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Discouraging Students from Taking Math
Coryoth writes "Following on from a previous story about UK schools encouraging students to drop mathematics, an article in The Age accuses Australian schools of much the same. The claim is that Australian schools are actively discouraging students from taking upper level math courses to boost their academic results on school league tables. How widespread is this phenomenon? Are schools taking similar measures in the US and Canada?"
This is what you get when schools do what it takes to look good. While they are too blame, the blame also lies on governments and parents who are looking for schools which turn out the most graduates.
Ideally a rating system should be based on the "quality" of those grades. What I mean by this is that the maths levels would be broken down into categories from easy to advanced. A school should be given higher marks if they manage to turn out a few good maths students as opposed to many low level maths students. I am not sure how this could be made to work in reality though.
Jumpstart the tartan drive.
There is little reason for most students to take upper level math. As a historian and a writer, i never EVER use anything more than arithmetic or geometry. Not being able to do calculus has never ones been a problem in my education or work.
In fact, when i was applying for grad schools a year ago, i asked the head of the department that i am in now if my VERY low GRE math score would be a problem. The answer was very clearly "no"
at any rate...American schools need to give kids the option of doing a calculus track in math or a statistics track in math.
Mikey
I've always been the kinda guy to fall for the girl dressed like an eskimo.
That's ridiculous--the moment there's even a shadow of that problem, you weight upper-level classes with a 1.1 or so. The idea is not to punish someone for taking a harder class, after all. (High school math was probably trivial for all of us, but it isn't for everyone.) My high school weighted honors classes at 1.05 when they averaged them into your GPA, and AP classes at 1.10; a similar technique would work here.
Maybe not intentionally. But the way math courses are setup discourages many otherwise capable students from being successful in the subject. My middle school district did a poor job of coordinating math courses with the high school district. As such, I was behind by the time I reached high school and struggled the whole way.
Couple this with the ridiculous "integrated math" fad that plagued countless districts (at least in California). We barely covered trig functions, factoring, and other critical topics. (Anyone else have a thought about integrated math?) High school physical science courses did a poor job of incorporating math.
In college, I changed to a geology major that required calculus courses. Having struggled with math in high school, I had to start from intermediate algebra and work my way up. At least college math curriculums were organized in a logical and relevant fashion. It helped when the professor said, "Yeah, pay attention to this because you might have to derive the formula for centripetal acceleration in a physics course." Connections are important, especially when dealing with abstract math concepts.
My friends had similar experiences and, not wanting to blow a year taking bonehead math like me, decided not to explore their interests in astronomy, physics, chemistry, and other math-intensive subjects. It's a shame, really.
There needs to better curriculum coordination at the middle- and high-school levels so kids understand the importance of math and have a foundation that preps them for college. I understand how easy it is for a student's math foundation to get ruined. Such foundations, at least in my case, take years to build. Oh yeah, and (excessive) testing doesn't help -- but that's a whole other rant! If you want to encourage kids to take math, do a good job of setting up the courses in the first place...and tell them how important it is!
I'm not being facetious at all when I assert this. A normal student in public schools in America will take at least two to three years of algebra, sometimes more, plus a year of trig or geometry. The ones who are interested in such things will take more advanced stuff yet, but those aren't the ones we have to more or less force into math classes anyway.
So we're looking at three to four years of mandatory math classes. For someone not strong in math, isn't that enough?
I am not saying that exposing the students to the classes is a bad idea. But by high school age, it is usually fairly apparent whether or not the student has an aptitude for math or not. If he doesn't, there is no point in making endure a forced march through a bunch of crap he'll never internalize, fully understand, or find any use for. Indeed, the article states precisely that
And why should a student weak in math be encouraged to pursue it? Let him focus whatever talents he has in other areas. I, for example, am hopeless when it comes to math, but was always strong in English and decent at visual arts. I'd have been ecstatic had an administrator said to me, "Your scores are consistently low in math but high in these areas. Would you like to shift your credit focus to reflect the subjects in which you excel?" Hell yeah.
