NOTE: Please leave your response to this discussion prompt below (on this site, NOT on the Spring 2019 site linked below)
In Spring 2019 I taught this course and at the end of the semester, I gave my students the following assignment:
Imagine that you are invited to speak on the first day of MAT 2680, to give advice to entering students. Write at least three sentences … describing what you would tell them.
To see the assignment and the students’ responses, follow this link.
Your assignment, due at the beginning of class next Thursday, September 9, is to:
- Read through ALL the responses (there are 44 of them, but many of these are short replies to other comments).
- Write a reply to this post (1 paragraph) responding to all of the following:
- What advice seemed most relevant to you personally? Why? (you can copy/paste a short statement, or put it in your own words)
- Based on this advice, what changes can you make right now to help you succeed in this course?
Extra Credit. For extra credit, write a response to one of your classmates’ comments. Do you have any advice? Be kind.
All of the advice provided by past students should be considered. It’s known that differentiation and integration techniques are the foundation of differential equations. I figured as much while entering this course. Personally, the piece of advice that resonated with me the most is to take advantage of your instructors Office Hours. I feel like not enough people talk about this. I’ve never taken advantage of office hours in the past. That’s something I’m actively working on this semester. It’s a good habit of a proactive student- to exhaust all possible resources, regardless of how “good” they think they are. You have the opportunity to build rapport with your instructor, and get some further guidance on topics that may confuse you. I’ll make it a priority to attend at least 10 office hour sessions for all my classes this semester.
Agreed, going to office hours is very important if there is not an understanding of a certain topic. Something I struggle with is also attending office hours as well. Knowing certain topics are definitely important in order to pass this class. Another thing I have learned is passing a class is one thing but understanding the class and the work is another thing. In order to do my best this semester I will study and review the topics needed to understand this class.
I agree strongly and greatly with office hours being an important resource for the class. There are always things that end up unclear or giving me a challenge after class, especially from past topics that we might not have time to cover in class due to new material. Office hours allows you to get those questions answered so you can get back on track. Very important and underrated element that I try to take advantage of whenever I can.
I agree with the using Office Hours because they are crucial time to learn outside the class to either clarify something or gain more knowledge on a topic. The fact that the school offers Office Hours means that they also know that students need help and provide it for them (which is great). Between the tutors and Office Hours the knowledge they can extend to us is immeasurable and they should be used if needed.
Thanks for getting this discussion started, Wadud! I can’t encourage you all enough to take advantage of my office hours – I’m paid to offer them, and often I spend the time just catching up on other work since no-one shows up. It’s okay to come and just listen to others’ questions, too – sometimes that can be helpful.
I agree with going to office hours because there are moments that after the lecture someone has a question about a certain part of a topic that could explain the process of solving a problem. That’s why going to office hours will help the student to understand a certain part of the topic that was unclear. Moreover, I will take this advice for myself of going to office hours.
I think going to office hours is very important for this course because sometimes it’s unclear what we should do because we have a very little time in class. It is difficult because of the short of time we are able to do one or two problem during the given time period and I this is not enough to understand a topic. So going to office hours would help us understand more deep and will help us to do good in this class.
The advice I would give to a new coming student is that a lot of knowledge from your previous math classes will be used such as Cal 1 and 2. From the start of the class there may be times you do not understand something, but always ask questions. Be prepared before you come to class, study the topic or at least get an idea of what it is about. From what I have gathered from past students I would say the most important topic of this class is first order differential equations. Based off the given advice I would say I need to focus on this class by studying and learning how delicate differential of equations are.
Very true. Fundamental differentiation techniques (calc 1) should be practiced until it’s an automatic impulse. As far as Integration goes, Integration By Parts, U-substitution, and Partial Fractions should make for a nice safety net in this class.
Definitely true, especially at this point in your academic career teacher will zoom by examples and even gloss over certain steps that may be obvious to some. Stopping to ask a question is always a good ide and should be encouraged.
Everything you said is very pertinent to the course. I think a great idea that you’ve mentioned is studying the topic of each lecture before actually attending the lecture and being in class. I have a habit of only getting exposed to a topic on the day of the lecture and then going into it and studying it more. I think having an idea on what is going to go on in the lecture would be a huge advantage because it would allow me to have questions in advance since Ive already processed SOME of the material.
Thanks, Ashley – these are great suggestions! I just posted a bunch of “Calculus Review” resources, and these include online lessons (and many videos with examples fully worked-out) for integration by parts, u-substitution, and more.
