Dumbing down of education

[chinesefireball]

Here's a sample of courses that fulfill the math requirement at some of the top universities:

Yale
MATH 101b, Geometry of Nature.
....

Harvard
Quantitative Reasoning 28. The Magic of Numbers
..........


Princeton
APC 199/MAT 199
Math Alive
.........

Just had to comment on the names - they actually bothered to come up with proper names. I had inspiring courses named "Mathematics 1A Part1/2"

 

[mangxema]

I wish it were. Most new college grads don't know arithemetic, much less Calculus. It's not required at Harvard or Yale or Princeton.

Those are liberal arts schools though... I had to take three semesters of calculus and differential equations for electrical engineering.

"Magic of numbers"...

 

[Fetus4188]

Those definitely aren't liberal arts schools.

 

[aneeshm]

Thankfully, we don't have the problem of dumbed-down education in India. For around 500 $ to 1250 $ a year, you can get a very good school education (thank god for private schools!), which covers all the fundamentals of "Physics-Chemistry-Mathematics" trio. I myself and my friends used a book used in MIT for for our eleventh and twelfth Physics. We covered all of 8.01, 8.02, 8.03, and a part of 8.04.

In mathematics, we covered all the fundamentals. The same in chemistry.



The biggest problem was, a thorough understanding of classical mechanics (which is what we did in eleventh) required you to know and understand calculus, but calculus was not introduced until the twelfth grade in mathematics! That really sucked, because for that year, we had to make do with blind faith and just a little bit of understanding. After we grokked calculus, however, everything became much easier.

 

[aneeshm]

But in general, you're right. The entire education system all over the world is skewed. All the stuff we did in eleventh and twelfth should not be introduced at such a late stage. It was in those two years that the concept of mathematical rigour was introduced for the first time.

Ideally, education should start when the child is eight years old, and it should not be dumbed down EVER, it should be rigorous from the very start. That way, the child's ability to think is not stunted with the usual crap that is fed to children nowadays. He will be able to use rigorous thought since the very beginning, and this will tremendously increase the general awareness and intelligence level of the population.

 

[Uiler]

Four years at an inner city public school yielded me perfect knowledge of the times tables, and not much else. Well, I knew more math by fourth grade, but not from the school. It was kinda sad though how some kids still didn't understand single digit multiplication by fourth grade. Then I moved to the suburbs and guess what the first thing we did in math was? Times tables. Then... word problems using those times tables. Then... word problems combining adding and multiplying. Then... the year was over. By the end of next year, though, we had all been taught how to solve linear algebraic equations.

I don't think people at my old school actually used the school library to borrow reading books. The public library was much bigger and better.

Whenever I have a teacher that doesn't understand the material any more than I do, I umm... just do whatever he/she says. I used to point out everything he/she got wrong, but that's really not a smart thing to do.

Another thing about maths, maybe it's just me but I think the way they teach arithmetic totally sucks. I find it much easier, especially in mental arithmetic to "divide" the problem up into separate easier components. I remember in school something like 256+145. They'd teach you to add the 6 to the 5. Then carry the one over to the tens column etc. That sucks, especially in mental arithmetic. Also it doesn't give you a good "feel" for what addition is anyway. It's an abstract "formula" you are supposed to memorize and apply like a robot. I hated it in school. I used to like going - OK, it's 200+100=300. Then 56+45=56+40+5=96+5=101. So 300+101=401. Of course in tests and homework I'd always do it the "proper" way, even though it never made much sense to me...Now that I'm out of school I never do it the "proper" way. Though when you think about it the formula was really reproducing the process I used above. You separate it into (200+100)+(50+40)+(5+6). "Carrying the 1" is because (5+6)=11. You do (5+6) first and then separate the resulting 11 into 10+1. But why on earth don't they just *tell* you this instead of making it into some "formula" you are supposed to rote memorize? Never once in any of the years I was forced to do this "formula" addition did any teacher tell any student I know of this.

 

[Shaihulud]

I don't think it gets easier, the maths and science i learnt in school were definitely much harder than in my dads time. However i am ambivalent towards the use of programmable calculators, i feel that it is cheating to use them for calculus, gives too much advantage to people who doesn't understand the subject.

 

[warpus]

Here's a sample of courses that fulfill the math requirement at some of the top universities:

But what sort of program/major are these a requirement for?

I hope you don't say Math or Computer Science...

