Article: Why do Americans Stink at Math

[redsquirrel]

http://www.nytimes.com/2014/07/27/magazine/why-do-americans-stink-at-math.html?hpw&action=click&pgtype=Homepage&version=HpHedThumbWell&module=well-region&region=bottom-well&WT.nav=bottom-well

 

It is a NYT article and they have a limit on how many views you can have in a 30 day period.

 

But I found it interesting, especially having read Liping Ma's book, and I thought some of you might find it interesting as well.

[maize]

Thanks for sharing the article. It really struck me when reading Liping Ma's book that math teachers in China--and from this article I think in Japan as well--are specialists. They have time and opportunities to really know their subject and study and practice teaching methods. I think we do ourselves a great disservice by turning elementary math instruction over to non-specialist teachers many of whom do not understand or like math themselves.

[Eagle]

What a fascinating article! It was so interesting to learn about the Japanese method of training teachers. I found myself wishing I could attend some of their 'jugyokenkyu'.

 

It was also eye-opening to see the amount of time spent on various types of work in the classroom:

"96 percent of American students’ work fell into the category of “practice,†while Japanese students spent only 41 percent of their time practicing. Almost half of Japanese students’ time was spent doing work that the researchers termed “invent/think.†(American students spent less than 1 percent of their time on it.)"

[ErinE]

Thanks for sharing the article. It really struck me when reading Liping Ma's book that math teachers in China--and from this article I think in Japan as well--are specialists. They have time and opportunities to really know their subject and study and practice teaching methods. I think we do ourselves a great disservice by turning elementary math instruction over to non-specialist teachers many of whom do not understand or like math themselves.

When I first started homeschooling, I asked for math help from an elementary school teacher with a math specialization.

 

She didn't remember inverse operations or reciprocals.

 

I stuck to the Hive for math advice after that.

[MarkT]

Don't get me going on the American education system. My son attended a public charter school for 7th and 8th grade. The charter schools can be more flexible but seem to be run by the same failing Edu-crats. I tried to give them advice on their math program (they did make the placement test harder) but they did not even consider some other easy common sense changes I suggested.  Their HS Algebra 1 and Geometry classes were accredited even though they are quite incomplete.

[MarkT]

from the article comments:

http://www.americanthinker.com/2013/09/common_core_standards_flunk_logic_101.html

 

http://www.americanthinker.com/2013/10/common_core_standards_flunk_logic_101_again.html

[FaithManor]

I've gone shopping before with a group of elementary teachers after conferences we've attended together to get CEU credits. Not one of them can find 25% of a $40.00 item without a calculator. Every time there is a discount they ask me for help and giggle about being "no good at math" with zero thought as to tne concerns that should present as professional teachers. They also think I'm a virtual genius because I know how much an 1/8th of a yard of fabric is and how to price it.

 

THIS is a huge reason why American students perform so poorly. Then when these students land in algebra 1 with someone who had to actually major in math in college to get certified to teach it, the poor teacher is reduced to having to teach rudimentary arithmetic skills. It snowballs from there and tne only kids who ever master any algebra or geometry skills are a select few whose parents saw to it that they learned the topics, hired tutors, or were naturally very talented in the subject.

 

One of our local, regional, crappy uni's allows students to fail the test of basic skills up to four times and still apply for an elementary education major, and the only math required is a "having fun with math" which concentrates on ways to bribe students to do math homework and designing creative math bulletin boards.

 

So, there you go. In my area, incompetent teaching is very much at the heart of the issue. Followed by bizarre curriculum that is visually overwhelming and so disorganized it should be burned!

[FaithManor]

Oh, and since the only thing that counts around here is standardized test scores, calculator dependence and guessing is emphasized.

[MomtoCandJ]

Because only a very few teachers have the skills to teach math to a large variety of learning styles. I loved my Algebra-geometry-algebra 2- teacher. She could teach anyone, too bad I didn't have her in elementary when I really needed her to help with those foundation skills. I know some may frown on this but she used to give credit for trying, but you had to show your work in order to prove you were actually trying. She would do anything she could to try to get you to understand.

[Liz CA]

I've gone shopping before with a group of elementary teachers after conferences we've attended together to get CEU credits. Not one of them can find 25% of a $40.00 item without a calculator.

