Failing trigonometry = the death of a amatuer physicist

[ObHassell]

Well, honestly you shouldn't beat yourself up bad about it, as long as you get at least a C you're doing well enough. To me it's the lowest acceptable grade in a math class...and besides...at least it's not a D!

At my high school I had a HORRIBLE teacher for Intermediate Algebra. He was from Colombia and after living here for like 20 years he still hadn't lost a pinch of his accent. Well I failed the first semester and barely got a D in the second, so I retook it next year and replaced that F with a C (it was a B for the longest time, but i think i messed up on one exam). There were other kids in that class that were getting high A's and High B's and I was getting a C, but since my teacher knew that I could do the math and was pretty good at it, he would use my papers (homework and classwork) as the answer key!

So just because you aren't doing well (gradewise) you might just not be cut out for math! But physics is different from Math, it's got math, and some of it is very close to just being another math class, but Physics is NOT math (again, very math intensive, but a totally different thing at the same time). I took Physics for a semester to try it out and loved it! In all of the class I was in the lowest level math in all of my physics class, I was in the first semester of Precalc and everyone else was in AP Calc BC (that's Calculus 2). I did exceptionally well! Again, my grade was like a B, but I did really well with the topics and the math and everything (I just didn't really do any homework...neither did anyone else). Out of all 12 of us, only two of us could actually understand what was happening in that class and that was me and this kid named Jonjon, and jonjon went to the best high school in the country up until 10th grade, BASIS Charter School (if you don't start at that school in 4th or 5th grade, you WILL fail...horribly...Algebra 1 in 7th, Algebra 2 in 8th, and Precalc in 9th)

So don't feel bad, you can be decent or even horrible at math and still do great! As long as you like doing Physics, you should do perfectly fine...This is from my experience though...so yeah...Good Luck!

 

[Cantab Morgan]

High school is a joke anyway, don't worry.

What could that possibly mean? I'm serious, what does that even mean? In what universe is that constructive advice?

 

[thrill3rnit3]

Don't even get me started with high school math.

 

[Cantab Morgan]

Don't even get me started with high school math.

Respectfully, that's not an answer.

 

[thrill3rnit3]

Respectfully, that's not an answer.

I wasn't trying to answer the original poster. I was following up the previous posts which were about how bad high school is.

 

[ObHassell]

i totally agree with thrill. High school math is ridiculously strange...most of the teachers aren't doing it because they love math or teaching, it's because they didn't do well enough in college to get a good job or into a grad program so they thought "hey, what the heck...How bout teaching?" and that's the way it goes. My senior year Precal/Trig teacher wasn't very good at teaching, but at least he did love math...he had a doctorate in math. But most other teachers were just plain difficult...all my life before high school i heard that algebra 2 was easier than algebra 1 because it was the same thing just a little bit more advanced (which was supposed to be easy because you already knew the material, so you were just doing more advanced versions of it)...then when i get to algebra 2 it's like "OMG! This has got to be the hardest thing I've ever done in my life!"...my teacher was horrible. and that's all I have to say

 

[thrill3rnit3]

i totally agree with thrill. High school math is ridiculously strange...most of the teachers aren't doing it because they love math or teaching, it's because they didn't do well enough in college to get a good job or into a grad program so they thought "hey, what the heck...How bout teaching?" and that's the way it goes. My senior year Precal/Trig teacher wasn't very good at teaching, but at least he did love math...he had a doctorate in math. But most other teachers were just plain difficult...all my life before high school i heard that algebra 2 was easier than algebra 1 because it was the same thing just a little bit more advanced (which was supposed to be easy because you already knew the material, so you were just doing more advanced versions of it)...then when i get to algebra 2 it's like "OMG! This has got to be the hardest thing I've ever done in my life!"...my teacher was horrible. and that's all I have to say

My Algebra 2/Trig teacher 2 years ago is so bad, like seriously. She teaches the classic plug and chug method. Doesn't teach the most important stuff because it's "too hard for the rest". Like I remember when I was taking her class, and we were doing trigonometry, she didn't even touch on the identities...and half her class was planning to take ap calculus the next year.

