me angry and frustrated, thus I had to write something. I was born in Luxembourg, got my high school education in Luxembourg, I then went to a German University and I currently work as a Mathematician at an University in Germany.
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On December 02 2014 07:06 Symplectos wrote:Show nested quote +On December 02 2014 05:22 Nyxisto wrote:On December 02 2014 04:35 Symplectos wrote:
so why not teach them the algebraic rules to work with multiplication and division, then they will see that such expressions are easy to work with and they don't need to use "cheap" tricks.
The did this in the 60's and 70's in Germany actually and started mathematical education in university like fashion, starting out with set theory and such in an attempt to "build up" mathematics. Like a toned down version of how it's done in university basically. Turned out to be pretty bad as the kids actually didn't really understand what and more importantly why they're learning the stuff. It's just hugely impractical to start out that way. Obviously most parents didn't get the purpose of it, too. From my experience children like to learn in a more holistic way. Stuff they learn should be easily applicable and practical rather than formal. Music is another example, too. If you try to teach young kids formal music theory you'll find yourself in an empty classroom rather quickly. I did learn Mathematics like that, set theory, an introduction to groups, rings and fields at the age of 12. It was the best that has ever happened to me, it helped me immensely to see the true beauty of Mathematics. I don't see why it is impractical and I definitely do not see why everything must be based on applications, especially seeing how bad those "applications" are in most modern high-school text books.
Out of your classmates, how many saw what you saw and how many were put off mathematics forever. I bet the ratio is quite unfavorable for mathematics, hence the impracticality of it. And this is coming from someone who agrees with you that mathematics should be as vital as basic literacy, and that the idea that someone proudly proclaims "I dont do math" should be viewed as much contempt as someone proclaiming "I dont read!"
Speaking for myself, I was educated in mathematics in the Soviet system and then the North American system and while the Soviet system prepared me better -- in American high school we were doing the math I did in grade 5 in the USSR, it instilled nothing for me about math. (and as an aside, I dont actually think the Russian system as it is set up today is as good as the Soviet system. Judging by my relatives kids who are going through it now, they are actually been 'Americanized' in terms of the rigor that math is pursued, and these are kids who go to kind of expensive private schools in Moscow. Which means whats happening in the provinces is even worse)
The quicker I quit it the better I felt -- and now I regret it and am correcting my earlier mistake by re-learning it from the ground up. But the reality is I am fortunate enough to have the time and the interest to do it. Quite frankly to me the applications of it -- being able to understand how to take the area under a curve for practical purpose of -- is exciting but the beauty of it is elusive (except for super clever proofs. but in that case its the cleverness, the fact that 'aha, that fellow saw it so elegantly' and now the beauty of 'aha, the underlying law of the universe is cute'.
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On December 02 2014 06:39 GreenHorizons wrote:Show nested quote +On December 02 2014 06:14 xDaunt wrote:On December 02 2014 04:00 GreenHorizons wrote:On December 02 2014 03:53 Introvert wrote:
This whole pursuit is useless. I know that teachers write the questions. Lordy. You used a math problem as an example then got unhappy when I displayed a little concern over the exact same problem. I don't have to satisfy the strange demand for lots of specifics when you fail to provide them yourself. I have seen no reason to think anything new is actually superior. And I don't need a list of examples because such a demand is unreasonable considering the topic and forum. You introduced a new criteria, as is normal. Is it useless because you don't know what standards, if any, are 'crappy' and you just said it without thinking? It's not strange to ask for at least 1 specific problem you have with the 'crappy standards' or 1 example of what the federal governments involvement influenced or changed to your dismay. Or to ask XDaunt who's main concern is defeating common core to prevent school from getting worse, what specifically about it (like an example or 2) is troublesome. You called the standards 'crappy' and have no identifiable reason as to why you believe they are 'crappy', your position here is quite telling. @Edit: Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. SourceYour turn 0.0........... Still waiting... I'm not sure where this came from. I don't really have a position on common core. My oldest child is 3 1/2, so we're starting to look at schools. We visited a charter school last month that teaches a "core knowledge" curriculum as opposed to common core. I'm not entirely sure what the difference is, other than that core knowledge is more rigorous (which is certainly appropriate for my children). I was fairly impressed by what I saw. Alegebraic concepts are introduced far earlier than I remember learning them. You're right, I'm sorry, it was Danglers. I'll make sure to correct it where I find the mistake. I don't think most people would be opposed to hearing what the differences in rigor is between the two and if it's a gap that can be bridged. The concept that Common Core is a lower standard is prevalent, but it's virtually impossible to tell what it's specifically being based off. As in, what do "more rigorous" curriculum like "Common Knowledge" have that "Common Core" doesn't? I can believe it is, I am just not sure how others are so sure? For clarity do you mean rigorous like "extremely thorough, exhaustive, or accurate" or more as in "a rule strictly applied or adhered to"?
