The evolution of math in the US

[IronBrig4]

Fifty Years of Math 1959 - 2009 (in the USA )

Last week I purchased a burger at Burger King for $1.58. The counter girl
took my $2 and I was digging for my change when I pulled 8 cents from my
pocket and gave it to her. She stood there, holding the nickel and 3
pennies, while looking at the screen on her register. I sensed her
discomfort and tried to tell her to just give me two quarters , but she
hailed the manager for help.. While he tried to explain the transaction to
her, she stood there and cried. Why do I tell you this? Because of the
evolution in teaching math since the 1950s:

1. Teaching Math In 1950s

A logger sells a truckload of lumber for $100. His cost of production is
4/5 of the price. What is his profit ?

2. Teaching Math In 1960s

A logger sells a truckload of lumber for $100. His cost of production is
4/5 of the price, or $80. What is his profit?

3. Teaching Math In 1970s

A logger sells a truckload of lumber for $100. His cost of production is
$80. Did he make a profit?

4. Teaching Math In 1980s

A logger sells a truckload of lumber for $100. His cost of production is
$80 and his profit is $20. Your assignment: Underline the number 20.

5. Teaching Math In 1990s

A logger cuts down a beautiful forest because he is selfish and
inconsiderate and cares nothing for the habitat of animals or the
preservation of our woodlands. He does this so he can make a profit of $20.
What do you think of this way of making a living? Topic for class
participation after answering the question: How did the birds and squirrels
feel as the logger cut down their homes? (There are no wrong answers, and
if you feel like crying, it's ok. )

6. Teaching Math In 2009

Un hachero vende una carretada de maderapara $100. El costo de la
producciones es $80. Cuanto dinero ha hecho?

The above story is from a friend. It raises an interesting point about the state of American education.

In California public schools, the average class size is at least thirty. Many non-involved parents expect teachers to teach their kids basic social skills as well. As a result, less time is spent on actual learning. It's not really the parents' fault since both have to work sixty hours a week to scrape by. What really sets me off is teachers are expected to discipline the kids, but self-righteous parents throw screaming fits whenever that happens.

Compare that to the class I teach in South Korea. The MAXIMUM class size is fifteen. The kids are socialized at home, and teachers have a lot more leeway with discipline. Smacking students who misbehave is common, although I don't do that. As a result, Korean kids are just so much more knowledgeable than their American counterparts. As one of my teacher friends back home told me, "Send me a retarded Korean second-grader. I'm sure he could beat the pants off my whole class of eighth-graders.

[bushbush]

Compare that to the class I teach in South Korea. The MAXIMUM class size is fifteen. The kids are socialized at home, and teachers have a lot more leeway with discipline. Smacking students who misbehave is common, although I don't do that. As a result, Korean kids are just so much more knowledgeable than their American counterparts. As one of my teacher friends back home told me, "Send me a retarded Korean second-grader. I'm sure he could beat the pants off my whole class of eighth-graders.

i honestly think that's the biggest problem with education system in North America. Everyone is worried about those kids who can't finish school and drift into poverty and crime. Honestly? they just need more ass kicking from their teachers and parents when they are young to learn wut's right and wrong.

[IronBrig4]

Like I said, I don't hit my students. I pound my desk and yell instead. It's a terrific way of expressing your displeasure. Some of my friends hit their kids and it works quite well. If the kid ever disrespects a teacher it's a guaranteed beat-down. And they get manhandled even more when they get home. Their parents won't sue the school district into oblivion.

Is it just me, or does the world need more drill instructors? Kids today, and especially American kids, are so coddled. They'd probably toughen up if a gunnery sergeant was screaming at them.

"You feel DEPRESSED because you got an F on your spelling test? It's hurting your SELF-ESTEEM?! Don't give me that psychobabble ! You worthless sack of !"