This "one size fits all" approach to education -- the idea that we must churn out "well-rounded" students no matter what an individual student's strengths and weaknesses may be -- is patently idiotic.
mirrorshades radio -- darkwave, industrial, futurepop, ebm.
Absolutely - I think the NCLB should be unceremoniously dropped, the Department of Education abolished, and the money saved used for debt reduction.
Wait - you want to KEEP the money given to states under NCLB? Just not comply with the terms? I understand now.
"As God is my witness, I thought turkeys could fly." A. Carlson
Math still has its place. If you want to go to graduate school in humanities, then you may still need some advanced math. In particular, many students from medicine, political science, humanities, and the arts, do advanced multi-variate statistical studies as part of their post-graduate studies. Understanding the tools used in these advanced statistical studies typically requires first or second year statistics skills. If you want your Master's degree, you need your undergraduate math.
As such, a significant number of undergraduate degrees require "Math for Humanities" or "Statistics for Non-stats Major" courses. It is a good idea to keep math throughout high school. It gives you many more options when you reach university.
Indeed. The NCLB folks need to realize that if you only teach what the least capable students can learn, the class will only be taught what the least capable student can learn.
(IANAL)
If you never learned calculus or any higher maths, how do you know that you would have never used them? Math is used for all kinds of research in history: population extrapolations, statistical correlations, dynamic modeling, hypothesis testing, etc.
You're like a blind person who has found ways to cope with what you're missing, but that doesn't mean that you wouldn't benefit from sight.
That might be true, but why doesn't the "well rounded education" argument ever come up when math and hard science classes are in jeopardy?
There's no shortage of people willing to defend the liberal arts because a well rounded education is so necessary to being a good person, but they're strangely silent when attendence in technical courses is dropping.
If moderation could change anything, it would be illegal.
Teaching people to learn to think is a worthwhile endeavor. Especially in the age of Wikipedia teaching people facts is somewhat useless. I can lookup almost anything I want to know on the Internet, but I can't necessarily interpret what I've read or tell if there's any value to it.
Teaching a vocational education sounds good in theory, but what happens when your job gets moved over to a cheaper country? You have been left with no skills to learn a new trade.
Not to mention the fact that I use a large amount of what I learned in high school. When my wife got pregnant my Biology came in handy, as it does when planting a garden and deciding the best types of plants and where to plant them. I needed my Geometry and calculus to build a non-rectangular deck behind my house. I use English when writing programming documentation and to communicate with other people. I use German and Latin in deciphering words I come across as well as some low-level communication. I use Chemistry in cooking. I use History, Government, and Economics to analyze the world I live in and truly understand the news. I use theater with my theater company. I use musical concepts I learned in band to understand my musician friends. I'll be honest, I haven't really used by health education much, but I think that was probably just because it was covered better in my two years of biology. Frankly, I've found my high school education immensely helpful.
There are people who don't seem to have needed their high school education, but is it the fault of the education that the recipient doesn't want to use it?
When you are being bred to be a bunch of mindless controllable sheep?
A country of dishwashers and burger flippers dont really need an advanced education.
Eventually it will backfire of course, when the country slips into place as a 3rd world nation that cant even support itself. But until then, it keeps the ones in power, in power.
---- Booth was a patriot ----
True education has been replaced by the ersatz education of testing and scoring, which is one big, complex game which has little to do with the true advancement of knowledge.
It helps to think about this in economic terms (by the way, feel free to shoot me down here, I'm not that good with economics). With fewer new schools being built and more students wanting to go to college because it is increasingly a factor in one's success, there is a lot of competition to get into college. One would think that more competition would result in brighter kids in college overall. However, colleges are increasingly complaining that incoming freshmen are not prepared for work at the college level.
However, we do not select freshmen based on factors which will lead them to success in college, such as reasoning, curiosity, or perseverance. We select them mostly based on grades and test scores. The tests test the student's ability to solve brain teasers. They are easily subverted, and there are myriad non-cheating ways to game the system in order to inflate your score. Also, classes are increasingly being taught to the tests, because that's what the parents want.