 

[Wellesley]

Recently I've heard that the US math teaching system is very poor now.

An excellent example of currently used teaching methods for math classes:

This seemed appropriate material for this Forum, I wasn't sure what section.

http://www.bryanappleyard.com/blog/2008/04/teaching-maths.php

1. Teaching Maths In 1970
A logger sells a truckload of timber for £100.
His cost of production is 4/5 of the price.
What is his profit?

2. Teaching Maths In 1980
A logger sells a truckload of timber for £100.
His cost of production is 4/5 of the price, or £80.
What is his profit?

3. Teaching Maths In 1990
A logger sells a truckload of timber for £100.
His cost of production is £80.
Did he make a profit?

4. Teaching Maths In 2000
A logger sells a truckload of timber for £100.
His cost of production is £80 and his profit is £20.
Your assignment: Underline the number 20.

5. Teaching Maths In 2008
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. )

 

[Wellesley]

So just because you aren't doing well (gradewise) you might just not be cut out for math! But physics is different from Math, it's got math, and some of it is very close to just being another math class, but Physics is NOT math (again, very math intensive, but a totally different thing at the same time). I took Physics for a semester to try it out and loved it! In all of the class I was in the lowest level math in all of my physics class, I was in the first semester of Precalc and everyone else was in AP Calc BC (that's Calculus 2). I did exceptionally well! Again, my grade was like a B, but I did really well with the topics and the math and everything (I just didn't really do any homework...neither did anyone else).

Not to be critical, but...I think physics has a lot of math in it, especially if you make it a career. I know that it goes well beyond Calculus II.

There were other kids in that class that were getting high A's and High B's and I was getting a C, but since my teacher knew that I could do the math and was pretty good at it, he would use my papers (homework and classwork) as the answer key!

 

[Count Iblis]

it won't do anything but confuse him further

This mentality is the cause of the problem in the first place. I mean, if we were to only teach spelling and grammar and postpone letting students read books until university, because "you should first learn to master the basics perfectly before you move on", then children would grow up to become illiterate. It is precisely because we teach math in this way that grown up people don't know much about math.

 

[millitiz]

This mentality is the cause of the problem in the first place. I mean, if we were to only teach spelling and grammar and postpone letting students read books until university, because "you should first learn to master the basics perfectly before you move on", then children would grow up to become illiterate. It is precisely because we teach math in this way that grown up people don't know much about math.

Hmm, very interesting. While it sounds reasonable, I kinda wonder, then where is the cut off point?
Just take the complex relation here. So if the HS teacher teach it in a HS trig course, then doesn't s/he also need to introduce what complex number is? The complex plain? Why is this true? and what exactly is i, How to derive it, etc...I mean you can go on and on and on. And the problem is, where should the teacher stops? It is easy to introduce this concept, but it would take a lot much more time to integrate this concept into students' head.
And btw, if the students couldn't grasp the ideas of trigonometry, would using some even more advance way of explaining it be appropriated, or is it going to be more confusing?

 

[Count Iblis]

The teacher should teach about complex numbers, but that should be done when the students are about 12 years old. Not when they are 14 or 15 and starting to learn trigonometry.

Complex numbers, complex plane, etc. can be taught to 12 years olds without much problems. You can use elementary geometry, you don't need to be proficient at being able to use trigonometric formulas like cos(2 alpha) = 2 cos^2(alpha) - 1.

Then when the students learn about exponential function they can learn about Euler's identity as well. Now trigonometry is different from just simple geometry in that you now have to be able to manipulate expressions involving trigonometric functions in a more abstract way. Being able to use the algebra of complex numbers then helps.

 

[ank_gl]

The teacher should teach about complex numbers, but that should be done when the students are about 12 years old. Not when they are 14 or 15 and starting to learn trigonometry.

