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A new study shows US students’ advanced math skills trail those of students in most other industrialized nations (the US came in 31st among 56 nations in the study). The same study also measures how each of the 50 states compare to each other. Oregon students actually did fairly well, scoring 8th in the nation.
Oregon’s Department of Education says those results validate its efforts to raise education standards. But when compared to the other 55 countries in the study, the Oregon students were outperformed by 25 countries.
Susanne Smith of Oregon's Department of Education says some parents, as well as educators, fear students won't be able to meet raised standards. Those sentiments partly reveal an aversion to math that is common among adults. Many of us don’t want anything to do with math once we’re out of school and in the working world.
How can we better teach math to kids? Is there still a gender gap in math? Why do so many of us dislike math? Why is it so important?
Can you solve this math "puzzle?" Tune in to hear the solution from our "mathemagician."
If a driver has a 30 mile commute, and it takes 30 minutes to get from home to work, and it takes an hour to get from work to home, then what was the average speed for the trip?
ANSWER: The car drove a total of 60 miles in 90 minutes, which is 60 miles in 1.5 hours, so the average speed is 60/1.5 = 40 miles an hour.
GUESTS
- Sarah Schuhl, math instructional coach at Centennial High School in Portland.
- Dawson Green is a 2004 graduate of Cleveland High School and a part time math tutor to high school students.
- Janet S. Hyde is professor of Psychology and Women's Studies at University of Wisconsin, Madison.
- Rebecca Goldin is associate professor of mathematics at George Mason University and director of research at STATS (Statistical Assessment Service).
- Arthur Benjamin is professor of mathematics at Harvey Mudd College in Claremont, California.
Photo credit: cherrina / Creative Commons
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maybe the lack of math skills has declined since the use of food stamp credit cards took all the math out of paying in food stamps
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The "lack" of math skills has increased, not declined.
Apparently the "lack" of language skills has increased also, an example being your comment.
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TYPICAL>>.attack the messenger>>. rules for radicals
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The reason I suggested learning math earlier and as a language is because of the story of Paul Dirac. His mother was a professor of mathematics and for a reason I don't recall, worries about sickness and disease or something, she kept him out of the schools. So he learned to read at home and the only material in that home was books about mathematics. So he learned math as a language, in the same way that most children learn their own spoken and written language.
Now Paul Dirac might have been born with exceptional mental abilities, but I think his example shows that it is possible to start earlier to learn the language of math and science. Paul Dirac learned Math as a first language while most kids try to learn it as a second language.
Evidently, Dirac was pretty socially inept but he was extremely able mathematically in that he would have a room full of professional mathematicians working on problems and he would walk around to each person and show them what to do about their math problems! And now mathematicians have set up a hierarchy of "Dirac Numbers" similar to the six degrees of separation from the actor Kevin Bacon, in which each mathematician can say with his number how close he/she worked with Dirac.
So let's learn From Paul Dirac about the possibility of earlier childhood education in math.
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Another example of why we ought to teach kids math earlier is the comparison to religion. Parents take their kids to religious services almost from the day they are born, and so the kids are constantly submersed and suffused in the beliefs of religion, growing up in it as a normal part of their lives.
I suggest that we can take a lesson from religion and provide similar experiences for babies and young children but this time in mathematics. My hypothesis that if math is a normal part of life from the day they are born it will tend to be normal in their adult life also. Can you imagine math seminars every Sunday morning, and evening math group meetings every Wednesday and Friday? How about a math Sunday school?
And I would point to the example of musicians; children who grow up in a household of musical parents tend to become well versed in music themselves.
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I might be inclined to agree with your analysis that math is a language, but it's no more or less a language than the jargon involved in banking companies, in cooking, or any of a host of other topics. Adults are able to get involved even at a late age with sports and learn the language and jargon surrounding it without ever having to actually sit down in a classroom to learn "a freethrow is ____, while a tightend does ____".
Certainly, there is an indication that students find the language of Mathematics to be daunting, but they find the entire field to be daunting in general. Is it because of the language? I have taught students without using any mathematical notation. My first proofs in college were actually more essays than the elegant mathematical symbology that defines proper math papers. The reason why I started using the notation is because my wrist started to get tired having to write "For all x, there exist gamma such that cheese plus pizza equals a good dinner." When I got comfortable with what I was writing, I found it was just faster to write "{V x, E y | cheese + pizza = good dinner}"
I think what might feel more natural is to let kids write essays instead of forcing the symbology on them, and then just hand them a reference chart. Believe me, they'll get tired of writing it long form in no time.
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Dawson Green.
I read your reply.
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Tom makes a very good point about musicians, I never met a rapper who didnt know how many grams were in a 8-ball.
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Kids learn to reply on a portable pile of silicon chips to do their adding and subtracting. You've probably seen one -- it will have the name Texas Instruments or Casio on it. Students are even told it is required for some math classes at college, such as for Pre-calculus or Calculus. If we were to BAN calculators from the classroom from Kindergarten through High School, we would be doing kids a big favour -- they would actually have to learn the skills, like we did before the age of coddling childrens' self-esteem.
Also, when they get their first jobs (at McDonald's or WalMart) they tend to rely on the pile of microchips in front of them for knowing how much change to give back to the customer. Why do merchants no longer value the skill of counting back change the old-fashioned way? I think most of us over 30 have seen it -- you make a purchase of $6.38 and pay with a $20 and the clerk counts back the change: "62 cents makes seven, eight, nine, ten, and ten is twenty."
