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@ bill83-Using some "quick math" myself, I calculate that the US' math score was about 15% lower than the highest country's. The science score was about 10% lower. I'm not sure what the Pew Research Center considers "significantly" higher/lower.
I am not sure neither. I didn't post that charts. How are those scores calculated?
Relevant to cognitive stages and why many of us believe that the Math processes embedded in Common Core will crash and burn, but not before ruining an entire generation for math. Much like the constant switching between teaching of Reading methods did 25 years ago:
1) The stages proposed by this theory of child development is a theory based on the observations of one guy. While it is a very good theory, I haven't actually seen any scientific studies that confirm this theory. It currently has about as much validity as the theory of childhood development that holds that all boys unconsciously want to kill their fathers and marry their mothers.
2) Even if we were to take the stages proposed by this theory, that would have us teaching all basic arithmetic to kids by the age of 7 (end of first grade), during their preoperational period when they are developing symbolic thought. Then it would have us applying arithmetic to concrete events, like applying arithmetic to things like fractions, ratios, and percents, through age 11 (end of fifth grade). After that (sixth grade and above) is when you get into abstract math, starting with pre-algebra and going up through calculus.
Which incidentally is the progression used in Singapore Math and Montessori. Which incidentally is the same progression used in Common Core, except for common core is a year or two behind. So by your argument, we should keep common core, but make it a year or two faster than it is.
Is that why you think common core will crash? Because it's too slow? If so I agree.
Are you familiar with Kahn Academy on youtube? What do you think of it?
Khan Academy is a fantastic resource. We often watch the math videos. It is especially useful for parents who are not confident enough in their own math ability to teach it themselves.
Yes, but that is not learning math concepts. That's just memorizing and parroting information.
This is why it is important to work out and test word problems. "Days" and "weeks" are abstract concepts in themselves. So, initially it may be difficult for some students to understand that you can do math with them.
However, once a student is taught that days or weeks can be thought of as concrete objects like abacus beads, it will become clear to them that you can do addition, subtraction, multiplication and division with them just like you can do with beads.
By the way, this a good example of an abacus that is very easy to learn math on:
We agree with all this. Earlier you said that there was no "right way" or "wrong way" to teach math. I disagree with that. I think that the method you just described above, teaching first with concrete objects, then moving into applying it to abstract concepts with word problems, is a "right way" to teach math. And that memorizing and parroting information without understanding it first is a "wrong way".
1) The stages proposed by this theory of child development is a theory based on the observations of one guy. While it is a very good theory, I haven't actually seen any scientific studies that confirm this theory. It currently has about as much validity as the theory of childhood development that holds that all boys unconsciously want to kill their fathers and marry their mothers.
2) Even if we were to take the stages proposed by this theory, that would have us teaching all basic arithmetic to kids by the age of 7 (end of first grade), during their preoperational period when they are developing symbolic thought. Then it would have us applying arithmetic to concrete events, like applying arithmetic to things like fractions, ratios, and percents, through age 11 (end of fifth grade). After that (sixth grade and above) is when you get into abstract math, starting with pre-algebra and going up through calculus.
Which incidentally is the progression used in Singapore Math and Montessori. Which incidentally is the same progression used in Common Core, except for common core is a year or two behind. So by your argument, we should keep common core, but make it a year or two faster than it is.
Is that why you think common core will crash? Because it's too slow? If so I agree.
You're incorrect in a couple things.
One, while Piaget is theory "based on observations of one man" those observations have been reaffirmed by nearly 100 years of observation by others. Those observations are the why that Math education in the US was set up the way it was. Which, by the way, is what you described as the ideal progression and is what is outlined in another link I posted a bit later.
What Common Core does is shove everything down about two grade levels, so it's not "behind" but ahead. Pre-Algebra is now, under Common Core, being introduced not around 6th/7th grade but 4th and in some school systems 3rd grade.
Our kids aren't dumber stock. They're just coddled. American math programs SPIRAL. You touch a topic and move on then come back to it again and again and again and again and again over the next several years. Our expectations are that kids won't get it the first time and that they don't need to remember it because we'll spiral back to it so they don't. We've trained them to think shallowly and not remember what they're taught. It's like pulling teeth to get kids to use algebra in chemistry. Even parents cry foul saying that their child should not be graded on math (or English) ability in science class.
THIS. The problem isn't the common core, the problem is the spiral.
But kids at that age do not think abstractly, do they? They're still in the concrete thinking stage.
I tutored high school students in math for the CAHSEE (California High School Exit Exam). I was astounded at the number of them who did not know their multiplication facts. While they might have had great "math logic," they became so frustrated at doing even two-step algebra problems that they skipped problems or had so many wrong answers that they gave up.
Also, my own kids were taught creative math in elementary school because that's what the state math curriculum demanded at the time. They solved problems such as, "If you have 12 containers, with two seeds in each, how many flowers are produced?" and that type of thing. Memorization of multiplication facts was not required.