I can't really speak to the differences between common core and core knowledge. The presentation that I received suggested that core knowledge pushes more advanced concepts sooner and requires that students do more work. Think of the difference between AP/IB and regular classes in high school. The former is clearly more rigorous than the latter. All I know is that common core is designed as more of a baseline-type of curriculum, and my children are almost certainly going to need something significantly harder than that given their pedigree.
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Cayman Islands24199 Posts
disagreement about common core math rests on some divergent perceptions of reality. on one hand if you think traditional math teaching can turn out students who only learn rote application of rules (like engineers or economist "math" huehue etc), there's a deficiency to be addressed by conceptual teaching. on the other hand, and this would require looking at how the theory is put into practice, mathematical rules are a language of their own, and application or memorization of those rules is not automatically rote/nonconceptual. rather, math class should get students acclimated to how the language of math is used in higher level studies.
both sides should agree that, bridging the gap between applying a rule and understanding the mathematical language of the rule is important in learning. but do you do this by forcing kids to go through some explicit visual representation of intuitions, or only tailor demonstrations to the extent that the intuitions are shown, and then internalized? the former method is misguided imo.
at the very least, don't make tests or homework over those representations. test the math not the particular pedagogical tool.
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On December 02 2014 07:50 oneofthem wrote:
at the very least, don't make tests or homework over those representations. test the math not the particular pedagogical tool.
You're preaching to the choir here.
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On December 02 2014 07:50 oneofthem wrote:
disagreement about common core math rests on some divergent perceptions of reality. on one hand if you think traditional math teaching can turn out students who only learn rote application of rules (like engineers or economist "math" huehue etc), there's a deficiency to be addressed by conceptual teaching. on the other hand, and this would require looking at how the theory is put into practice, mathematical rules are a language of their own, and application or memorization of those rules is not automatically rote/nonconceptual. rather, math class should get students acclimated to how the language of math is used in higher level studies.
both sides should agree that, bridging the gap between applying a rule and understanding the mathematical language of the rule is important in learning. but do you do this by forcing kids to go through some explicit visual representation of intuitions, or only tailor demonstrations to the extent that the intuitions are shown, and then internalized? the former method is misguided imo.
at the very least, don't make tests or homework over those representations. test the math not the particular pedagogical tool.
Yes, but this is all old hat. Everyone knows math education is broken, both for developing good mathematicians or mathematical professionals and for increasing the level of the general population. Common core has some interesting ideas and as a person who does some Khan Academy math every day, it arguably sets the stage better for higher level math by gently introducing and emphasizing concepts rather than good old fashioned rote drilling and grunt work in the trenches of basic math doing long division.
The problem is the old way has some ancillary benefits, such as discipline and constantly reinforcing the basics. Introducing advanced concepts too soon is confusing and abusive for students who aren't strong in the basic skills and quickly end up hopelessly lost in the wilderness, which in the case of common core seems to apply to parents and teachers as much as kids (which is alarming in itself).