Maybe if we go back to the basics, kids will actually learn to do math on their own again. (I sincerely hope I'm not just dreaming, here.)
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Oops...that should be "Kids learn to rely on a..."
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Back in the 1960s the US tried to bring our measuring system up to date by converting to the metric system, which is the system of science, mathematics, and the economy in most of the world. For some reason that attempt failed. I suggest that our system is a very big speedbump in the way of our kids learning math.
Learning math by adding, subtracting, multiplying, and dividing feet, inches, yards, sixteenths, eighths, miles, gallons, quarts, pints, ounces, pounds, tons and long tonnes, oil barrels versus 50 gallon barrels, and the rest of that ilk, ought to be rendered over to people who are only interested in the esoteric oddities of history.
Building construction uses feet and inches but civil construction, which is roads, parking lots, sidewalks, bridges, and underground utilities, uses feet and tenths and hundredths of feet. So the person in charge of lay out, of measuring and marking on a project, has to have two sets of measuring tapes and surveying stadia rods. That's nuts!
And in the air and on the sea, we have fathoms of depth, nautical miles of distance, knots of speed, and all of that arcane stuff.
Mechanical stuff is coming around, but there used to be multiple measuring systems of bolts, flat to flat or point to point, on the bolt heads, or the actual diameter of the shaft without threads, and length, three different systems, wih names like Whitworth, etc. Metric is just bolt diameter and shaft length.
Kids ought to learn the metric system, which is incredibly easy, and would not turn them off and away from math.
And we ought to totally convert over to metric, that would create new jobs and products, and put people to work teaching how and why metric is better. Our economy would win, our kids would win, and eventually we would all become more efficient with the metric system.
A win-win-win!
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Oh and how about recipes? Tablespoons, leveled tablespoons, rounded tablespoons. Teaspoons, heaping teaspoons. Three teaspoons equal to a tablespoon, where did that come from? One tablespoon equals one sixteenth of a cup.
And Drams? Grains?
http://www.sciencelab.com/data/conversion_calculators/weight.shtml
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ur gonna confuse the dope dealers >>. does mexico use the metric system??
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You know, Vitalpac, if you would actually LISTEN once in a while, you would know that the United States is the ONLY hold-out against conversion to the Metric System. Both of our closest neighbours (Canada and Mexico) have converted, and years ago at that!
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I hated math thru high school... that didn't turn around until my first year at university, all it took was one teacher who made math fun and taught in a simple, practical manner for me to unlock the door to advanced math... math has been a joyful challenge ever since. It was then that I realized that the general problem with math wasn't the student, but the teacher.
Most math teachers I've had (thru calculus in hi-school and ~48 units at university) fell into two broad buckets:
1) They didn't know the material and couldn't explain it for toffee.
2) They knew the material well (maybe too well), but couldn't explain it if their life depended on it... these are the ones who would look at me like I was the village idiot because to them the path to the solution was intuitively obvious.
I've had exactly one who was different and without him my career (and life) would have been fundamentally different.
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I don't dislike math, I dislike the way I was taught math.
Early in my education teachers became frustrated with me when they tried to explain something easy to grasp that I found difficult to comprehend. I sensed their frustration and believed something was wrong with me.
In those days we gave lip service to the idea that individuals have different ways to learn. Education wasn't customized to each students' needs or abilities. Teachers were confronted with the task of getting the majority of 30-35 students through class with a passing grade.
Even though I got through Algebra, Geometry and Trigonometry, I remember two teachers came to my home to discuss their frustrations regarding my math skills with my parents. Teachers saw me put in the effort and participate in class but they didn't understand why I did poorly on tests.
I hated tests because I feared wrong answers and feeling stupid. Wrong answers perpetuated performance anxiety and intensified my vortex of suffering. Teachers said relax but that felt like telling a struggling non-swimmer to relax in the middle of the ocean as shark fins closed in circles of ever-decreasing diameter.
Out of frustration I'd badger teachers, "What the heck am I going to use advanced Algebra for in real life?" If I were going to be a mathmetician or scientist, advanced math would be beneficial, but I don't need polynomials to puree pumpkins.
I took umbrage when teachers said, "Learn this so you can pass the tests and get out of my class." This wasn't teaching, this was akin to moving widgets down an assembly line. Dangerous if the widgets manage to design future bridges and buildings with a barely adequate grasp of fundamental math and science.
The struggle to learn math has been beneficial and destructive. Continuous failure made me steer clear from math and puzzles until I decided to stop fighting and re-convinced myself to learn. Fear of wrong answers had metastacized mole mounds into mountains that had to be bull dozed away with extraordinary effort.
The benefit of pugnacious tenaciousness encourages me to learn math today as I gently shoo away vultures awaiting my fall. Stock investing requires lots of simple math but an even greater understanding of how our psychotic business world lurches off its medications in fascinating and terrible ways.
Math underpins the design and operation of the Universe, it's too bad many of us have suffered unnecessary trauma regarding a science and art that is fundamental, beautiful and amazing when considered in the larger context of comprehension, wisdom and experience.
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I wonder if it would help to search out the best storytellers of math.
I suspect that most people have very little understanding of physics but we have had some very good storytellers of physics like Richard Feynman, Neil DeGrasse Tyson, Brian Greene, Carl Sagan, and a very few others. They were/are able to translate all those arcane and weird sounding theories and equations and symbols into words and stories that the public can understand and relate to.
So I suspect that there are a few mathematicians who are good storytellers and who can translate what seems mathematically opaque to the public into transparent and easily understandable stories.
