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I agree; however, frustrating younger children by attempting to give them more than one simple way to do it and not allowing them to master that before they find another (in my experience anyway) can backfire. That's when parents start to hear the dreaded "I hate math! I'm stupid!" etc. etc. I like the part where they are trying to get them to understand vs. memorize, but I have a real problem with the pacing and spiraling aspects of it. Most of the time they don't have time to play the games that are supposed to help them learn their facts, and therefore, they don't.
Also, many of the newer programs hand them manipulatives and say 'figure it out" (more or less) and when a parent tries to help, they are often told by their children that their teachers told them "Don't ask your parents for help because they won't know how to do it."
Schools want parents to be more proactive in their child's education which is a good thing; however, it's nearly impossible for many parents to relearn how to do it when they have a measly so-called "reference book" that doesn't have clear steps how to show them.
I am not a math teacher and I don't know beans about teaching math. I do know, however, that the average elementary teacher didn't like math him/herself.
In re: the average person's knowledge of math, I got into a, ahem, discussion with a guy on another forum who is a lawyer, who didn't understand math. He couldn't figure out that if "City A" has 45% of possible sunshine, and "City B" has 54%, that City B is 20% sunnier than City A. This guy argued that the difference is only 9%. He didn't know how to figure out the problem. Even after I worked it out for him, he said, "you're doing a percent of a percent".
Well, I guess critical thinking is lacking in the United States, isn't it? This is something I really don't like. Where is the U.S. failing? Why do some students from other countries come out of high school with more knowledge than the average U.S. college graduate? Since some other countries seem to be quite advanced in math, science, reading, etc., why doesn't the U.S. follow their model?
Well, I guess critical thinking is lacking in the United States, isn't it? This is something I really don't like. Where is the U.S. failing? Why do some students from other countries come out of high school with more knowledge than the average U.S. college graduate? Since some other countries seem to be quite advanced in math, science, reading, etc., why doesn't the U.S. follow their model?
Not completely disagreeing, but which countries would you be talking about and what is your evidence for same?
Here is a crucial quote from the TIMSS article and it is what I see as the most important deficit in the US curriculum
"A typical U.S. eighth-grade math textbook deals with about 35 topics. By comparison, a Japanese or German math textbook for that age would have only five or six topics."
We could so improve our math and science if we went to fewer topics covered in depth.
Well, I guess critical thinking is lacking in the United States, isn't it? This is something I really don't like. Where is the U.S. failing? Why do some students from other countries come out of high school with more knowledge than the average U.S. college graduate? Since some other countries seem to be quite advanced in math, science, reading, etc., why doesn't the U.S. follow their model?
Generally India and China or Japan are the countries that our students are compared to. The thing is, it's not necessarily that they're teaching it better over there. It's not a simple comparison. The entire mentality of education is different over there.
For one, there is no "we will educate everyone" policy. If you don't test into the schools, you don't get to go. If you have a learning disability or are physically handicapped, you don't go to school. If you can't keep up with the material, they kick you out of class. They teach the cream of the crop, and that's it. If America wanted to do that, we could--but it goes against a lot of the values of our society.
Second, these kids are tracked from an early age. You test into your high school, pick a career path, and go. Kids in India know from the time they are 13 that they are going to be engineers, and they work their tails off for it. They go to school 6 days a week and go to tutoring before/after school. They don't play 3 varsity sports, perform in the school musical, or volunteer at the animal shelter after school. They work solely towards getting into their college of choice to get a well paying job.
When asked what they wanted for their child, parents in the different countries had telling goals. In India, parents hoped their children made good money (which makes sense, since much of the country is impoverished). In China, parents wanted career success. In the US, parents wanted their children to be happy. It's not wrong, it's just a different goal. In China or India, no parent would want their child to be the artist who lives in a studio apartment on the beach. In the US though, we tend to celebrate that--if they're happy and can pay the bills, great.
It's a different set of values. Unless we are willing to select careers for our children and force them into those paths, I don't think we'll ever see the same results as China or India.
generally india and china or japan are the countries that our students are compared to. The thing is, it's not necessarily that they're teaching it better over there. It's not a simple comparison. The entire mentality of education is different over there.
For one, there is no "we will educate everyone" policy. If you don't test into the schools, you don't get to go. If you have a learning disability or are physically handicapped, you don't go to school. If you can't keep up with the material, they kick you out of class. They teach the cream of the crop, and that's it. If america wanted to do that, we could--but it goes against a lot of the values of our society.
