My Struggle with Math: Understanding Real-World Applications

[Tyrion101]

It seems often in math you are taught to do seemingly meaningless series of problems until you reach college (or actually arrive at a class where it is useful) where you find out solving for x and y does actually have a purpose, and that graphing thing you learned in high school is kind of important, maybe I wasn't paying attention in middle school or high school, but I hated math with a passion, because it felt precisely like I described, I was being told to do a bunch of things that had no real connection to me, and I didn't get an explanation of why I'd need them some day. I don't hate math as much now, but did I simply miss those lectures that explained why I was learning the stupid adding x and y and why I'd need to know this for later?

 

[Vanadium 50]

Do you think that you should only learn things of immediate practical value?

 

[Tyrion101]

No but I'd like to learn why I'm doing something, rather than just here is an equation here is how you solve it. Does that make any sense?

 

[SteamKing]

No but I'd like to learn why I'm doing something, rather than just here is an equation here is how you solve it. Does that make any sense?

Only if you need the solution to the equation to apply to something else.

Analyzing projectile motion often involves solving quadratic equations. The quadratic formula comes in pretty handy in those situations.

Optimizing certain things not only involves taking the derivative, but you must set this derivative equal to zero and solve for the unknown value.

 

[edward]

I can relate to the OP a bit. For me and in high school it was factoring complex polynomials. I think that may be overkill for a person who is going to get a degree other than is the sciences.

 

[SteamKing]

I can relate to the OP a bit. For me and in high school it was factoring complex polynomials. I think that may be overkill for a person who is going to get a degree other than is the sciences.

Would that all of our future endeavors could be known with certainty when we were in grade school, we could tailor one's educational experience so.

 

[edward]

Would that all of our future endeavors could be known with certainty when we were in grade school, we could tailor one's educational experience so.

That is true and I appreciate your reply. My reply to the Op was partly in jest. Yet at the time when I was in high school factoring page after page of complex polynomials simply had no meaning. I remember when we were barely started on trig functions that teacher took us to the town's water tower. He showed us how to shoot an angle and then determine the height of the tower. Now that made sense. : )

I really do wish we had a test to be given in the sophomore year to decide which students would be more fitted for a trade school. And then actually have the applicable students start in the direction that many of them end up going anyway.

 

[Tyrion101]

That is true and I appreciate your reply. My reply to the Op was partly in jest. Yet at the time when I was in high school factoring page after page of complex polynomials simply had no meaning. I remember when we were barely started on trig functions that teacher took us to the town's water tower. He showed us how to shoot an angle and then determine the height of the tower. Now that made sense. : )

I really do wish we had a test to be given in the sophomore year to decide which students would be more fitted for a trade school. And then actually have the applicable students start in the direction that many of them going anyway.

That's exactly my point, my whole thing is, most students might actually understand math if you actually showed them practical uses, along with the pages of meaningless equations, you shouldn't have to wait until trig 1, to discover there was a point to all that. It also didn't help that a minus sign got entire problems wrong rather than just taking a point off if you showed you could do it. Mathematics needs feedback, in some cases lots of it, otherwise you get frustrated and more frustrated because you're expected to know what it was you did wrong.

 

[Evo]

That's exactly my point, my whole thing is, most students might actually understand math if you actually showed them practical uses, along with the pages of meaningless equations, you shouldn't have to wait until trig 1, to discover there was a point to all that. It also didn't help that a minus sign got entire problems wrong rather than just taking a point off if you showed you could do it. Mathematics needs feedback, in some cases lots of it, otherwise you get frustrated and more frustrated because you're expected to know what it was you did wrong.

A lot of people get it the first time though, should an entire field of study be redone for just a few students, or do you have actual numbers showing that most people don't get it. You are making claims but not backing them up. Please back them up.

 

[symbolipoint]

It seems often in math you are taught to do seemingly meaningless series of problems until you reach college (or actually arrive at a class where it is useful) where you find out solving for x and y does actually have a purpose, and that graphing thing you learned in high school is kind of important, maybe I wasn't paying attention in middle school or high school, but I hated math with a passion, because it felt precisely like I described, I was being told to do a bunch of things that had no real connection to me, and I didn't get an explanation of why I'd need them some day. I don't hate math as much now, but did I simply miss those lectures that explained why I was learning the stupid adding x and y and why I'd need to know this for later?

No but I'd like to learn why I'm doing something, rather than just here is an equation here is how you solve it. Does that make any sense?

You were missing instruction for Algebra. Elementary schools tell you what things are and what to do with them but do poorly on building your conceptual understanding. This is all mostly repaired when you study Algebra 1 in high school.

 

[zoobyshoe]

A lot of people get it the first time though...

If they do, why?

