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Rebroadcast: Math Appeal
Warning! Spoiler alert! If you check out the original show post for this program on the appeal — or lack of appeal — of math, you'll find out the answer to this question:
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?
Can you solve this math puzzle? On this program we'll get the solution from a "mathemagician." And we'll explore how we can 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?
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: Emily Greenseth / Creative Commons
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"...what was the average speed for the trip?"
There were two trips, one to work and one back home from work, so which average do you want?
Words matter. ;)
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Tom, there were really three trips (one to work, one home, and then the overall "trip" (total commute). I suspect it's the total commute in question. Given that problem (the other two averages are just too easy), I would say that the average speed was 40 mph: miles = 30 X 2 = 60; hours = 0.5 + 1 = 1.5. So, 60 miles / 1.5 hour = 40 mph, the overall average.
But you are certainly right that words matter in defining "the" problem!
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and if we ask about "velocity" the question becomes entirely different...
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And relative to what?
There is a speed limit sign posted in the ISS that reads "Speed Limit 17,500 mph." I love that every time I see it.
It reminds me that we are all moving at fantastic speeds relative to other objects in the universe.
So that commute is appropriately relative to the speed of the earth spin depending on which direction it takes. Or relative to the sun or the galaxy, on and on.
We usually assume context in math story problems without considering other affecting factors.
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Data on US' student test scores is utterly misleading if the following is not included: private school students in the US do not have to take state tests. When the news media doesn't include this caveat in their reports on student achievement levels, the public is receiving information about American students that is deeply inaccurate.
My strong professional opinion is that private school students would pass these tests in greater numbers than public school students. So presenting public school test results as "National" figures is untruthful and therefore unacceptable to an honest debate. One has to wonder why the public is hit with wave after wave of "Low American Test Scores!" stories in the mass media (not referring to NPR here) -- and why these stories do not remind Americans that millions of our students are not in public school and thus are not reflected in achievement data. Is it perhaps a familiar Alarm Button that brings in media consumers?
Private school students have family accountability and in-school resources that public schools do not have. Public schools are not given the resources to complete the task they are given. Let's please not pretend that they are provided the manpower necessary for the task. Private school teachers are asked to move students from one grade level of skill to the next. Public school teachers are ostensibly being asked to move students 3, 4, or 5 grade levels in one school year. All with less resources than private school teachers.
So yes, private school students would pass more tests. But they do not have to take them. (Perhaps because education research shows that high-stakes testing does not improve student learning? But that's another show.) US achievement data would be much less alarming if private school students were included in the results. Failing to include this in the national debate is deeply irresponsible on the part of the US media.
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"One has to wonder why the public is hit with wave after wave of "Low American Test Scores!" stories in the mass media ..."
Because Conservatives believe that public schools are Socialism and they want to get rid of them. And along with that they want to destroy Unions and especially Teachers.
So they attack public schools and teachers whenever and however they can.
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"Why do so many dislike math?" Lots of factors enter into this simple-looking question, but when I taught college math for a while, I learned four parts to the answer--one "R" and three "T"s: (1) poor explanation of math's relevance; (2) poor teacher(s); (3) poor texts; and (4) lack of tutoring.
The first three I learned from an excellent math textbook we used at the university where I taught part-time; the fourth I learned from my wife. She had to take college algebra three times in order to pass it, and she said the difference the third time was having a good tutor.
The relevance of math to the "real world" is greater than most folks might realize, and it's not hard to demonstrate if done well. In the algebra textbook my university used when I taught math, each new major section tied in the upcoming material with real problems people might want to solve or a dab of historical significance. This made the material come alive. We also assigned real-world work for the students, who were mostly working adults. They each had to bring in a story of how they had used, or seen applied, some aspect of algebra in their real world--usually from work, but it sometimes was from home.
With a proper focus on the above four factors, we can turn around the trend that spawned the not-so-old joke about today's kids: "Sixty percent of school students don't understand math; the other two thirds just don't care."
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Mathematics is the universal language. And it is one discipline where there is an absolute correct answer. You cannot massage, 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. I guess we are benefiting from cross border immigration in other ways as our education systems converge.
Students aren't used to doing homework. And with video gaming, the Internet, Facebook, Tweeting, Texting, digital music, and 3D TV, students spend 4-6 hours on media everyday. There is no time for learning.
Here is a simple solution that will never be implemented. Math, Engineering and Science are problem-solving based. Every night, students do 10 problems and work out their solution on paper. Then they can have their gadgets, txting and media. I guess to some this sounds like human rights abuse. Just call it the old-fashioned way that lead to great American achievements such as the Apollo Moon Landing.
Our weak math, science and engineering education has lead a great nation into decline.
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"Our weak math, science and engineering education has lead a great nation into decline."
Yep, thirty some years of decline into Conservatism is showing up in math and other scores.
It is shameful.
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I taught math fundamentals to high schoolers this summer. Too many of them come to us with the inability to multiply and divide. Teachers tend to give in to the calculators at the high school level because they feel the pressure to have them understand algebra before they graduate. What are your opinions about giving into the calculators before kids can do basic math functions?