 

Good Grief! That is scary. An eighth grader who is good at math and is working the cash register could really fool them...I don't like algebra that much but at least I can calculate my discounts.

[BlessedMom]

Interesting article!

Thank you for sharing the link.

[SKL]

I'm not drinking any kool-aid here, but that article did inspire me to give my daughter a little more time to figure out math problems.  Because she is slow at math, she generally expects the lesson to move on before she has a chance to think through challenging problems.  But she is able to work things out if she has time (and knows it isn't going to be done for her).

 

The way my kids' school handled common core in 2nd grade was:  they did Singapore math (2a-b ), plus binders full of worksheets that supposedly represent Common Core Math.  (You know, the ones where they make the kids draw a picture and write a word problem for 8+6.)  They rushed through both.  I think my kid would have flunked math if we hadn't done parallel work at home, for at least an hour per day.  There was so much to do, the idea of letting a slower kid actually work out a challenging problem must have seemed ridiculous.  Especially if she doesn't seem to be catching on after watching others perform the trick a number of times.

[bettyandbob]

I've been in and out of teaching a few times over the last 25 years. Each time I've reentered the profession I've had to take round of tests to renew my certifications. The tests are different each time, but they are always reading and writing. I have never been expected to prove I could solve a math problem. I am a sp ed teacher. Because I am certified K-12, I take the same tests elementary teachers take. The reason why students are not mastering the basics in elementary school is because the persons teaching the basics never learned enough to actually understand. So, they take the students through rote lessons and show them only one way to do a problem. They do not show multiple approaches. They do not know how illustrate with manipulatives. They just get through it. 

 

I think along with reading and writing tests, teachers ought to be required to take math tests that cover all arithmetic and basic algebra. 

 

I do know some one who is an amazing K teacher, who gives her students a solid foundation in math. When she was in high school, her physics and calculus teachers were insisting she go to engineering school, but her dream was to teach K. Her students are very lucky. I also know a girl who is entering college with hopes of teaching elementary school. She completed through multivariable calculus in high school. She has a firm understanding of math. She's also quite solid at other subjects. If she ends up as an elementary teacher, her students will be very lucky. 

[kwg]

VEry interesting article. I have learned more homeschooling my children than I ever did as a teacher.  Yes we had inservices and such but there were such pressures! (testing)  In the end, as a new teacher I followed what the other teachers were doing and now I wonder sometimes about those kids' number sense.  Pure memorization.

 

 

[kiana]

I've gone shopping before with a group of elementary teachers after conferences we've attended together to get CEU credits. Not one of them can find 25% of a $40.00 item without a calculator. Every time there is a discount they ask me for help and giggle about being "no good at math" with zero thought as to tne concerns that should present as professional teachers. They also think I'm a virtual genius because I know how much an 1/8th of a yard of fabric is and how to price it.

 

THIS is a huge reason why American students perform so poorly. Then when these students land in algebra 1 with someone who had to actually major in math in college to get certified to teach it, the poor teacher is reduced to having to teach rudimentary arithmetic skills. It snowballs from there and tne only kids who ever master any algebra or geometry skills are a select few whose parents saw to it that they learned the topics, hired tutors, or were naturally very talented in the subject.

 

One of our local, regional, crappy uni's allows students to fail the test of basic skills up to four times and still apply for an elementary education major, and the only math required is a "having fun with math" which concentrates on ways to bribe students to do math homework and designing creative math bulletin boards.

 

So, there you go. In my area, incompetent teaching is very much at the heart of the issue. Followed by bizarre curriculum that is visually overwhelming and so disorganized it should be burned!

 

Guhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh.

 

Honestly, I think this is one reason to teach algorithmic math in elementary school. I *like* the conceptual curricula, if you have a teacher who can handle them. But so many of the conceptual curricula, when taught by a teacher who doesn't understand the concepts, results in students leaving elementary school who can neither conceptualize nor compute. At least if they used an algorithmic curriculum, they'd have some foundation in computation that the high school teachers could build on.

 

I mean, I spent a few summers grading placement tests at a university. One problem was "What is 1/2 + 1/3?". The most common answer was 2/5. I wouldn't have made this error ... ever, that I can remember. I know 2/5 is less than 1/2, and I for darn sure know you can't add a positive number to 1/2 and make it smaller.

