Discouraging Students from Taking Math 509
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?"
Worrying (Score:5, Insightful)
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.
I am fine with this (Score:2, Insightful)
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.
Weight scores. (Score:4, Insightful)
Maybe... (Score:5, Insightful)
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!
Why is this a bad thing? (Score:1, Insightful)
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.
Re:in college this would make some sense (Score:2, Insightful)
Wait - you want to KEEP the money given to states under NCLB? Just not comply with the terms? I understand now.
Even in Art, Math has its place (Score:5, Insightful)
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.
Re:in college this would make some sense (Score:5, Insightful)
How do you know? (Score:5, Insightful)
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.
Re:in college this would make some sense (Score:4, Insightful)
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.
Re:Why is this a bad thing? (Score:5, Insightful)
Re:Heh. (Score:3, Insightful)
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?
who needs math (Score:4, Insightful)
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.
Re:in college this would make some sense (Score:5, Insightful)
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.
Don't need more math, more common sense (Score:3, Insightful)
Re:Worrying (Score:3, Insightful)
Ok, maybe it is fun to have such competition between schools once in ten or five years, but in long term it is hurtful. Education is NOT competition, when you learn, you just start to understand what to do with your power of knowledge and wisdom. Competition at such level crushes pupils which are emotionally weaker in time when they are not ready yet to stand on their own feet. It also popularizes more cynical point of view (versa friendlier, knowledge sharing like) to the world and can harm also motivation of smarter students.
When competition takes main role in the school, lot of students rushes trough material without trying really to understand it. Hapily, I spent my last secondary school's years in class which was full of "common man geniuses" (seven people tried to enter Med Academy, only two didn't succeded), I never felt to be in competition with them, because it was never forced. Yes, in the end, they dug material better, but I got my share of knowledge. And lot of very good friends.
In the end, it is not only knowledge that matters.
Re:Why is this a bad thing? (Score:3, Insightful)
(Also note that 99.9% of the time, if someone is "bad" at maths, it's because the instructor is incapable of teaching them, it has almost nothing to do with actual ability at all. A different instructor, working at a different pace, can turn a person with consistent scores of zero into a mega-star grade-A+ student - or turn a grade-A+ student into one with a score of zero.)
Then you get into the "real world". Those involved in computing do an extraordinary amount of maths - whether for 3D graphics, figuring out how to optimize the normalization of the databases, maximizing network performance, or performing non-trivial QA functions. Those in any research field also use extensive amounts of maths. Geological work? Maths - and bloody complicated wave functions through multiple boundary layers it is, too. This isn't the stuff of amateurs, this is seriously hard work.
What else. Engineering. Those who lack maths are doomed to rebuild roughly 14,000 incompetently-designed, incompetently-maintained bridges because those before them never applied the maths to spot design defects or prevent potentially catastrophic deterioration. Those who have maths are likely the ones to actually do the architectural redesigns and make bucketloads of money. Those who lack maths might weld, glue or rivet bits of aircraft together, but the designers - the ones doing the real work - are the ones with top-notch maths. Which is just as well, because those are the people who matter. The person gluing could be replaced by a robot - if they haven't been already - and you'd never notice or care.
Even at the cash register, you can spot the ones with strong maths skills. They're the ones telling you the total BEFORE the machine, who can get the change right by touch alone, who can process more customers than the rest of the lines put together. Yes, I've seen plenty of people that good, and I've seen plenty of morons who can add and subtract but that's it.
What about salespeople, cable runners and other high-travel folk? If you don't understand optimization, you will never minimize travel times. There is no computable solution, so you have to do the maths in real-time in your head.
Manufacturing? There's no high school I know of that teaches Operational Research and SIMPLEX. There's also not the remotest possibility of maintaining high profits and high quality without such techniques.
Journalism! Journalism can't need maths, can it? It's just writing skills. Uh, no. Packing the maximum number of key points into the least space is the packing problem. Anyone can write, anyone can (with practice) write something readable. But only those with a good understanding of the packing problem can write efficiently and effectively. That is why so few journalists are truly excellent and why so many are merely OK.
What about creative writing? That's an even clearer one. Look at the ground-breaking writers - Arthur C Clarke, Isaac Asimov, JRR Tolkien, C. S. Lewis. What do they have in common? They're ALL scientists, which means they're ALL maths-oriented. There's no point trying to say that the Lord of the Rings is science fiction and therefore needs science skills, because it isn't. It needs science skills because coherent, structured, self-consistent, efficient, disciplined stories cannot be written by anyone other than someone with a mathematical mind. It can't be done. Those who try will almost invariably be sloppier, produce formulaic work (or steal it outright), be inconsistent and/or be wholly lazy about the whole thing. It may be perfect by English class standards, it may eve
Re:in college this would make some sense (Score:5, Insightful)
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.
Re:How do you know? (Score:4, Insightful)
Can you tell whether you understand something or not? If he's grasped every graph or math-based explanation he's needed to, and knows only arithmetic and geometry, that means that he's never needed trig or calculus.
Other possible systems. (Score:3, Insightful)
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.
Re:Shhhhhh (Score:1, Insightful)
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.")
Re:Why is this a bad thing? (Score:5, Insightful)
The value of the math content in a curriculum is more than just "useful math", in the same way that composition, literature, art, science, and history courses have value far beyond the explicit content. It's true that the specific mathematical skills that are taught in high school and college math are not necessary for most people. However, the rigorous logical analysis and problem solving skills necessary in mathematics are absolutely essential to an educated person.
I've forgotten most of the specific content of my literature courses, but they were part of how I learned how to read critically. I don't remember much from my college chemistry courses, but they helped me to think scientifically. I've forgotten many of the details from my history, art, and social science courses, but along the way I learned to analyze and appreciate the world around me.
The purpose of an education is to learn to think, and mathematics is a crucial part of that process.
Re:Tinfoil (Score:5, Insightful)
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.
Re:Tinfoil (Score:3, Insightful)
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.
A math PhD student's perspective: this is good (Score:1, Insightful)
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.
Re:Math in Canada (Score:5, Insightful)
Re:It'll all work out (Score:3, Insightful)
Re:in college this would make some sense (Score:3, Insightful)
You've got a point on the Monet, though.
Re:in college this would make some sense (Score:4, Insightful)
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."
Selection criteria. (Score:3, Insightful)
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 [rmit.edu.au] (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.
Re:How do you know? (Score:3, Insightful)
Between 1400 and 1500 the population of Languedoc doubled, but the war in 1450 reduced it to 88% of what it was in 1400. During this time the average profits per household tripled, except the 40% dip in the drought of 1470. Can you estimate the taxes that kings collected over this period of time if records give you some absolute numbers to fit the curves to?
Re:in college this would make some sense (Score:4, Insightful)
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.
Re:in college this would make some sense (Score:3, Insightful)
Re:Tinfoil (Score:3, Insightful)
Re:Math? (Score:2, Insightful)
It's ironic that Mathematics is the subject to suffer, since it was used to create the situation.
Incentives (Score:4, Insightful)
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.
Re:in college this would make some sense (Score:1, Insightful)
Re:in college this would . . . Empirical evidence? (Score:3, Insightful)
Fun fun.
Re:in college this would make some sense (Score:2, Insightful)
Re:I dropped my math course (Score:2, Insightful)
"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'.
Re:in college this would make some sense (Score:3, Insightful)
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
Re:in college this would make some sense (Score:1, Insightful)
*) 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.