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Mathematics As the Most Misunderstood Subject
Lilith's Heart-shape writes "Dr. Robert H. Lewis, professor of mathematics at Fordham University of New York, offers in this essay a defense of mathematics as a liberal arts discipline, and not merely part of a STEM (science, technology, engineering, mathematics) curriculum. In the process, he discusses what's wrong with the manner in which mathematics is currently taught in K-12 schooling."
Basic math is easy enough for nobody to have an excuse for not knowing it.
No sig today...
This is exactly the kind of thinking that has got us into the mess we're into now.
Learning math is just as difficult as learning any other subject or content material. Deciphering poetry, learning programming, studying psychological theory, and learning calculus all involve concentration, study, and struggle from the learner. No one is born knowing any of those things, therefore they all must be learned. The entire point of the OP is to say that the way we go about teaching math is wrong and that people need to reconceptualize how they teach the information because it doesn't make sense to the learner. In the end, its all difficult to some degree. It's when you have that "A-Ha!" moment, it clicks, and you get it. But if you have some terrible algebra teacher who doesn't understand advanced math or someone who doesn't care that you learn, only that you can complete problems 1-50 in a mechanic fashion, then of course it's going to seem difficult (or more difficult than it should be).
Carl Sagan quotes get you an automatic +5 on all posts.
Well, we would likely all be malnourished, due to lack of fertilizers, at least those of us who hadn't died at childbirth or soon after. There wouldn't be an Internet to talk on, but that would be okay, since we wouldn't have time to use one due to the lack of engines and the resulting need to do backbreaking labour 16 hours a day. In short, our lives would be miserable, but due to lack of medicine, they would at least be short.
Missing these kinds of little details is why I have very little respect of philosophers. As far as I can tell, most of them chose their field because it doesn't punish sloppy work. And then there's idiocy like the Chinese Room, which assumes that a system cannot have properties its components don't have, yet hasn't been laughed out like it should had been.
Philosophy means you accept the human condition. Technorcacy means you try to do something about it. Hope for a better world in the future lies on the latter, not the former.
Forget magic. Any technology distinguishable from divine power is insufficiently advanced.
The way math is taught in schools is atrocious. Most math texts that I've used with 5th and 6th graders emphasize learning processes and methods for solving a set of problems. The texts do not hold all of the blame, however. The texts are written to follow state and national standards. The standards are written in such a way to emphasize process and not necessarily apprehension of greater concepts. For example:
5th Grade Level Expectation 1. Differentiate between the term factor and multiple, and prime and composite (N-1-M)
While these vocabulary items are important and these skills are definitely useful, learning this skill in isolation (which most texts teach) is pretty useless as students do not connect these skills to a greater picture.
A revision of mathematics standards and teaching methods will go a long way to improving the quality of mathematics education. A holistic approach that includes some wrote learning of basic skills and lots of real application problems. Real application problems are not word problems. How many "real" word problems have you had to solve in the last ten years?
Some texts such as Every Day Math from the University of Chicago does a much better job at integrating all sorts of skills and teaching in a much more holistic method. It includes some excellent modeling exercises, games that rely on a real understanding of mathematical principals for mastery and interesting lessons. But even the best text can't help a kid if they don't have a good teacher that really understands mathematics. Watching an uniformed teacher try to explain what a prime number is, or a different method for division (such as repeated subtraction) is painful. They simply can't do it. Unfortunately, in my experience most of the teaching candidates that were in my classes thought that math was "hard" and "didn't really matter." They scraped by with the lowest possible scores in the required math classes and one even told me she "wasn't going to bother teaching math." While this is pure anecdotal evidence, the declining math scores in the US show that we really do suck and producing math teachers.
The problem stems from bad math teachers badly teaching math which of course leads to more poorly instructed math teachers. Placing a real emphasis on reading and mathematics, with highly qualified and well-supported specialists is the only way we're going to solve this problem. Unless we have some real political will akin to that found during the space race, we're not going to solve this problem any time soon. We'll just keep cranking out kids that think that math is done by computers and a few nerds that wave their magic math wand over problems to find solutions.
This one's tricky. You have to use imaginary numbers, like eleventeen... --Hobbes
While agriculture requires backbreaking labour, hunter-gatherer societies only worked a couple of days a week. Not that I advocate a return to it, but backbreaking labour all the livelong day was not universal in ancient society.
Philosophical journals have the same rigorous standards for papers as journals for the various sciences. Your view of philosophy is about as valid as a grizzled mountain man who mutters about hard science being all book-learnin' and mumbo-jumbo.
Even that is a statement of philosophy. Furthermore, you seem unaware that many calls for improving human lives came from works of philosophy: More's Utopia, Kirkegaard's questions of metaethics, even what is often called the beginning of the Western tradition, when Socrates hung out in the agora and asked passersby "What if what you comfortably believe is wrong?"
Why are people even debating philosophy vs technocracy? Why should someone have to choose one over the other? How do people get dragged into such nonsense? Here a new subject for you: tomatoes vs rainbows. Go.
"Meanwhile we have turned the majority of Western humans from independent men into chair-warming consumers singing in lockstep for trinkets."
I suggest you take off your rose coloured glasses and go read some history, in particular just how "free" your average serf was in feudal times and even later. Don't like what your overload or king does? Tough. Complain and you'll probably at best end up homeless or at worst end up swinging from a tree.
People in the west have NEVER been as free as they are now.
So get yourself a fucking clue!
In mathematics it is the truthiness of the statement creates "credit" and then we search back in history to find who said it first and then we give the credit to him/her and that is how reputation/respect is created. It flows back in time. Credibility accrues from the statement to the speaker.
In philosophy a bunch of people agree that some one was/is a great philosopher and so they give more value to a statement from such person. The credibility flows from the speaker to the statement.
sed -e 's/Chuck Norris/Rajnikant/g' joke > fact