Complex numbers, complex plane, etc. can be taught to 12 years olds without much problems. You can use elementary geometry, you don't need to be proficient at being able to use trigonometric formulas like cos(2 alpha) = 2 cos^2(alpha) - 1.

one needs to consider that students at 12-14 have limited minds, they cannot compare to what you have. Students need to be fed slowly, so that they absorb things which are taught. Can you imagine how confused a child would be if he can prove trig relations by complex numbers, but is unable to recall any complex number at all?
quite frankly, have you ever taught a student? I teach my brother maths & physics an hour daily, he is in high school. Being an engineer, i do sometimes go in soooo much detail & depth, that the poor guy is left

Age is a serious factor, else I would have had 5 PhDs by now

 

[Wellesley]

one needs to consider that students at 12-14 have limited minds, they cannot compare to what you have. Students need to be fed slowly, so that they absorb things which are taught. Can you imagine how confused a child would be if he can prove trig relations by complex numbers, but is unable to recall any complex number at all?
quite frankly, have you ever taught a student? I teach my brother maths & physics an hour daily, he is in high school. Being an engineer, i do sometimes go in soooo much detail & depth, that the poor guy is left

Age is a serious factor, else I would have had 5 PhDs by now

If kids were exposed early enough, I don't think there would be any problems. The problem is, in schools, kids are not learning as much as they should be. For example, kids are coming into high school, not knowing how to graph a (X,Y) point, or can barely deal with fractions. It's the schools that are the problem, not the restraints of the kid's age.

 

[Count Iblis]

I agree with Wellesley. Kids of age 8 play computer games that require more logical reasoning than solving the average university homework math problem requires. So, kids at primary school are capable of learning much more mathematics than they are taught now.

Also, if you were to teach math at a younger age, the brains of children will develop differently so that they can more easily understand math. It is similar to how you wouldn't have been able to read and write properly if you had learned it after the age of 12. Reading a sentence would have remained as difficult for you as for a five year old who has just learned it.

 

[kaos86]

if you were to teach math at a younger age, the brains of children will develop differently so that they can more easily understand math.

It's true, I wish I was exposed to math soon in my younger days. Sadly, the education system in America sucks ***. Japan has robots already and yet America just have bad teachers, books, and no good plan for children to advance well in the schools. I agree with everyone on somethings about school and issues of the education system.

 

[thrill3rnit3]

The United States hasn't been about education.

It has been about sports, leisure, and partying. There's no way you can change that now.

 

[DarrenM]

Also, if you were to teach math at a younger age, the brains of children will develop differently so that they can more easily understand math.

I'm very wary of statements like this, as I cannot recall having read or seen a study that supported such claims...especially ones that were not first passed through the media hype-machine.

I'm also a bit amused by the invective I'm seeing hurled at the education system. I will very shortly be concluding my 2nd year as a high school teacher, and I can't help but wonder how many folks making these comments have taught before... or how many people saying these things even have children.

My own experience has led me to believe that the problem is caused by a multitude of various factors. Bad teachers may be one of those factors, but I seriously doubt they are the primary one. It is a systemic problem, and it is not something that an inane 4-year plan is going to fix. A child could have the best teacher in the world but if they go home to an environment that not only places little value on education but outright reviles it... well, I hope my magic wand arrives soon, because that's the only way that child will be able to break the cycle they're in.

I've seen a depressing lack of personal resposibility amongst students and parents. A teacher's job is to teach, true, but "to learn" is not a passive verb. We can not, no matter how much we may wish to, open up a child's head and impart knowledge or understanding when that child does not care to learn. We can try to plant those seeds, but if they're not in fertile ground we're out of luck.

When I was quite young, even before I started attending school, my mother spent a great deal of time with me reviewing flashcards. Basic arithmetic, multiplication tables, states and their capitols, as well as an assortment of other subjects and content. My mother did not have a college education, but she burned with a desire to see her sons obtain a degree, to go on and do "better" than she had. I would rather have been caught smoking than have brought home a report card with a C on it. We weren't struck, or abused, but the disappointment that it would have caused... I still shiver at the thought. We were taught to show respect to our teachers even--no, especially, if we did not like them. It was made clear that we were there to learn regardless of whether or not we "liked" the teacher.

If a student is not doing well the first questions I ask are these: has he been doing his homework? Has she been taking notes/paying attention in class? Has he been coming to the extra-help sessions that are available? Do you, the parent, see the child doing any schoolwork at home?