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On December 02 2014 07:46 xDaunt wrote:Show nested quote +On December 02 2014 06:39 GreenHorizons wrote:On December 02 2014 06:14 xDaunt wrote:On December 02 2014 04:00 GreenHorizons wrote:On December 02 2014 03:53 Introvert wrote:
This whole pursuit is useless. I know that teachers write the questions. Lordy. You used a math problem as an example then got unhappy when I displayed a little concern over the exact same problem. I don't have to satisfy the strange demand for lots of specifics when you fail to provide them yourself. I have seen no reason to think anything new is actually superior. And I don't need a list of examples because such a demand is unreasonable considering the topic and forum. You introduced a new criteria, as is normal. Is it useless because you don't know what standards, if any, are 'crappy' and you just said it without thinking? It's not strange to ask for at least 1 specific problem you have with the 'crappy standards' or 1 example of what the federal governments involvement influenced or changed to your dismay. Or to ask XDaunt who's main concern is defeating common core to prevent school from getting worse, what specifically about it (like an example or 2) is troublesome. You called the standards 'crappy' and have no identifiable reason as to why you believe they are 'crappy', your position here is quite telling. @Edit: Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. SourceYour turn 0.0........... Still waiting... I'm not sure where this came from. I don't really have a position on common core. My oldest child is 3 1/2, so we're starting to look at schools. We visited a charter school last month that teaches a "core knowledge" curriculum as opposed to common core. I'm not entirely sure what the difference is, other than that core knowledge is more rigorous (which is certainly appropriate for my children). I was fairly impressed by what I saw. Alegebraic concepts are introduced far earlier than I remember learning them. You're right, I'm sorry, it was Danglers. I'll make sure to correct it where I find the mistake. I don't think most people would be opposed to hearing what the differences in rigor is between the two and if it's a gap that can be bridged. The concept that Common Core is a lower standard is prevalent, but it's virtually impossible to tell what it's specifically being based off. As in, what do "more rigorous" curriculum like "Common Knowledge" have that "Common Core" doesn't? I can believe it is, I am just not sure how others are so sure? For clarity do you mean rigorous like "extremely thorough, exhaustive, or accurate" or more as in "a rule strictly applied or adhered to"? and my children are almost certainly going to need something significantly harder than that given their pedigree.
hehe
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On December 02 2014 09:05 Sub40APM wrote:Show nested quote +On December 02 2014 07:46 xDaunt wrote:On December 02 2014 06:39 GreenHorizons wrote:On December 02 2014 06:14 xDaunt wrote:On December 02 2014 04:00 GreenHorizons wrote:On December 02 2014 03:53 Introvert wrote:
This whole pursuit is useless. I know that teachers write the questions. Lordy. You used a math problem as an example then got unhappy when I displayed a little concern over the exact same problem. I don't have to satisfy the strange demand for lots of specifics when you fail to provide them yourself. I have seen no reason to think anything new is actually superior. And I don't need a list of examples because such a demand is unreasonable considering the topic and forum. You introduced a new criteria, as is normal. Is it useless because you don't know what standards, if any, are 'crappy' and you just said it without thinking? It's not strange to ask for at least 1 specific problem you have with the 'crappy standards' or 1 example of what the federal governments involvement influenced or changed to your dismay. Or to ask XDaunt who's main concern is defeating common core to prevent school from getting worse, what specifically about it (like an example or 2) is troublesome. You called the standards 'crappy' and have no identifiable reason as to why you believe they are 'crappy', your position here is quite telling. @Edit: Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. SourceYour turn 0.0........... Still waiting... I'm not sure where this came from. I don't really have a position on common core. My oldest child is 3 1/2, so we're starting to look at schools. We visited a charter school last month that teaches a "core knowledge" curriculum as opposed to common core. I'm not entirely sure what the difference is, other than that core knowledge is more rigorous (which is certainly appropriate for my children). I was fairly impressed by what I saw. Alegebraic concepts are introduced far earlier than I remember learning them. You're right, I'm sorry, it was Danglers. I'll make sure to correct it where I find the mistake. I don't think most people would be opposed to hearing what the differences in rigor is between the two and if it's a gap that can be bridged. The concept that Common Core is a lower standard is prevalent, but it's virtually impossible to tell what it's specifically being based off. As in, what do "more rigorous" curriculum like "Common Knowledge" have that "Common Core" doesn't? I can believe it is, I am just not sure how others are so sure? For clarity do you mean rigorous like "extremely thorough, exhaustive, or accurate" or more as in "a rule strictly applied or adhered to"? and my children are almost certainly going to need something significantly harder than that given their pedigree. hehe
Hey, mom has an applied math Ph.D., so I hope they got their brains from her.
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Some of the example questions for common core are just inane.
