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Marnetmar

The way math is taught to pupils

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I was pondering this the other night. In the environment of a high school or college algebra class, why aren't all of the problems that are given application problems instead of maybe 1 in 10?

It seems incredibly backwards for students to get good at algebraic thinking without context and then panic when the dreaded story problem comes along. It's like if somebody opened a boxing gym where the coach spent the whole time talking about boxing theory but never had anybody spar.

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Marnetmar said:

I was pondering this the other night. In the environment of a high school or college algebra class, why aren't all of the problems that are given application problems instead of maybe 1 in 10?

It seems incredibly backwards for students to get good at algebraic thinking without context and then panic when the dreaded story problem comes along. It's like if somebody opened a boxing gym where the coach spent the whole time talking about boxing theory but never had anybody spar.


Where and when are people panicking here?

Isn't the point of college/university specifically to learn practical application of said theory in a given context?

What the heck is a story problem?

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I never learned any of those maths because whenever anybody asked the teacher about anything he just told them to check their vocab. I hate the inclusion of technology and the internet into the classrooms, I don't even want to make an account for these stupid websites and emails or whatever, that shit's all a riot. It just lets the teachers put no effort into actually teaching a lesson whilst the computer does everything. What's even the point of going to school if the teachers don't interact with the students? People could just use the computers at home. There's not even the factor of social interaction because students are never allowed to speak at all, not even discussion amongst peers, or analysis of a given story in English class of all things. But oh no, that'd take resources away from having all the students sit in silence and do nothing for half an hour for the worthless advisory period.

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I did so many of those "story problems" in grade 9 I can still remember half the questions. They tended to reference "navy stew", the dimensions of catwalks on refinery tanks, destroyers chasing submarines, or grain silos. Math teacher was an American Vietnam vet who grew up in Idaho, you see. Well, at least he said he was. He was also a psychologist who always seemed to like spinning a web of pranks and lies.

Those kinds of problems were the fun ones. They always offered insight into the weirdness of teachers. Grade 10 physics had a lot of instances of Darth Vader dropping cannon balls on Phineas' head. What the hell did Phineas do to Ms Davidson?

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I was always horrible at Maths. I never liked it and I always had issues understanding the theory when it came to class room teaching and text books.

To pass my Statistics exam I had to hire a tutor which taught me more about stats in 4 two hour sessions in comparison to a lecture + tutorial for half a year. I do believe one of my issues with Math and Statistical theory is the lack of context. I need someone to plainly explain how it operates and answer any of my questions in a slow pace for me to comprehend. I found most teaching methods are "Memorize this formula because that's how it works. It will make more sense when you use it with a more advanced formula later, but don't become too familiar because it can alter for a different situation".

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I was good at math. That being said, I have retained barely anything, beyond simple algebra. Thankfully, I never needed or used it, in my life. (yes, yes, I know; we use algebra, and all that jazz more than we think, subconsciously)

Now if only we can teach it to people in a way that doesn't make them resent the discipline, itself.

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Marnetmar said:

I was pondering this the other night. In the environment of a high school or college algebra class, why aren't all of the problems that are given application problems instead of maybe 1 in 10?

It seems incredibly backwards for students to get good at algebraic thinking without context and then panic when the dreaded story problem comes along. It's like if somebody opened a boxing gym where the coach spent the whole time talking about boxing theory but never had anybody spar.


Disclosure: I'm in a mathematics and comp. sci. program and anything I say here will be about university-level mathematics, not high school or lower.

There's not enough time to cover applications and still meet the goal of the course, which is to gain skills in algebraic manipulations. And most of those "story problems" or "word problems" are extremely artificial and basically just test the student's ability to turn words into some kind of equation that can be solved using the methods they've been taught. When students have difficulties with these kinds of problem, this may be symptomatic of a problem with reading comprehension or critical thinking rather than mathematical skills.