[FaithManor]

I agree, they can't compute, they can't conceptualize, they can't balance a checkbook, they can't compare...it's total mathematical illiteracy. In my day, we may not have had a lot of conceptual math, but we darn well knew our arithemetic and at least the 6th and 7;h grade teachers did not start from scratch.

 

My boys always laughed when I pulled out "Basic College Mathematics" for a quick 7th grade review of the last 5 chapters before algebra 1. They couldn't believe people go to college not being able to add, subtract, multiply, divide, work with fractions and percents. Yes boys, there are a lot of 18 year olds and even older adults taking the Compass Exam and testing into this class.

 

But, if the adult in charge can not do it and is unwilling to learn to do it so he or she can teach it, then all you have is k-6 blind leading the blind!

[Rosie_0801]

I've gone shopping before with a group of elementary teachers after conferences we've attended together to get CEU credits. Not one of them can find 25% of a $40.00 item without a calculator. 

 

Not good enough! I can do that even with severe preggie brain!

[SKL]

I was just remembering the "college" math book for the only math course (2 semesters) that I was supposed to take to become an elementary (K-8) and special ed (K-12) school teacher.  "Basic Math Concepts."  (This was 1983, not sure what it's like today.)  I looked over the book and thought, there is no way I can do this.  I cannot sit through a course that is this simple, I will kill my GPA because I just can't.  This was stuff from mid-elementary school at best.  I got permission to switch to a sequence that went from algebra through calculus in 2 semesters.  But yeah, it is a bit disturbing that they are requiring higher thought at a younger age when the teachers may never have learned the logic it requires.

[TrixieB]

Not good enough! I can do that even with severe preggie brain!

 

Did I miss an announcement?

[Rosie_0801]

Did I miss an announcement?

NO!!!!!!! I AM SINGLE, VERY, VERY SINGLE and while I'm good, I'm not good enough for immaculate conceptions and I'm getting wigged out because dd woke up this morning and told me I was pregnant. (Perhaps she got the wrong mum and her step mum had better watch out!)

 

I was talking about previous pregnancies.

 

Anyway, that's a bit off topic for a maths thread. 

[kiwik]

I had maths teachers right up to the equivalent of 10th grade who complained about being forced to teach maths when they signed up to teach science. The teachers at primary were even more anti-maths. We got new maths combined with complete lack of understanding. There were some really obvious things I never understood. On paper I was good at maths but in reality not so much.

[Alessandra]

Wouldn't it be nice to hear Takahashi (or Liping Ma) speak at a homeschool conference?

[Scarlett]

When I first started homeschooling, I asked for math help from an elementary school teacher with a math specialization.

 

She didn't remember inverse operations or reciprocals.

 

I stuck to the Hive for math advice after that.

I remember when ds was in third grade. I ran into a 3rd grade teacher at swim and started talking to her about ds's math. She said she didn't bother teaching what borrowing meant because it was easier to just show them the algorithm . But she didn't use the word algorithm even. Her explanation sounded like SHE was the third grader. I was gobsmacked.

 

Speaking of specialists....my mom was a 5th grade teacher who specialized in teaching math ot elementary..beginning pre k. She didn't learn the methods in college...she learned them from special math classes she went to on a special program after she began teaching. She went to a weeks worth of training at least 3 or 4 times a year. She is the reason I was able to teach my son math from the beginning...heck I learned a lot myself!

 

I totally agree specialists are needed for early math. If everyone had the ear of someone like my mom a lot more kids would excel in math.

[magnificent_baby]

Guhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh.

 

Honestly, I think this is one reason to teach algorithmic math in elementary school. I *like* the conceptual curricula, if you have a teacher who can handle them. But so many of the conceptual curricula, when taught by a teacher who doesn't understand the concepts, results in students leaving elementary school who can neither conceptualize nor compute. At least if they used an algorithmic curriculum, they'd have some foundation in computation that the high school teachers could build on.

 

I mean, I spent a few summers grading placement tests at a university. One problem was "What is 1/2 + 1/3?". The most common answer was 2/5. I wouldn't have made this error ... ever, that I can remember. I know 2/5 is less than 1/2, and I for darn sure know you can't add a positive number to 1/2 and make it smaller.