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On December 02 2014 07:50 oneofthem wrote:
disagreement about common core math rests on some divergent perceptions of reality. on one hand if you think traditional math teaching can turn out students who only learn rote application of rules (like engineers or economist "math" huehue etc), there's a deficiency to be addressed by conceptual teaching. on the other hand, and this would require looking at how the theory is put into practice, mathematical rules are a language of their own, and application or memorization of those rules is not automatically rote/nonconceptual. rather, math class should get students acclimated to how the language of math is used in higher level studies.
both sides should agree that, bridging the gap between applying a rule and understanding the mathematical language of the rule is important in learning. but do you do this by forcing kids to go through some explicit visual representation of intuitions, or only tailor demonstrations to the extent that the intuitions are shown, and then internalized? the former method is misguided imo.
at the very least, don't make tests or homework over those representations. test the math not the particular pedagogical tool. Reality: Parent's support of common core dropped 18% in one year (Rasmussen)
New York was one of the early adopters of the program. It's African American students in third grade that scored "below standard" in English has grown from 15.5% to 50%. In seventh grade, the same underachiever grouping grew from 16.5% to 70%.
(But I'm sure this is just consequences of a change, and not anything about the program itself ... of course)
If we were to evaluate its effects thus far, it would not receive a passing grade. We can argue pedagogy all day long. This particular conception of it appears to be idiotic, no need to bend reality to suit needs. The math portion is frequently put into concrete visual representations, yours and my anathema. Forced compliance from state-down forces the selection of these books and these styles, and parent's can't help with their kid's frustrations (most famously, Louis CK's) and it breeds and festers.
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Cayman Islands24199 Posts
not sure if you are reading my posts on the matter.
i've basically said that they are trying to patch a fundamental lack of teaching engagement/effective application of hands on instruction with a badly designed implementation of a vague nice idea. you can teach intuitions just as well under the old system with some hands on tutoring with students who don't get the conceptual heuristics
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On December 02 2014 07:33 Sub40APM wrote:Show nested quote +On December 02 2014 07:06 Symplectos wrote:On December 02 2014 05:22 Nyxisto wrote:On December 02 2014 04:35 Symplectos wrote:
so why not teach them the algebraic rules to work with multiplication and division, then they will see that such expressions are easy to work with and they don't need to use "cheap" tricks.
The did this in the 60's and 70's in Germany actually and started mathematical education in university like fashion, starting out with set theory and such in an attempt to "build up" mathematics. Like a toned down version of how it's done in university basically. Turned out to be pretty bad as the kids actually didn't really understand what and more importantly why they're learning the stuff. It's just hugely impractical to start out that way. Obviously most parents didn't get the purpose of it, too. From my experience children like to learn in a more holistic way. Stuff they learn should be easily applicable and practical rather than formal. Music is another example, too. If you try to teach young kids formal music theory you'll find yourself in an empty classroom rather quickly. I did learn Mathematics like that, set theory, an introduction to groups, rings and fields at the age of 12. It was the best that has ever happened to me, it helped me immensely to see the true beauty of Mathematics. I don't see why it is impractical and I definitely do not see why everything must be based on applications, especially seeing how bad those "applications" are in most modern high-school text books. Out of your classmates, how many saw what you saw and how many were put off mathematics forever. I bet the ratio is quite unfavorable for mathematics, hence the impracticality of it. And this is coming from someone who agrees with you that mathematics should be as vital as basic literacy, and that the idea that someone proudly proclaims "I dont do math" should be viewed as much contempt as someone proclaiming "I dont read!"
Two out of 23 are now Mathematicians, but that isn't really the point. The point is that we all got a good general mathematical education. Out of my head I know that 7 out of my old classmates have a Ph. D. in a STEM-field and are working at an University or a research institute.
On December 02 2014 07:50 oneofthem wrote:
disagreement about common core math rests on some divergent perceptions of reality. on one hand if you think traditional math teaching can turn out students who only learn rote application of rules (like engineers or economist "math" huehue etc), there's a deficiency to be addressed by conceptual teaching. on the other hand, and this would require looking at how the theory is put into practice, mathematical rules are a language of their own, and application or memorization of those rules is not automatically rote/nonconceptual. rather, math class should get students acclimated to how the language of math is used in higher level studies.
both sides should agree that, bridging the gap between applying a rule and understanding the mathematical language of the rule is important in learning. but do you do this by forcing kids to go through some explicit visual representation of intuitions, or only tailor demonstrations to the extent that the intuitions are shown, and then internalized? the former method is misguided imo.
at the very least, don't make tests or homework over those representations. test the math not the particular pedagogical tool.