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Tosi said:

Disclosure: I'm in a mathematics and comp. sci. program and anything I say here will be about university-level mathematics, not high school or lower.

There's not enough time to cover applications and still meet the goal of the course, which is to gain skills in algebraic manipulations. And most of those "story problems" or "word problems" are extremely artificial and basically just test the student's ability to turn words into some kind of equation that can be solved using the methods they've been taught. When students have difficulties with these kinds of problem, this may be symptomatic of a problem with reading comprehension or critical thinking rather than mathematical skills.


I agree with this, based on my experience from working in a university for the past 12 years. There are people that go on to become teachers that don't even know how to properly write sentences!

The biggest issue with education is that a lot of the teachers today were underachievers themselves.

If you want to improve upon education, than we need to raise the standards of what it takes to become an educator. Anyone with less than a 3.6 GPA in college, doesn't have any business teaching children.

EDIT: Which implies, less teachers, but higher-quality ones. Thus teachers should be given the higher salary they deserve. If anyone really wants to stand up for teachers, than they should stand against the deluge of incompetent faculty that poisons their profession.

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Kontra Kommando said:

If you want to improve upon education, than we need to raise the standards of what it takes to become an educator. Anyone with less than a 3.6 GPA in college, doesn't have any business teaching children.

Hard college GPA requirements are silly, since that's a measure of how easy your major was just as much as it is how well you performed.

There's a good reason why, at the college I graduated from, nearly 100% of the students who graduated cum laude were art majors. And it's not because they were better students (most of them were business or engineering majors during their first semester, and changed when they realized that they'd fail the program horribly).

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Cynical said:

Hard college GPA requirements are silly, since that's a measure of how easy your major was just as much as it is how well you performed.

There's a good reason why, at the college I graduated from, nearly 100% of the students who graduated cum laude were art majors. And it's not because they were better students (most of them were business or engineering majors during their first semester, and changed when they realized that they'd fail the program horribly).


Yes, and no. There's a lot of business and engineering majors that would fail horribly at art. If it was easy, than everyone could do it. But that's not the case, because someone could be great with accounting, but barely be able to draw stick-figures. You probably wouldn't be able to differentiate their effort, from the work of a 3 year old.

Also, maybe they excel at majors they are actually good at.

But the point is, a lot of people are underachievers, in the field of education. That is the profession that is in question. Not engineers or business majors. If you can't write a sentence properly, how are you expected to teach children?

This whole lackadaisical attitude towards getting a good GPA is the reason why we have these problems in this country. Also, its the reason why other nationalities, like Chinese, and Indians, are getting ahead of the average-american. Because they believe in a culture of academic excellence.

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Kontra Kommando said:

Yes, and no. There's a lot of business and engineering majors that would fail horribly at art.

Also, maybe they excel at majors they are actually good at.

But the point is, a lot of people are underachievers, in the field of education. That is the profession that is in question. Not engineers or business majors. If you can't write a sentence properly, how are you expected to teach children?

This whole lackadaisical attitude towards getting a good GPA is the reason why we have these problems in this country. Also, its the reason why other nationalities, like Chinese, and Indians, are getting ahead of the average-american; because they believe in a culture of academic excellence.

I assure you, the people who became art majors at this particular school weren't the cream of the crop. The college was well known for its business, computer science, and electrical engineering programs; its art school building was literally a corrugated tin shed referred to by students as the "art barn". Talented art students weren't going to that school.

I know a lot of really great engineers who are perfectly capable of writing in complete sentences whose GPA is is in the 3.2-3.5 range. Again, GPA is as much a measure of how difficult the courses you took were as it is a measure of how good you were as a student. In most of my upper-division computer science courses, the median grade was a C-, and it wasn't because people weren't working (this school actually had a lot of foreign students from India, and their grades were similar to the native students).