[Arjun]

i honestly think that's the biggest problem with education system in North America. Everyone is worried about those kids who can't finish school and drift into poverty and crime. Honestly? they just need more ass kicking from their teachers and parents when they are young to learn wut's right and wrong.

i totally agree, lol when i was in school we could be caned even while in high school. believe me, it works. Nothing makes a student concentrate on studies more like the specter of caning looming over them.lol

Also, parents should become much more involved in the education of their kids. Active parental participation is essential for kids to learn well. Last but not the least, respect for teachers is something that is sadly lacking here. Its impossible for students to take what teachers say seriously, if they do not respect teachers in the first place.


another pet peeve of mine is how often kids are using calculators in school. It might come a surprise to many, but when i was in school, calculators were not allowed. and no...i got out of high-school less than 10 years ago(even now calculators are not allowed). Mental arithmetic is very important. not only does it enable us to do fairly complex math without a paper or pen(let alone a calculator) studies seem to show that it also makes the brain more sharper.Other mathematical problems can be solved with pen and paper. Yes..a calculator would shorten the time drastically, but unless a student has a very firm basis on doing math by hand; he would not understand how its done. and when a calculator is not nearby...he would not be able to do anything!


and as for possible cases of abuse; no, there are ways that students/parents could have a teacher reprimanded for unreasonable punishment.


@ topic

I have so many such horror stories from shop-counters.

[IronBrig4]

My friend who teaches 8th grade Stateside says that a lot of his kids are atrocious writers. They write essays like they text. For example, they will write "l8r" instead of "later." Yeah, it's THAT bad.

Another buddy of mine scheduled parent-teacher conferences. He made himself very available so parents could come in from after school until six or seven in the evening. He was even there all day Saturday. Only about one-third of the parents bothered to show up.

Again, not all of them are necessarily at fault. American parents are working longer than they used to. Single parents often have to work two jobs, and even two-parent families are working all the time now. Still, don't they even care about their kids' educations?

[I Am Herenow]

When I first read your story, I thought you were just joking, but having looked at some past papers, I can see your point. Compare a Massachusetts 10th grade maths paper with a GCSE one. Although both exams are mind-numbingly easy in places, the UK paper does at least have some questions where one might be required to think, and, most heinously of all, the US paper is multiple choice!

I Am Herenow

[Saturn]

Is it just me, or does the world need more drill instructors? Kids today, and especially American kids, are so coddled. They'd probably toughen up if a gunnery sergeant was screaming at them.

"You feel DEPRESSED because you got an F on your spelling test? It's hurting your SELF-ESTEEM?! Don't give me that psychobabble ! You worthless sack of !"

Starting this year I actually WANTED to go to military school. That is not a joke. I really am pissed off about teachers wasting my time. I'd rather be learning something than listen to them talk to their students about what they did last weekend for the first twenty minutes of class. Teachers spend too much time trying to be the "cool" teacher these days instead of teaching their students. I'm not saying all of them are like this. It seems to be the younger teachers. There are good teachers still, but I sense their numbers are dwindling.

[Arjun]

Starting this year I actually WANTED to go to military school. That is not a joke. I really am pissed off about teachers wasting my time. I'd rather be learning something than listen to them talk to their students about what they did last weekend for the first twenty minutes of class. Teachers spend too much time trying to be the "cool" teacher these days instead of teaching their students. I'm not saying all of them are like this. It seems to be the younger teachers. There are good teachers still, but I sense their numbers are dwindling.

The main problems are not the teachers but the educational system itself, and the students who do not want to work hard. No use blaming the teachers when the system itself is progressively dumbed down

[Viking Prince]

You do not need to be a cool teacher. You also do not need to bang on the desk and scream at the classroom full of children. I had a 4th grade teacher who lost her temper and threw a desk against the wall. That was her last day in that classroom. I have no idea what happened to her.

I am not suggesting the classroom of children be treated as if they are little adults. They are children. The teacher is supposed to be an adult and should behave in that role. To do anything in the classroom that would get you kicked out of a business or arrested on the street is simply not acceptable. Children can have consequences for their actions and lack of attention without caning, paddling, desk pounding, and screaming. Parental involvement helps, but the lack of such involvement cannot excuse the actions in the classroom.