Therefore, there is increased competition, but due to highly imperfect information on the part of the colleges about which kids will perform best, they make worse choices as to who gets in. Furthermore, because the kids are less prepared, and there's nothing to do about it, they must make the courses more remedial. And then, everyone in the educational system gets stupider.
Screw math, we need a class on general problem solving and trouble shooting. In IT we have to understand *everything* in order to help someone. My CIS teacher told me "The client doesn't know what he wants or needs, you need to find this for him" and the client being the owner/CEO/whatever. "my speakers stopped working" = the *green* plug is plugged into the *blue* port next to the *green* port.. WTF?! This is your average person. How can the speakers stop working if they couldn't have worked in the first place. We need people capable of figuring out stuff on their own and researching. Once we can start getting this down, math will come naturally. The only thing I've learned as IT is "Never underestimate the stupidity of average intelligence." I love working with and helping people... but wow.. it's never ending
NCLB does not divert resources away from teaching. It influences what is taught. If one happens to think the standardized tests actually test what we want students to learn, then this is a good thing. If one happens to think the standardized tests fail to measure what we want students to learn, then it's a bad thing.
In either case, however, the solution is to make sure the tests are measuring the right things. There are a lot of people who feel the tests aren't doing that - so let's fix the tests.
What we should NOT do is abandon the whole premise of measuring progress just because the tests could be better. (I'm not saying you did or did not advocate this. But a lot of anti-NCLB folks do just that). The only real way to know where a school needs improvement, and whether attempts at improvement are actually working, is to get some sort of empirical evidence, which pretty much boils down to testing.
The expected change in ability will roughly follow an S-curve. Those who know very little will need to learn a lot to advance just a little. Those who know a lot must learn a lot more for it to make any difference. Those in the middle have the tools to learn rapidly and will do so.
All you need to do is have a test at the start of the year, extrapolate from prior years the constants needed to define the curve, then use that to determine where the student can be expected to be at the end of the year. The end of year exam is then normalized the same way. Your actual grade would then be equal to ((normalized end of year) - (normalized start of year) + (mid-point score)) * (multiplier needed to stretch/shrink scores over traditional range).
If you do this, any student who works consistently will score consistently. Any student who achieves better than they could have been expected to will always score well, no matter what their abilities are like compared to others of their own age. Likewise, someone who learned a lot once upon a time and is now sleeping through lessons will automatically fail, no matter how good their knowledge.
To make this system fair and easy to apply, you've also got to stream classes. Mixed-ability classes would not work well with a relativistic rating system. Ideally, each subject would be broken into 5 or 7 streams, giving you 2 or 3 subdivisions from neurotypical ability on either side of the bell curve. For large enough schools, I'd expect such a system to use standard deviations from average. With smaller numbers, you'd need to narrow the bands more. You'd also have multiple classes of the same ability, as needed. You need an age-appropriate number of instructors per student in each class, but no class of any age should exceed about 15-18 students.
The multiple classes would allow you to cover different styles and methods of covering the same material, so students who did poorly with one style/method could find one that worked better for them, as learning - not ability - is the part that is truly individual. Ability places demands on learning, but has no direct impact at all.
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
Nah, that's where he works now. See, he's a math genius -- he threw you off the trail. You must have been a math professor at Western Washington University in the early 1960s, because he is clearly smarter than you.
(I, being a math super-genius, followed the link to his homepage and clicked "Resume.")
Stick it to da' man: factor a polynomial!
Funny but also kinda true. Math is a gateway to Critical Thinking or Logic. The kind of accuracy and clarity you get with math isn't something that most modern governments really want to encourage in the populace. Not the math itself, but the kinds of thinking you learn by way of math. It's much easier to sway them with a convincing soundbite than to actually have to have a through and logical understanding of an issue. Factoring a polynomial teaches you break things down into clear components in a much different way than you will get if you are only ever exposed to literature,history,and civics. A well educated thinking man is going to be a politicians toughest constituent.
We are all just people.