I haven't found any statistics, but the percentage of students who have difficulty with math is high enough that it's of constant concern to educators:

http://www.education.com/reference/article/why-students-struggle-mathematics/

http://www.pbs.org/wgbh/misunderstoodminds/mathdiffs.html

https://www.louisianabelieves.com/d...handout-conceptual-understanding.pdf?sfvrsn=2

From the first link:

Mathematics has often been termed the “gatekeeper” of success or failure for high school graduation and career success (National Research Council [NRC], 1989). It is essential that “mathematics . . . become a pump rather than filter in the pipeline of American education” (NRC, 1989,

 

[zoobyshoe]

It seems often in math you are taught to do seemingly meaningless series of problems until you reach college (or actually arrive at a class where it is useful) where you find out solving for x and y does actually have a purpose, and that graphing thing you learned in high school is kind of important, maybe I wasn't paying attention in middle school or high school, but I hated math with a passion, because it felt precisely like I described, I was being told to do a bunch of things that had no real connection to me, and I didn't get an explanation of why I'd need them some day. I don't hate math as much now, but did I simply miss those lectures that explained why I was learning the stupid adding x and y and why I'd need to know this for later?

I'm with you on this. I never had any luck getting an explanation of what we were all working toward in acquiring an apparently endless succession of procedures that only became more and more abstract. Math became overbearingly tedious. Later in life, though, whenever a practical use for math came up, I embraced it and became quite enthusiastic about it.

I think the problem might be that many grade school and high school teachers, themselves, don't understand real world applications of math. If you ask a math teacher what the use of math is, the only honest answer they can give from personal experience is that it can be used to get a paycheck for teaching it. They, themselves, don't have any experience in the careers they are supposed to be preparing you for.

 

[Psinter]

Do you think that you should only learn things of immediate practical value?

I would like to very respectfully tell you that I don't think that's the point of OP. :) (No hard feelings)

I think the point of OP is that you are being ordered to do something and not being told why, like a soldier: just do it and that's that. And that bothers some people because it's not 1 year or 2 years that you are being ordered around and not being told why. It's 11 or 12 years of the same sad story. It feels like you waste your energy for no tangible benefit other than passing your grade. The same old sad story that never ends.

I don't hate math as much now, but did I simply miss those lectures that explained why I was learning the stupid adding x and y and why I'd need to know this for later?

I don't think you missed them. It's just that it is so much material that at most places teachers are not given time to tell you why you are learning what you are learning or make practical exercises. Teachers are simply ordered to follow a syllabus and teach the fundamentals. Not tell you why or help you do something practical with it. If they'd do they would need more time. Time which the hiring institution doesn't give and/or pay them.

Although it is impossible for me to tell you an answer because I wasn't at your school, I don't think you lost that material you talk about (the why and practical uses) because you weren't paying attention. I think you were simply not shown to it.

 

[AlephNumbers]

I think the point of OP is that you are being ordered to do something and not being told why, like a soldier: just do it and that's that. And that bothers some people because it's not 1 year or 2 years that you are being ordered around and not being told why. It's 11 or 12 years of the same sad story. It feels like you waste your energy for no tangible benefit other than passing your grade. The same old sad story that never ends.

Excuse me if I don't shed a tear for all the people in the world who had access to an education.

Okay, that was a bit of a low blow. I'm sorry.

I do think that not nearly enough emphasis is put on the practical application of math.

 

[AlephNumbers]

I do think that not nearly enough emphasis is put on the practical application of math.

I should clarify that I don't mean that math classes should emphasize practical application. That's for science class. I mean that in the US, I think that maybe students should have classes beginning earlier on that focus on applying the math they are learning. I couldn't take physics until my third year of high school.

 

[Mark44]

I think the problem might be that many grade school and high school teachers, themselves, don't understand real world applications of math.

And in many cases, don't really understand math, let alone applications of it. My evidence is somewhat dated (a short brochure from GRE titled "Interpreting Your GRE General and Subject Test Scores"). In it there's a table of average test scores of the three parts of the GRE (Verbal, Quant., and Analytical) for tests given between 1983 and 1986. The scores are broken down by intended graduate major field. Education was included among the Social Science.

In Verbal Ability the average score for Ed majors was 450 (out of 800), the lowest of the 11 major areas. The average scores ranged between 450 and 540 (Languages and other Humanities group).

In Quant. Ability, the average for Ed majors was 479, again the lowest of all 11 major areas. The average scores ranged between 479 and 674 (Engineering) with Math Sciences and Physical Sciences scoring 657 and 635, respectively.

Finally, in Analytical Ability, the average for Ed majors was 506, yet again the lowest of the 11 areas. The average scores ranged between 506 and 596 (Mathematical Sciences).