I completely agree with this. Visualizing Mathematics and staying away from the "harder" topics will lead to better results (obviously) at the beginning, parents will be happy, because now their children "understand" Mathematics, but at some point Mathematics will strike back and then the children, that are now teenagers or young adults, are lost and by that time it is a lot harder to close the knowledge gap - I see this happening in Germany at the moment and with horror I have to watch as Luxembourgish politicians are destroying a system that was once quite good.
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The simple fact is that math education has failed generations of students. This is not a new phenomenon and I would be surprised if it really was substantially different in Luxembourg. Math is generally the most hated subject, the subject people are worst at and even the subject it is most socially acceptable to fail at (btw it does not look like your class is the norm at all Symplectos, perhaps you shouldn't extrapolate too much from your experience).
Obviously, people who are mathematically inclined tend to defend the way it was taught or even demand that it should be taught more abstractly or more difficult. For them the system worked fine and that the majority got very little out of their math classes never crosses their mind or is chalked up as individual failure/stupidity.
Note that I am involved with math at the university level as well and not only can I see that this attitude is the norm for mathematicians, I myself had (or even have) the same gut reaction towards this kind of new math. Once you understand something it becomes difficult to relate to how someone else could not understand it. Because we try to do everything as general and abstract as possible, we tend to think that this is the best way for everyone. However, that most children at the beginning have a fundamentally different approach seems not only possible but very likely.*
As mathematically inclined people we should realize that we are not the norm and ask ourselves why this is the case.
*This holds even at the university level. I have seen professors using way too abstract concepts in introductory classes and then be proud when 50% fail the exam after the majority already dropped the class.
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Let me just add a few thoughts as someone who studied math and stats at university and working as a statistician.
Teaching math from set theory at a early age is generally not a good idea, it was tried in the New Math movement and it failed. I was introduced to set theory around the start of secondary school. It seemed completely pointless to me at the time. And it was. Set theory is useless for understanding early secondary school level math, but invaluable for understanding university level math. So the timing for when to introduce these concepts is important. Primary or early secondary school is no place for set theory, group theory, or ring theory. These concepts should be introduce when they are needed. Moderate levels of mathematical rigor should generally start around grade 10, increasing incrementally.
I see applications of math everywhere, for example, in the image filtering algorithms used in the photo app on your phone, in Twitter analytics or in the statistical theory used to design the SC2 MMR system and other games. But shoehorning applications of math into primary or secondary level math is pointless and counter-productive. Any serious application of math involves serious mathematics, far beyond the scope of pre-university level math. Moreover, any sort of application of math at primary or secondary level would be so artificial and convoluted, unrealistic, and boring, that it detracts from the joy of learning math. Mathematical theory is beautiful, even at high school level, both calculus and pre-calculus are remarkable enough and interesting enough to stand alone. The connection between trigonometry and complex numbers via Euler's formula, or the fact that the area under the curve is the inverse operation to finding the slope of a curve, or the connection between set theory and probability theory, are all remarkable and interesting and no contrived applications is needed to teach and appreciate these amazing facts.
In general, the content of the basic math curriculum is mostly fine. How it's taught can be improved, especially through having better teachers who don't teach it as just a series of tedious, uncreative exercises and unmotivated algorithms and facts to be memorized, but rather explained as a remarkable theory to learn, understand and explore.
However, I don't buy the notion that we need more mathematicians or STEM majors or mathematically-literate people. In economics, prices--including the price of labor--adjusts so that supply equates to demand (unless there's some form of price control or rigidity preventing price adjustment). So if there is a shortage of STEM skill, then show me the money. I don't see the wage of people with STEM skills going through the roof. Indeed, the more mathematically stupid the general population is, the higher my wage should climb.
Thus, I see little compelling evidence that people failing in math, is somehow worse for society than people failing at, say, dance or music.
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EPT