Which leads us back to the original question; others have stated that failing a single math class is not the apocalypse. However, I would reiterate that the single most important person in your education is you. You may have a bad teacher, yes, but ultimately you determine how much you get out of a class. Barring certain extenuating circumstances, a poor grade is almost always a reflection of a lack of ability, lack of effort, or both.

 

[millitiz]

It seems like the direction of thread is spinning off from the main course :D

I agree with Wellesley. Kids of age 8 play computer games that require more logical reasoning than solving the average university homework math problem requires. So, kids at primary school are capable of learning much more mathematics than they are taught now.

Also, if you were to teach math at a younger age, the brains of children will develop differently so that they can more easily understand math. It is similar to how you wouldn't have been able to read and write properly if you had learned it after the age of 12. Reading a sentence would have remained as difficult for you as for a five year old who has just learned it.

I think I am pushing it a bit too serious, I am wondering the credibility of your first statement of your first statement " Kids of age 8 play computer games that require more logical reasoning than solving the average university homework math problem requires."
Because I have the feeling that the statement is more like "there exist some kids of age 8 that play computer games that require more logical reasoning..."
If so, then the statement really means nothing. Yea, that it is nice, but so what? Statistically speaking, it doesn't not draw any useful conclusion other than confirming the Gaussian bell shape curve.
If the statement is "The average kids of age 8 that play computer games..."
Then I would suggest to fire all of the high school, middle school, elemental school teachers. They AREN'T teaching anything! Furthermore, I propose to let the average 8 year old kids to study in universities! Why? They could already do universities' works, why should we keep them in elementary school while they have the capability to be Einstein? (Well, this make me feel dumb. I have about the same intelligent level of 8 year old kids?)

And the brain develops differently. Well, is it a good thing? I have the feeling (with no solid evidence support) that this type of changing the structure of brain sacrifices the flexibility of the young minds. Assume so, then personally I don't think that it is a good thing.

 

[DrummingAtom]

... However, I would reiterate that the single most important person in your education is you. You may have a bad teacher, yes, but ultimately you determine how much you get out of a class. Barring certain extenuating circumstances, a poor grade is almost always a reflection of a lack of ability, lack of effort, or both.

I agree with this; Darren has brought up some great points. For me, especially with Math/Physics classes, the teacher has very little impact on my understanding. I have to work on a lot of problems and with various resources to gain mastery of a topic. The teacher does, however, reinforce topics that you've worked on. To me, the most important thing a teacher can do is show the ideas of what's to come. This makes me motivated to learn the new ideas and builds confidence of my previous learned topics.

 

[ank_gl]

If kids were exposed early enough, I don't think there would be any problems. The problem is, in schools, kids are not learning as much as they should be. For example, kids are coming into high school, not knowing how to graph a (X,Y) point, or can barely deal with fractions. It's the schools that are the problem, not the restraints of the kid's age.

talkin about US??
I dunno, its not so in the world 180degrees past US.

I agree with Wellesley. Kids of age 8 play computer games that require more logical reasoning than solving the average university homework math problem requires. So, kids at primary school are capable of learning much more mathematics than they are taught now.

hold on,, which game requires logical reasoning?, as in quake?, calculation of projectile motion, NFS?, automotive engineering?, blah... what?. only game requiring any mental exercise is solitaire or spider solitaire or freecell i guess, but then, how many 8 year olds play these?(i only see my dad playing it)

Also, if you were to teach math at a younger age, the brains of children will develop differently so that they can more easily understand math. It is similar to how you wouldn't have been able to read and write properly if you had learned it after the age of 12. Reading a sentence would have remained as difficult for you as for a five year old who has just learned it.

early starters learn more! is this what you mean? I don't see anyone who can support this 100%. it might be the case, but it won't be the case always.

will to study & understand comes with maturity, not by forcing tykes to remember sin(90) = 1. when did Einstein start?

Children are not computer, they are not meant to be programmed, they are meant to be nurtured. I seriously advice you try to teach a 12 year old.

