Math education - Why is US not solving this problem?

[Anonymous]

Anonymous wrote:

Anonymous wrote:While I appreciate all the opinions, can anyone point me to articles or other research that digs into these issues in depth and supports positions with research? I'm kind of a "show me" person, so I need to see the research myself.

Here is an excellent article that was developed by the National Science Foundation's National Science Board.

http://nagc.org/uploadedFiles/Information_and_Resources/Hot_Topics/NSB%20-%20Stem%20innovators.pdf

Many thanks for this. Thanks also to the Liping Ma reference. I will check them out.

I'm not looking for anyone to "do the research for me" but rather just to see whether anyone here has ever looked into this before and might have suggestions about good places to start my own research. It's sort of like asking for a book recommendation; I hope no one would begrudge me that.

[Anonymous]

Anonymous wrote:People seem to have different approaches to solving problems involving division with fractions. How do you solve a problem like this one? 1 3/4 ÷ 1 /2=
Imagine that you are teaching division with fractions. To make this meaningful for kids, something that many teachers try to do is relate mathematics to other things. Sometimes they try to come up with real-world situations or story-problems to show the application of some particular piece of content. What would you say would be a good story or model for this problem.

The answer is 14/4, right? But I can only do that conceptually - I can't understand how you'd teach that one as a story problem.

[Anonymous]

Anonymous wrote:

Anonymous wrote:People seem to have different approaches to solving problems involving division with fractions. How do you solve a problem like this one? 1 3/4 ÷ 1 /2=
Imagine that you are teaching division with fractions. To make this meaningful for kids, something that many teachers try to do is relate mathematics to other things. Sometimes they try to come up with real-world situations or story-problems to show the application of some particular piece of content. What would you say would be a good story or model for this problem.

The answer is 14/4, right? But I can only do that conceptually - I can't understand how you'd teach that one as a story problem.

it is 1.75x2=3.50

[Anonymous]

Anonymous wrote:The key is "knowledgeable teachers". The best book explaining the difference between math education in the U.S and China is a book by Liping Ma called Knowing and Teaching Elementary Mathematics. The book compared a group of US teachers that were rated above average and Chinese teachers when they were asked how to solve four different types of problems. For example Ma asked the teachers:

People seem to have different approaches to solving problems involving division with fractions. How do you solve a problem like this one? 1 3/4 ÷ 1 /2=
Imagine that you are teaching division with fractions. To make this meaningful for kids, something that many teachers try to do is relate mathematics to other things. Sometimes they try to come up with real-world situations or story-problems to show the application of some particular piece of content. What would you say would be a good story or model for this problem.

Only 9 of the 21 U.S. teachers who worked the problem produced the correct numerical answer to the division problem. This clearly points to a problem with the teachers’ algorithmic competency. In contrast, all 72 Chinese teachers performed the computation correctly. Only one of the U.S. teachers generated a story that corresponded correctly to the given division. In contrast, 90% of the Chinese teachers generated appropriate stories for the division. U.S. teachers were taught by teachers without a profound understanding of math so they teach the way that they were taught which creates a never ending cycle of incompetent teachers. One way to change the system would be for math to be taught by math teachers/specialists at the elementary level instead of elementary teachers.

This seems impossible to believe. The problem is simple and I wasn't a standout math student. There's nothing like someone called Liping Ma writing about how the Chinese are superior. I'm sure she's totally unbiased.

[Anonymous]

The quality of life is too high here. People usually pursue the difficult subjects to better their situation. I wouldn't be surprised if most of the STEM jobs held by US born citizens are AAs in the next decade or two.

[Anonymous]

Make every teacher get a degree in the subject they are teaching plus a certificate in education vs a degree in education.

[Anonymous]

The problem in a nutshell? Look at the University of Chicago math curriculuum, much vaunted by schools across the country. It was developed by the university Education department and not their Math department. There's a reason so many fads come and go in education- old fashioned algorithms (and phonics, for that matter) don't get you published in professional journals....

[Anonymous]

It is a good question and I think the answer is that standards have dropped at every level. I am a liberal but have to say that the curiculm culture wars of the 60's and 70's especially on the left destroyed high quality standarized education. E.D. Hirshe writes about this alot. That and it is really hard for parents to be on top of their kids education when they both work or they are single parents. I know I personally feel that I am somehow shorting my kid and despereately want to relay on the babysitter in the box. Finally college does not really appear to require it. http://thechoice.blogs.nytimes.com/2011/01/17/academically-adrift/

So is our economy screwed, yes unless figure out how to continue to drain the rest of the world of their high performing graduates,

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:People seem to have different approaches to solving problems involving division with fractions. How do you solve a problem like this one? 1 3/4 ÷ 1 /2=
Imagine that you are teaching division with fractions. To make this meaningful for kids, something that many teachers try to do is relate mathematics to other things. Sometimes they try to come up with real-world situations or story-problems to show the application of some particular piece of content. What would you say would be a good story or model for this problem.

