Career options when not good at math

[Electro97]

I take a big interest in science mainly chemistry and physics. My dream is to be an engineering technologist and move on to be a scientist, chemist or a physicist, in not sure yet, the problem is I wasn't the best in my math class because I never really paid attention, I suddenly take an interest in it know and I'm trying to increase my math skills. Is there any physicist on this forum that have been in my shoes, is it possible to succeed under extreme studying and hard work?

 

[axmls]

is it possible to succeed under extreme studying and hard work?

That's the only way to succeed.

Just pay attention in your classes and work hard. In your case, extra hard if you need to catch up due to poor math prerequisite skills.

 

[symbolipoint]

I take a big interest in science mainly chemistry and physics. My dream is to be an engineering technologist and move on to be a scientist, chemist or a physicist, in not sure yet, the problem is I wasn't the best in my math class because I never really paid attention, I suddenly take an interest in it know and I'm trying to increase my math skills. Is there any physicist on this forum that have been in my shoes, is it possible to succeed under extreme studying and hard work?

Some people are both not good at math and not bad at math; they are something in between. Such people can work hard and at least learn mathematics well enough to be able to use it as a tool, both for application and as a tool for understanding.

Effort to learn is very important, and also it is important for those who are "good at math".

 

[jackmell]

I take a big interest in science mainly chemistry and physics. My dream is to be an engineering technologist and move on to be a scientist, chemist or a physicist, in not sure yet, the problem is I wasn't the best in my math class because I never really paid attention, I suddenly take an interest in it know and I'm trying to increase my math skills. Is there any physicist on this forum that have been in my shoes, is it possible to succeed under extreme studying and hard work?

I had a similar problem when I first became interested in Chemistry: I was weak in math. So I embraced and immersed myself in working hard to learn and become good at math and soon began to enjoy and even love math. My chemistry classmates thought I was silly for taking a (non-required) class in differential equations. Then Physical Chemistry happened (highly mathematical) which you'll need to get a degree. We were all there and since I had grown to love math, I basically zipped through (the math part of) it while the same people who thought I was silly for taking DEs had to drop it.

I can't speak for Physics, but can for Chemistry: If you want to do well in Chemistry, then work very hard to excel in math before you begin a degree program in math. Even the very first (degree) course in Chemistry is very mathematical. A minimum rule of thumb is to take the first course in Calculus at the same time you take your first (major) class in Chemistry, then take all four semesters of Calculus even though your degree may only require 2 or three, then go on to take differential equations preferably before taking Physical chemistry which is generally a senior-level course so you have time.

Therefore if you're weak in math, like I was, then take 4-6 months to study pre-Calculus and do all the problems, then register for Calculus and freshman Chemistry even if that means you have to sit-out a semester to do so because otherwise you won't be ready.

 

[Ali.B.]

If you have really made your decision on catching up on working with math, nothing helps you but "perspiration ". As the great "Thomas Edison" says " genius is one percent inspiration and ninety nine percent perspiration "

 

[JakeBrodskyPE]

I suffered math teachers ranging from bad to utterly dreadful at every stage of my education. My grades were nothing to brag about. And yet, I persevered. I studied on my own. I bought extra books and read all I could stand about the subject. To this day, I'm not all that glib with math. I can get by. I understand the broad concepts, but I will never be one of those geniuses.

Math is often used, in my not so humble opinion, as a hazing tool for science and engineering students. Then people sit and wonder why STEM is not popular. Get a clue: IT'S THE MATH! This subject causes more angst than any other in the STEM fields. This is not made any easier because in every subject people tend to use slightly different notations and conventions. Furthermore, many discussions assume exposure and comprehension of these different notations and concepts while poorly designed curricula often fail to teach it or teach it after it was needed in the first place.

It is indeed infuriating. If I were made king of all STEM for a year, I'd spending aligning curricula with the math foundation and attempting to show examples in various other notations and conventions instead of those used just by the math teacher. I'd also spend more time working on applications, REAL applications, not just a few silly word problems, that can't easily be cross checked.

So my advice to you is to forge ahead. You have a lot of work before you. I get it. Many of us have been through it. It's not fun. But if you persevere, it can be very rewarding.

