Applied math
From a December 2004 article:
U.S. high school students match their peers in other nations when it comes to math skills. But ask them to apply those skills to real-world situations and things begin to look a bit bleak, a new study suggests.
The nation's 15-year-olds make a poor showing on a newly released international test of practical math applications, ranking 24th out of 29 industrialized nations, behind South Korea, Japan and most of Europe. U.S. students' scores were comparable to those in Poland, Hungary and Spain.
. . .
The test goes far beyond the multiple-choice questions many students see on standardized tests these days.
. . .
[Jack Jennings, president of the Center on Education Policy] adds, "Maybe American kids know more math than they did before, but they don't know how to apply it in practical situations."
Or, take this report from early this year:
More than half of students at four-year colleges and at least 75 percent at two-year colleges lack the literacy to handle complex, real-life tasks such as understanding credit card offers, a study found.The literacy study funded by the Pew Charitable Trusts, the first to target the skills of graduating students, finds that students fail to lock in key skills no matter their field of study.
. . .
They cannot interpret a table about exercise and blood pressure, ...compare credit card offers with different interest rates and annual fees, or summarize results of a survey....
. . .
Almost 20 percent of students pursuing four-year degrees had only basic quantitative skills. For example, the students could not estimate if their car had enough gas to get to the service station. About 30 percent of two-year students had only basic math skills.
I've been pondering why so many of us are unable to apply math in everyday life. Is the problem that we introduce concepts too early, before we can really "get" the techniques involved in solving a problem? (Take carrying and borrowing: if you really understand the ones, tens, and hundreds places, these are obvious tricks to use. If you don't have a gut-level grasp, these are just cookbook rules one must memorize.)
Is it that "kill and drill" ignores the conceptual and demands rote memorization in its place? Is it that "story problems" are those last few items in the homework assignment, almost like extra credit, rather than the meat and potatoes of math? Is it that we teach a superficial overview of too many concepts in math, instead of taking techniques one at a time, examining each one in depth in a dozen different contexts?
And furthermore, why is "math phobia" a widely recognized phenomena? I haven't heard anyone say they had "reading phobia" or "science phobia" or "history phobia." Yet a sizeable proportion of Americans experience an impenetrable brain fog when confronted with math.
I don't have a theory to put forth here, really, to explain why learning mathematics is so fraught. But I've been pondering it, and thought I'd post about it. Anyone have any ideas?
posted by Production Is Wealth | 3:06 PM
4 Comments:
Let's say that a child isn't ready for certain math skills or concepts, but she has to sit through the same math class as her peers, some of who DO understand, day after day. She feels like a failure, unable to comprehend. To top it off, math is a class in which there is ONE right answer (and usually ONE right way to reach that answer). Now combine these two things. Here you have a person with no confidence in her ability to perform--something that will stay with her even if she improves--and yet she knows she's going to be tested again and again, and every assignment or test will be graded. Fear of a bad grade leads to more anxiety. Anxiety interferes with comprehension and performance, and the vicious circle is established.
It's arguable that any learning area shows this dynamic, but it seems that there is less room for maneuvering in math: less opportunity to explain your thinking, less personal flexibility, fewer ways to compensate for a weakness in one aspect by excelling at another and so evening out one's grade, and above all, only one right answer. I think it's really easy for a child to simply assume that "math is hard" because that child is fulfilling the prophecy/expectation she's all too aware of.
Here's a few random problems that come to mind:
1. We don't explain the difference between math and arithmetic. I personally am glad that I know how to multiply large numbers by hand, but I can't begrudge anybody finding it boring - it is after all, a mechanistic and boring process. By not explaining that arithmetic is not the same as math, we teach people that math is a boring, mechanistic process -- and by extension, that people who enjoy math are coldly logical and are not creative. This last lesson has permeated so deeply that one symptom of "Autism Spectrum Disorder" (at least according to pop-health mags) is "finds numbers interesting / enjoys math".
2. "Story problems" are crap. I'm referring not to the idea, but to the implementation. Q: If Joe the handy-man can fix three windows in an hour, how many windows can he fix in 4.5 hours? A: No one gives a crap! Kids are plenty curious about the world, but "story problems" are hardly concrete - they don't relate to the world that kids actually live in. How about asking interesting questions - like "how fast can I go on my bike", or "how many words are there in all the books in the school library?" or "how fast does the space shuttle go?".
3. The example questions lead to my final point: Teach math in context. I don't think I had any science courses that really put any of my math in context until the 11th grade, in chemistry. That's way too late to establish that math is relevant to the real world. And math doesn't have to be taught in science only - the front page of the new york times probably provides a full day's worth of math discussion every single day.
Another anxiety-producing factor with math is that speed is considered of the essence. Some teachers want students to be able to complete 30 simple arithmetic problems in 60 seconds, as if "math facts" should be so strongly emblazoned in one's memory that one can parrot them like an automaton. Although speed is a goal with reading, it is not tested in this high pressure fashion. I would imagine that speed will be more and more emphasized due to the advantage it gives you on a standardized test.
You know, kids would see the utility of math if they were doing things like mapping the playground, building a birdhouse, planting rows of seeds, buying and selling things (and making change), doing science at an earlier age, conducting short surveys and summarizing the results, etc.
In short, if they were pursuing real life instead of learning "the basics" without any context whatsoever. If you want to know how to use a wrench or a screwdriver you seek out a project which requires their use; what students do is analogous to reading about wrenches and screwdrivers instead of using them.
I read some standardized math test questions recently that made the most pointless attempts at being concrete or real world... stuff like "Beatrice bought a cookie for 42 cents. Which set of coins equals 42 cents?" As if throwing "Beatrice" and "cookie" in there makes it somehow more real or interesting.
I was also surprised at questions like "Which of these equations might Henry use to solve this problem?" So you don't actually get the answer, you just find the equation you would use to get the answer... talk about boring!
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