I have two books on the history of mathematics, and I find it very interesting to read about who developed what, when they did it, and why, and what effect their work has had on all of the rest of us.
So why not find the good storytellers of math and create programs on video of their enthusiasm for whatever parts of math that they particularly like? Tell those histories in ways that are interesting to kids and adults and generate some interest in that way. If you can generate some adult enthusiasm, that will rub off on their kids, and maybe a few more percentage of kids will stick with it.
Like anything, there is a lot of hard work slogging through the parts that are not really exciting in order to get to the part where you are competent and have that base of learning supporting you.
And I would teach kids the "why' of homework and practice, to establish and build neural pathway connections in the brain and reinforce them, like riding the same mountainbike path through a forest until the path is well worn and well known to the rider. Homework is important and I only learned its importance years after I got out of school. I was smart enough to get away with it, but most people are not and even I would have been better off if I had done all of my homework and fully established that foundation base.
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Homework is like basketball practice, or choir or band or football or dance or skateboard or soccer. Kids ought to learn that fact early. Homework is practice for the brain, just like sports practice is for the muscle strengthening and memory. Homework creates strong brains.
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cant make a silk purse out of a sow's ear >.. alot of learning is controlled by genetics
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Mathematics is the universal language. And it is one discipline where there is an absolute correct answer. You cannot message, mollycoddle or whitewash an answer with bs.
And it is probably the fairest comparison for international student achievement. And unfortunately the truth is stark.
In the 2006 International Assessment of Maths Skill of OECD Nations, American students ranked not in the top 5, top 10, top 20 or even top 30 places. It ranked 32nd, just ahead of Turkey and Mexico.
Students aren't used to doing homework. And with video gaming, the Internet and 3D tv, students spend 4-6 hours on media everyday.
It has a real economic cost. I once went to a lumber yard and asked the lumberman to cut a 2x2x 8ft piece of wood into thirds. He handed me three unequal pieces because he could not do the long division, deal with fractions and apply measurements. He offered to lop off the tops, but he wasn't going to do math.
And the Space Telescope Hubble was hobbled because someone neglected to convert some measurements from English to Metric. And Boeing has problems engineering their new 787 airplane and it is more than 4 years overdue. By comparison the North American Mustang fighter was designed and flown in 6 months and the Boeing 747 in 28 months--both designed with sliderules without the use of supercomputers!
We once built rockets to the Moon. Now we are farther away from the Moon than Kennedy was in 1960. We use sophisticated GPS technology for treasure hunts for plastic Pokemons instead of diving to the oceans depths for Spanish dubloons. We use the Internet to Facebook and Tweet 'Wassup' instead of sequencing DNA. And if we had a Saturn V Rocket engine we would probably use it to roast marshmallows. We have great technology like polio and menningitis vaccines, and parents reject it based on old wive's tales.
Our weak math, science and engineering education has lead a great nation into decline.
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Students aren't used to doing homework. And with video gaming, the Internet and 3D tv, students spend 4-6 hours on media everyday. -- jacob — Thu Nov. 18th 5:03p.m.
It doesn't help that they are screwing around with their cellphones in class, tweeting, and updating their fakebook status, and texting their bff's and sexting their boyfriends or girlfriends.
Your encounter at the lumber yard should have been simple...and they should have given you three 32" lengths of 2 x 2. (I didn't even need a piece of scratch paper for that one!)
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Actually you have to subtract the width of the sawcut twice and then divide by three. So each piece will be just under 32 inches by between a thirty-secondth and an eighth depending on the blade width.
And the Japanese thought up the idea of narrow saw blades with carbide teeth and so they cut easier and faster and the lumber manufacturer loses less material to sawdust. Those Japanese blades also make a carpenters work easier in pushing a saw through the wood, making for less problems with carpal tunnel wrist problems. A money saver all around.
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Point taken, Tom...but if I could figure it out in my head, then surely a lumber sales person should be able to figure it out with a pencil and paper (or scrap wood), if available, or a calculator if necessary.
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You are right Penny, about it being 3 pieces 32" long, and I would think that a retailer would put a knowledgeable person on the cut saw, because cutting the wrong lengths can get expensive in a hurry.
I was just being carpenter nerdy about the actual final lengths. Most people figure close is good enough.
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2 thoughts. Before being allowed to use a calculator in math class, kids need to know how to do basic math in their heads. Knowing the "times table" we used to learn in grade school is critical to note fearing math and moving on to a higher level.
Secondly, we as parents, grandparents and teachers need to make math fun for children so they can enjoy it and crave more.
Chatting with my 4-year-old grandson while eating lunch, I'll sometimes scribble on a piece of paper and ask him things like, "If 2+3=5, and 2+a=5, how much is "a" worth? He giggles and says "3!" He is so proud when I tell him, "Hey! You can already do algebra!" He loves it.
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Before being allowed to use a calculator in math class, kids need to know how to do basic math in their heads. -- keithinbend — Fri Nov. 19th 10:27a.m.
Agreed! In fact, that was the attitude of one of my junior high school math teachers, Mr. Richardson. He would allow us calculators in class, provided we could show that we knew how to set up the problem and work it with pencil and paper. Calculators back in the day (mid-1970's) were very basic, no one had even heard of a graphing calculator and having a scientific calculator meant you had one with a square root key.
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The Stanford mathematician, Professor Keith Devlin, who often comes on Science Friday and other NPR shows, has said that the problem that most kids have and the point where they give up on math is in algebra when they encounter "variables". So, keithinbend, you're giving your grandson a great running head start and I'd bet that he'll blow right through the variable barrier.