 

[micromass]

I'd also spend more time working on applications, REAL applications, not just a few silly word problems, that can't easily be cross checked.

I get your frustration, but what you propose here is almost impossible to pull off. Sure, there are applications of math, there are a huge number of applications to math. But the applications of math are usually more difficult than what you can do in a math class, because those applications require more knowledge than just math. In order to show an application, you'll need to spend a significant amount of class time working out the prerequisites and the application itself. That goes to cost of other math material which is very much needed for actual other applications.

I get it, word problems are silly. But I don't see a good way to improve upon them. The class is about math, and therefore the problems need to be simple enough to just illustrate the math. Those word problems will then inevitably be too simplistic to model anything interesting.

 

[axmls]

I agree with micromass. Unfortunately, a good application problem requires too much prerequisite knowledge to assume that students in a standard math class would know, and I doubt there's time to teach that knowledge. Of course, I could be wrong.

 

[JakeBrodskyPE]

I get it, word problems are silly. But I don't see a good way to improve upon them.

The problem with teaching pure math, as opposed to applied math, is that there are no practical personal experiences, phenomena, proceses, or other understanding to hang it on to. It exists in abstract, waiting to be used. This is WHY so few people remember this stuff well enough to apply it to anything.

There is well known psychological research that documents how people remember and process information. It has to relate to something they already know. The problem with way we teach math is that it is rarely ever discovered that way. New mathematical concepts usually come about because someone is itching to solve a particular problem in a particular application. Then everything is abstracted from it and they teach the abstraction with no trace of the original history behind it.

It would be better if we started from the application, and then abstracted it rather than teach the abstraction which few can remember or comprehend, and then leave the application as an exercise to the reader.

But let's face it. Math teachers don't give a fig about application. They think they ARE the application. And that's how the hazing happens. Basically, students see some pompous nitwit who probably thinks he or she is way too intelligent to be teaching this class, but they'll throw it at the students anyway and see what sticks. Sure enough, they don't understand much, and then the teacher will smugly walk away wondering why everyone around them is so stupid.

 

[micromass]

It would be better if we started from the application, and then abstracted it rather than teach the abstraction which few can remember or comprehend, and then leave the application as an exercise to the reader.

That is a good theory, but it doesn't work in practice. For example, I would have no idea how to properly motivate "factoring polynomials" through an application that high school students would understand. Factoring polynomials is very important and it is something you need to know, but its importance is not something a student can immediately grasped.

Remember also that a lot of math was invented without an application in mind. I think of Euclidean geometry which was mainly done to train the mind, but which does end up being very useful.

And then there's math whose applications are outdated. The main application for logarithm was to be able to do calculations faster. Not really a compelling reason now that there are calculators. So we'll need to go to other applications which are more difficult to understand.

But let's face it. Math teachers don't give a fig about application. They think they ARE the application. And that's how the hazing happens. Basically, students see some pompous nitwit who probably thinks he or she is way too intelligent to be teaching this class, but they'll throw it at the students anyway and see what sticks. Sure enough, they don't understand much, and then the teacher will smugly walk away wondering why everyone around them is so stupid.

Yes, and you clearly have never taught math before. Teaching is a very difficult job. So perhaps try it before you start throwing insults around.

 

[symbolipoint]

#9, JakeBrodskyPE,
Good mathematics courses usually include applications. The emphasis for a mathematics course is learning the mathematics, and not studying applications of the mathematics. Heavily mathematical reliant subjects like engineering, physics, chemistry, and so much other natural sciences develop students in the way you want for them. University & college math programs always require students to learn subjects or courses which are mathematically intensive. You can check this in the institutions' catalogs.

 

[JakeBrodskyPE]

One of the most difficult things for educators to understand, and I say this as the son of two educators (a university professor and a high school teacher), is that when you finally comprehend something, the way you remember it changes. You see all sorts of interesting correlations and understandings that you didn't have before, and you think that if you could just teach those things, that somehow it will be easier to understand.

WRONG!

You have to understand that the view of someone who knows nothing about the subject is different from your understanding. You want them to get that level but you can't do it by showing them all the insights you learned after the fact. You have to realize that all those insights you learned had a backdrop against which they can be remembered and applied. ONLY THEN will they be able to understand what you know.

