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firefly124I doubt anybody wants to listen to this, so it's all going under a cut. But when I woke up for work tonight and checked my Twitter feed, there was this Washington Post editorial about the state of math education in the US. I actually agree with some of his points. A lot of textbooks have gone in bizarro and unhelpful directions trying to stir up math interest in students and in the process have completely missed the point. Unfortunately, so has the person who wrote that editorial. Among other things, so far as I can tell, no we didn't "survive the new math of the 60s," in the sense of it being a fad that came and went, we just now call it plain old "math."
It's true. Nobody needs to be able to calculate the rate at which one's martini's volume is depleting in the glass as it's being sipped, and even attempting to do so suggests that anyone would ever sip or gulp it in a pattern that could be captured as a differentiable function, which, er, no. Problems like this are why I spend an inordinate amount of time having to explain to those of my tutees who actually have critical thinking skills why they are being asked to do such asinine problems. Honestly, by the time they're taking calculus, they're either motivated enough to handle word problems that are a tad less patronizing or else it's time for them to pack up their abacus and pick another specialty.
The real issues, though, are much further down the chain. The author of that editorial says that most of us can get by with the math we learned in grade school. Considering the number of tutees I've seen at both four-year universities and now two-year community colleges who have to take pre-algebra and can barely add, subtract, multiply, and divide, I'd have to say no. Basic math skills of the sort that one needs in order to function in society without being continually ripped off or at least taken for a ride are not being taught in a manner that is actually sticking for a large subset of our population.
I used to work in the marketing department for a publishing company that specialized in math textbooks. Their entire line was predicated on heavy calculator use to let students focus on the critical thinking aspects of problems. I still think that's an entirely valid approach, but only after you've already established strong basic skills. The problem is, the educational system has run with it without making sure that foundation is there first, or so I keep hearing. Not having kids of my own, I lack first-hand experience with the state of elementary math ed, but I hear it continually second-hand, and I'm seeing it in my younger tutees. Some of whom are early childhood and elementary ed students! I'm not sure that's actually scarier than when I see it in pre-nursing students, but on a societal level, it's a bigger problem.
(That said, if I never have to remind another pre-nursing or nursing student that yes, it is possible to be stuck having to calculate your drug dosage or iv drip rate without benefit of calculators, it'll be entirely too soon. Here in New England, we get these things called blizzards and ice storms that can take out a big chunk of the electrical grid. Head for warmer climes, and it's hurricanes or tornadoes. Pacific Rim? Earthquakes. Every place has some sort of natural disaster potential that can take out your precious technology. Yes, hospitals have generators, but those can go down too.Especially when the local alien hunters commandeer the MRI to kill some virus in the phone system and incidentally take out all the local electronics. I do not want to end up someday the only person in the whole damned hospital calculating everybody's drip rates for the duration of a week-long power outage because nobody knows how to handle basic multiplication and division on their own and all their calculator and phone batteries have died after a day or two! Besides which, if you have no math sense, then you won't realize that you've just punched up a fatal dosage of heparin because you mis-keyed a decimal someplace. You should recognize that the result staring at you looks like no dose you've ever administered in your life, but if you're truly as number-phobic as some of my tutees and peers, maybe not. *shudder*)
Now, this is where I actually agree with the editorial writer again. If your career path is early childhood or elementary ed, or even nursing or social work, there is no sane reason to put you through some of the crap they are currently cramming into "intermediate algebra." Why the hell is there suddenly this massive unit on logarithms and exponential functions? Yes, the nursing students will need some passing familiarity with them to deal with bacterial colony growth in micro, but frankly, that's it. I'm less bothered by introducing trig at this level, though even that, I think, could be better left for pre-calculus in favor of focusing on problem-solving.
Because that, or so I was taught back in the days of dinosaurs, is the reason intermediate algebra is required of everybody who gets a college education. Algebra teaches strategies for applying critical thinking to problem-solving, and everybody needs that. Hell, everybody needs that whether they have a college education or not, but at a minimum, we should be making sure people who get to stick alphabet soup after their names have it. Except instead, we're making them jump through hoops of how to make numbers dance on a page without any real understanding of why they're doing it. In some cases, there are still profs leaving word problems out of their homework and exams entirely so they can cram this shit in, which defeats the entire purpose of the fucking class and leaves their students woefully underprepared for, well, just about everything.
Now, math is only one way to accomplish this. That's why there's often an option to take logic through a philosophy department-supplied course as a way to fulfill one's math requirement. Preferring to dance with numbers, I never went that route, so I can't comment on how effective that really is. Theoretically, it should be actually even better at teaching critical thinking because it's taken any math-phobia out of the, erm, equation.