 

[warpus]

Another thing about maths, maybe it's just me but I think the way they teach arithmetic totally sucks. I find it much easier, especially in mental arithmetic to "divide" the problem up into separate easier components. I remember in school something like 256+145. They'd teach you to add the 6 to the 5. Then carry the one over to the tens column etc. That sucks, especially in mental arithmetic. Also it doesn't give you a good "feel" for what addition is anyway. It's an abstract "formula" you are supposed to memorize and apply like a robot. I hated it in school. I used to like going - OK, it's 200+100=300. Then 56+45=56+40+5=96+5=101. So 300+101=401. Of course in tests and homework I'd always do it the "proper" way, even though it never made much sense to me...Now that I'm out of school I never do it the "proper" way. Though when you think about it the formula was really reproducing the process I used above. You separate it into (200+100)+(50+40)+(5+6). "Carrying the 1" is because (5+6)=11. You do (5+6) first and then separate the resulting 11 into 10+1. But why on earth don't they just *tell* you this instead of making it into some "formula" you are supposed to rote memorize? Never once in any of the years I was forced to do this "formula" addition did any teacher tell any student I know of this.

I never liked many of the ways of solving problems that were presented to me in school, so a lot of the tiems I would just come up with my own. Sure, sometimes there exists a very established way of doing something that is expected to be memorized for tests and exams (ie. completing the square), but.. well, let me give you an example.

I took grade 11 chemistry in High School. I was always keen on math, so when we got into the chapters dealing with moles, I came up with my own way of solving these problems. I hated the formulas that were spoonfed to us, so I actually sat down, figured out what the hell was going on, saw the big picture.. and anytime after that, if I was given a question involving moles and any sort of conversion involving that, I could just look in my head, figure out what number crunching was required.. and put it down on paper. I got 100% on all tests involving moles. The teacher stopped asking me to go to the board to show how I solved a particular problem (he would pick people randomly to check if they did their HW), because he couldn't figure out how I arrived at my answers. The class got confused too because I wasn't using any of the formulas that were given to us.. but I always arrived at the right answer.. even on the "hard" bonus questions on tests.. I just had the whole system figured out. There was no need for formulas. Most of the things were just a matter of number crunching and making sure that you don't make a mistake in the process - but the process was always easy.

In any case.. It's good to memorize formulas and accepted methods of solving problems. But if you truly see the big picture and understand the question given to you, you can just.. do it. So if you can figure out a better way to solve a problem (like addition in your example), why not just run with it?

 

[ShannonCT]

But what sort of program/major are these a requirement for?

I hope you don't say Math or Computer Science...

Those were math courses that fulfilled the general education requirement. I was just trying to show that even the top universities do not require students to take Calculus.

 

[Irish Caesar]

Those were math courses that fulfilled the general education requirement. I was just trying to show that even the top universities do not require students to take Calculus.

Harvard, Yale, and Princeton aren't exactly representative of the "top universities" that would require knowing calculus. It might be better to show what students at MIT, Caltech, and Georgia Tech have to take. And I assure you, there's calculus.

 

[Sparta]

I had to take three semesters of calculus and differential equations for electrical engineering.

Ditto (plus quantum physics!). I agree with Irish Caesar - being specific on majors would make a big difference. At my school alone (Wisc, FWIW) you could've gone from Calc III and Dif EQ being requirements for a BSEE down to something pathetic like "applied math" being required for a D-I football player with a major in "Sports Therapy" or some such nonsense.

(and FWIW, they all had 'tutors' doing all their work for them anyway, even for such lowbrow studies as that - maybe if they'd paid more attention, they wouldn't have all sucked at cards as horribly as they did (seriously, I have never played poorer card players in all my life than some of those collegiate athletes, and I used to play against several high-school dropouts back in the day).)

On the overall point though, I'll concede that IMHO it is much easier to squeak by with very little proficiency in school these days than in the past, if that is your intention. Oh and also, FW(little)IW, I completely agree with you, Uiler, on mental addition being far more intuitive and quickly accomplished when approached the way you describe it.

 

[ShannonCT]

Harvard, Yale, and Princeton aren't exactly representative of the "top universities" that would require knowing calculus. It might be better to show what students at MIT, Caltech, and Georgia Tech have to take. And I assure you, there's calculus.

Well people don't usually go to MIT to be English majors do they? Of course "tech"-nical schools are going to require more rigorous math and science courses. My point was that Harvard, Yale, and Princeton are considered among the top universities in the US and they do not require Calculus. The Ivy mystique loses a bit of its luster when you can graduate without ever having taken a math class harder than "Math Alive" or "The Magic of Numbers".

I think if you're smart enough to get into a top-25 school, you're smart enough to understand basic Calculus: limits, methods of derivation and intergration, and applications to the sciences.

 

[ShannonCT]

Oh and also, FW(little)IW, I completely agree with you, Uiler, on mental addition being far more intuitive and quickly accomplished when approached the way you describe it.