The data listed in the brochure is about 30 years old. Even so, I doubt that much has changed. I would be surprised to see much change in more current data.

If you ask a math teacher what the use of math is, the only honest answer they can give from personal experience is that it can be used to get a paycheck for teaching it. They, themselves, don't have any experience in the careers they are supposed to be preparing you for.

 

[Evo]

I guess I was lucky to have taken math before the "new math" came out. The elementary school math many younger people took is not the math I took. Math in my day made sense.

 

[symbolipoint]

I guess I was lucky to have taken math before the "new math" came out. The elementary school math many younger people took is not the math I took. Math in my day made sense.

Most of Mathematics was both difficult and made little sense, UNTIL the college-preparatory sequence of courses in high school, starting with Algebra 1.

 

[Tobias Funke]

Most of Mathematics was both difficult and made little sense, UNTIL the college-preparatory sequence of courses in high school, starting with Algebra 1.

Do you have much experience with high school (now commonly middle school) Algebra 1 courses? I think you're giving them far too much credit for making sense. The books are mostly bad, the students aren't ready, and they're often taught poorly. Even "good" algebra (2?) books and courses tend to do unbelievably stupid things like "a matrix is an array of numbers, and here's how you add them, and you multiply them like this...yep, like that...now there's a soccer team that needs 12 jerseys at $15 and a basketball team that needs 14 jerseys at $12, or something, use matrices because we're in that section of the book to find the total cost."

That doesn't make sense.

 

[WWGD]

I have had the impression that few people, not just few teachers, are good in setting the context for an explanation to make sense.

 

[micromass]

Alright, we get a lot of people "blaming" the teachers. And sure, you're right. But let me put in a different perspective:

1) Teaching children is difficult. Really difficult.
It was 10 years ago. I was young and naive, and a local high school searched somebody to teach math. So I accepted and went to teach math for a month. For free. I had a lot of nice plans. I would show them the beauty of math. I would show them how it's applied. I would do a lot better than how my teachers taught me. So first day of school and I stood before the class and I just couldn't get them to pay attention. I would ask for attention, they would shut up for a minute and then start all over again. I had to spend half the class asking for people to pay attention. Sure, I was inexperienced, but that didn't really encourage me to go into teaching. And I'm hardly the only one, a lot of teachers quit after a year or after a few years. Some even come home crying every day. I saw much good intentions and wonderful teachers got really demotivated. I can fully understand why some people after a few years just start teaching from a standard syllabus without trying to do anything innovative.
Granted, there are some people who are good at everything: the subject matter, explaining and class managament. I truly envy those people. But I cannot do it. And I think there are few of those people as well.

So sure, you can go and blame the teachers. But take a look at yourself first. Do you always pay full attention in class? Are you always respectful? Are you motivated and do you engage with the teachers? etc.

We want teachers who are experts in their field. But wait... why would experts in the field even want to teach? The pay is much lower than what you get in industry. And the job is so immensely difficult for most people that they just give up after a few years. There is really no incentive for experts to go into teaching. I surely don't want to go into teaching for the experience I had. So what is left are people (not all of them, mind you), who really don't have much other options than to go into teaching.

2) Teaching applications is difficult
You want math to be more practical? Well, why don't you try it yourself. The issue is that most practical applications require a solid understanding of the matter and of several other matters as well. Try it: find a child who is learning multiplication and teach him/her why we care exactly. They won't get it. The same really holds for much other math (trigonometry being an outlier here). For example, I was teaching topology to my university class. And they complained that they didn't see applications of it. But I couldn't give applications! Not because I didn't know it, but because it would take out too much time, and because they weren't mentally ready for them. Maybe I'm just a lousy teacher, but teaching well is a rare skill.

 

[AlephNumbers]

So sure, you can go and blame the teachers. But take a look at yourself first. Do you always pay full attention in class? Are you always respectful? Are you motivated and do you engage with the teachers? etc.

You make an excellent point.

I used to have to tell people in my English class to shut up so I could hear the teacher. One kid even started eating a thanksgiving turkey during class. I would actively encourage the teacher to give disrespectful students detentions, but he told me that that didn't work, in his experience. I don't blame him one bit for the failing grades that many of those students received.

I am lead to believe that the problem is more of a cultural one, and needs to be addressed at the familial level. Children should be taught at a young age to respect knowledge, and by extension, those with more knowledge than them. Namely, teachers. American society, from what I have experienced, places little value on knowledge compared to collectivist cultures. And it certainly shows.

 

[symbolipoint]

Most of Mathematics was both difficult and made little sense, UNTIL the college-preparatory sequence of courses in high school, starting with Algebra 1.

