Bumpy Road Thus far; Am I Too Far Gone?

[Cosmophile]

Hey, everyone. First and foremost, I assume you clicked on this out of willingness to offer some insight, so thank you for that. This will be a bit long, and for that I apologize.

I am currently 22 years old and I am wanting to double major in physics and mathematics. I am currently attending a community college to get my Associate's Degree so that I can transfer to a university for my undergrad career. This is my second attempt at community college. When I first started college, I placed out of precalculus and into Calculus I. My first community college was not a good one; the instructors weren't able to answer detailed questions and my needs as a student weren't met. During my first semester, I experienced some medical issues and was in the hospital for some time. My teachers agreed to allow me to do an independent study, but upon the semester's completion, I was marked as failing Calculus (this is the day I learned to get such agreements in writing).

The next semester, I took Calculus I again with the same instructor (this college only had two Calculus instructors). I kept record of all of my grades, the lowest of which was a 96. When I tried to register for Calc II the next semester, I was told I couldn't do so because I made a D in Calculus I. I figured this was simply an issue with entering grades, so I requested that my instructor and I go over the grades, and she declined.

So, the next semester, I took Calculus I again with a different instructor. Because I had taken the class twice before, I had to fill out surveys asking what my weak points as a student are and if I would like to consider additional assistance to overcome any learning obstacles I may have. While I understand that these systems are good to have, it was unsettling to be subjected to them. My father died right before the semester began and I became responsible for all of the legalities involving his property, debts, etc. These external stressors, as well as an overall lack of satisfaction for that school, caused me to withdraw from the school altogether.

I took a year off to handle my father's estate and other issues, and re-enrolled at my community college. This semester is my fourth semester taking Calc I. My final grade will most likely be a C. My current instructor is much better than previous instructors in the sense that he knows mathematics to a much higher degree (no pun intended). That being said, he's a bit ridiculous when it comes to grading. For instance, I made a 69 on my first exam even though no answer was wrong; his issue was that my method of showing my work didn't match his exactly (he has notations that he made up and prefers that we use those). If our work isn't a mirror copy of what his would be, points are deducted. I've always worked for an understanding of material, so mimicry isn't my strong suit. Anyway, this has resulted in quite a few point deductions. When I try discussing my grades with him, he simply says "when you have 20 years of experience, we can discuss the grade I've given you."

That being said, I definitely have some responsibility for my grade's not reflecting my knowledge. Throughout high school, I was a poor student; I always aced my exams but never did the homework and often missed days (I averaged roughly 15 absences per semester in high school). As a result, I never developed good homework habits. My calculus homework is all online (MyMathLab, if you are familiar with it) and points are deducted if the system doesn't agree with the way we put answers in. Being online work, I have had a difficult time remembering to do the work and have missed a few assignments. I accept full responsibility for those instances. The labs that we turn in would easily make up for it, but he invokes the same grading mentality on the labs as he does for tests. For instance, when I had to minimize the distance between two points, I opted to minimize the square of the distance for the sake of simplicity and clarity. I received zero points for doing so and made a C on the lab.

So, here's my question: Am I screwed? I've taken Calculus I four times and won't have an A in the class (unless, for whatever reason, I make a D and have to retake it. I don't want to think about that). I love mathematics and physics. I want to go to a good school and be surrounded by like-minded people, but I'm extremely worried that my bumpy road has doomed me to mediocrity. When I think of applying to schools, all I can think of is admissions seeing my history in Calc I and rolling their eyes, even if I make all A's in the rest of my math courses.

What insights can you all give?

 

[axmls]

I personally don't believe your hopes of getting into a good school are lost. After all, people doing admissions understand bad things happen, and you certainly have a good reason for performing less-than-stellar during those semesters.

I'm an undergrad, so take this with a grain of salt, of course, but the main point is that you really can't go back and fix those past semesters, so focus on doing well now, and if you ever have the opportunity to explain your grades, explain everything.

I am however curious about your professor's homemade notation. Also note, professors often test not only the material at hand, but also your proficiency in applying the techniques you learn in the course. Some people might view this as stifling creativity, but it very well may be the case that the methods you use are much less efficient than the course methods when it comes to more advanced problems, and that's why they teach the way they do.

Have you taken other courses and done well in them? That would probably help too.

Ultimately, I'd say keep working hard (go to office hours!) and you'll be able to move on. No one can guarantee a spot in a great university, but as long as the university you go to is doing some good research and has the courses you need, you'll be fine, especially if you were planning on going to grad school.