What I think is going on at the intermediate algebra level is trying to better prepare students for pre-calculus. There is a really problematic gap in college-offered basic math tracks, in that if you didn't take geometry in high school, you won't get it in college. Therefore, students who have to start out with the more basic math courses and actually want to go into the hard sciences are often at a fairly serious disadvantage when they make the jump from intermediate algebra to pre-calculus. That is, I agree, a problem that needs solving. Considering the tiny proportion of intermediate algebra students going in that direction, though, I don't think cramming more into that class is the answer. How about, oh, I dunno, offering geometry at the college level? Teach proof construction! Teach all the funtastic angle equivalencies! Because for all the crap they're cramming into intermediate algebra, there's still no place to get all that at the college level. And considering how many people aren't getting it in high school, either because they weren't "tracked" for college prep or whatever, there really needs to be.
Because in this increasingly technological world, we need to be better preparing people to potentially go into the sciences, or to at least have a firm grasp of all the science they interact with every day. But that doesn't come from eschewing the basics and making people completely dependent on their calculators so that we can cram the upper-level stuff into lower and lower level classes. It comes from making sure the basics are solid enough that people actually feel that going further in math is an attainable possibility, whether it's something they choose to do or not. And this is where the bit about the early childhood and elementary ed teacher prep comes in. I'm seeing the pattern continue of scaring the crap out of these students who are going to be teaching young children, so that these future teachers are just crossing their fingers to get through their math requirement that they may never need to touch it again. These are the people who will then communicate their own math phobia to the next generation, not to mention have such weak skills that they may mis-teach some of the basic concepts and/or turn math into this sort of quasi-magical thing that no one should expect to really understand, and voila, the cycle continues. And for that, I do have first-hand knowledge, because I ran into it with my own elementary school teachers, and dude, that was 30+ years ago. This is a problem that should've been fixed by now but clearly hasn't.
So, after all that, I guess my point is that yes, there is a huge problem in math education in this country. Yes, some of it is the patronizing dumbing-down of concept applications and some of it is the cramming of advanced concepts and operations into what should be basic courses. But not because "there's no need to love math," but rather because there should be no need to fear it. If we would actually give people a solid foundation in their basic skills, then spend algebra focusing on true problem-solving techniques instead of over-emphasizing "how to make numbers and letters dance on a page" ad nauseam, we might actually make some progress in math and science education. Because seriously, those of us who are destined to be math geeks will go off on our own and have fun with making numbers dance on a page, seeking out or even creating bizarro setups to play with laws of exponents and rules of logs, because it really can be fun if that's your thing. But there's no reason to torture people with it who don't have any reason to care, especially at the expense of teaching the actual core concepts and how they apply to the real world.
Speaking of the real world, now that I've got this rant out of my system, I suppose I should get to work.
It's true. Nobody needs to be able to calculate the rate at which one's martini's volume is depleting in the glass as it's being sipped, and even attempting to do so suggests that anyone would ever sip or gulp it in a pattern that could be captured as a differentiable function, which, er, no. Problems like this are why I spend an inordinate amount of time having to explain to those of my tutees who actually have critical thinking skills why they are being asked to do such asinine problems. Honestly, by the time they're taking calculus, they're either motivated enough to handle word problems that are a tad less patronizing or else it's time for them to pack up their abacus and pick another specialty.
The real issues, though, are much further down the chain. The author of that editorial says that most of us can get by with the math we learned in grade school. Considering the number of tutees I've seen at both four-year universities and now two-year community colleges who have to take pre-algebra and can barely add, subtract, multiply, and divide, I'd have to say no. Basic math skills of the sort that one needs in order to function in society without being continually ripped off or at least taken for a ride are not being taught in a manner that is actually sticking for a large subset of our population.
I used to work in the marketing department for a publishing company that specialized in math textbooks. Their entire line was predicated on heavy calculator use to let students focus on the critical thinking aspects of problems. I still think that's an entirely valid approach, but only after you've already established strong basic skills. The problem is, the educational system has run with it without making sure that foundation is there first, or so I keep hearing. Not having kids of my own, I lack first-hand experience with the state of elementary math ed, but I hear it continually second-hand, and I'm seeing it in my younger tutees. Some of whom are early childhood and elementary ed students! I'm not sure that's actually scarier than when I see it in pre-nursing students, but on a societal level, it's a bigger problem.