I treated most of the math I learned in the context of the classroom as a plug-and-chug exercise. I hated doing that, but I didn't have the time or the resources to do better. Months and in fact many years later, I got flashes of insight as to what it was I was plugging and what I did when I chugged. I get it now. Only as my understanding matured, was it possible for me to turn the subject around far enough to appreciate the abstractions.

I still have notes I wrote to myself about the frustrations I experienced in college. Yes, the abstractions are gorgeous when you already understand them. Euler's forumula is absolutely one of the most sublime pieces of math that I have ever encountered. But it has an application. And that's how I first learned it. The understanding and appreciation came later.

 

[Electro97]

I take a big interest in science mainly chemistry and physics. My dream is to be an engineering technologist and move on to be a scientist, chemist or a physicist, in not sure yet, the problem is I wasn't the best in my math class because I never really paid attention, I suddenly take an interest in it know and I'm trying to increase my math skills. Is there any physicist on this forum that have been in my shoes, is it possible to succeed under extreme studying and hard work?

Update: ok so I got a lot of comments saying yes, some saying no, and some saying it depends on how its taught. My other question is can math be picked up through neuroplasticity? I heard there was a man named rudiger gamm that was not a math person until he trained his brain and become a human calculator.

 

[axmls]

Update: ok so I got a lot of comments saying yes, some saying no, and some saying it depends on how its taught. My other question is can math be picked up through neuroplasticity? I heard there was a man named rudiger gamm that was not a math person until he trained his brain and become a human calculator.

There is no special secret that people use to become good at math. All it takes is going to class every day, going to the professor when you need it, doing all the homework, and making sure you fundamentally understand what you're doing.

 

[JakeBrodskyPE]

and making sure you fundamentally understand what you're doing.

That's the hard part. Too many teachers themselves do not fully understand what they're teaching. Imagine lecturing about a subject one had never applied beyond the classroom exercises. Is it really possible to comprehend the subject with so little experience? Many will go through the motions without actually thinking the whole process through. If one were to stop them and ask (for example), "I see that you equate these terms, but what does it mean when we presume they are equal?" --More than half of the time in my experience, there would not be a comprehensible answer. After a while, many realize the futility of asking such questions, so instead they study WHAT the instructor did instead of why. Often these classes are paced so fast that the time or the mental capacity to ask such questions just isn't available.

Plugging and chugging through algebraic and trigonometric, and various other identities is pretty straightforward. The hard part is comprehending how and why the equations were set up the way they were and the an understanding of what the result actually implies. This is the coping mechanism that many use. Some are gifted with an intuition that makes such leaps of comprehension immediately obvious. I'm not one of them; nor, I suspect, are most students.

 

[symbolipoint]

That's the hard part. Too many teachers themselves do not fully understand what they're teaching. Imagine lecturing about a subject one had never applied beyond the classroom exercises. Is it really possible to comprehend the subject with so little experience? Many will go through the motions without actually thinking the whole process through. If one were to stop them and ask (for example), "I see that you equate these terms, but what does it mean when we presume they are equal?" --More than half of the time in my experience, there would not be a comprehensible answer. After a while, many realize the futility of asking such questions, so instead they study WHAT the instructor did instead of why. Often these classes are paced so fast that the time or the mental capacity to ask such questions just isn't available.

Plugging and chugging through algebraic and trigonometric, and various other identities is pretty straightforward. The hard part is comprehending how and why the equations were set up the way they were and the an understanding of what the result actually implies. This is the coping mechanism that many use. Some are gifted with an intuition that makes such leaps of comprehension immediately obvious. I'm not one of them; nor, I suspect, are most students.

JakeBrodskyPE, maybe you received less than mediocre instruction in Mathematics. Instruction quality varies. High school math teachers are typically qualified enough (have studied the course themselves at one time) for the courses they teach. College and university teachers are more than typically well qualified for what they teach. From their instruction, the rest of the learning is the students' responsibilities. Sometimes this means repeating a course. Sometimes this means studying more on your own. Other courses which are not Mathematics courses but are mathematically intensive, usually do not teach the Mathematics, but in these, the students APPLY the mathematics which they had studied.

 

[JakeBrodskyPE]

[...]maybe you received less than mediocre instruction in Mathematics. Instruction quality varies.