As for the classroom having changed since the 1950's -- there are fewer changes than you think. I think most of the changes are improvements, but some are not. That is the way with progress in any field. Side tracks, back alleys, and steps back are part of the process.

Remember that segregation, two track systems, no eye exams, no specialist in reading and language, etc. I think that we are better today than in the 1950's. The good aspect of education is that the developing world is getting closer to the developed world with education.

Oh -- and there is nothing wrong with some of the testing to be multiple choice. I fail to see how a standardized test of 100,000's of sudents can be short essay.

[Arjun]

You do not need to be a cool teacher. You also do not need to bang on the desk and scream at the classroom full of children. I had a 4th grade teacher who lost her temper and threw a desk against the wall. That was her last day in that classroom. I have no idea what happened to her.

I am not suggesting the classroom of children be treated as if they are little adults. They are children. The teacher is supposed to be an adult and should behave in that role. To do anything in the classroom that would get you kicked out of a business or arrested on the street is simply not acceptable. Children can have consequences for their actions and lack of attention without caning, paddling, desk pounding, and screaming. Parental involvement helps, but the lack of such involvement cannot excuse the actions in the classroom.

As for the classroom having changed since the 1950's -- there are fewer changes than you think. I think most of the changes are improvements, but some are not. That is the way with progress in any field. Side tracks, back alleys, and steps back are part of the process.

but its a fact that students are expected to do less now than what they were expected to before.

Remember that segregation, two track systems, no eye exams, no specialist in reading and language, etc. I think that we are better today than in the 1950's.

I thought they were social issues and not to be confused with Educational issues.

The good aspect of education is that the developing world is getting closer to the developed world with education.

not true. The only area a lot of developing nations are lacking in education is the availability of resources such as computers and even chalk...in fact a lot of developing nations rank much higher than America and some western nations when it comes to how well their students perfom in exams..especially in the sciences and geography/history fields.

Oh -- and there is nothing wrong with some of the testing to be multiple choice. I fail to see how a standardized test of 100,000's of sudents can be short essay.

what the poster most probably meant is that instead of having say..5 possible answers to a math question; let the student write the answer instead.

[Viking Prince]

but its a fact that students are expected to do less now than what they were expected to before.



I thought they were social issues and not to be confused with Educational issues.

not true. The only area a lot of developing nations are lacking in education is the availability of resources such as computers and even chalk...in fact a lot of developing nations rank much higher than America and some western nations when it comes to how well their students perfom in exams..especially in the sciences and geography/history fields.




what the poster most probably meant is that instead of having say..5 possible answers to a math question; let the student write the answer instead.

In bullit points to your bullit points:

• Students are not expected to do less. Please support such a claim.
• There has always been a mix of social issues with education. The entire concept of a publicly funded education system is a social issue.
• Ranking higher on a particular area or not --- my point is that these nations lagged behind the developed world in the 1950's. Many were still colonial possessions and many lacked any attempts at universal education for the masses. I would hope that every developed nation feel the pressure of competition.
• You explanation of what the poster meant is precisely my point of what a standardized test must be. Fill in the blank does not work as well as multiple choice. It does not mean the test cannot be effective though.

[I Am Herenow]

Fill in the blank does not work as well as multiple choice. It does not mean the test cannot be effective though.

Of course writing the answer yourself is better than circling an answer given to you. Marking it is very simple, especially for sciences. For instance, consider a longer question of a basic statistics exam:

When onion seeds are sown in a greenhouse, the seed manufacturing company claims that the germination rate is 90%. A gardener suspects that the rate will not be as high as this, and carries out a trial to investigate. 18 randomly selected seeds are sown in the greenhouse and it is found that 14 germinate.

Write down suitable hypotheses and carry out a test at the 5% level to determine whether there is any evidence to support the gardener's suspicions.

