First time taking Calculus 1 and I only got a B

[stivodivo]

I tried very hard studying calculus before my semester started. I self-taught myself for months and realized that I was actually good at it. I felt very confident, so I decided to take a online summer class. This was my first calculus class ever. Rather than a 15 week semester, the class is only 8 weeks long- start to finish. Ended 07/08/22.

Unfortunately, I did very poorly on the final exam. Long story short, it made my grade from an A to a B. Personally, I don't feel good about using excuses. However, test anxiety combined with brain surgery (right hippocampus removed tumor), was a big weight during my tests.

Studying by myself cam get very obsessive, I sometimes go for days binge watching math videos; writing and studying for 9 hours per day. Practicing my math then getting burned out. This is one of those cases.

I was furious when I saw my final calculated grade (82%); I was really hoping for a 92% minimum. I don't know how this will look to the graduate school I apply to. Also don't know how retaking would look; I understand the material of calculus 1 very well. It's either I can't accept that I can't do calculus correctly, or I felt nabbed of my A because I have very poor lose short term memory (hippocampus).

it's important to include my thoughts about my instructor. I'm not sure if this is common practice or not, but my teacher does not tell you what you did wrong on tests. His teaching skill was not exactly good. He only answers questions during office hours on a piece of paper in front of a webcam. Just going through the problems without explaining why the result is correct. 80% of the content we asked help for, wasn't even on the final exam.

I'm being a crybaby and I'm blaming my instructor. I'm not happy with my grade and I feel like it will ruin applications to grad school/etc. I want to be an astrophysicist, and I have this feeling that I must be a straight A student. This final grade was a gigantic punch to my confidence. I don't want to start calculus 2 until I study it awhile beforehand. The only way to recover my grade appearance is to Ace calculus 2.

I love astrophysics, and I think about it every day. I enjoy math a lot, I was having a good semester until the final. Too much pressure is a weakness for me. I'm typing this post to cope, I want to know if someone has experienced something similar. Or are all of you straight A students?

TL:DR - Got a B in calculus, is this going to look bad for an application to a grad school?

 

[symbolipoint]

it's important to include my thoughts about my instructor. I'm not sure if this is common practice or not, but my teacher does not tell you what you did wrong on tests. His teaching skill was not exactly good. He only answers questions during office hours on a piece of paper in front of a webcam. Just going through the problems without explaining why the result is correct. 80% of the content we asked help for, wasn't even on the final exam.

I'm being a crybaby and I'm blaming my instructor. I'm not happy with my grade and I feel like it will ruin applications to grad school/et

You want the full semester-length course. NOT a 8 week class during a summer session. You complain too that you earned a B instead of a A. DID YOU LEARN? You still may not know if you did, until you enroll in and study Calculus 2. If you do poorly in Calc2, then this is a strong indication you did not learn Calc1 well enough regardless of "grade earned".

 

[Mark44]

NOT a 8 week class during a summer session.

Minor point, but this was not a summer session, as it ended on July 8, which is only about three weeks after the start of summer. The point about an 8-week class vs. 15-week class is germane, though.

I sometimes go for days binge watching math videos

I'm not sure watching math videos is as helpful as you probably think it was. And self-study is not as fruitful as being able to get feedback on your work from an instructor, IMO.

 

[Vanadium 50]

If it's all your teacher's fault, what do you want us to do? Won't all these problems go away as soon as you get another instructor?

Of course, if you bear some non-zero responsibility, maybe we can help.

 

[symbolipoint]

I tried very hard studying calculus before my semester started. I self-taught myself for months and realized that I was actually good at it. I felt very confident, so I decided to take a online summer class. This was my first calculus class ever. Rather than a 15 week semester, the class is only 8 weeks long- start to finish. Ended 07/08/22.

Did I misunderstand something there?

 

[symbolipoint]

Part of what I meant is that, being issued a letter grade of B does not mean that you are ready for the next course in sequence.

 

[Vanadium 50]

Part of what I meant is that, being issued a letter grade of B does not mean that you are ready for the next course in sequence.

Is there a missing (or extra) not in there?

 

[malawi_glenn]

However, test anxiety combined with brain surgery (right hippocampus removed tumor)

I hope you recover well from this bro

I still have a hard time understanding the entire situation, you took your first calculus class and are already thinking about grad school? Why not just take one step at the time, like applying for an undergraduate physics program?

 

[gmax137]

you took your first calculus class and are already thinking about grad school? Why not just take one step at [a] time

That's what I was going to say.

 

[nuuskur]

First time I took analysis I got a B, too. You're fine.