I think a lot of schools are re-realizing the value in being able to crunch numbers quickly. For the past two decades, math curricula had been based on the "New Math" model that said students didn't need to know their math facts because they could do calculations on a calculator. The "New Math" model said that rote learning was evil and that students should be able to explore math and discover its many beautiful applications. Publishers started churning out textbooks that were half pictures and very light on traditional math problems. The problem with the "New math" was that students couldn't really develop any deep understanding of applications because they didn't understand the fundamentals. So a lot of students left school having very little concrete understanding. I think schools are now moving away from this disaster. Recent studies by math education scholars have realized their earlier errors and have begun promoting math fundamentals once again. They accept that rote learning (like math facts) is necessary in the early grades to establish a basis for theoretical understanding later.

 

[Irish Caesar]

Well people don't usually go to MIT to be English majors do they? Of course "tech"-nical schools are going to require more rigorous math and science courses. My point was that Harvard, Yale, and Princeton are considered among the top universities in the US and they do not require Calculus. The Ivy mystique loses a bit of its luster when you can graduate without ever having taken a math class harder than "Math Alive" or "The Magic of Numbers".

I think if you're smart enough to get into a top-25 school, you're smart enough to understand basic Calculus: limits, methods of derivation and intergration, and applications to the sciences.

Yes, but if you're going to one of those schools, wouldn't you be better off spending your time taking law and medicine classes which are insanely rigorous and leave multivariable calculus to engineers and physicists?

 

[ShannonCT]

Yes, but if you're going to one of those schools, wouldn't you be better off spending your time taking law and medicine classes which are insanely rigorous and leave multivariable calculus to engineers and physicists?

Certainly there are majors where Calculus is not going to help you (I would disagree with your implication that pre-meds don't need Calculus, as they need to take physics to pass the MCAT). But does an engineer need to know anything about the Humanities or a physicist about Western Civ? And yet those courses are part of the general ed requirements at the top schools. It seems that math, as a subject that every high school grad has been studying for the last 13+ years, should be a subject that the nation's top students should know well enough to take single-variable Calculus in college.

There is an idea that universities should have a core curriculum that all students must take so that the students become well-rounded individuals and share a common knowledge base with their fellow students. A university, by Latin definition, is a community of scholars. There can be no community if students are compartmentalized by their major and have nothing in common with their fellow students. A university is more than merely a place to get trained for a career. But alas, the idea of a university as a community of scholars is all but dead in many schools...

 

[Tomoyo]

Another thing about maths, maybe it's just me but I think the way they teach arithmetic totally sucks. I find it much easier, especially in mental arithmetic to "divide" the problem up into separate easier components. I remember in school something like 256+145. They'd teach you to add the 6 to the 5. Then carry the one over to the tens column etc. That sucks, especially in mental arithmetic. Also it doesn't give you a good "feel" for what addition is anyway. It's an abstract "formula" you are supposed to memorize and apply like a robot. I hated it in school. I used to like going - OK, it's 200+100=300. Then 56+45=56+40+5=96+5=101. So 300+101=401. Of course in tests and homework I'd always do it the "proper" way, even though it never made much sense to me...Now that I'm out of school I never do it the "proper" way. Though when you think about it the formula was really reproducing the process I used above. You separate it into (200+100)+(50+40)+(5+6). "Carrying the 1" is because (5+6)=11. You do (5+6) first and then separate the resulting 11 into 10+1. But why on earth don't they just *tell* you this instead of making it into some "formula" you are supposed to rote memorize? Never once in any of the years I was forced to do this "formula" addition did any teacher tell any student I know of this.

Firstly, I can't believe that a word I learned today from doing a crossword actually appeared in my life today. (Rote - the clue was "education by memorization")

In elementary school, I hated to do problems that way too. The way I'd do that addition problem would be 256+145 = 255+145+1 = 400+1. There were also those word problems where, for the word, I would write something like "3+7=10, 10*3=30, 30/120=1/4" instead of writing the required "Because the three children each held seven marbles in one hand and three in the other, each child hold ten. 3+7=10. There are three children. 10*3=30 marbles. There are 120 marbles in the room. 120/30 = 1/4, so the three children hold a total of 1/4 of the marbles."

Now, of course, I'd do x = [(3+7)3]/120.

However, there is one thing that has always plagued me in my math life. The quadratic formula. I used to keep trying to derive it when I needed it, like any other formula. I would fail on occasion due to not having a good grasp of completing the square. Eventually I just memorized it. Sing along with me, it goes to the tune of "Pop Goes the Weasel".

X equals negative b,
Plus or minus square root,
B squared minus four ac,
All over two a!

On a separate note, knowing that tan(x) = sin(x)/cos(x) would have helped me a lot in physics...