When I was doing A-level physics, I discovered just how dumbed-down the course had become. The pre-requisite for the course is only a C at GCSE in maths. It's possible to get a C (the lowest passing grade, below B, A and A*) by taking a simplified paper, which caps your mark at a B (I think; it may be a C). This simplified paper does not include solving quadratic equations. As such, the A-level physics course could not require them. Similarly, it could not rely on any knowledge of calculus (taught in A-level maths). This meant that you were expected to remember a load of equations for motion, rather than just a couple and how to integrate / differentiate the rest. Worse, you would not get all of the marks for showing your working if you used calculus to solve the problems. That was when I stopped regarding the course as worth anything, and gave up doing any work.
I was glad when I got to university to discover that the dumbing down hadn't reached quite that far, but I discovered that universities were having a problem selecting from applicants, because A-level performance was not any kind of indication of ability at degree level.
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Whether this is good or bad depends on if students are being encouraged to drop math altogether, or merely to avoid taking advanced math courses. Let me explain.
/lot/ of calculus classes in my day. There's a consensus growing within the undergraduate math education community -- and very visible at my school -- that calculus is being pushed way, way too hard, at the cost of more important, basic math. In the US, one of the metrics used to evaluate high schools is how many AP exams their students take; it's in the school's advantage to toss kids into advanced classes whether they're ready or not. Kids muddle through a compressed algebra sequence by relying on their calculators, and then get to advanced placement calculus having no idea what they are doing.
I'm a fourth year math PhD student at a school with a top-notch engineering program, so I've taught a
The result is this: In our freshman calculus course for engineers, SEVENTY PERCENT of the students have taken a calculus course before. They are no better prepared -- and often worse off -- than the students who have never seen the material in their life. That senior calculus sequence was a waste of an entire year for most of these students. The problem is that they are taking calc before they are ready -- they have no command of basic algebra skills. Here's a nice example of a mistake we see all the time:
sqrt(a^2 + b^2) = a + b
This is a mistake that a high school sophomore shouldn't be making, much less a college freshman. It's too easy to teach these kids to pass a multiple-choice national calculus test without ensuring that they actually know what's going on, and if calculus is pushed at the expense of algebra skills that's exactly what will happen.
The point is, it's good that weaker students are being discouraged from taking calc. The course is a waste of their time, and it will ultimately hurt them in college. They should instead be taking more basic preparatory classes that will prepare them better.
No, you're not a former Math teacher. You're still a Math teacher, only now you're a math teacher with integrity. That's a former school. You're still a Keeper of the Flame of Knowledge. That building used to be a place where Knowledge was passed on. Now, like me, you're probably making the money you should have made as a teacher doing something else. And, yes, our world is poorer for it.
He put his boots up on the table and made a face. "The sig," he smirked. "You can waste your life in search of the sig."
This isn't about each student's ability to gain admission into college. The schools are doing this because when students get good grades, the school gets recognition and money. If more students take harder classes and therefore get lower grades, the school gets less money and less recognition. Therefore, make everyone take classes they will get A's in and all is good.
Three days from now?? Thats tomorrow!! ~Peter Griffin
Yes, because it makes the difference between watching a movie and saying "by golly, thems some purty pictures" and "oh, that's directly influenced by this classic play, that's neat."
You've got a point on the Monet, though.
You would absolutely love having a background in EE.
It makes the difference between shopping for a CD player and saying, "Oh, so they put fun inside" and "it's still going to be limited by the sensitivity of the DAC, so I don't need to pay extra for the oversampling."
If moderation could change anything, it would be illegal.
"I think they should take the same approach in this situation."
I'm an Aussie with two grown kids and a partner who selects students for a university degree in the state of Victoria. I can attest to the fact that your post describes the way the system works in Australia fairly accurately, the math to determine the final "score" is quite complex and the "score" cannot be determined before all year 12 students in the state have taken the test.
Truth is some people can't do math just like some people can't kick a football or paint a picture. To be able to do the "hard math" in the final year (year 12) the student must do the preparatory "hard math" in the preceding two years, if (as many do) they can't cope with the year 10-11 "hard math" I can understand why teachers suggest a less demanding course. It's the same as a kid who never practiced football but suddenly wants to be picked for the school's senior team, it's simply not going to happen that quickly.
