This has been the summer of our numerical discontent.
As a nation, we've been riveted by the debates over the debt-ceiling crisis, the credit downgrade, the dizzying ascents and descents of the stock market. But how many people actually understand the numbers they're watching?
It's not just how many zeroes in a trillion that's so hard for us to track. My own day-to-day observations confirm that many Americans can barely make change. At the supermarket where I buy groceries, I've watched more than one encounter at the cash register where both customer and clerk are befuddled at the prospect of double-checking the sums.
"Is this is the right change?'' a customer will say, looking at the coins in her hand.
"I don't know,'' the clerk answers. "It's what the machine says.''
I'm an astrophysicist and a professor, so my day job involves manipulating intractable numbers that characterize our universe. This renders me a dinner party curiosity item. "That must involve a lot of hard math,'' the guest next to me admits cheerfully. "I can't even balance my checkbook!''
The numbers back up this distressing lack of numerical dexterity.
According to the International Center for Education Statistics, in 2009, the average U.S. mathematics literacy score for 15 -year-old students fell below the average score of students in more than 30 developed countries, including the United Kingdom, Germany, France and Korea, to name a few.
Earlier this year, the United States hosted the first-ever International Summit on Teaching, gathering instructors, union leaders and education ministers from 25 countries to a meeting in New York. One of the striking results from this meeting: our math education doesn't come close to the way students are trained in countries where math scores are higher.
In countries that lead math education rankings, schoolteachers are not judged only on the basis of their students' test scores, but rather on their success at developing well-rounded, high-performing students. In addition, teacher pay is higher.
There is a correlation between math education and the innovation needed to create jobs and spark an economy. Just look at the fact that the United States is outranked both in math education rankings and in the Global Innovation Index by countries such as Singapore, Finland, Korea and Japan.
Our numbers, in other words, simply aren't adding up.
We are failing to teach our children the fundamentals of mathematics and quantitative reasoning skills. These skills form the foundation upon which future technical education is based. Children do not attain adequate proficiency, develop math phobia and as a result we lose a vast talent pool of potential engineers and scientists. Most of the high-paying jobs of the future will require mathematical fluency -- a skill that most American students leaving school do not come close to possessing.
So how do we fix this math problem? We need more creative government and private sector partnerships to support numerical literacy programs to keep the US competitive. Earlier this year, Intel, for example, made a 10-year, $200 million commitment to promote math and science education. Many non-profits are active in this arena -- one is Math for America that helps recruit talented young people into teaching mathematics in schools.
In addition to a well-funded school system, we need to encourage and exploit innovative approaches for learning outside the classroom. An example is the Khan Academy. Starting with a set of YouTube math video tutorials for his cousins, Sal Khan has developed a library of 2,400 instructional videos, each 12 minutes long on a range of topics. After every math lesson that focuses on a conceptual theme, students can assess their progress while working at their own pace.
One of the nagging problems with math in schools is that the weaker students never catch up. Self-paced learning outside the classroom offers a unique way forward. Sal's videos offer concepts in bite-sized chunks and the ability to return to these videos repetitively ensures that students learn difficult mathematical ideas effectively. These new learning methodologies could augment and transform math education, and ensure that no child is truly left behind.
Finally, it's time to return to old-fashioned rote learning. My work now involves complicated and abstract math, but I started where everyone can: with the multiplication tables. Here are two truths: 7 x 5 = 35 and developing dexterity with mental arithmetic leads to comfort with quantitative reasoning.
We also need to pay math teachers more and create incentives, like a bonus system modeled on how Wall Street compensates its highly productive cadre.
As Congress battles over spending and cost cutting, it is imperative that funding for math education programs does not fall victim. Our future rests on fixing math education now.
David Mumford and Sol Garfunkel: Bottom Line on Mathematics Education
In my view, this is incorrect. My wife and I, as our kids parents, are responsible for our children's educations. We delegate this work to the schools and teachers, but the responsibility is ours. You can delegate authority. You can't delegate responsibility.