 

Completely agree with your first paragraph. In fact, this was one of the reasons I pulled Dd to homeschool. Teacher had no clue what she was doing with this math (granted, they had just trained that grade of teachers) and Dd was confused and so frustrated. Now that they are all back in, I'm fairly impressed what my kids can do in their heads, now that all of the teachers have been heavily trained in conceptual math. My 1st grader was adding/subtracting 3 digit numbers in his head one day, I was quite surprised he could do this. Still a fan of a good balance of traditional/conceptual, which they are *somewhat* doing in our district. 

[TrixieB]

NO!!!!!!! I AM SINGLE, VERY, VERY SINGLE and while I'm good, I'm not good enough for immaculate conceptions and I'm getting wigged out because dd woke up this morning and told me I was pregnant. (Perhaps she got the wrong mum and her step mum had better watch out!)

 

I was talking about previous pregnancies.

 

Anyway, that's a bit off topic for a maths thread. 

 

Oh, previous pregnancies.  I certainly recall struggling with simple math during those!

 

[umsami]

I read the article and really enjoyed it.

 

It seems that our country is also missing the public lessons aspect… but knowing the US, they would be used to criticize rather than help teachers, which would ruin the point.

 

It's sad that so many of the wonderful ideas that the Japanese and Chinese use came from the U.S., but we still teach the same way.

 

So…how can homeschoolers access master teachers, so to speak?  Who are the "masters' who you turn to?

[kiana]

You might note that the article never said math teachers were idiots, (as is implied so many times on this thread) but rather that better teaching methods were not being taught in teacher training and quality training on new curricula not provided.

There is a big difference between thinking someone is an idiot and thinking that someone is innumerate and has been graduated and is responsible for the education of other people's children while still being innumerate.

 

Someone who can't do the elementary school math they're supposed to be teaching is pretty innumerate, just as someone who can't read elementary school-level books is pretty illiterate. I'd have been just as shocked at finding an elementary school teacher or a large group of them who were surprised at someone able to read ... oh, let's say Harry Potter #1.

[redsquirrel]

If elementary teachers aren't being taught and supported in math education, I see that as a reflection on of the values of the district. If they value math then they will ensure, not assume, the teachers know what they are doing. I also know that some states don't require public school teachers to have specific teacher training or any certification beyond any  4 year college degree. And I know that in private and charter schools some states have zero mandates of qualifications. I had a few friends from high school who dropped out of college, because they couldn't cut it. who are now teachers in private schools. In my state, public school teachers are required to have a Master's degree to be a certified teacher, but private schools are free to hire anyone they like. Come to think of it, one friend who couldn't maintain a passing GPA, Colleen, went on to be a high school math teacher at our local Catholic high school. And her area of study in college was history. How she ended up a math teacher I never understood.

 

My district has 'master teachers' in both math and ELA. Not every school has a master teacher in those subjects, but they are available to all teachers in the district. I know all elementary teachers alternate with weekly meetings about math and ELA with the master teachers.In those meetings they practice lessons, sharing ideas, try out new things. New teachers are mentored and monitored in math and ELA by the master teachers. When the district switched over to SM,a couple years ago, a couple master math teaches were taken out of the classroom and worked full time to mentor and train and help with the transition.

 

[maize]

There is a big difference between thinking someone is an idiot and thinking that someone is innumerate and has been graduated and is responsible for the education of other people's children while still being innumerate.

 

Someone who can't do the elementary school math they're supposed to be teaching is pretty innumerate, just as someone who can't read elementary school-level books is pretty illiterate. I'd have been just as shocked at finding an elementary school teacher or a large group of them who were surprised at someone able to read ... oh, let's say Harry Potter #1.

This exactly. If you read Liping Ma's book, her research demonstrated horrifically deficient conceptual understanding of mathematics among elementary school teachers. That does not mean the teachers are idiots--but it does indicate a serious problem in the selection and training of teachers.

[ErinE]

There is a big difference between thinking someone is an idiot and thinking that someone is innumerate and has been graduated and is responsible for the education of other people's children while still being innumerate.

 

Someone who can't do the elementary school math they're supposed to be teaching is pretty innumerate, just as someone who can't read elementary school-level books is pretty illiterate. I'd have been just as shocked at finding an elementary school teacher or a large group of them who were surprised at someone able to read ... oh, let's say Harry Potter #1.