They were promptly sent to Kumon. One of them told us years later that he could never have passed Alg II or Trig in high school if he hadn't gone to Kumon. (Of course they hated going at the time.) And Kumon is simply drilling, over and over, until the kid has mastered that particular level of math and can move on to the next level.
1) The question "how many days are in 3 weeks" is a concrete question. Not an abstract question. Days and weeks are concrete things that you can manipulate (using a calendar, for example). "3 x 7 = ?" is an abstract question. The numbers and symbols are abstractions of the concrete things.
2) You identified the main down side of the math spiral. They do not truly "master" any topic.
The correct way to teach math is to take one topic at a time, and first teach them how to understand the concept. Do the "if you have 12 containers, with two seeds in each, how many flowers are produced" problems. Those are good, but they only get you half way there. Once you understand, then you memorize. You drill your multiplication facts until the are memorized, until they are reflexive, and you know how to use them because you understand why you need these facts. Then you have mastered the topic.
Its like piano practice. When you are given a new song, first you figure out what all the notes are and what the timing is, and get to the point where you are able to play though it correctly. But that's only half way to mastering the song. After you can play it correctly, then you practice and practice until you have it memorized, and then you practice it memorized over and over until it is reflexive, and then you are able to inject emotion in it, and perform it, and use it to convey emotion to an audience (even if your audience is only yourself). That's the point of playing the piano. If you only do the first part, you are missing the whole point.
You did right, IMO. If your kids' school only taught the first half of math (understanding) and skipped the second half (memorization and mastery), then Kumon is perfect for fixing that. That is exactly what Kumon is for. So far my first grader has had no problem memorizing her multiplication tables at home with the amount of drill they have in Singapore, but when my 4 year old gets to that point, if he has trouble, he will absolutely be going to Kumon.
I am not sure neither. I didn't post that charts. How are those scores calculated?
Oh, sorry, it was Matadora. I have no idea how the scores were calculated. It talks about a base of 1000. It looks kinda like this "How to Lie with Statistics" stuff. I mean, yeah, it'd be great if we were up there in the top 5 or even 10 countries, but note how there are a lot of scores bunched up around 500. The US is within 4% of that at 481.
Quote:
Originally Posted by North Beach Person
You're incorrect in a couple things.
One, while Piaget is theory "based on observations of one man" those observations have been reaffirmed by nearly 100 years of observation by others. Those observations are the why that Math education in the US was set up the way it was. Which, by the way, is what you described as the ideal progression and is what is outlined in another link I posted a bit later.
What Common Core does is shove everything down about two grade levels, so it's not "behind" but ahead. Pre-Algebra is now, under Common Core, being introduced not around 6th/7th grade but 4th and in some school systems 3rd grade.
And even of more simple societies. Most societies have a coming of age thing at around age 13. Here it's 8th grade graduation, which is a big deal in some places; confirmation in many Christian churches, Bar/bat Mitzvah in the Jewish religion, etc.
One, while Piaget is theory "based on observations of one man" those observations have been reaffirmed by nearly 100 years of observation by others. Those observations are the why that Math education in the US was set up the way it was. Which, by the way, is what you described as the ideal progression and is what is outlined in another link I posted a bit later.
Yes, I agree it's been reaffirmed by observations and is a great theory. But I have not seen the science. I would love to see the scientific method applied to this work and published.
Quote:
Originally Posted by North Beach Person
What Common Core does is shove everything down about two grade levels, so it's not "behind" but ahead. Pre-Algebra is now, under Common Core, being introduced not around 6th/7th grade but 4th and in some school systems 3rd grade.
I just reviewed the Common Core standards, and it has math standards for Kindergarten through 8th grade, and then goes on to have standards for "High School Algebra". I'm not seeing pre-algebra in the standards for 4th grade. I am seeing "algebraic thinking" in 4th grade, which is basically teaching that 7-3=? is the same as 3+?=7, which is good, but is not really "pre-algebra" in the sense of what you actually learn in a pre-algebra course. I mean, my first grader understands "3+?=7" with no problem, but she's not ready for pre-algebra by far. She's on track to get there at 6th grade, and she's a year and a half ahead of common core.
What am I missing? Is there some curriculum out there that claims to be common core that's doing pre-algebra in the 4th grade?
White Americans scored higher than large western countries like the U.K, France and Germany.
Asian Americans scored higher than Japan and South Korea.
Hispanic Americans scored way higher than all Latin American countries.
That doesn't sound to me like something is terribly wrong with the U.S. primary educational system.
Fascinating. It sounds like the glass is both half-empty and half-full at the same time! lol
Interesting that they measure 8-th grade science performance. The schools I went to didn't even have science instruction until HS. Part of the problem with US education is that it can be all over the place, like when some school districts decided to teach reading by the see-and-say method, which ended up leaving a lot of kids out of the loop entirely. Weird fads sometimes sweep through an entire state, though I suppose initiatives like "No Child Left Behind" were an attempt to standardize instruction more?
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The problem isn't the common core, the problem is the spiral.
lol