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Please consider that the study of math is a complete waste of time for many of us. I have a Ph.D. in German Literature and wish I had been able to devote more time in high school and college to learning subjects that really interested me and would have been useful in my future profession as a teacher. Instead, I was required to study algebra and trig and hated every second of this drudgery.
Unless a student is clearly heading for a vocation or profession requiring math, I believe one should not have to learn more than addition, subtraction, multiplication, division and fractions.
Sata
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I totally agree!
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So you believe in creating a world of uninformed consumers of financial products? That seems to be what has happened with the latest generation and their view on debt.
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Sata
What an ironic comment.
The Germans used to be the world standard in math, science, and engineering and people had to learn German in order to learn those subjects.
That was still true back in the late 1960s.
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Sorry to hear that you consider math study a "complete waste of time," but if you are open minded, you can learn some good ideas from the posts of several others here.
Learning math is a way of learning critical thinking--which is essential for life in any field. Try voting without being able to assess ballot measures; try shopping without understanding how to analyze the misleading hype that high-paid marketing types throw at us every day.
You won't get a good understanding of analysis from studying just addition, subtraction, multiplication, division, and fractions. Besides, these are the most boring aspects of numerical operations! Once you get beyond those fundamentals, you will (if you have a good teacher, a good text, and if necessary a good tutor) find yourself enjoying the study of solving problems. Consider teaching yourself from a good textbook if you don't like math teachers. Just don't give up on yourself or the value of a good education in critical thinking.
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I had my moments of struggle with math. For me it is all about the teachers. Once in college I enjoyed math until Calculus. It made no sense and the teacher was less than helpful when approached.
Now that I am a mother to a girl we are very careful about what we say about math. I don't want her to have that preconcieved notion that math is hard. I want her to think of math problems as puzzles waiting to be solved.
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"I want her to think of math problems as puzzles waiting to be solved."
I think you are right. Nobody likes to have "problems" but most people love mysteries and puzzles, just look at how popular Jeopardy is and all of the other puzzle, game, and mystery shows.
Math teachers ought to reframe the words describing math like you have.
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Most of the math I had to take for my schooling, from public school to college has been intriguing, challenging, and even fun -- UNTIL I GOT TO CALCULUS! (MTH241, MTH242) Then it was just annoying and damn near unintelligible -- I gotta confess, I really do not know when, as an accountant or bookkeeper, I will EVER use Calculus! Algebra, maybe, but Calculus?!?!?
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I love story problems, the problem here is in defining the terms. For example to me a "commute" would include both directions of travel.
As such the answer to me is 20 miles per hour (average speed for the entire commute), however without properly defining the variables (such as the term commute) these problems are androgenous.
I absolutely love math and I find that the problem with people not caring about math is partially caused by teachers not properly developing real world situations and story problems to make a student think how Math can be useful.
I love story problems and enjoy finding ways to use mathn in real world situations, however many people are frustrated with story problems and have a hard time understanding the real world value of math.
I had great teachers and parents who always were asking me to use math in real world situations rather than with arithmatic problems.
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So when he stated it on the radio he changed the terms and definitions. This is indicative of how important that math teachers know language, just as language students must know math.
Unfortunately when math teachers aren't good at english their story problems are confusing and make students angry and frustrated with mathematics.
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"I love story problems, the problem here is in defining the terms. For example to me a "commute" would include both directions of travel."
I agree.
There an old engineer slogan that "When you define the problem, you define the solution". One of the hardest things to do is figure out the right question to ask. And that is the main task in story problems, where words can be obfuscating and confusing, like the Car Talk guys do with their Puzzlers.
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Something that is almost always left out of these math conversations is Dyscalculia. Schools, parents, and students need information on this. http://www.dyscalculia.org/
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40 mph is the answer to your math question
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I use math on a daily basis, though it's not always done with pencil and paper. My degree is in civil engineering and I work with a company that develops high voltage power lines. Without my strong foundations in simple algebra and geometry, I could never understand the static and dymanic elements of my job. I actually just used simple addition to check an employee's work. I get much more stimulation when i do hand calculations than let, say, Excel or AutoCad software do it for me.
Terry, 25, Portland, OR
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As a child of an immigrant and a laborer, one of which spoke very little English I could not expect help from my parents. I myself put myself through University and studied Geology but it was a struggle.
If this is the case for others, how, by whom and at what juncture in an educational experience can be help all different types of learners earn competencies in Math?
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Perhaps the true utility of mathematics lies beyond how often one uses it on the job. Studying math you find difficult - whether it's arithmetic, calculus or multivariable partial differential equations- develops systematic and organized patterns of thought which are useful in all areas of life requiring critical thinking.
Understanding at least some abstract mathematical concepts is also a part of being a well-rounded, educated person. There's a difference between education and job training.