Agreed. This was my point. My eldest was having trouble with the idea of inverse operations and reciprocals. So I asked this teacher for additional approaches. The teacher did not know either term. After I explained, the advice was, "In the classroom, the students would keep practicing until they 'got' it." This person teaches at a school rated 10 on Great Schools and is certified to specialize in teaching math. The teacher is not an idiot, just not the level of math instructor I'd like for my kids. In my view, a certified elementary math teacher would have many ways to teach basic math concepts, beyond rote practice.

 

I've read numerous threads on this board describing different ways to teach elementary math. When I'm looking to improve my math teaching skills, I'm not looking for brilliance, just experience.

[kiana]

I've read numerous threads on this board describing different ways to teach elementary math. When I'm looking to improve my math teaching skills, I'm not looking for brilliance, just experience.

 

And the biggest difference I noted in Liping Ma's book was the search for continual improvement in knowledge, understanding, and teaching methods.

 

We (in the US) tend to have have the erroneous idea that having taken a course in something, and possibly even gotten an "A" in it, we know everything about it.

[Erin]

In thinking back to my math methods classes, I'm not sure how it could be that {elementary} teachers still aren't being prepared for teaching math in the classroom.  :confused1:

For every new skill, we learned at least two or three different ways to teach it (multiplication is a number of sets of things, multiplication is repeated addition, etc.)

Trap used to tease me about the manipulatives I had to buy for math methods or doing origami, basically, for discovering area of different shapes.  All we did in class was learn to play with new toys.   ;)

[kiana]

In thinking back to my math methods classes (three of them that I can recall), I'm not sure how it could be that {elementary} teachers still aren't being prepared for teaching math in the classroom.

For every new skill, we learned at least two or three different ways to teach it (multiplication is a number of sets of things, multiplication is repeated addition, etc.)

 

There are a number of reasons.

 

1) Some states require more or fewer math methods classes. Some require as few as one semester, which really isn't enough to get someone up to speed if they're far behind.

 

2) Some were competent when they learned it, but promptly forgot.

2b) Some really loathe math and simply learned to fake it long enough to pass the class.

 

3) Some were trained in outdated methodology.

 

4) Some are seriously resistive to trying new methods simply because it wasn't how they learned.

 

Some of these are obviously easier to address than others. It's pretty difficult to measure continuing competency unless you start randomly testing all your teachers every couple of years.

 

Upon reading your updated post, clearly you were a great student and probably a pleasure to have in class. I have friends who teach that class who repeatedly hear things like "Whyyyyy do I hafta learn fraaactions when I just want to teach Kindergaaaarten" -- some of them fail, some fall into 2b) above, and some get convinced.

[Erin]

I don't think I was anything special, really.  Most of us got a kick out of methods classes.  

And there was a common complaint of, "Why wasn't I taught this way in school??"  (This was 20 years ago, btw)

 

ETA:  I will agree that there was always a battalion who were completely resistant.  Interestingly though, they were usually older (aka non-traditional) students.  

 

Something I've found in the years since, though, it's not the teachers who are the problem.  It's the parents and administrators.  

I've always done a lot of activities like estimating the length of the playground and then measuring it.  Or calculating the circumference of the merry go round, then measuring it with a rope to see how close we can get.  ...Playing with paper projects for area and volume.  That sort of thing.  Stuff that doesn't necessarily produce something tangible
But parents want to see worksheets.  I can't even guess how many times I've heard "But how will I know how little Johnny is doing??"   :001_rolleyes:  Consequently, when parents are complaining about not getting enough worksheets, administrators crack down that we need to be doing more seat work!  It's a painful cycle.  

[kiana]

But parents want to see worksheets.  I can't even guess how many times I've heard "But how will I know how little Johnny is doing??"   :001_rolleyes:  Consequently, when parents are complaining about not getting enough worksheets, administrators crack down that we need to be doing more seat work!  It's a painful cycle.  

 

This is another huge issue. There's definitely a battalion out there of parents who want to see that little Johnny is doing work exactly the same way that they were taught in elementary school. I know a mom who keeps boasting about how they're having the kid do math all these confusing ways and she's making him do the standard algorithm instead. The "confusing ways" are standard early grades Singapore stuff. It's even explained in the worksheets but she is utterly resistant.

 

Also remember -- most teachers are not incompetent, and I don't claim that they are. But like cops, or social workers, or judges, or any other public service worker -- one bad one can outdo the good done by ten good ones.