(That said, if I never have to remind another pre-nursing or nursing student that yes, it is possible to be stuck having to calculate your drug dosage or iv drip rate without benefit of calculators, it'll be entirely too soon. Here in New England, we get these things called blizzards and ice storms that can take out a big chunk of the electrical grid. Head for warmer climes, and it's hurricanes or tornadoes. Pacific Rim? Earthquakes. Every place has some sort of natural disaster potential that can take out your precious technology. Yes, hospitals have generators, but those can go down too.
Now, this is where I actually agree with the editorial writer again. If your career path is early childhood or elementary ed, or even nursing or social work, there is no sane reason to put you through some of the crap they are currently cramming into "intermediate algebra." Why the hell is there suddenly this massive unit on logarithms and exponential functions? Yes, the nursing students will need some passing familiarity with them to deal with bacterial colony growth in micro, but frankly, that's it. I'm less bothered by introducing trig at this level, though even that, I think, could be better left for pre-calculus in favor of focusing on problem-solving.
Because that, or so I was taught back in the days of dinosaurs, is the reason intermediate algebra is required of everybody who gets a college education. Algebra teaches strategies for applying critical thinking to problem-solving, and everybody needs that. Hell, everybody needs that whether they have a college education or not, but at a minimum, we should be making sure people who get to stick alphabet soup after their names have it. Except instead, we're making them jump through hoops of how to make numbers dance on a page without any real understanding of why they're doing it. In some cases, there are still profs leaving word problems out of their homework and exams entirely so they can cram this shit in, which defeats the entire purpose of the fucking class and leaves their students woefully underprepared for, well, just about everything.
Now, math is only one way to accomplish this. That's why there's often an option to take logic through a philosophy department-supplied course as a way to fulfill one's math requirement. Preferring to dance with numbers, I never went that route, so I can't comment on how effective that really is. Theoretically, it should be actually even better at teaching critical thinking because it's taken any math-phobia out of the, erm, equation.
What I think is going on at the intermediate algebra level is trying to better prepare students for pre-calculus. There is a really problematic gap in college-offered basic math tracks, in that if you didn't take geometry in high school, you won't get it in college. Therefore, students who have to start out with the more basic math courses and actually want to go into the hard sciences are often at a fairly serious disadvantage when they make the jump from intermediate algebra to pre-calculus. That is, I agree, a problem that needs solving. Considering the tiny proportion of intermediate algebra students going in that direction, though, I don't think cramming more into that class is the answer. How about, oh, I dunno, offering geometry at the college level? Teach proof construction! Teach all the funtastic angle equivalencies! Because for all the crap they're cramming into intermediate algebra, there's still no place to get all that at the college level. And considering how many people aren't getting it in high school, either because they weren't "tracked" for college prep or whatever, there really needs to be.
Because in this increasingly technological world, we need to be better preparing people to potentially go into the sciences, or to at least have a firm grasp of all the science they interact with every day. But that doesn't come from eschewing the basics and making people completely dependent on their calculators so that we can cram the upper-level stuff into lower and lower level classes. It comes from making sure the basics are solid enough that people actually feel that going further in math is an attainable possibility, whether it's something they choose to do or not. And this is where the bit about the early childhood and elementary ed teacher prep comes in. I'm seeing the pattern continue of scaring the crap out of these students who are going to be teaching young children, so that these future teachers are just crossing their fingers to get through their math requirement that they may never need to touch it again. These are the people who will then communicate their own math phobia to the next generation, not to mention have such weak skills that they may mis-teach some of the basic concepts and/or turn math into this sort of quasi-magical thing that no one should expect to really understand, and voila, the cycle continues. And for that, I do have first-hand knowledge, because I ran into it with my own elementary school teachers, and dude, that was 30+ years ago. This is a problem that should've been fixed by now but clearly hasn't.
So, after all that, I guess my point is that yes, there is a huge problem in math education in this country. Yes, some of it is the patronizing dumbing-down of concept applications and some of it is the cramming of advanced concepts and operations into what should be basic courses. But not because "there's no need to love math," but rather because there should be no need to fear it. If we would actually give people a solid foundation in their basic skills, then spend algebra focusing on true problem-solving techniques instead of over-emphasizing "how to make numbers and letters dance on a page" ad nauseam, we might actually make some progress in math and science education. Because seriously, those of us who are destined to be math geeks will go off on our own and have fun with making numbers dance on a page, seeking out or even creating bizarro setups to play with laws of exponents and rules of logs, because it really can be fun if that's your thing. But there's no reason to torture people with it who don't have any reason to care, especially at the expense of teaching the actual core concepts and how they apply to the real world.
Speaking of the real world, now that I've got this rant out of my system, I suppose I should get to work.