I think other kids could do the same if we used your idea.
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I know that I always look forward to it when I hear Scott Simon say, "and know a visit from Weekend Edition Saturday's Math Guy, Keith Devlin..."
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Back in the '60s when we learned how to use a slide rule at OSU, they taught us how to perform calculations, but maybe more importantly, in my view, they taught us how to check whether our calculations were correct or even in the ballpark. And they had us write out each step of our calculations and they would give us credit for getting the steps correct even if we got the wrong answer.
I think that would be useful for kids and calculators. Things like calculating just the orders of magnitude and comparing that in order to check if your answer ends up in the correct order of magnitude. How many zeros should you have? And keeping constant track of your degrees of accuracy + or -.
Calculators can give you answers that seem accurate to many decimal places for measurements that are only accurate to the precision of your measuring instrument, like an eighth or a sixteenth.
So I think kids ought to learn the processes of math and also to learn how to check their answers through other processes. There can be many ways to an answer and they ought to use them to self check.
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MATH IS JUST TOO HARD AND POINTLESS FOR MOST JOBS! I have 2 degrees and had to suffer through trig and calculus. I had to take calculus 3x before I passed in the class of those “fun” math teachers. (That's why some math and science classes are used as “weed out” classes. Congratulations, these classes finally worked! That's why there are 2-year waiting lists for law and MBA schools.) Later, when I got my job for which I had studied, all the math was done on specialty computer programs, MS Excel templates, or some specialist was in charge of “cranking the numbers” for me. I never used trig nor calculus—only algebra on MS Excel. So, these classes were just so much “fluff” requirements to graduate, but not necessary for actual work. With the costs of education continuing to rise, students can only afford to take the classes they actually need for work, not what academics in ivory towers pontificate and require.
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Thanks for addressing this topic. I'm the Director of Professional Development in Mathematics for an international not-for-profit company. (I formerly taught public school in Wilsonville, OR for 8 years). I travel all over the U.S. (and U.K. and Australia) working with teachers in grades pre-k through 12, helping them to better understand:
a. math content itself
b. how and when children develop mathematical concepts
c. the impact of teacher's pedagogical choices on how children learn math
Rather than focussing the country on a new collection of Common Core Standards, which, by the way, were NOT endorsed by many of the top educational researchers in the country, I would like to see us focus on developing standards for professional educators in the area of mathematics at ALL levels.
Many of the teachers of elementary age students whom I work with feel it is culturally acceptable to excuse themselves as being 'no good at math'. When I ask them if they would find it acceptable to hire a teacher who could only read at the third grade level, they begin to question the 'acceptableness' of their self-imposed labels, and we begin talk about our professional responsibility to work on those areas that we don't feel as confident.
Professor Deborah Lowenberg Ball at the University of Michigan is a leader in the area of identifying all the necessary components an effective teacher of mathematics needs. (Degrees or courses taken in college math are not indicators effective math teaching). The result of our current system of teacher preparation is that many teachers teach math the way they were taught mathematics which, in this country, has generally been a very superficial series of applying algorithms without understanding and memorization.
Mathematics leads to choices. As soon as students in the U.S. enter middle school, their schedule and access to classes is determined by their mathematical proficiency. What they study in Middle school will affect what classes they can take in High School, which in turn will determine their options for higher education. Not all children need to become professional mathematicians, but the should have the choice to choose.
I hope that my work with teachers will translate into students who feel like they have choices about their future, as well as releasing the unlocked potential of many would-be thinkers for our community.
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I'd like more information about what you do and the components that Prof Ball has come up with. Will you direct me to some sources?
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Our mediocre standing in math (and science) is 100% predictable. Looking deeper into the statistics, one finds that if children living in poverty are eliminated from the U.S. data, our standing in mathematics improves dramatically, placing us among the elite nations.
Everybody agrees that children's learning is adversely affected by poverty. As it turns out, the leading nations in math achievement have economic and political systems that are much more effective at mitigating poverty. On the other hand, we have, as a nation, made a conscious decision to tolerate levels of poverty that make predictable our mediocre math education ranking.
It isn't just poverty. In the U.S. we are also uncomfortable with the level of taxation and government responsibility needed to ensure an excellent math education for all. In order to protect the economic freedom to earn and spend money as we see fit, we decline to provide excellent education of other people's children. The result is that poor children often get not excellent education, but "basic" education, with predictable results.
Furthermore, we have maintained a system of textbooks, curriculum, and testing that protects the rights of publishers and evaluation firms to profit from K-12 public schooling; the result is that the tail (efficiency and profit), wags the dog (learning). Mass implementation of excellent math education and assessment is not as profitable as a "basic," drill-and-kill approach with multiple-choice, standardized tests. Our sinking math standing in the world is a predictable result.
We may actually have, or middle class and above children, the best education (and health care) system in the world. But children of poverty often end up in the educational "emergency room," already too sick, receiving "basic care" that often comes too late. The U.S. may never decide to move in the economic and political direction of math-smart nations like Denmark, Finland, and Taiwan; we want our economic freedom. But, as we are told, freedom isn't free; it comes at a cost; in this case the cost of a fully math literate society.
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I agree it's predictable. No amount of failure ever changes things in public schools in the US. The incentives are too perverse to have positive academic outcomes.
Any public outrage for poor performance is followed by an increase in the education monopoly. Education is a very profitable monopoly who's customers are supplied by the police power of the state. The investment in education only increase when it does poorly. When schools do poorly what else can one expect but cries and calls for more funding - for the children. It's inevitable that the monopoly will expand demanding more and more tax dollars and the outcomes will not improve or continue to deteriorate.