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I am an advocate of teaching applied mathematics as opposed to pure math at early educational stages. What we really want to achieve is a population capable of higher reasoning and advanced problem solving skills than we currently have. Math is essential to the understanding of physics, biology, computer software, computer technology, music, economics, business, etc. and can be taught, thoroughly, through these subjects. Math is better learned and appreciated when taught as a tool used in reasoning processes related to the subjects that interest the student the most. Course work structured to teach the student the beauty of deeper understanding leads directly to a deeper appreciation of mathematics and a more creative, confident and contributive individual.
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Thanks for letting me comment. Excellent topic and guests!
It's not just about math. The question is, do we really want a well-educated thinking population? Other nations do and there is no mystery about how to accomplish this goal. Instead, we continue to treat the issue as if it's a conundrum to be endlessly discussed and debated. Process is no substitute for the commitment of shared resources, family support, value development, and all the other things that we know are necessary to accomplish something important as a society. No amount of good intentions and great ideas are going to make much difference.
The formula for improving math scores, and the quality of education generally, is simple: 1) we must learn to value and respect educators (view them as authority figures, pay them more, and expect more from them as professionals), 2) we must reverse the trend toward anti-intellectualism and learn to revere knowledge and intellect for its own sake, and 3) we must provide the social safety net required to make children physically and mentally prepared to learn. Without these, any plan to improve education in this country succumb to continued dithering and mediocrity. Could we do what it takes?
Maybe. There are many good examples from our nations past. I think back to the way we taught our people to stop littering and become environmentally aware in the 1970s. It took the combined effort of schools, the mass media, government, individuals and families. It took a willingness to stand up to vested business and political interests and a willingness to make a change within ourselves. Unfortunately, we may no longer have the requisite sense of unity as a people and a national consciousness anymore.
The one bright spot is our education system itself. Over the last 30 years, educators have done a marvelous job making improvements considering the paltry amount of moral and financial support we give them. The quality of my children's public education is much higher than the one I received. The problem is not the educators. We have an education system ready for the task. It's up to the rest of us to change our values and commitment, to give it life, and let it give us the knowledge and intellectual freedom everyone deserves.
Badspellar
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I appreciate your remarks, pkollas, but do not agree that a grasp of mathematics in any way enhances critical thinking. Have taught a good number of literature classes over the past 20 years; in very few instances have my math, chemisty and physics majors excelled in truly discerning thinking, and a good number of them have seemed very poorly equipped for grasping abstracts.
With regard to math assisting us in practical areas of our lives - most of us can probably call upon tech friends to figure out this sort of stuff whenever the rare instances (at least, in my life) calling for such skills arise.
Sata
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Sata,
How much math did you take, and what types? You mentioned algebra and trig in your earlier comment. If you indeed struggled with algebra, it was probably not taught well, unfortunately, leaving you with not only a bad taste in your mouth for math but also a lack of understanding of what good math courses can do for one's analytical ability. I should note that this analytical ability doesn't necessarily appear overnight after one completes a single math course; it builds over time.
Your math, physics, & chem majors may not have gotten to that point in their development either, especially if they were early in their school programs or were themselves struggling with the coursework.
Belive it or not, I had trouble with math, too, in college; a lot of it was a struggle. But I didn't lose sight of what it offered, and now I'm glad I kept an open mind about the subject. It is useful probably every day, in things both mighty and mundane.
One of the jobs I interviewed for (and got) required that I prove the ability to perform math operations with nothing more than a pencil and paper--yes, including longhand division, which I'd not done in decades!--and I was really glad I didn't just say, "Why should I do this; when would I need it on the job?" But the employer wanted to be sure I could do calculations even if no calculator or computer (or tech friends) were available--which could have happened, as a lot of the work was on airborne aircraft. This was in the days before laptops were common.
My point is, you never know when you might wish you had math in your hip pocket. And even when you don't think you need it, you could use it to understand things better, like medical studies that get splashed onto the news with little analysis by the media.
And no, I'm not a uni-dimensional math geek, in case you wondered. I've also taught business communications (including international comm.), medical topics, and more, and I ran an editing business for well over a decade. Studied and practiced law, too. I've never considered anything I ever learned to be a waste of time; everything builds on everything else . . . including math.
Cheers,
P
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Comments are now closed.
It’s a fast, competitive world. The more skills your child has at using their brain to mentally address and solve problems, the more successful they will be. Very few ‘school’ subjects are geared toward teaching children to use their whole brain to solve problems, particularly in mathematics. With the advent of technology, children have become overly dependent on calculators to solve even basic math problems. That over-dependency denies them the opportunity to learn how to handle mental math calculations, as well as fostering the ability to focus on a problem and enhance their concentration skills, thus the fear of Math.
My daughter has learnt the skill of Japanese Abacus and Anzan (mental math) from a local Japanese Abacus Math School in Bethany Village, Portland,OR she has excelled not only in math but has transfered these skills to other subjects, her teacher Sensei Miwako teaches life long skills, its worth the investment I have made in my child who will carry this onward and pass it on to her children.