By the way, if you do plan on going to grad school, they're be much more willing to let you in if you show improvement and excel in your upper level courses even after failing calculus, anyway. This would be especially true if you explain your extenuating circumstances in your statement of purpose.

But like I said, focus on doing well now. You do have some areas you need to improve, and you need to do so before moving on to a different school (completing online homework in time particularly).

 

[Cosmophile]

Before I reply, can someone fix the title? I have no idea why it doesn't say "bumpy," and why "thus far" is one word...

I am however curious about your professor's homemade notation. Also note, professors often test not only the material at hand, but also your proficiency in applying the techniques you learn in the course. Some people might view this as stifling creativity, but it very well may be the case that the methods you use are much less efficient than the course methods when it comes to more advanced problems, and that's why they teach the way they do.

I'd argue that the notation he requires is pointless (and that his explanations are sometimes wrong). For instance, if I were to find

$$\lim_{x \to -1} \frac {2x^2 -2x -4}{x^2 -1}$$ I would first factor the expression and get

$$\lim_{x \to -1} \frac {(2x+2)(x-2)}{(x+1)(x-1)}$$

Here, our instructor tells us that we can not divide the $(x+1)$ terms to get $\frac {2(x-2)}{(x-1)}$. Instead, he asks that we do this:

where the "EL" over the equal sign stands for "equivalent limit." When I asked him about this, he said that the reason the limits are equal is because of L'Hopital's Rule, which we hadn't covered yet because that involved differentiation. I approached him in office hours about this showed him a proof that if $f(x)$ and $g(x)$ agree $\forall x \neq c$ in an open interval containing $c$ and the limits as $x \to c$ of $f(x)$ and $g(x)$ exist, then the limits are equal. I proved this using the epsilon-delta definition of a limit and he dismissed it before I could begin.

On-topic: Thank you for the helpful words. It's an extremely stressful situation to be in. I seek the best textbooks and post here pretty frequently in hopes that I'll gain a better understanding, but none of that matters when I have instructors like I've had in the past. What advice do you have for dealing with instructors like this? I'm sure I'll come across more.

 

[axmls]

It's difficult to assess what exactly your professor had in mind when saying that (your reasoning is correct when you say cancellation is possible in the limit). That said, unfortunately, the only path to take is to do it your professor's way and avoid taking those professors for future courses. Self study if you need to. Sometimes you just get a semester where that's the only option (as is the case for me this semester).

 

[Cosmophile]

It's difficult to assess what exactly your professor had in mind when saying that (your reasoning is correct when you say cancellation is possible in the limit). That said, unfortunately, the only path to take is to do it your professor's way and avoid taking those professors for future courses. Self study if you need to. Sometimes you just get a semester where that's the only option (as is the case for me this semester).

Certainly, and really, I've worked on making sure I follow his methods more carefully now. I still lose points here and there (if it isn't exactly as he'd do it, he deducts points), but it is what it is, I suppose. It's just very frustrating to be in a position where the instructor can clearly see you know the material but doesn't care to give you a grade based on that.

 

[Choppy]

Sorry to hear you've had such a bumpy road.

Part of success in academia though is learning to navigate the bureaucracy. Sometimes that stuff that "doesn't precisely match" what the professor says is important. Although, as a student, you do have a right to know why. Sometimes, it's just the professor being difficult.

But the major issue that I see is that you've taken a single class four times and there's a massive wall of text, much of which is shifting the blame to others. (I'm not making a call on whether this is justified, I'm just trying to give you a sense of what it comes across as to an outsider). People who look at your transcripts will see how you did and compare you to the rest of your class. That's the reality you have to deal with.

While you're not in a great position, I don't think you've doomed yourself. First-year calculus is first year calculus. What matters is that you learn it well and then go on and are successful in the more advanced classes. The issue you need to focus on though is how, when you go on to Calc II, or III, or differential equations, etc., you are going to avoid falling into the same situations. Do you need to spend more time researching a school and program to make sure it fits with your learning style? Do you need a program where the professors have more time to talk with students?

 

[jtbell]

Before I reply, can someone fix the title?

Done. I also merged your two threads and deleted the duplicate opening post.

 

[Cosmophile]

Sorry to hear you've had such a bumpy road.

But the major issue that I see is that you've taken a single class four times and there's a massive wall of text, much of which is shifting the blame to others. (I'm not making a call on whether this is justified, I'm just trying to give you a sense of what it comes across as to an outsider).