Below are links to two PISA studies for 2003 and 2006 showing pretty much the same mediocre scores for the US.
http://nces.ed.gov/surveys/pisa/pisa2003highlights_2.asp In 2003:U.S. performance in mathematics literacy and problem solving was lower than the average performance for most OECD countries (table 2 and table 3).
2006: On average, U.S. students scored lower than the OECD average on the mathematics literacy scale (474 vs. 498). http://nces.ed.gov/surveys/pisa/pisa2006highlights.aspPossibly solutions?
Less is more: Take a look at Finland. Finland has scored in the number one spot or in the 95th percentile over the last decade. Not just in math but in science and all academic endeavors. What are they doing? Compulsory education does not start until children are 7 years old. The entire Finish school sequence is NOT 12 years. It's only 9 years. Not only are the Fins among the best in world they are doing it more cheaply and in less time. This is not an anomaly. Swedes don't score as high as the Fins but are close. There school sequence is 9 years also. And the children start a age 7 as well.
You'd think Americans would be all over that. Instead we've got an entrenched educational/union bureaucratic complex that's second only in goverment funidng to the Department of Defense. Poor academic means more funding equals job security. Too many people have a financial stake in academic mediocrity for there ever to be real academic improvement.
I'll bet you in 3, 6, 9 years the new study with the same head lines or worse will come out. The money given to solve the education crisis will be even greater. And we can listen to this same show again.
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IT is a fallacy to attribute education failure to simple Poverty and Diversity.
If we exclude the poorest performers, and concentrate on the Elite Math Students, America also lags in particular to much poorer Asian countries. A recent Stanford University study looked at the advanced math students highlighted in The Atlantic Magazine Dec2010.
http://www.theatlantic.com/magazine/archive/2010/10/your-child-left-behind/8310/
The number one country for Elite Advanced Performing Math Students was China(F) with 28%, followed by Hong Kong with 24% and Korea with 23%. Only 6% of Americans are considered advanced in math. We also lag Estonia, Lithuania and Slovakia. And ALL these countries are considerable poorer in per capita GDP compared to America.
More money does NOT lead to better results.
Smaller class sizes do NOT improve learning.
In Taiwan, classes are much larger. Students are self disciplined and want to learn. Students sit in a descending hierarchy reguarding standings. In this meritocracy, every student knows were he sits, and everyone wants to become the best.
We can't increase budgets in a Recession. We have to work Smarter.
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DUMBING DOWN THE LANGUAGE
It's interesting how everyone has "done the math," whether it's adding two plus two or solving a complex equation. The word arithmetic will soon be tossed into the bin of antiquity.
Does using the word math make people think they are more intelligent or is using a shorter word just part of today's truncated lexicon?
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The Solution to Math Defficiency is quite simple but difficult to achieve. It is similar to the problem of Obesity. The solution is simple: EAT LESS and EXERCISE MORE. However we are not inclined to active and painful behaviors.
Like the Romans, We ARE A HEDONIST SOCIETY.
Math skills are problem solving. All children should do more math problems, which means more homework. But homework competes with a lot more fun activities.
The average teen ager text msgs over 100 times a day. If they used a scientific calculator for just 10 times a day plotting a graphing equation, they would be brilliant.
Boys can spend all night playing a new first-person shooter game or car theft game. They actually pull ALL-NIGHTERS--not studying --but rather playing video games nonstop on weekends. If they spent just two hours reading a textbook per night they would be world leaders.
I remember a college math professor who was a bit of a school marm and wet-blanket. Too driven and less social--no talking or texting in class. Classes met three times a week MWF and at each meeting we progressed through one chapter in statistics and had to hand in 10 problems from the last last chapter. It was a a lot of hard work and time. And the pace made it difficult to keep up and easy to fall behind.
BUT we finished the text book, gave me a great grounding in statistics, armed me with quantitative tools, and equipped me with skills that I use everyday, from poker to reading dry journal articles.
How to Gain Math Skills: DO 10 Math Problems a Night....But no one will crack a textbook when you can watch Bristol Palin cut a rug on Dancing with the Stars on Prime Time TV. We are becoming couch-bound obese imbeciles.
Know every wasted hour, will never be regained. And we live in Global Competitive World. And our skills need to be World Class if we are to remain on top.
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It makes a bit of sense that current Americans don’t excel in mathematics, because math is a frugal discipline and Americans are not a frugal people. It is the sort of thing that is mainly creative at the higher, theoretical levels. Yes, much of our world functions on the principles of mathematics, but much of math is esoteric. It can be useful to understand the foundations, the nuts and bolts, but sometimes one just wants to live in the building. As much as I like math, and did fairly well in it, it is essentially a dead end, except for the most brilliant mathematicians. Math is pure elegance, but it is elegant at the most banal level, it lacks the philosophical interests that other fields hold. Math has been glorified for too long. For most people math is not much more than a foundational tool, and the real excitement begins in the things one can do with math, not in the ‘math’ itself. Math is like linguistics---sure, it would be great to know about the science of language, but personally I’d rather spend my time writing 'the book.'
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I am a 41 yo single mom going back to college (my second degree) to get my BSN. I was very nervous to take the required math classes. I have not taken math since 1985 in high school! In my first degree, I avoided math and actually changed my major from psychology to anthropology so that I would NOT have to take a single math class. It was a bragging point for me that I had managed to avoid it for so long.