Personally I dropped out of high school at 16 and ended up going to uni at about age 30, however having dropped out of HS I could not just waltz in as a mature age student, I had to do a year 12 math course by correspondence and sit the HS "hard math" test to meet the selection criteria (also it was a good way for the uni to see if I was serious).
A good high school "score" is important when you are young because it gives you an advantage over others entering the workforce/uni. It's basically societies reward for your efforts to complete the "grasshopper" stage. It's not a guide to "intelligence" or "wisdom" any more than a fat wallet is, and it's most definitely not a "make or break" moment that follows you around society for the rest of your life.
And did you exchange a walk on part in the war for a lead role in a cage? - Pink Floyd.
I'd give you +1 insightful moderation points if I had any.
The best teachers we had were those that had the entire syllabus on glossy workcards (glossy to stop them getting all torn and smudged). In that way every student could more or less work at their own speed. If anyone missed or fell behind a lesson for any reason, they could quickly catch up by working at home. The worst teachers were the ones that made everyone work in lock-step from the blackboard - mainly wordy subjects like history.
The best books were the Lett's study guides for A-levels. They had the entire syllabus for every exam board listed on the front pages, along with each module in a separate chapter. Combined with past exam paper questions, anyone who
wished to learn a subject could simply work from home in this way.
Vintage computer adverts: http://www.vintageadbrowser.com/computers-and-software-ads
If you want the state to create you a job move to China.
you hit on something that nobody is teaching stuff to know it and love it, merely to have the mark on their records that they took the class and the school offered it. Mastery of material is not really something taught anymore. It doesn't fit in the neat little 13 week class to learn 500 pages of math concepts. Nothing about how to use them, what you might do with them, or how to pursue the field I have the typical "technical" round of 4-5 semesters of math in college and while I like it, none of it means anything. The really cool stuff is reserved for "math majors" and hobbyists aren't really welcome or encouraged. It's quite dismal really.
This is what happens when a target is allowed to be more important than a purpose; school staff may have to choose between their families' welfare and that of the people they are paid to help.
It's ironic that Mathematics is the subject to suffer, since it was used to create the situation.
In *general* (not in *all* cases but in the majority of them) people tend to do whatever they have been given incentive to do. When you judge the success of a school by how many A's they give to their own students, you have given them just as much incentive to exercise statistical manipulation and practice grade inflation as you have to provide an education.
I believe that the people who test students, and the people who educate students, should be different people. The educators should not be able to rate their own success by giving whatever grades they please to their own students. Instead, the public school should only provide the education. Then, at the end of the year, the students are sent off to take some standardized tests which are graded by people who do not work for the school board, and who focus primarily on objective criteria.
Since the educators will no longer be able to determine the grades, and since the grades will still be used as a determination of the success of the educators, they now have to focus their efforts on the providence of a good education (rather than the grade inflation and what have you).
I think it would help. It would create its own set of problems (schools trying to expel special-needs students rather than help them, for example), so it is not a perfect solution. But I do think it would help.
I haven't read much Shakespeare, but I do recall some good insights here and there. Sallust, Machiavelli, Plutarch, Sun Tzu, and basic courses in the social sciences have been more helpful.
Then you set up a moral hazard. ( http://en.wikipedia.org/wiki/Moral_hazard ). A school would have the incentive to not improve, because improving would mean being punished with their funding being cut.
Fun fun.
The standardized tests also need to vary tremendously from year to year. A major problem with No Child Left Behind is damn near every school district in the US is "teaching to the test" the state administers. If the test format were highly unpredictable from year to year then designing curricula around it would be of little help and the tests might then actually measure something.
"Yay, cancelled!" is in the same catagory as "Well nobody else did it either". People who think that is OK will be happy when they are talking about passing their course, which to them means 'getting a high paying job'.
The same argument could be made against honors math classes.
When I was an MIT freshman, many, many moons ago, the European students were from the elite. They had tons more calculus than the Americans. This was a big advantage -- for about half a semester. By the end of freshman year, there was no difference in mathematical skills between European and American students.
In the end what matters is the ability to reason mathematically, not having a checkmark on your transcript, or a high grade on a test.