Do you have much experience with high school (now commonly middle school) Algebra 1 courses? I think you're giving them far too much credit for making sense. The books are mostly bad, the students aren't ready, and they're often taught poorly. Even "good" algebra (2?) books and courses tend to do unbelievably stupid things like "a matrix is an array of numbers, and here's how you add them, and you multiply them like this...yep, like that...now there's a soccer team that needs 12 jerseys at $15 and a basketball team that needs 14 jerseys at $12, or something, use matrices because we're in that section of the book to find the total cost."

That doesn't make sense.

What I say makes sense according to MY EDUCATION WHICH I RECEIVED. I agree that several of the textbooks that students have in the recent few years are harder to use (and not designed as well as in a few decades previous). Still, what weaknesses occur in modern textbooks is something that the teachers can remedy in the classroom - at least for junior high and high school level. High school mathematics teachers would be expected to have enough credits of their own in Mathematics to be qualified to teach the subject; they are usually graduates with degrees in any of Mathematics, Engineering, Computer Science, or nearly any physical science.

 

[zoobyshoe]

Alright, we get a lot of people "blaming" the teachers...
... but teaching well is a rare skill.

Good points, micromass. There are, at least, two separate skills required for a teacher, "class management" being the one that must precede the other.

During my years in grade and high school, the teachers had no problem with this. It was against a background of good class management that they, never-the-less, could not connect most math to my, or anyone else's, reality. One high school algebra teacher in particular answered my query about this with the vague information that engineers use algebra a lot and then he changed the subject, which gave me the impression he had no idea what specific sorts of problems an engineer might actually be confronted with.

I feel he failed me when I was most receptive. If he could have gotten me interested in some real world engineering problem at that point, it could have lit a fire under me to be hungry for more math.

 

[WWGD]

As a(n) (unemployed) teacher and student, I don't think much useful can be reached in this (nor, really most, if not all others) by making this into an "us against them" discussion. Not a brilliant insight, but sometimes discussions (de)evolve in this direction.

 

[Tyrion101]

That was not my intent, to start an us them argument. Now when I had the choice of an algebra class that was just that, or one that used real world modeling techniques, I jumped at it he latter, and I have a far better appreciation of math now than I did, I have an innate need to know how and why things work, it makes things more interesting and part of why I am working to be an engineer now, I just think there's a better way of doing mathematics in lower grades than the current standard. I do not have the answers for everyone but in my case if you give me what it leads to, and help me see how it is used, I'll be far happier to work harder in something I know is actually useful.

 

[WWGD]

That was not my intent, to start an us them argument. Now when I had the choice of an algebra class that was just that, or one that used real world modeling techniques, I jumped at it he latter, and I have a far better appreciation of math now than I did, I have an innate need to know how and why things work, it makes things more interesting and part of why I am working to be an engineer now, I just think there's a better way of doing mathematics in lower grades than the current standard. I do not have the answers for everyone but in my case if you give me what it leads to, and help me see how it is used, I'll be far happier to work harder in something I know is actually useful.

Sorry, I didn't mean to imply that was your goal, only that discussions degenerate somewhat naturally in this direction.

 

[Tyrion101]

Sorry, I didn't mean to imply that was your goal, only that discussions degenerate somewhat naturally in this direction.

Only too true.

 

[WWGD]

But you see, some see an intrinsic esthetic quality of sorts in the way Math works, which sucks them in. I guess something similar happens in other areas.

 

[Tyrion101]

I believe it is aesthetic? But I see your point, language drew me in that way,

 

[zoobyshoe]

As a(n) (unemployed) teacher and student, I don't think much useful can be reached in this (nor, really most, if not all others) by making this into an "us against them" discussion.

I don't even know what this means. Are you saying it's fruitless to question the way math is taught?

 

[AlephNumbers]

As a(n) (unemployed) teacher and student, I don't think much useful can be reached in this (nor, really most, if not all others) by making this into an "us against them" discussion. Not a brilliant insight, but sometimes discussions (de)evolve in this direction.

I don't even know what this means. Are you saying it's fruitless to question the way math is taught?

I find the post equally perplexing. What is an "us against them" argument?

 

[WWGD]

I don't even know what this means. Are you saying it's fruitless to question the way math is taught?

I find the post equally perplexing. What is an "us against them" argument?

I mean a thread in which some blame the teaching/teachers and other blame the students

 

[SteamKing]

I find the post equally perplexing. What is an "us against them" argument?

http://en.wikipedia.org/wiki/You're_either_with_us,_or_against_us

There are several other rhetorical devices with which one should be familiar. Straw Men, anyone?

 

[AlephNumbers]

There are several other rhetorical devices with which one should be familiar. Straw Men, anyone?

Don't question my rhetorical skills. I am a defensive jerk by profession.

Anyways, I'll have to read up on those rhetorical devices. Thanks for the link.