[7 marks]

Method (from the mark scheme):

Let X ~ B(18, p) [1 mark for definition of p]
Let p = probability of germination (for population)
H₀: p = 0.90 [1 mark for H₀]
H₁: p < 0.90 [1 mark for H₁]

P(X ≤ 14) = 0.0982 > 5% [You get that from these tables they give you - I Am Herenow]
So not enough evidence to reject H₀ [1 mark for probability]
Conclude that there is not enough evidence to indicate that the germination rate is below 90%. [1 mark dep for comparison; 1 mark [not sure what for, though; I don't understand their jargon]; 1 mark for conclusion in context]

Thus, even though you don't circle the right answer, there is still a clear system for awarding marks for working and for the answer you get.

I Am Herenow

[Viking Prince]

Of course writing the answer yourself is better than circling an answer given to you. Marking it is very simple, especially for sciences. For instance, consider a longer question of a basic statistics exam:

When onion seeds are sown in a greenhouse, the seed manufacturing company claims that the germination rate is 90%. A gardener suspects that the rate will not be as high as this, and carries out a trial to investigate. 18 randomly selected seeds are sown in the greenhouse and it is found that 14 germinate.

Write down suitable hypotheses and carry out a test at the 5% level to determine whether there is any evidence to support the gardener's suspicions.

[7 marks]

Method (from the mark scheme):

Let X ~ B(18, p) [1 mark for definition of p]
Let p = probability of germination (for population)
H₀: p = 0.90 [1 mark for H₀]
H₁: p < 0.90 [1 mark for H₁]

P(X ≤ 14) = 0.0982 > 5% [You get that from these tables they give you - I Am Herenow]
So not enough evidence to reject H₀ [1 mark for probability]
Conclude that there is not enough evidence to indicate that the germination rate is below 90%. [1 mark dep for comparison; 1 mark [not sure what for, though; I don't understand their jargon]; 1 mark for conclusion in context]

Thus, even though you don't circle the right answer, there is still a clear system for awarding marks for working and for the answer you get.

I Am Herenow

I agree for me as a teacher in a classroom to assess my students I prefer the big tests to be more written. The quizes a are quick and easy means to insure they stay on schedule and are always multiple choice and true/false.

Standardized tests need to be multiple choice when testing 100.000 kids on a single exam. The issues with hand grading greatly outweigh the issues of test methods for assessment. No two teachers will grade hand written tests identically. How can a standard sore be determined?

btw -- way back in the dark ages I was in high school. My zoology teacher always gave t/f tests and the median was near 50% all the time. The only flaw in the method was when the final exam came up. I needed a 70% to average with my other grades to get an A. Not being a fool, I flipped a coin for each and every question that I had any doubt on rather than to try to outthink the tricky ones. It worked.

[Eric]

Oh, as a student in Canada these days, I can completely see what you mean. And if Canada, in general, has a better education system than the US, I shudder to think what the Americans are going through.

One of the big problems is the students. So many of the people at my high school have this damned sense of entitlement, they expect everything to be given to them on a silver platter, and are shocked when it isn't, and complain and carry on when it isn't. For example, just the other day I heard a girl complain that her History teacher didn't give out 'enough' free marks. The fact that she thinks that marks can be given without effort says a lot about education these days. It's damn depressing, especially since the History teacher is a very good one, he doesn't put up with any bull, and he expects high quality work from us.

[Tiberius Tosi]

Oh, as a student in Canada these days, I can completely see what you mean. And if Canada, in general, has a better education system than the US, I shudder to think what the Americans are going through.

LOL, as someone who had brothers go through the Canadian school system for half their life, I can tell you that Canadian school are, on average, about 2 years BEHIND American schools. Even transfer students we get from Canada always have to be dropped a grade or two because they just can't understand what we are doing.

[Eric]

LOL, as someone who had brothers go through the Canadian school system for half their life, I can tell you that Canadian school are, on average, about 2 years BEHIND American schools. Even transfer students we get from Canada always have to be dropped a grade or two because they just can't understand what we are doing.