 

[Choppy]

I would take this all as a learning experience...

• A single B grade on a first year calculus course is not going to play a major role in graduate school admissions if you end up with A grades everywhere else. The key concern is that introductory calculus is foundational for a lot of other stuff. If there are aspects of it that you're still struggling with, whatever the reason, it will be difficult to get top grades without mastering them.
• Many students learn that university-level math is different from what they're used to in high school. Professors don't give the same level of feedback and coaching as high school teachers.
  You're also now in a pool of students who did well enough in high school mathematics that they purposely chose to study it in university. You've got through an aptitude bottleneck.
• Condensed summer courses are often like drinking water from a firehose.
• The problem with self-study is that it's done in a vacuum. It's easy to believe that you understand more than you really do in the absence of critical feedback.
• If text anxiety was an issue this time, it's going to be an issue again. There are different strategies for dealing with it. Most universities will have some sort of academic guidance services that can help with this.
• Studying obsessively and then burning out is not a healthy habit. Find balance. Again this is something where there should be services available through your school that can help.
• If medical issues played a role, the lesson may be that you need to make sure you're healed and in an optimal position to learn before challenging yourself again.

 

[CrysPhys]

...
Unfortunately, I did very poorly on the final exam. Long story short, it made my grade from an A to a B. Personally, I don't feel good about using excuses. However, test anxiety combined with brain surgery (right hippocampus removed tumor), was a big weight during my tests.

...

I was furious when I saw my final calculated grade (82%); I was really hoping for a 92% minimum.
...

I'm not sure I'm parsing your post correctly. But did you have brain surgery in the midst of your condensed course? If so, you should be congratulating yourself for getting a final grade of 82%, rather than beating yourself up for not scoring at least 92%.

But as others have written, you've several years ahead of you before grad school. This one early B per se is nothing to be concerned about with respect to grad school applications.

 

[gmax137]

"Calculus 1" is probably the last course that should be compressed into an 8-week schedule. It is the foundation of nearly every STEM course.

 

[mathwonk]

In my first 2 semesters of calculus I got B-, D-. Much later I got a PhD in math and had a long career as a successful research mathematician / professor. So things can and do change if you hang in there. So don't take your first calc grade too seriously. Also I agree that this difficult course is not suitable for learning in an 8 week summer class. It takes time to absorb calculus. good luck, and try to relax.

 

[malawi_glenn]

Also I agree that this difficult course is not suitable for learning in an 8 week summer class. It takes time to absorb calculus.

What mass classes do you, and others, recommend taking during a 8 week class? Which math is "easy" to absorb?

 

[vanhees71]

Minor point, but this was not a summer session, as it ended on July 8, which is only about three weeks after the start of summer. The point about an 8-week class vs. 15-week class is germane, though.

I'm not sure watching math videos is as helpful as you probably think it was. And self-study is not as fruitful as being able to get feedback on your work from an instructor, IMO.

I'm not too convinced about didactics/pedagogics as a science, but many studies in this field come to the conclusion that the best way to teach/learn STEM subjects is the good old lecture with a professor using a black board writing everything by hand (it doesn't matter if it's a usual true black board with chalk or writing on a tablet and projecting it in class) plus doing a lot of problems (also writing by hand).

Powerpoint lectures or, even worse, videos on the internet are the worst. If you have a "good speaker", it may suggest to you much more understanding than you really gained. You can figure out, whether you understand the subject by (a) deriving everything yourself without looking at the book/lecture notes and/or (b) explaining it to others, and (c) solving a lot of problems.

 

[malawi_glenn]

the best way to teach/learn STEM subjects is the good old lecture with a professor using a black board writing everything by hand

I found these lectures to be the most productive for my students as well, also taking some breaks now and then and letting everybody finishing their notes, and asking questions and discussing with peers (like "why did we do this step", "what do you think we will do next") to keep them engaged. Problem is, this takes time, and time in classroom is often very limited due to money constraints.

Powerpoint lectures or, even worse, videos on the internet are the worst. If you have a "good speaker", it may suggest to you much more understanding than you really gained

I often provide these as supplementary sources of information, which I publish after the real lectures, but not all the time. I stress that they have to make that material their own, that they should take notes, and write down questions and help each other understand too - if they can not sort it out together, they can ask me during my office hours. I never give them "summaries" and such, they have to write those on their own, and compare with other students summaries "why did you think this formula was important, what about this"?

Students must also learn how to take own responsibility. Same with reading through a physics/math book, they can not just read and think they will learn. They have to write down the steps, fill in the blanks, and ask questions to the text and to themselves "why is this valid" "why not this instead" "why was this step so imortant".