Now, after 4 quarters of college Math, I actually enjoy it. (but don't tell my facebook friends who are forced to listen to my rants about it!) It's concrete and there are rules to follow and if you do them in the right order, you get rewarded with the correct"answer". In my crazy life, nothing else is so streamline and simple. I sort of NEED this math class as a touchstone. I'll be sad when the quarter is over and I'm on to less concrete classes with out "right" and "wrong" answers!
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I left high school without an understanding of even basic algebra. I ended up in college graduating with a minor in mathematics. Learning about the fascinating history of mathematics in college made me fall in love with the subject. I think teaching math from the foundations of Euclid through Newton in high school would really help encourage students to learn math. I don't remember any teacher in high school mentioning anything about the origins of what they were trying to teach.
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We short change our students by not requiring math classes. Yes it is drill drill drill but so is learning to read and write. As an engineer I have been subject to many poor teachers; people who did not understand math nor did they like it. Most importantly many instructors did not know how to find WHY students were not understanding the math problem or subject.
We also need to change society views that to show that math and logical thinking is valuable. Look how we as a society progressed in during the 60's when we focused on math and science as part of the space program. -
I never considered myself very good at math while growing up. I was taught traditional algorithms and just never understood any of it. The teachers didn't seem to care, as long as I could do them. When I became a teacher, is when I really started to understand math and get excited about it. I taught K/1 and never taught my students 'how' to do a problem, but let them work it out on their own and then explain how they got there. I was always amazed at the different ways students came up with the solution, if I just allowed them to explore on their own. This, I believe, was teaching them not only to understand what they were solving, but also allowing them to figure it out based on what made sense for them. I also made sure I brought in math that was all around us in our world. This lets students know that math is not only important but is a natural part of our world and worth knowing. Your discussions have been great and I am hopeful by what I see and hear happening about math.
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Well, you come up on my screen as one of the best kinds of heroes and heroines to be admired and learned from.
Thank you for your service.
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If a driver has a 30 mile commute, and it takes 30 minutes to get from home to work, and it takes an hour to get from work to home, then what was the average speed for the trip?
My answer: move closer to work, ride your bike, keep the air clean get good exercise and don't be a chump putting thousands of dollars a year into the pockets of Big Oil, and the Automotive Industry. or 45mph.
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I like your answer, Fred....move closer to work and mothball the car, except for semimonthly trips to the grocery and the rare late night trip to the ER when the little ones are screaming from the earache they have as a result of one of the many ear infections that children are subject to.
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Dear Penny. Thanks! I think having kids totally justifies having a car and the reality of our culture makes it difficult to lead a "modern adult life" with out one. It's also really nice to have the option to drive in, like I did this morning, and be warm and listen to OPB - for me, as a treat on a cold and potenially snowy day.
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My son's experience illustrates a problem with math teaching. He's current a PhD candidate in Computational Biology, with a BS in Computer Science. You'd think he'd be pretty good in math, right? Yet when he got to grad school he felt he needed to re-educate himself in math from the ground up, because it was clear to him that he had never really understood much of it.
Thinking back, I remember one Grade 2/3 teacher who was incapable of distinguishing between calculating area and volume, and another who openly admitted to the children that she had never been any good at math and it was okay not to be good at it. She also insisted on teaching "touch math" to 2nd/3rd graders, so they could perform addition by counting dots rather than by simply knowing basic sums.
So whatever we do now is going to be a problem for a long time, because the teachers we have now are products of this same system, and may very well not truly understand math. How do we address that as we go forward?
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I was fortunate at a young age to have an amazing math teacher. He made much of the work very interactive and fun. I believe that this is when I started to love math. This was an honors math program that had a large number of girls in it. Many of us joined the math team and all went on to take high school math classes in junior high.
Like anything, making the learning process fun will help anyone to understand and be interested in the subject matter
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The earlier comment on the air regarding having spreadsheets and specialists to do the math misses the point. Unless that person has the basic understanding to evaluate the results from his resources, or understand the limitations and applications of those results, he's not really doing his job . . . blindly accepting results from a "black box" solution is very dangerous . . . "Trust but verify."
On another note, there have been some studies that suggest that there may be indidvidual differences in the ability to understand and visualize multidimensional concepts, which may lead to a "brick wall" for some at the level of Calculus . . . does your guest have any info on that theory?
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My thoughts exactly - trust but verify - understand context.
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Something that I haven't seen mentioned in the discussion (that I am admittedly late to...) is the condition dyscalculia. The condition is often overlooked and under or misdiagnosed. Often sufferers as labeled as "just bad at math." Dyscalculics often mix up the operations of a math problems, have difficulty with sequence, keeping score in a game, telling time on an analog clock, and counting change. These symptoms can make math and numbers in general very challenging and frustrating. Without assistance people, especially children will shy away from numbers.
I didn't realize that what I was struggling with had a name! Educators need this information.
http://en.wikipedia.org/wiki/Dyscalculia
http://www.dozenlilacs.com/A%20Dozen%20Lilacs%20In%20A%20Shoebox/Dyscalculia.html
Also, my children were educated in a type of home-schooling referred to as "unschooling". This approach to education has no mandatory curriculum, and we approach learning as a way of life and a natural by product of living. My children never had a forced mathmatics lesson, but were instead encouraged to see math as a part of the world. Games, recipes, shopping, art, and etc were all math, and my kids were not faced with the boring dry way math is often taught. The approach can make all the difference!
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An earlier caller indicated that they 'didn't use math' at work although they used excel based formulas and other tools to do their job.