So obviously the Canadian education system does everything slower than the American, the quality of education is still pretty reasonable here, but we share a lot of the same faults that the American system does. Lack of supplies, underpaid teachers and too many self-centered students who rarely give a . Take my school. We've got a number of modern computers, but we also have people trying to run XP on computer models that were produced sometime during the Cold War . We also have some of the worst students in the city, despite our generally good quality teachers (that's why I signed up for this school, the teachers are all very good and competent). These are students who write essays like they chat on Twitter, who believe that Canada was once a US State which gained independence sometime in the 1950s, who ask what the square root of 1 is, AND who have to ask whether or not the Allies won the Second World War.

[Phier]

So obviously the Canadian education system does everything slower than the American, the quality of education is still pretty reasonable here, but we share a lot of the same faults that the American system does. Lack of supplies, underpaid teachers and too many self-centered students who rarely give a . Take my school. We've got a number of modern computers, but we also have people trying to run XP on computer models that were produced sometime during the Cold War . We also have some of the worst students in the city, despite our generally good quality teachers (that's why I signed up for this school, the teachers are all very good and competent). These are students who write essays like they chat on Twitter, who believe that Canada was once a US State which gained independence sometime in the 1950s, who ask what the square root of 1 is, AND who have to ask whether or not the Allies won the Second World War.

Oh if only someone survived from the days before computers were in every class room, those '80's' and could teach us how to teach without said devices.

You don't need a computer to teach a child, you need a chalk board, paper and pencils.

I don't know about the Canadian system, but one factor thats an issue in the US is the quality of the teachers. Back when I took the GRE, they used to break down scores by major. Education majors had by FAR the lowest scores (they no longer show this breakdown), it wasn't even close to the next lowest.

Teaching pays relatively well in my area, but I have to wonder if they constant 'poor teachers, so under payed and over worked, mantra has convinced more able students to avoid the field.

This of course is not the only factor. I see parents more interested in sports and cheerleading then grades, and it seems generation, well whatever one is before X is into spoiling their kids, but the overall quality of the teachers protected by the main teachers union (I forget the name) isn't helping either.

[LSJ]

We learn more than kids did in the 50s - for example, you weren't taught quantum mechanics in high school in the 50s. That was a university course.

But it is true that the quality of education has fallen. Kids don't learn math as quickly, they do poorly in science, most of their essays are crap, and they don't know their history at all...

One part is definitely that the teachers suck - half of them pretend to care about the kids while not considering helping students who are struggling. They can't teach - most of my teachers were so awful I learned most of what I know in every subject through the internet and books.

Also, they never give quizzes - you only get one test every while, which is about 5% of your grade, and if you do poorly you see that you must study, but then they never come back to that subject until the final exam. After the test you don't use your knowledge until months later. Then the exam is a mix of everything you've learned throughout the year, much of which you can't remember because you only talked about it for one week last year. So you have to relearn everything. As well, they decide to give you projects or presentations the same time you are supposed to be studying, resulting in a brain melt where you forget your own name.

At least that's my experience.

[Phier]

@Ironbrig4 - Look on the bright side, in 20 years other countries will be outsourcing to US and we can make all the plastic crap cheaper.

[C-Rob]

OP, that scares the out of me. But I'm glad to see that once we all learn spanish, the questions will be just as difficult as the nineteen fifties.

speaking of education and the amount of work that students are expected to do... I have a 158 point webassign in physics due tomorrow night at 9. I REALLy have to get on that. 12% done just wont' cut it.
See? I can be academically motivated!

I can relate to the complaining about the lack of free points. In physics I hear complaints all the time. "is this for bonus?" is a common question.

Perhaps get rid of the four possible answer multiple choice tests and make them 10 possibl eanswers. Effectively eliminates the, "well, I'll just guess" factor. Not completely, I suppose, but a 1/10 shot is not at all very good.