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Cynical said:

I assure you, the people who became art majors at this particular school weren't the cream of the crop. The college was well known for its business, computer science, and electrical engineering programs; its art school building was literally a corrugated tin shed referred to by students as the "art barn". Talented art students weren't going to that school.

I know a lot of really great engineers who are perfectly capable of writing in complete sentences whose GPA is is in the 3.2-3.5 range. Again, GPA is as much a measure of how difficult the courses you took were as it is a measure of how good you were as a student. In most of my upper-division computer science courses, the median grade was a C-, and it wasn't because people weren't working (this school actually had a lot of foreign students from India, and their grades were similar to the native students).


I understand what you mean about STEM degrees being more rigorous. But what I'm saying is that, if you can't get a high GPA within that field, than how could you be expect to teach it? I'm sure your professors were not C- students. If they were, than maybe that's why they're producing C- students.

But also, there's always a chance to re-comp those failed classes.

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Kontra Kommando said:

I understand what you mean about STEM degrees being more rigorous. But what I'm saying is that, if you can't get a high GPA within that field, than how could you be expect to teach it? I'm sure your professors were not C- students. If they were, than maybe that's why they're producing C- students.

But also, there's always a chance to re-comp those failed classes.

My professors obviously weren't C- students, and I'm not certain that I'd want even those C- students teaching at a high school level, but I'd have no problems with most of the ones whose GPA hovered at around the 3.0 area teaching STEM areas at a high school level.

In fact, I'd go so far as to say I'd rather have the STEM major with a 3.0 teaching a math class than the Education/Teaching major with a 3.6.

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Cynical said:

My professors obviously weren't C- students, and I'm not certain that I'd want even those C- students teaching at a high school level, but I'd have no problems with most of the ones whose GPA hovered at around the 3.0 area teaching STEM areas at a high school level.

In fact, I'd go so far as to say I'd rather have the STEM major with a 3.0 teaching a math class than the Education/Teaching major with a 3.6.


I'm sure they weren't C students, because getting two Bs gets you thrown out of a doctoral program, usually.

You can choose to be a 3.0 stem major, but that's hardly a skill set required to be a teacher. Would you trust someone like yourself to be as an effective teacher? Would you rather have your professors be A students or C students?

Knowing something, and knowing how to teach something, are different. The appeal I am making here, is that teachers should be expected to be academic elites.

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Kontra Kommando said:

I'm sure they weren't C students, because getting two Bs gets you thrown out of a doctoral program, usually.

You can choose to be a 3.0 stem major, but that's hardly a skill set required to be a teacher. Would you trust someone like yourself to be as an effective teacher? Would you rather have your professors be A students or C students?

Knowing something, and knowing how to teach something, are different. The appeal I am making here, is that teachers should be expected to be academic elites.

I don't feel like the requirements to be a high school teacher should be as high as the requirements to be a college professor. The requirements should probably be higher than they are now, yes, but requiring someone to be an "academic elite" to teach high school is wasteful of resources -- we have better things for the academic elites to be doing.

I doubt I'd be an effective high school teacher (and my GPA was a 3.5 -- I was well above the median), but that's entirely because I'm not good with kids (I'd also make a terrible parent), and I'd fail miserably at the "classrom control" parts of the job. I'm quite confident I could teach high school level STEM material to adults who wanted to learn.

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Cynical said:

I don't feel like the requirements to be a high school teacher should be as high as the requirements to be a college professor. The requirements should probably be higher than they are now, yes, but requiring someone to be an "academic elite" to teach high school is wasteful of resources -- we have better things for the academic elites to be doing.

I doubt I'd be an effective high school teacher (and my GPA was a 3.5 -- I was well above the median), but that's entirely because I'm not good with kids (I'd also make a terrible parent), and I'd fail miserably at the "classrom control" parts of the job. I'm quite confident I could teach high school level STEM material to adults who wanted to learn.