I graduated from the Johns Hopkins University nearly 25 years ago. If that's a mediocre example of a university education, I have to wonder what bad is.

When I read the career guidance, and engineering questions that people ask in these forums I can't help but notice that a high percentage of the problems are due to difficulty understanding the math or a misapplication of the mathematical abstraction because they do not understand the underlying relationships it describes. It is a very common theme. Another common theme is students assessing difficulty of courses based upon how much mathematics background is required. Would they really do that if they had a solid background in math? We don't see nearly as many people assessing the difficulty of courses in the Humanities in terms of reading comprehension, why is math different?

As I pointed out before, there are students who can intuitively understand new notation systems, new derivations, and immediately understand what an equation implies. I know such people. But they are very few and very far between. They were perhaps a few percent of the students in my engineering classes at Hopkins.

I think we are teaching math very poorly. I know, professors and academics of all stripes adore abstraction. I like it too. But most people study, learn, and apply in specific instances. The abstractions come later.

 

[StatGuy2000]

I graduated from the Johns Hopkins University nearly 25 years ago. If that's a mediocre example of a university education, I have to wonder what bad is.

When I read the career guidance, and engineering questions that people ask in these forums I can't help but notice that a high percentage of the problems are due to difficulty understanding the math or a misapplication of the mathematical abstraction because they do not understand the underlying relationships it describes. It is a very common theme. Another common theme is students assessing difficulty of courses based upon how much mathematics background is required. Would they really do that if they had a solid background in math? We don't see nearly as many people assessing the difficulty of courses in the Humanities in terms of reading comprehension, why is math different?

As I pointed out before, there are students who can intuitively understand new notation systems, new derivations, and immediately understand what an equation implies. I know such people. But they are very few and very far between. They were perhaps a few percent of the students in my engineering classes at Hopkins.

I think we are teaching math very poorly. I know, professors and academics of all stripes adore abstraction. I like it too. But most people study, learn, and apply in specific instances. The abstractions come later.

Jake, first of all, when you talk about the teaching of math, are you talking about college/university level instruction, or are you talking about math instruction at the K-12 level? Because the issues you raise about the quality of the teaching of math are, as I see it, different in both areas.

You state that math has to be tied into specific instances or applications, but I would have to agree with micromass that this is simply not possible at the K-12 level. At that level, math should best be thought of as a language where children are learning the "syntax" and "grammatical rules" and the methods of proof and problem solving associated with learning that language. Once a certain maturity and foundation is established, it is only then that one can look at specific instances or applications to tie in that mathematical knowledge into practical situations or problems.

At the college/university level, my feeling is that problems with abstraction comes in largely because the people who may be teaching math to engineering students are the same people who are teaching math to math students. This could be a problem, however, as engineers are, for the most part, not interested in abstraction per se, but would need to know math to be able to specifically apply to various problems that they are required to solve (e.g. learn differential equations to solve problems in fluid flow), whereas the math student will need to know the firm foundation, including the solving of proofs, etc, and at least some of those instructors who are trained to think abstractly in math may not have the comfort level or understanding to specifically see from the applied perspective of the engineer.

 

[JakeBrodskyPE]

I think elementary and middle schools do a better job teaching math than high schools and colleges. Even though they do teach abstractions, it is possible to visualize what those abstractions are --that is until at some point when the subject of Algebra gets going. That's when some kids decide they're going to do something else.

From that point on, more and more kids get flummoxed. Some are lost when learning Geometry, even more are lost during Algebra II, and by the time they take Trigonometry/Pre-Calculus, many have learned to plug and chug. I'm watching my middle school and two high school kids go through this. It is not a pretty sight. By the time they're picking out courses for college, most of those headed for some kind of STEM studies have figured out coping mechanisms.

We encourage kids to explore the STEM subjects, but then they have to deal with learning everything backwards. And we wonder why so many of those who study STEM are skewed toward introversion. It's because only introverts can devote the mental bandwidth needed to overcome the extraordinary effort of integrating abstractions into their understanding, and then remembering it well enough for it to be useful later on.