Second, these kids are tracked from an early age. You test into your high school, pick a career path, and go. Kids in india know from the time they are 13 that they are going to be engineers, and they work their tails off for it. They go to school 6 days a week and go to tutoring before/after school. They don't play 3 varsity sports, perform in the school musical, or volunteer at the animal shelter after school. They work solely towards getting into their college of choice to get a well paying job.
When asked what they wanted for their child, parents in the different countries had telling goals. In india, parents hoped their children made good money (which makes sense, since much of the country is impoverished). In china, parents wanted career success. in the us, parents wanted their children to be happy. it's not wrong, it's just a different goal. In china or india, no parent would want their child to be the artist who lives in a studio apartment on the beach. In the us though, we tend to celebrate that--if they're happy and can pay the bills, great.
It's a different set of values. Unless we are willing to select careers for our children and force them into those paths, i don't think we'll ever see the same results as china or india.
Well, I guess critical thinking is lacking in the United States, isn't it? This is something I really don't like. Where is the U.S. failing? Why do some students from other countries come out of high school with more knowledge than the average U.S. college graduate? Since some other countries seem to be quite advanced in math, science, reading, etc., why doesn't the U.S. follow their model?
IMO, "critical thinking" is not limited to math instruction. Many other subjects/tasks require the ability to take apart a problem piece by piece and put it back together again correctly.
One reason why I carp on about giving younger kids more than one simple way to solve a problem and let them master it, is that in addition to getting the correct answer and thereby building confidence, they are also learning to take steps to an end.
I'm also a fan of having a child copy problems to solve from a book vs having a workbook. Why? Because in addition to learning to solve a problem, IMO, the child makes the connection between lining up the numbers correctly, writing the numbers correctly, and taking the necessary steps to solve the problem. This also reinforces which way a 9 is written, checking your work, etc.
Yes, it's slow, yes it's tedious, but to me there is intrinsic value to learning to take your time and not rush for a solution.
The questions is: Is it useful for a math teacher to know?
Does a pitcher need to understand the game of baseball?
It's part of the big picture. In math, the pieces fit together. The student learns 6^3, 6^2, 6^1, and he wonders . . .
So he asks, and the teacher explains . . . or tells him it doesn't matter, or not to worry about it, or that she doesn't know, or to stop asking questions, or to be quiet and finish his worksheet.
How much of this before he decides math doesn't make sense, after all?
Or the student listens to his teacher and quits wondering about it. Then he gets to junior high and learns about negative exponents.
6 to the second = 36
6 to the first = 6
6 to the negative first = 1/6
6 to the negative second = 1/36
Huh? Where'd this all come from? Why skip 6^0? That doesn't make sense. But that's okay, math is just magic tricks anyway, right? Or maybe he thinks, "It must be undefined, like dividing by 0." And because he doesn't understand what the teacher/book meant by "Division by 0 is undefined" in the first place, this makes sense to him. He's put in a puzzle piece - but it's the wrong piece. And math makes less and less sense.
Okay, here's a simpler example of a problem from teachers who don't understand math:
First grade: 3 + 4 =
The child puts 7. Yep. Nothing wrong with that.
Unfortunately, most kids come to think that "=" means "put the answer here." Maybe the teacher said it at some point; maybe she didn't realize he was getting that idea; but maybe she just didn't realize it was important. At least half of my middle schoolers came to me with this idea. They see the left side as the "problem" and the right side as the "answer." This causes confusion when the student is learning to solve equations.
Another: fractions and division
I tried to get third grade teachers to use different ways of writing division when the kids were learning it, including 36/4 (36 over 4) I had previously done this with second graders, and they learned it smoothly with no problems, not having any prior experience to confuse them. The third grade teacher didn't want to do it because they couldn't see 36/4 as being 36 divided by 4. To them, 36/4 was an improper fraction, and improper fractions were stored in a completely different category in their brains. Yes, both equal 9, but . . . . It just didn't fit in with how they understood math.
Then, when the kids learn about improper fractions, they learn that they are supposed to divide to change them into whole or mixed numbers. Each piece of math is taught separately, like it is a new concept - but it isn't. So math becomes fragmented, and it looks like our texts have 35 concepts instead of six. (I think someone said that's what Japanese texts have.)
Oops. Long post. I get into this.
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