I actually believe the opposite. At one point, high school was a lot more rigorous, and people received a higher quality education. College was an institution for academic elites, which in-turn almost guaranteed upper-middle class to rich status. Today, the standards of education have fallen to the point that a high school degree is basically meaningless. Furthermore, many people are now encumbered in student loan debts, because they want to forge a better future for themselves with a college degree. But now, they can only hope to at least retain their middle-class status, lest they fall into poverty. It is disgusting what has happened in the past 30 years to this country. A person SHOULD be able to receive a quality education in high school, that prepares them for the real world. Not that they should be expected to be saddled with debt to receive a sub-standard degree.

The reason why a college degree doesn't mean much, is because employers know that colleges are turning out ignorant people. This is why people are "forced" to get into even more debt, with a masters, so they may distinguish themselves from their peers.

Forget about raising the ceiling, we need to raise the floor.

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The standards of a high school education falling has less to do with the teachers themselves and more to do with the curricula that they are being made to teach. The reasons for the curricula being made simpler are entirely political ("every kid has to pass, or we're failing them!" sounds great as a campaign slogan), and have nothing to do with the teachers we have available. High school teachers weren't academic hot-shots in the "good old days", either.

The main reason for lowered standards in college is political, as well -- it was a way for the academic left to exempt people from the Vietnam War draft.

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Cynical said:

The standards of a high school education falling has less to do with the teachers themselves and more to do with the curricula that they are being made to teach. The reasons for the curricula being made simpler are entirely political ("every kid has to pass, or we're failing them!" sounds great as a campaign slogan), and have nothing to do with the teachers we have available. High school teachers weren't academic hot-shots in the "good old days", either.

The main reason for lowered standards in college is political, as well -- it was a way for the academic left to exempt people from the Vietnam War draft.


Based on my experience, as I have stated, it has a lot to do with the quality of teachers, who are a product of a sub-standard educational system.

But I agree that it is political as well. A lot of teachers I speak to, from public schools, right here in the north east, dislike the idea of common core. They complain that they barely get to actually teach the children, because they constantly must prepare for standardized tests; as much as 5 a year! They hate it, and the students hate it as well.

EDIT: as a matter of fact, I don't know a single educator, that ever had anything good to say about common core. I understand that its intended to ensure quality; but its facilitating the exact opposite.

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I didn't read the thread, but let me tell you, college math has gotten crazy. The new system(I forget what it's called in the US) is absolutely retarded. My community college only gives you four weeks to complete a unit, which consists of quadratic equations in the more advanced sections. I'm about 50% done with my associates in Mech/Ind Engineering degree, though I do have a GPA of over 3.5.

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In what fairyland are quadratic equations the advanced part of college-level engineering math? That's grade 10!

Quality teachers are important, but educational standards depend mostly on the society that supports them. Many of the countries the USA compares itself to have pretty weird ideas about education. Koreans study like crazy. Indians cheat like crazy. I'm not sure either of those systems works better than America's lax standards.

Well, then there's America's teaching-the-test problem that even seems to lead some districts to encourage the teachers to cheat for the students! That's crazy stuff.

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Marnetmar said:

I was pondering this the other night. In the environment of a high school or college algebra class, why aren't all of the problems that are given application problems instead of maybe 1 in 10?

It seems incredibly backwards for students to get good at algebraic thinking without context and then panic when the dreaded story problem comes along. It's like if somebody opened a boxing gym where the coach spent the whole time talking about boxing theory but never had anybody spar.


Thinking about maths from only the standpoint of "how can I use it in the *real* world?" is a mistake imo. Certainly it's useful to be able to translate words into equations, but the real reason EVERYONE should go through the maths gauntlet is because it rewires the brain to think differently (unless you were a special snowflake who already had a superior mind for logic). If one really strives to understand algebra and basic calculus, it helps in all facets of one's life because one will be better at following chains of logic and the ability to discard unnecessary information in favor of truly relevant information.

edit: and I mean to say focusing only on "application" type word problems will be insufficient in this goal.

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