Thus we check and monitor what they are being taught. If we detect what we take to be gaps, we fill them in. The kids already know that there are two standards; ours and the schools'. They have to meet both, and I give homework. We review his assignments as well. At times we have told him to improve his writing. His reply that it is acceptable to his teacher does not matter. It was not acceptable to us.
I had my son reviewing pre-algebra material over the summer because I knew he would be starting algebra this year. He is in 6th grade taking 7th grade math. Did he like it? NO! Did he do it? Enough.
My wife is a linguist. I am a physicist/engineer/scientist. So I handle the math and science topics. I expect them do do their best. If they have done so, I have no criticism. I will help them work on their weaknesses. But slacking and sloppy work is not acceptable.
Only a fraction of American students are in school this summer. The ostensible reason is that all these children are helping their parents harvest corn and herd cattle to the rail head. Since this hasn't been true for almost a century it might be time to consider increasing the number of days in the American school year to match those of more advanced countries.
Most of our children spend the summer in front of their TV, computer or video game. Actually, they spend most of their free time all year there. Has anyone missed the flash of insight provided by this fact?
In school they sit in rows of desks facing a blackboard while a fairly boring middle aged adult lectures them. This has about the same appeal as a root canal. If Intel wants to throw money at the problem, they could pay for some of their young, hip employees to monitor classes where kids played math-themed video games or watched historically accurate movies--designed by those same young, hip employees.
I would put the progress of the "entertained" students up against traditionally schooled kids any day of the week. A kid who is engrossed in trying to score points against the other members of his class in an on-line math game is not going to be hurling spitwads--or profanity--at the teacher.
Those children who are a problem need to be placed in special classes where their individual needs can be addressed. This may involve a certain amount of @sswhooping. It certainly won't involve letting them drop out to become a drain on the community exchequer.
Rather than traditional classwork during the summer, we need to organize programs for the lower class kids that they will enjoy, but also use some of the skills learned in the classroom. Fill their summer with field trips, crafts and hobbies instead of reruns on TV.
Step 2. See step 1
It doesn't hurt reciting the rudiments of maths at random times. It's quite easy to ask, "What is the square root of 25?", and other such things on the drive to school, ballet, sports, etc.
The issue is not that students are not learning computations, it's that they are rarely learning these computations in useful contexts. The "fake" textbook word problems that are presented to students are an attempt to develop some sense of context for students, but most of these fail to address the cultural and socio-economic differences in students.
Keith Devlin talks about this issue in, "The Math Instinct", which is part of the required reading for all who are interested in math education reform. Further, I would add "A Mathematician's Lament" by Paul Lockhart and " The Four Pillars Upon Which the Failure of Math Education Rest" by Matthew A. Brenner (see http://www.k12math.org/doclib/4pillars.pdf).
Another useful video to watch (created by Gord Hamilton of http://www.mathpickle.com) has another perspective on this issue. Watch it here: http://www.youtube.com/watch?v=3sN3dEVeMb8
As for the utility of the Khan Academy videos, see Derek Muller's video where he demolishes the notion that kids learn effectively from standard video lectures: http://www.youtube.com/watch?v=eVtCO84MDj8
The issue in math education is complicated. We don't live in a world where memorizing everything (note: memorizing some things is still useful) is necessary. We don't need to carry rote memorization in our heads as much, so long as we understand how and why we can access the information.
Modern mathematics is taught from the bottom up universally, and it shouldn't be. To the language oriented like me that approach is ineffective. Had someone ever just explained to me what algebra was instead of simply attempting to get me to memorize a set of meaningless numbers in new ways, I might not have driven myself and a succession of elementary and high school teachers crazy.
http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers.html
So, yes, I have stared dumbly back at customers when they ask if I gave them the correct change and said "Ummm", but it is entirely unrelated to my math SAT score. I'm not denying that there are MANY cashiers who simply can't do the math, but don't be so quick to judge.
Maybe public schools shouldn't be kicking students up to the next grade unless they've earned it and actually know the material? Just a thought. It used to work in the good ol' days, before a students' potentially hurt little feelings became more important than their actual education.