No worries; that's a totally fair criticism, and, as I mentioned, some of the blame certainly falls on my shoulders. Poor organizational skills on my part has resulted in a few missed assignments here and there, which absolutely contributes to my grade not reflecting my ability.

 

[Mark44]

I'd argue that the notation he requires is pointless (and that his explanations are sometimes wrong). For instance, if I were to find

$$\lim_{x \to -1} \frac {2x^2 -2x -4}{x^2 -1}$$ I would first factor the expression and get

$$\lim_{x \to -1} \frac {(2x+2)(x-2)}{(x+1)(x-1)}$$

Here, our instructor tells us that we can not divide the $(x+1)$ terms to get $\frac {2(x-2)}{(x-1)}$. Instead, he asks that we do this:

where the "EL" over the equal sign stands for "equivalent limit." When I asked him about this, he said that the reason the limits are equal is because of L'Hopital's Rule, which we hadn't covered yet because that involved differentiation. I approached him in office hours about this showed him a proof that if $f(x)$ and $g(x)$ agree $\forall x \neq c$ in an open interval containing $c$ and the limits as $x \to c$ of $f(x)$ and $g(x)$ exist, then the limits are equal. I proved this using the epsilon-delta definition of a limit and he dismissed it before I could begin.

You have my complete sympathy here. The current instructor, whom you describe as the better of the two you've had at your school, sounds like either a pedant or someone whose grasp of mathematics is so tenuous that he can't comprehend that there might be other ways of solving a problem that are equally valid. I'm very sorry you have had to spend so much time at that school, as the two calculus instructors you mentioned don't seem to be all that knowledgeable in mathematics. The limit that you showed above does NOT need L'Hopital's Rule to evaluate it. Simply cancelling the x + 1 terms is perfectly legitimate inasmuch as $\frac{x + 1}{x + 1} = 1$ for all values of $x \ne -1$, hence the limit of this fraction is 1 as well.

On-topic: Thank you for the helpful words. It's an extremely stressful situation to be in. I seek the best textbooks and post here pretty frequently in hopes that I'll gain a better understanding, but none of that matters when I have instructors like I've had in the past. What advice do you have for dealing with instructors like this? I'm sure I'll come across more.

Is there some possibility of going to a different school? It sounds like they've been jerking you around at that school.

I have followed many of your posts, and in all of them you have showed very good work, certainly better than would call for C or D grades as you say.

 

[Cosmophile]

Is there some possibility of going to a different school? It sounds like they've been jerking you around at that school.

I have followed many of your posts, and in all of them you have showed very good work, certainly better than would call for C or D grades as you say.

This is, unfortunately, the best school in my area, and is the second school I've tried. The first was even worse. I already am driving 45 minutes to get to my school. I've slept in my truck at a Walmart nearby the school because I didn't have the gas to drive home and back to school. Times are hard.

I always see your responses to my posts, and they're always appreciated. For the most part, I'm self-taught, so getting help and insight from the PF community is invaluable.

 

[micromass]

Is this the same instructor who argued with you over the constants of integration? The guy sounds like a piece of work then. It doesn't sound to me that he really hasa deep grasp on calculus at all! I'm sorry you had to suffer this kind of introduction to calculus. Sadly, there is not much you can do about horrible instructors such as this one. Just see that you pass the class. Then take classes which avoid this guy completely. You will likely not get in top schools, but try to get in as best schools as you can. You will be able to get in somewhere. If you apply yourself there and really make use of the opportunities there, a good grad school is not impossible. But you absolutely can't afford this kind of situation where you take the same course 4 times and end up with a bad grade. Even though it's not entirely your fault, do try that this does not happen again.

 

[Cosmophile]

Is this the same instructor who argued with you over the constants of integration? The guy sounds like a piece of work then. It doesn't sound to me that he really hasa deep grasp on calculus at all! I'm sorry you had to suffer this kind of introduction to calculus. Sadly, there is not much you can do about horrible instructors such as this one. Just see that you pass the class. Then take classes which avoid this guy completely. You will likely not get in top schools, but try to get in as best schools as you can. You will be able to get in somewhere. If you apply yourself there and really make use of the opportunities there, a good grad school is not impossible. But you absolutely can't afford this kind of situation where you take the same course 4 times and end up with a bad grade. Even though it's not entirely your fault, do try that this does not happen again.

Yes, this is the same instructor. Thanks for the help as always, Micromass.