I hope they aren't designing anything important. Using and understanding math is also about understanding the concepts and context of the application.
Just doing the calculations isn't math. Understanding it is.
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Math is critical for every US citizen to be prudent consumers. If the average American were better at math, we would not be in this recession. People entered into ridiculous mortgage contracts, they bought houses they had no business buying and they spent money with no grasp of the interest rate consequences.
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I would guess that there is a good percentage of families who read to or with their children most nights before bed (or at least that is a goal). Think of the impact, the message that is sending to our children- that reading is important. Now how many families do math problems with their children daily? I think another way to convey the importance of math is for children to see its value each and every day. If this importance is conveyed at a young age, this will grow with the child and at some point change how math is perceived.
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What a great idea!
This opens up a huge new market for math writers to write age appropriate books for all ages. Whew! I am overwhelmed with the possibilities; essays, short stories, poems, novels, histories, even fictions with a math thread through them. Childrens math books, etc.
How about the Weekend Edition Sunday Math Puzzle, just like the current word puzzle.
Sherlock Holmes, Agatha Christy, boy could you write up some math mysteries and romances. Ha! How about those bodice ripper romantic novels with beating heart, heaving breasts, mathematicians, whoa!
And math science fiction? Heck, those guys write that all of the time, exploring so many different paths to try and explain physics and even pure math research, all they need is good storytellers to translate the weirdnesses that they imagine and work on, into generally understandable forms.
Geez, you have a great idea!
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I always thought I hated math all through high school and college, even though I was really good at it, because I was an artist and I thought math was pretty much the opposite. I went on to become a professional knitwear designer, using all my art education in my career, but also using math every day! Algebra is a huge part of knit design, and I love it! Writing patterns is like solving math puzzles, which I totally nerd out about. Never would have guessed I'd end up doing math in my career when I was in high school!
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The Most Amazing Math Resource For Teachers and Parents:
www.worldmathday.com
It is an online competition that runs for 48 hours beginning on March 1st.
Kids compete against similar-aged kids around the world.
I have never seen my students more captivated by math...they'll be begging to stay up late to work on it!
-Scott Rodman
Tillamook, OR
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Good idea but it requires FlashPlayer, the very evil, computer memory, and resource hogging, program that is responsible for overloading, hanging, and crashing computers all over the world.
No thanks.
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I'm glad that caller brought up Danica "Winnie" McKellar, I couldn't remember her name or I would have posted about her too, she is an inspiration. She has been on Science Friday every time she brings out a new book. She is all about getting girls to learn math but I think boys ought to learn from her too!
Her website is Kissmymath.com, if I recall correctly.
Yes:
http://www.kissmymath.com
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What's the answer to the question posted?
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the answer on the air this morning was 40 mph. I was in correct at stating the average speed was 45. I did that in my head. Maybe i should dust off my "statistics for dummies" and do a refresher.
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This discussion on math in school reminded me of this instance in my past. I'm 76 years old. So past, is very past.
Back in grade school i had this teacher who was good at english & math. and the way he thought us how to do word problems was through these little rhymes:
" Object of prep, out of sight in the sky, divide by the top, then multiply."
Problem: Sixty is what percent of five thousand?
" No percent given, you'll sure lose you rep, unless you divide by the object of the prep. "
Problem: Six is equal to what percent of ninety?
This tool has helped me over the years not only remember basic ways to solve math problems, but also remember some basic english grammar. I passed these little reminders onto my kids, both of which are in college, one who happens to be a pre-med student, the other who is going for an english teaching degree.
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Our public schools have, in the last 10 years or so, worked to increase literacy by implementing reading programs for both accelerated and struggling readers. There is plenty of time and energy spent every day in classrooms encouraging reading and writing.
I would love to see this same effort put into mathematical literacy. An important aspect of understanding math, from my experinece, is understanding that it is a language.
I am a TA for a physics class at WSU Vancouver. I am regularly surprised at how difficult it is for students to translate physical phenomena into mathematical expressions. I have also noticed a distinct lack of the ability for students to follow a simple derivation.
I think that increasing mathematical literacy would strengthen students' ability to understand simple proofs and derivations which are a huge part of science and math texts at the college level.
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OK I know the people on the show know this:
It is all Calculus!!!!Geomotry, area, slope of curves (trig) are all calculus you just remember the short cut 4/3*Pi*r^3 not understanding that that is an integral of the area of a circle.
Stats and probability: Calculus, You just forget that you are finding the area under that probability to give you your chance.
Physics, engineering, all the sciences: D=V*T integrates to D=V0T+.5at^2 to allow you to calulate speed. Electronics L R C is the perfect model for a diff eq.
Finance: A= Pe^(rt) (continuous compunding interest) Is a diff eq. of course the banks would rather compund interest you owe this way and interest they owe at a rate less than this as it makes them money.
Distince = Rate x time
integrate:
d=Vi *t + .5*a*t^2
(Distance with acceleration)
Force = Mass x Acceleration
but what if the mass is alrady traveling at 200 miles an hour does it not add to the force? Well we have forgot that this too is a diff eq and a more complete formula is (looking a lot like distance):
F= Ma + .5Mv^2
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I wonder if kids would do better if they were always taught that they were doing calculus and just progressing fom the simplest questions towards the more difficult. Take the fear of calculus out of their way by getting them to own it.
If every kid is already doing calculus from early on, would they do better when they study it specifically?
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I really liked what Dawson Green said about his ten weeks of learning math by going back through history and deriving the equations while learning the who and why of the equations. I think that is great.