 

[Irish Caesar]

Certainly there are majors where Calculus is not going to help you (I would disagree with your implication that pre-meds don't need Calculus, as they need to take physics to pass the MCAT). But does an engineer need to know anything about the Humanities or a physicist about Western Civ? And yet those courses are part of the general ed requirements at the top schools. It seems that math, as a subject that every high school grad has been studying for the last 13+ years, should be a subject that the nation's top students should know well enough to take single-variable Calculus in college.

I think it's good to know more than just your own major, and certainly through history the engineers were also well-versed in history and architecture and physics and whatnot, but I think it's more important that an engineer know some history than a lawyer know some calculus.

There is an idea that universities should have a core curriculum that all students must take so that the students become well-rounded individuals and share a common knowledge base with their fellow students. A university, by Latin definition, is a community of scholars. There can be no community if students are compartmentalized by their major and have nothing in common with their fellow students. A university is more than merely a place to get trained for a career. But alas, the idea of a university as a community of scholars is all but dead in many schools...

I go to an institute!

 

[ainwood]

Dumbing down of education? Well, read this....

http://www.nzherald.co.nz/section/story.cfm?c_id=1&ObjectID=10410338

Pupils given NCEA credits for just turning up to chat

Sunday November 12, 2006
By Catherine Woulfe


Schools are awarding students NCEA credits for simple tasks such as knowing how to apply for a benefit, having a conversation or simply turning up to school on time.

A Herald on Sunday investigation has also revealed credits awarded for doing the washing, gift-wrapping a present or buying groceries.

The NCEA unit standards were written by the New Zealand Qualifications Authority, are internally assessed, and are often given more weight than mainstream subjects such as science or maths.

Hundreds of schools are accredited to assess the standards and they are available to all students at those schools.

One of the standards appears on students records as "Work and Study Skills: Demonstrate Care and Timeliness as an Employee" - but to get it, pupils simply have to attend school on time and behave for 20 consecutive school days.

Other credits are awarded for:

* role-playing applying for a benefit

* keeping healthy

* holding a conversation with a friend

* gift-wrapping an item

* choosing appropriate clothing

* doing the washing

* working with a group

* istening

* buying groceries

* understanding friendship

* asking about or ordering goods or services, face to face or over the phone.

In 2004 Cambridge High School was slammed for "credit-cramming" to boost pass rates - but it used legitimate standards such as "Interpersonal Communications: Participate in a team or group to complete routine tasks", to do so.

The school made students pick up rubbish as their "routine task". That standard is still available to schools.

The qualifications authority said on Friday that the standards uncovered by the Herald on Sunday were from a special Supported Learning section and that this would be marked on students' records. But yesterday it admitted the credits were mainstream and not differentiated on NCEA records. Bali Haque, deputy chief executive of qualifications, said level one was "absolutely basic" and the delivery of unit standards was "a developing process".

"There's no doubt that you will find anomalies.

"The intention here is to recognise the learning that people have done, and give them credit for it."

Haque said the situation "is not perfect" but he had faith that teachers and schools were not exploiting the system to boost pass rates.

"It is better to offer people those sorts of simple, unsophisticated qualifications than not to - as long as people understand the purpose."

Graham Young, head of the Secondary Principals' Association of New Zealand, said the NCEA system put pressure on schools to accumulate credits - and the easiest way to do that was to encourage students into internally assessed unit standards.

"There are some very low-level unit standards which are extraordinarily easy to pass... For people with above-average or average abilities to be using those unit standards is absolute nonsense."

Gilbert Peterson, spokesman for the Employers and Manufacturers Association, said the titles of particular standards meant nothing to employers faced with "a big grab bag of assessment".

"It's going to cause bewilderment and confusion, quite frankly.

"Getting credits for doing the washing or talking to your mate is just amazing. Any businessperson reading this would be quite appalled. We're absolutely sure of that."

Haque said he was confident employers would recognise the standards as basic, and that they were not misleading.

Level one students have to collect 80 credits to pass the year. Eight of those have to be literacy, and eight numeracy. Students are free to choose which standards they attempt. The number of credits given for completing the tasks range between two and four. Yet some mainstream standards - such as understanding atomic structure and fission reactions, giving a speech in French, or using geometry to solve problems - are worth only two credits.

John Langley, dean of education at the University of Auckland, said the other standards were meaningless.

"I turned 51 last week and I still can't gift wrap a parcel - and actually, it doesn't matter."

Langley said the authority needed to look at what the NCEA standards were and how they were applied.

National's education spokesman, Bill English, said the "easy credits" demotivated students. "Take someone who's struggling with maths and works hard to get four or five credits - and then they see their mate getting three credits for holding a conversation... That's something that children learn when they're 2, 3, 4... It hardly seems credit material."