Here's a story I often tell. In one of my jobs after school, I was the company geek. People came to me when they needed their newfangled digital watches set (this dates me pretty well). I once had a guy come to me with a problem: he had a friend who made penny whistles, and that friend knew the correct length to make a B flat whistle, and he had a formula that, given a properly sized whistle, yielded the correct length for a whistle a half note higher. But he wanted to make an A whistle, and couldn't figure out how to do it. He went to his friend, who went to me.
After rearranging the formula, I calculated the correct length, and then plugged it back in to the original formula to show it was right. I then asked this guy whether he had taken Algebra in high school. He said he had, and he had done well in it. In fact, he was perfectly capable of doing the operations I did, but it didn't even occur to him to use anything he'd learned. He actually seemed surprised that I had found a practical application for Algebra..
So -- I don't think it matters that much. A lot of people graduate with what I call a "cargo cult" math education: they can go through the motions, but they don't know what it all means. I'd rather have people entering college with strong math reasoning skills and solid math through algebra and trigonometry, than entering with the ability to manipulate symbols in a Calculus-y sort of way without grasping the significance of what they are doing.
There's nothing intrinsically wrong with testing, as there is nothing intrinsically wrong with honors math courses. The problem with testing is how much harder it is to create a good test than a hard test, and how few people realize the distinction between the two. Tests that are inordinately hard generate a flurry of action; they make things happen. Unfortunately, it's pure luck whether those things are really useful things. A good test tells you things you really need to know. It is neither so hard that most people fail it, nor so easy that everybody passes. Difficulty is the least important aspect of a test; you simply calibrate the difficulty to yield the most information. Difficulty is almost not a policy issue at all, or shouldn't be. The test difficulty is simply calibrated to yield the highest entropy in score distribution. It is the nature of the challenge that is critical. Does it really require the student to engage in mathematical thought, as opposed to procedure?
A retreat from offering advanced math courses is not necessarily good, or bad. If you are doing less advanced math, the question is what are you doing in its place. If you are concentrating on bringing your school's pass rate up, it is a sign that the tests you are teaching to are (a) too difficult and (b) bad.
Here in the States, we have a law called "no child left behind", which is basically a "states rights" version of ed reform. States are free to create their own tests, so everything depends on what state you're in. I've looked at some of the questions in my state, and I actually think the questions are pretty good. Much of the emphasis is in converting problems into mathematical representation -- precisely what my post-Sputnik generation needed most. As a result, my children got intensive practice in reasoning with mathematics from the first grade. As soon as t
Post may contain irony: discontinue use if experiencing mood swings, nausea or elevated blood pressure.
For all those pushing some form of privatization, I'd like to add the following force for market discipline within the public school system.
*) Empower teachers to hire/fire their own administrators.
The natural unit of teaching in lower grades is the classroom, not the school and certainly not a district. The administration is just there to support this process. Give the teachers a budget that they can spend. Let competing administrations jostle to best provide this support rather than empowering some paper-pusher behind a desk somewhere to make a uniform decision across the entire district. The teachers can then advocate for an increased budget without having the cloud of "administrative waste" covering the discussion.
We have computers now. If teachers want to delegate responsibility to an outside entity, then let them. If they want to handle things on their own with multiple vendors, let them do that. If some teacher gets very good at this and other teachers want to let her handle it for them, explicitly allow this kind of "intrapreneurship" in the teaching contracts to grow responsive administrations.
The same "classroom centric" philosophy applies to testing. Classrooms should be tested, not just individual students. This means using random sampling and administering more in-depth oral exams to some of the students to see how they are doing, and using statistical methods and *adaptive group sampling* to deal with the "laws of small numbers" involved.
For example: First group classrooms at the same achievement level into random bins. Test a random sample of students from the bin with an in-depth oral exam. If they do acceptably, then fine --- mark the whole bin as clean. If it is not o.k., then subdivide the bin and repeat to isolate classrooms that might have problems. When it comes to the classroom level, do in-depth testing for the entire classroom to see what is wrong. Add some random chance for these processes to be triggered so that the mere fact of in-depth testing does not carry a stigma being attributable to random chance.