I think it all boils down to the amount of passivness vs. activeness, and that some types of "teaching medias" encourage one of them more than the other.

 

[vanhees71]

Learning and passiveness are excluding each other! There's no way to learn anything in a passive way!

 

[malawi_glenn]

Learning and passiveness are excluding each other! There's no way to learn anything in a passive way!

Exactly, but the syllabus is packed to the rim. I would rather teach 1/3 less material, but making the students learn the remaining 2/3 really really well. Unfortunately, what is written in the syllabus is beyond my radius of convergence so to say... same with time assign to spend on teaching in the classroom. I stress to my students that they are each others teachers as well, and that they together can learn more than what anybody would do on their own. Student having access to classroom and study rooms are essential imo.

 

[vanhees71]

Of course, getting active should take different forms. It's not only sitting alone behind you desk and solving dull problems, but also meeting with other students and discuss the material, solving the problems together, explaining each other something not yet understood etc. If the "Corona semesters" with online lectures have taught me one thing: There's nothing that can substitute for personally discussing the material among students also also among students and professors.

I think compared to "self-learning" everything with a textbook this additional methods to learn and teach enable you to learn all this much material in one semester. Self-learning the same amount of material for yourself alone from a textbook takes much longer!

 

[gmax137]

What mass classes do you, and others, recommend taking during a 8 week class? Which math is "easy" to absorb?

Maybe number theory or probability? Not that you can be complete in 8 weeks (obviously) but I think you can get a good intro in that time.

"Calculus 1" on the other hand includes limits, differentiation, and integration. It's not that it is harder, it is more that the scope is defined and I just don't think cramming that defined scope into 8 weeks is fair to the material.

 

[malawi_glenn]

Maybe number theory or probability? Not that you can be complete in 8 weeks (obviously) but I think you can get a good intro in that time.

"Calculus 1" on the other hand includes limits, differentiation, and integration. It's not that it is harder, it is more that the scope is defined and I just don't think cramming that defined scope into 8 weeks is fair to the material.

limits, differentiation and integration is already covered in high school math. I teach that to 17 y old kids. I can understand calculus 1 is difficult if you have never seen a derivative or an integral in your entire life, but basic high school math is required for calculus 1.

I had a look at my old grades and such, I finished calculus 1 in 10 weeks with perfect score. And during that time I also took Elementary algebra (euclid algoritm, congruences and such topics) not perfect score on the final, but still an A. Teachers were awful save for one teacher assitant, I learned basically all material on my own and studying with some friends now and then. This was before youtube existed I should say.

 

[CrysPhys]

limits, differentiation and integration is already covered in high school math. I teach that to 17 y old kids. I can understand calculus 1 is difficult if you have never seen a derivative or an integral in your entire life, but basic high school math is required for calculus 1.

Not sure that's true of all high schools. It's been mucho decades since I was in high school in the US. I had those topics in my senior year, but that was only because I elected Advanced Placement (AP) Math, which was introductory calculus. The standard math did not cover them. But your profile indicates that you're in Europe, so maybe standard for your country?

 

[malawi_glenn]

maybe standard for your country?

You have to have completed high school maths at a certain level to even be eligible to take Calc 1 or any other math class at university here.

What are the requirments to enroll in Calc 1 in US?

 

[CrysPhys]

You have to have completed high school maths at a certain level to even be eligible to take Calc 1 or any other math class at university here.

What are the requirments to enroll in Calc 1 in US?

First off, high school in the US runs through grade 12. I believe in some countries it runs through grade 13. So that would make a difference. What is it in your country?

Curriculum varies by state. Here's the one for New Jersey: https://www.nj.gov/education/modelcurriculum/math/. The standard curriculum stops at Algebra I & II and Geometry.

Here are the requirements for Calculus I at MIT (highly demanding undergrad curriculum): http://catalog.mit.edu/subjects/18/. There are now two versions: 18.01 for students with no previous calculus in high school, and 18.01A for students with previous calculus in high school (and appropriate placement exam scores). When I was there many moons ago, there was only one option 18.01. At the time, MIT gave no consideration for high school Advanced Placement courses, even if you scored a 5 (highest score) on the advanced placement exam.

 

[malawi_glenn]

First off, high school in the US runs through grade 12. I believe in some countries it runs through grade 13. So that would make a difference. What is it in your country?

No idea how you count those grades, but here they start primary school at age 7 and finish at 15-16 so that's 9 years, then most of them go high school which is 3 years. But I teach this stuff to 2nd year high school kids.