Let's face the reality: this is not an "Engineering" thing. It is a mad rush to abstract concepts before they're even understood. Those who get it, don't seem to understand what all the fuss is about. I made a deliberate effort to remember my frustrations and what it felt like while trying to learn this stuff. I knew that eventually I would understand this stuff and then I'd look back and wonder what the confusion was about. I try to remember that confusion and what triggered it so that I could help others get past those problems.

Despite my grousing about how we teach this subject, I do appreciate a wide variety of mathematics. It is a truly a thing of beauty. But the frustration of learning it is not something I'm likely to forget. I've seen math teachers in many different school systems. I've yet to meet one who inspired even a small fraction of the students in a class.

If we were to change one thing to encourage more kids to embrace the STEM fields, it would have to be to find a better way to convey and teach Mathematical concepts.

 

[symbolipoint]

Posting #19:
The discussion indicates a change has happened in the way Mathematics is being taught. Much the same human responses are happening, but Math courses were once taught differently than today; and maybe in the future the way will change again.

In elementary and middle school, the smart students do well (mostly) in Mathematics. Suddenly in high school, many of the smart students struggle with Algebra and learn less well in this than they were accustomed. Hard to say why or what confuses them. Each student would best speak for himself about this.

 

[StatGuy2000]

I think elementary and middle schools do a better job teaching math than high schools and colleges. Even though they do teach abstractions, it is possible to visualize what those abstractions are --that is until at some point when the subject of Algebra gets going. That's when some kids decide they're going to do something else.

From that point on, more and more kids get flummoxed. Some are lost when learning Geometry, even more are lost during Algebra II, and by the time they take Trigonometry/Pre-Calculus, many have learned to plug and chug. I'm watching my middle school and two high school kids go through this. It is not a pretty sight. By the time they're picking out courses for college, most of those headed for some kind of STEM studies have figured out coping mechanisms.

We encourage kids to explore the STEM subjects, but then they have to deal with learning everything backwards. And we wonder why so many of those who study STEM are skewed toward introversion. It's because only introverts can devote the mental bandwidth needed to overcome the extraordinary effort of integrating abstractions into their understanding, and then remembering it well enough for it to be useful later on.

Let's face the reality: this is not an "Engineering" thing. It is a mad rush to abstract concepts before they're even understood. Those who get it, don't seem to understand what all the fuss is about. I made a deliberate effort to remember my frustrations and what it felt like while trying to learn this stuff. I knew that eventually I would understand this stuff and then I'd look back and wonder what the confusion was about. I try to remember that confusion and what triggered it so that I could help others get past those problems.

Despite my grousing about how we teach this subject, I do appreciate a wide variety of mathematics. It is a truly a thing of beauty. But the frustration of learning it is not something I'm likely to forget. I've seen math teachers in many different school systems. I've yet to meet one who inspired even a small fraction of the students in a class.

If we were to change one thing to encourage more kids to embrace the STEM fields, it would have to be to find a better way to convey and teach Mathematical concepts.

My sense here is that the abstractions taught in elementary and middle schools in the US (and also in Canada, at least when I went to school) covers topics at too slow a pace, and so abstract concepts are rushed from middle school to high school. I recall that kids are still learning the multiplication tables by the time they are in Grade 4, when this is something that should be mastered by a student is in Grades 1 or 2 -- students should be learning the basics of algebra and geometry by the time the student finishes Grade 6, including the ability to do proofs and solve word problems (similar to the curriculum offered in Japan, my mother's home country). I learned algebra by the time I finished Grade 8, and learned calculus in Grade 10, and I was almost completely self-taught (although I was lucky to have several inspirational math teachers in high school).

I suspect that part of the problem with math instruction is that many teachers in schools in the US (and Canada) do not have an especially strong command of the subject themselves, and therefore are unable to effectively teach the subject. The other part of the problem is a widespread belief within North America that math ability is somehow a "genetic" ability (i.e. people are born with this ability), so many teachers and parents believe that if children initially struggle with the subject, then somehow those children are "incapable" of learning the subject. This has always been ridiculous to me -- we don't believe that children who struggle with learning to read are "incapable" of learning to read -- why do we believe that math is somehow different? If a student struggles, then isn't it logical to assume that this may be due to poor instruction, as much as due to any inherent ability?

In countries outside of North America, there is an expectation that anyone can and should learn math. That's how I was brought up, and I also believe that anyone can learn math with enough effort and good instruction.