 

[ank_gl]

anyways, skimming through the post, DarrenM has made the colossally right point & the best so far

 

[Wellesley]

talkin about US??
I dunno, its not so in the world 180degrees past US.


hold on,, which game requires logical reasoning?, as in quake?, calculation of projectile motion, NFS?, automotive engineering?, blah... what?. only game requiring any mental exercise is solitaire or spider solitaire or freecell i guess, but then, how many 8 year olds play these?(i only see my dad playing it)


early starters learn more! is this what you mean? I don't see anyone who can support this 100%. it might be the case, but it won't be the case always.

will to study & understand comes with maturity, not by forcing tykes to remember sin(90) = 1. when did Einstein start?

Children are not computer, they are not meant to be programmed, they are meant to be nurtured. I seriously advice you try to teach a 12 year old.

Since this thread went off-road a while ago,
ank_gl, I'm not quite sure what you meant by the comment about the U.S. Did you mean other countries are worse, or better than America? What's "180 degrees past the U.S."?

Regarding the games: any strategy (Real time, turn-based), adventure (Traitors Gate, etc.), or role-playing (Star Wars, Knights of the Old Republic) game requires a certain degree of reasoning. I have seen plenty of 11 and 12 year old kids (sometmes even younger kids) playing games geared towardadults and 16-18 year olds play.

I don't necessary believe we should start teaching 8 year olds trig identities. Rather, the courses taught in middle school and high school (in the U.S.) should be streamlined so that courses in High school, (i.e. Trigonometry) are more meaningful and integrated with more advanced courses.

 

[calceus]

Trigonometry is a one page subject:

That requires only two real numbers to fully comprehend, after "learning" the basics.

However, do to the generically defined concepts of inversion, reflection, and rotation, that must be "preformed" in a very specific order: mistakes are common.

Trig is the most "efficient" branch of mathematics when used correctly.

But the ease of making "mundane" simple clerical mistakes, can cause one to loose comprehention all together.

 

[kaos86]

The United States hasn't been about education.

It has been about sports, leisure, and partying. There's no way you can change that now.

We can change that. We just need to make education serious for today's Americans (like me.) and have books that can help students understand the subject at hand. well, maybe if possible.

 

[thrill3rnit3]

It CAN be done...it's going to be a major overhaul and change in the curriculum especially at the high school level.

It's pitiful how the U.S. has one of the worst education systems in the world, and California, being the worst state in terms of education, decides to cut down its budget through a HUGE budget cut in education.

 

[Wellesley]

We can change that. We just need to make education serious for today's Americans (like me.) and have books that can help students understand the subject at hand. well, maybe if possible.

But why would the teachers want to change? That means more work for them. Note, I am not saying all teachers don't do work. The work ethics follow a bell curve.

 

[maze]

hold on,, which game requires logical reasoning?, as in quake?, calculation of projectile motion, NFS?, automotive engineering?, blah... what?. only game requiring any mental exercise is solitaire or spider solitaire or freecell i guess, but then, how many 8 year olds play these?(i only see my dad playing it)

Starcraft is one that immediately comes to mind.

 

[Count Iblis]

If we again compare the way math is taught to other subjects then we also see that part of the curriculum of most subjects will also consist of activities that are fun. In case of language lessons we can think of activities like reading books, even watching t.v. (e.g. during French lessons in high school the teacher sometimes brought her video and we watched some t.v. program).

Another thing is that unlike the other subjects, the goal of learning math is not clear to students. Students are not told how math is used in the real world. The problems they solve are artificial useless problems with little application to either practical application or even as good practice problems to learn more advanced math.


So, there is a lot of room for improvement. One can invent new computer games for small children that will automatically train their logical thinking skills without the children even getting the idea that they are doing anything else than playing. You can imagine children in kindergarten playing such games instead of wasting their time doing nothing as is the case now.

 

[thrill3rnit3]

Another thing is that unlike the other subjects, the goal of learning math is not clear to students. Students are not told how math is used in the real world. The problems they solve are artificial useless problems with little application to either practical application or even as good practice problems to learn more advanced math.

blame that to the plug and chug approach by most of the math teachers