There are now two versions

I see, that makes sense. In my country there is some kind of transition program, for students who choose like social sciences and stuff for high school. The transition program is 1y and it covers the math, physics, chemistry and biology taught at natural science and engineering high school programs. There are no university level courses on math that is not based on natural science high school maths.

 

[Vanadium 50]

At the time, MIT gave no consideration for high school Advanced Placement courses, even if you scored a 5 (highest score) on the advanced placement exam.

When I was there, they paid little attention to that as well, but you could take the final exam, and if you scored well enough (B- maybe?) you could skip ahead.

That definitely has its pros and cons.

 

[CrysPhys]

No idea how you count those grades, but here they start primary school at age 7 and finish at 15-16 so that's 9 years, then most of them go high school which is 3 years. But I teach this stuff to 2nd year high school kids.I see, that makes sense. In my country there is some kind of transition program, for students who choose like social sciences and stuff for high school. The transition program is 1y and it covers the math, physics, chemistry and biology taught at natural science and engineering high school programs. There are no university level courses on math that is not based on natural science high school maths.

Just for comparison, here's the math curriculum at a less demanding state university (University of Massachusetts); same state as MIT: https://www.math.umass.edu/course-descriptions. For Calculus I, we have:

MATH 131: Calculus I​

See Preregistration guide for instructors and times
Prerequisites:
High school algebra, plane geometry, trigonometry, and analytic geometry.
Description:
Continuity, limits, and the derivative for algebraic, trigonometric, logarithmic, exponential, and inverse functions. Applications to physics, chemistry, and engineering.But note all the introductory university math courses offered to students without a good grounding in high school math.

 

[Vanadium 50]

same state as MIT

<cough, cough> Commonwealth <cough>

It's a little unfair - or possibly a little too fair - but MIT covers what most colleges cover in three classes, Calc I, II and II, in two: 18.01 and 18.02.

 

[mathwonk]

Here is essentially all the theory of one variable calculus in outline form. The proofs of the two first principles take a couple pages more. We also need to define "continuous" and "differentiable" functions. All this assumes that a real number is represented by a unique never - terminating infinite decimal. (If you think real numbers are what your calculator gives you, namely finite decimals of fixed length, then none of these theorems are true, although of course then every function on a finite interval does take a maximum, since then a finite interval would only contain a finite set of numbers.) You can decide how many weeks it would take you to understand this material. You can also check whether you agree that everything after principles I and II does follow from them logically.

There are 4 basic principles.

I. (Intermediate value theorem) If a function f is continuous on an interval, then the values it takes also form an interval.
Hence if there exist points a,b in the domain interval where f(a) < K < f(b), then f(c) must equal K for some c between a and b.

II. (Extreme value theorem or max-min theorem)
If a function is continuous on a closed bounded interval, then its values also form a closed
bounded interval, i.e. particular there is a (finite) smallest and a (finite) largest value.

I.e. if f is continuous on [a,b], there exist c,d in [a,b] such that for every x in [a,b],
f(c) ≤ f(x) ≤ f(d).

III. Cor: (Rolle’s Theorem) If f is continuous on [a,b] and differentiable on (a,b), and if f(a) =
f(b), then there is a point c between a and b where f’(c) = 0; (choose c as an interior “critical point” where f achieves either its maximum or minimum).

Cor: If f is continuous on [a,b] but has no critical points in the interval (a,b), then f cannot take the same value twice in [a,b], hence cannot change direction, i.e. f is strictly monotone on [a,b]. In particular, f has an inverse function defined on [f(a),f(b)], (which by I is also continuous).

Cor: If f ’’ exists but is never zero on [a,b], then f’ is monotone, hence f never changes concavity on [a,b], i.e. f is either concave up or concave down on all of [a,b].

Cor: If f and g are continuous on [a,b], differentiable on (a,b), and agree at a and b, then they have the same derivative at some interior point. (apply Rolle to f-g.)

IV. Cor: (Mean value theorem) If f is continuous on [a,b] and diff’ble on (a,b), there is a point c with a<c<b, where f’(c)(b-a) = f(b)-f(a). (apply the previous corollary to f and the linear function for the secant line joining (a,f(a)) and (b,f(b)).)

Cor: If f’ = 0 everywhere on (a,b), and is continuous on [a,b], then f is constant on [a,b].

Cor: If f’= g’ on (a,b), and f and g are continuous on [a,b], then f - g is constant, on [a,b]. Thus (f-g)(b) = (f-g)(a), hence f(b)-f(a) = g(b)-g(a).