That's the storytelling that I think is essential.
It's kind of like putting all of the muscles, hair, skin, blood, brain, and nerves back onto the bones of the skeleton. It puts it in context.
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I thought the Professor Benjamin’s suggestion to aim math more towards statistics was absolutely brilliant, and I couldn’t agree more. I am a woman who was always found math quite easy and a little bit interesting as a game, but beyond that rather pointless. My life experience has born that out: in the 38 years since I graduated from college, calculus been completely irrelevant. I almost never need to use anything more than a little simple algebra and some geometry.
More grounding in statistics, though, would have been very useful. I had several teachers whose eyes would light up when they began to talk about statistics, how powerful it is and how frequently misunderstood and misrepresented. But they only had time to give us a taste of it before getting on with the rest of the curriculum; it was always an extracurricular side topic.
Finally I took a course in it, unfortunately presented in such a dry, rote manner that I promptly forgot it all. I regret that each time I want to follow up on some news story by looking into the original research, which is so easily available now on the internet. So often what is reported in the media is quite a distortion of the real results of a study, and the study itself may or may not be a good one.
By the way, I generally avoid using calculators unless I have a lot of repetitive calculating to do. Even simple arithmetic skills can be forgotten if you never use them. But if you use them even occasionally, they are always there for you, and problems like the one Benjamin presented are easy.
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As I said on the show, there's a nuance to Dr. Benjamin's point that was of concern to me and that I think should be looked at more closely. My reaction to Dr. Benjamin was a rejection of the idea that either calculus or statistics can just be claimed to be "better" than each other. What is key to understanding professional mathematics is that regardless of the field you specialize in, be it Number Theory, Statistics or Matrix Algebra, no one cares what you know in the field if you can't actually prove what you're saying. And like in other fields of study or hobbies in life, it's being able to prove things that matters more than just being able to say you can do it or you have a trick for that particular problem. The reason is because the trick is unique, the skill is not.
I suspect there have been many skills you have developed in life since graduating from college. How did you develop those skills? When did you actually feel like the skill had "developed" and wasn't just something you were doing? In going through your career, did you shine when you could just recite some factoid or when you could make a passionate plea with a listener or client about the value of a product or a method of problem solving?
In Mathematics, this art is the Defense of Proof, and it's what separates the good mathematicians from the ones who merely hold degrees in it. When a mathematician is done talking about a subject, there shouldn't be any questions left to ask. No extra scenarios, no possibilities that are waiting to be discovered... adding "QED" after a result on a math paper is like putting "The End" when you finish a book: nothing else happens next, the story is over, move on.
But defending an idea isn't unique to mathematics... it's something everyone does for all of the hobbies and jobs they hold. If you need to learn this art by studying statistics because you have a natural ability to defend your ideas in there, that's great! But the same techniques you use to prove yourself right in statistics is the technique you use to derive the correct solutions in all other fields of Mathematics and beyond.
That's why I stressed analysis. That's the crux of the problem. That's where I was weak and what I finally had to learn at that 11th hour. And once I did... everything else was finally able to fall into place.
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Technically the answer is that there at two separate trips and each has its own average. Words matter.
Now if you ask for the average time for the "round trip", that is something else and you have to specify that the time does not include the time spent at work. Because 30 minutes going, plus one hour returning, plus eight hours at work, plus lunch and break times which are government requirements, makes for a very slow roundtrip.
I suspect that what the Professor meant was what was the average speed for the combination of the trip to work and the trip returning home from work, excluding all other times.
Words matter.
Wow! I must have been seen by teachers as really obnoxious in school for nerdiness like that, I won a lot of arguments correcting teachers and I hope that they have forgiven me.
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It bothered me that a Professor from California thought it natural to use a "30 mile commute". That so plays into my despise and predjuce that Californians are more self-centered than Oregonians and think nothing of using up resources. It could easily be re-worded:
Fred has a 8 mile bike commute, and in the morning, it takes him 30 minutes, and in the evenings it takes him an hour, what's his average speed? The answer is 18 mph, and he stops for half an hour on the way home to have a beer with the money he saves on gas and car maintainance. Now that's the upside of math, knowing that you save enough by biking to have a regular beer.
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Excellent point, FredPDX.
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I just want to make clear that my comment about "storytellers" was not about "story problems", it was about people with the knowledge about math and its history who can make it come alive in peoples minds and excite kids.
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I've wondered if it is because we don't learn it early like we do regular language. Like maybe we ought to learn it as a language, which in some ways it is.
Mathematicians have created special symbols and language to simplify their equations, to make them "elegant" and I wonder if we ought to reverse that trend for the very early ages and use the full english language descriptions of what is being done.
"2+2=4" is not the same as the words "two plus two equals four".
Or look at the equation "2+2=", a teacher would use words more like "what does two plus two equal?" Kids learn those question symbols, words, and vocal inflections very early and so I would use that early learning and write "2=2=?" placing the question mark where it belongs and so connecting math and word language early on.
And in order to start them on variables, I would add a letter right after the question mark, "2+2=?a", "3=3=?b", and so on. And the next lesson would reuse those letters, "4+4=?a", "5+5=?b", so that they learn that the letters a and b are variable answers. Then later at some appropriate time, start dropping the question mark and just leave the a and b variables.
I'd be lost without math and the accompanying logic and reasoning and so I'd like for kids to get a better start on it from the earliest possible time. They can learn those weird, somewhat arcane, math words and symbols later on when they are more comfortable in their math skins. Integrals, derivatives, and all the rest.