The answer is 14/4, right? But I can only do that conceptually - I can't understand how you'd teach that one as a story problem.

it is 1.75x2=3.50

14/4 = 3.50

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:People seem to have different approaches to solving problems involving division with fractions. How do you solve a problem like this one? 1 3/4 ÷ 1 /2=
Imagine that you are teaching division with fractions. To make this meaningful for kids, something that many teachers try to do is relate mathematics to other things. Sometimes they try to come up with real-world situations or story-problems to show the application of some particular piece of content. What would you say would be a good story or model for this problem.

The answer is 14/4, right? But I can only do that conceptually - I can't understand how you'd teach that one as a story problem.

it is 1.75x2=3.50

14/4 = 3.50

Oh, and if you have 1 3/4 pizzas, and you want to serve each person 1/2 a pizza, how many people can you serve? Answer: 3, with half a serving left over for the dog.

[Anonymous]

Anonymous wrote:The key is "knowledgeable teachers". The best book explaining the difference between math education in the U.S and China is a book by Liping Ma called Knowing and Teaching Elementary Mathematics. The book compared a group of US teachers that were rated above average and Chinese teachers when they were asked how to solve four different types of problems. For example Ma asked the teachers:

People seem to have different approaches to solving problems involving division with fractions. How do you solve a problem like this one? 1 3/4 ÷ 1 /2=
Imagine that you are teaching division with fractions. To make this meaningful for kids, something that many teachers try to do is relate mathematics to other things. Sometimes they try to come up with real-world situations or story-problems to show the application of some particular piece of content. What would you say would be a good story or model for this problem.

Only 9 of the 21 U.S. teachers who worked the problem produced the correct numerical answer to the division problem. This clearly points to a problem with the teachers’ algorithmic competency. In contrast, all 72 Chinese teachers performed the computation correctly. Only one of the U.S. teachers generated a story that corresponded correctly to the given division. In contrast, 90% of the Chinese teachers generated appropriate stories for the division. U.S. teachers were taught by teachers without a profound understanding of math so they teach the way that they were taught which creates a never ending cycle of incompetent teachers. One way to change the system would be for math to be taught by math teachers/specialists at the elementary level instead of elementary teachers.


Don't think it's the teachers. Rather, the problem is american parents and culture don't have the stomach to push their kids the way parents in math focus counties do. Believe me I know. Also, american math teachers learnt from the same culture they're teaching in, not in foreign math focus countries.

[Anonymous]

Op, to answer the question about why we are not solving the problem: the problem keeps being solved for us, with immigration.

[Anonymous]

I have to agree with 17:12 and that it goes back to the elementary age teachers teaching math. Math concepts are a skill that needs to be taught by a math professional with the teacher as facilitator. It's like a foreign language, if the skills are taught correctly and early, it becomes a natural foundation for the kids to use in MS and HS math. The concepts and skills have to be drilled in for easy access later in life.

As a teacher who did student teaching in 4th grade, I can tell you that we had no idea how to do the above. We just explained the ideas from the worksheets and kids either learned how to do the worksheets OR if they were "math brains" they actually absorbed the concept/skill to use later.

[Anonymous]

Anonymous wrote:I have to agree with 17:12 and that it goes back to the elementary age teachers teaching math. Math concepts are a skill that needs to be taught by a math professional with the teacher as facilitator. It's like a foreign language, if the skills are taught correctly and early, it becomes a natural foundation for the kids to use in MS and HS math. The concepts and skills have to be drilled in for easy access later in life.

As a teacher who did student teaching in 4th grade, I can tell you that we had no idea how to do the above. We just explained the ideas from the worksheets and kids either learned how to do the worksheets OR if they were "math brains" they actually absorbed the concept/skill to use later.

You had no idea how to do it? But it's not advanced math. I'm not a mathematician either but this is a simple fraction problem. Why do you need mathematicians to teach elementary school math???

[Anonymous]

I'm wondering if it is partly because people with inherently strong STEM ability tend to be introverted, socially awkward and gravitate toward isolated research, academia or think tank work rather than teaching? Or jobs that pay a lot more than teaching.