Cor:(FTC) Since for continuous f, d/dx ( the area under graph f, from a to x) = f(x), then for any G with G’ = f, the area under graph f from a to b equals G(b)-G(a).

[Definitions: Assume f is a positive function. If M is the area of a family of (non overlapping) rectangles each reaching from the x-axis to a point above the graph of f, and m is area of a family of (non overlapping) rectangles each reaching from the x-axis to a point below the graph of f, then the area under the graph of f is the unique number A such that m≤A≤M for all approximating families of rectangles.
Such a unique number exists if f is continuous (Riemann), or piecewise monotone (Newton).
For piecewise monotone functions, continuity is equivalent to principle I. A general function f is continuous at x=a if f(x) can be made as close as you wish to f(a) by choosing x close enough to a.
A function g(h) is tangent to zero at h=0 if the ratio g(h)/h can be made as small as desired by choosing h small enough. Geometrically, the graph of g is tangent to the h axis at h=0.

A function f(x) is differentiable at x=a if there is a scalar c = f'(a) such that the function g(h) = (f(a+h)-f(a) - c.h) is tangent to zero at h=0. Geometrically the graph of f(x), where x = a+h, is tangent to the line f(a) + c.(x-a) at x=a. ]

[Computations: if f(x)-f(a) is tangent at a to c.(x-a) and g is tangent to d.(x-a), then (f+g)(x)-(f+g)(a) is tangent to (c+d).(x-a), hence (f+g)' = f'+g'. (sum rule)
And f(x)g(x)-f(a)g(x) is tangent to c.g(x).(x-a) which is tangent to c.g(a)(x-a), and f(a)g(x)-f(a)g(a) is tangent to f(a).d.(x-a), so f(x)g(x)-f(a)g(a) = f(x)g(x)-f(a)g(x)+f(a)g(x)-f(a)g(a) is tangent to [c.g(a)+d.f(a)](x-a) so (fg)' = f'g + g'f. (product rule)
And f(g(x))-f(g(a)) is tangent to c.(g(x)-g(a)) which is tangent to c.d.(x-a), so (f0g)'(a) = f'(g(a)).g'(a). (chain rule)]

One should also discuss special functions like trig and exponential functions, inverse functions, and expression of functions as integrals, power series, and Fourier series.

 

[symbolipoint]

Of course, getting active should take different forms. It's not only sitting alone behind you desk and solving dull problems, but also meeting with other students and discuss the material, solving the problems together, explaining each other something not yet understood etc. If the "Corona semesters" with online lectures have taught me one thing: There's nothing that can substitute for personally discussing the material among students also also among students and professors.

I think compared to "self-learning" everything with a textbook this additional methods to learn and teach enable you to learn all this much material in one semester. Self-learning the same amount of material for yourself alone from a textbook takes much longer!

The posting deserves at least a few more LIKES than you will receive.

 

[symbolipoint]

limits, differentiation and integration is already covered in high school math.

Where? Which "high school math" courses?

 

[symbolipoint]

Curriculum varies by state. Here's the one for New Jersey: https://www.nj.gov/education/modelcurriculum/math/. The standard curriculum stops at Algebra I & II and Geometry.

Some high schools also offer a Trigonometry or a "Pre-Calculus" course (supposed to be like "Elementary Functions" but can often be much weaker).

 

[malawi_glenn]

Where

In Europe. I knew things were different in the US, but not learning basic calculus in high school is shocking to me! Do you know of any website I can learn about high school curricula / programs in the US?

 

[CrysPhys]

In Europe. I knew things were different in the US, but not learning basic calculus in high school is shocking to me! Do you know of any website I can learn about high school curricula / programs in the US?

Not a simple task.

* As I mentioned before, in the US, each state sets its own school curriculum. As a starting point, you can Google: "<name of state> high school mathematics curriculum" . You will typically be directed to a state Department of Education site.

* But the curriculum typically specifies the minimum requirements for public high schools in the state. In the US, a 'public' school is a school funded by tax dollars; students pay no tuition. Actual course offerings vary substantially among specific public high schools, even within a local municipality. Within a single large city (such as New York, Boston, Chicago, ...), the curriculum can range from egregiously abysmal to suberbly excellent (some probably will meet even your expectations ). In a previous post, I cited the New Jersey state curriculum. Is calculus required? No. Is calculus offered in the high school down the street from me? Yes.

* Adding to the complexity, there are also private schools in the US. Here students pay tuition. The variation in curriculum is even greater.

* So, for a comprehensive view, you would need to sample the websites of individual public and private high schools across the US.