Calculus Review resources:
https://openlab.citytech.cuny.edu/2021-fall-mat-2680-reitz/2021/09/08/calculus-review-some-helpful-hints/
The advice that seemed the most relevant with me personally would be the remembering of differentiation and integration. Although I’ve been learning these concepts since high school and generally remember the basic rules to these mathematical methods, I still tend to forget small little rules here and there. Every semester that I would have a math class I would have a somewhat slow start, I keep up until I have to come back to the few rules and methods I may have forgotten. Considering the class is literally called Differential Equations, I would say it would be very helpful to review derivative and integration methods you know like chain rules and what not. Current changes would definitely surround that, it would be most helpful to stay sharp on these concepts.
Dbudhi, I agree with your statement. I tend to struggle at times with math as well getting a slow start. During my previous classes or Cal 1 and 2 I learned that derivatives play a big role in this class. That being said in this class I hope to learn more about derivatives and integration and applying those rules.
Correct, as far as differentiation, we should be confident with Chain Rule,Product Rule, implicit differentiation. For integration, integration by parts, u-substitution, and partial fractions should be a good safety net.
Yes, I agree with you Dbudhi, laws, rules, identities and properties for both integration and differentiation are very essential when tackling a course like this. Like I mentioned in my post the “under-the-hood” concepts are what we should go over again so that we can apply those methods to the bigger scheme.
I agree with you 100 percent. I personally have the same issues, remembering the small little rules that help with integrating. But hopefully we can all work together to overcome our struggles and do good in this class
The math advice that connects to me personally, is when my calculus two teacher stated how important it is to practice the problems from previously done quizzes and exams even if it’s a question that you got right easily. At the time I figured since I practiced the exam and homework problems that were difficult to me, I would be fine. A specific question on a previous quiz was easy to me, so when it came time to study for the final I didn’t think that I would need to practice that question. When the final exam came around I was able to get through the questions, then I was faced with the one on the quiz that I never practiced after getting it correct on a quiz that I had completed earlier and it showed up twice on that exam. I passed the exam, but I could have done better if I had listened. Based on the advice from the past I will continue to practice questions that I got correct on a quiz or exam because they will most likely pop up again in the final exam.
This is excellent advice, Rashan – thanks for bringing it up. Unlike riding a bike, you don’t necessarily remember mathematical procedures forever – sometimes, even just a quick refresher and a problem or two is enough to get your brain back into the groove for those problems again.
The advice that stood out the most from me from the responses of past students was the one mentioned by a student regarding having to prioritize this class over others. I typically give all my classes, about, more or less, the same amount of time, give or take taking more time out for an upcoming exam. This is in general, practice that had served me well throughout my academic career. However, I can already feel that this class is going to be taking more from me than my other classes this semester and that I may risk falling behind come exam time.
To remedy this, I think I will do the obvious, spend less time on my other courses and more time on differential equations. This doesn’t mean I will neglect my other courses, but rather for simpler ones, take the extra study time and apply it to the class here. Given how challenging the material of this class is, I think it would be a wise thing to do.
100% agree with everything said. Prioritizing classes at this stage of college is very important I feel. Not neglecting courses but more so exerting more effort into something that holds more value in the long run. The challenges will eventually be worth it in the end.
The advice that stood out the most from me from the responses of past students was the one mentioned by a student regarding having to prioritize this class over others. I typically give all my classes, about, more or less, the same amount of time, give or take taking more time out for an upcoming exam. This is in general, practice that had served me well throughout my academic career. However, I can already feel that this class is going to be taking more from me than my other classes this semester and that I may risk falling behind come exam time.
Some advice that is most relevant to me personally would be to take advantage of the teacher whether it be through conversation in class or email, or rather going to office hours. This would help because if I don’t understand something who better to clarify than the teacher. This would also work for if I have a question about anything pertaining to the class. Some changes I could make to help me succeed in this course would be to rely on the teacher more and re watch the zoom recordings. I look forward to a knowledgeable class where I can learn and understand.
I 100% completely agree with your comment. This tool is extremely helpful as you get can get extra time with a prof to help you understand the material better. I myself didn’t take advantage of this opportunity as much as I should’ve and I definitely regret it. With our classes being online, this opens doors much easier to different things that we can take advantage of such as the online office hours and also the record zoom recordings. Being able to go back to a certain part in the class and re-listen is very useful if not the most useful thing about online learning. You could re-watch the whole class if you wanted to.
As I scrolled down and read the comments made on the post proposing a similar question to what we have, what stood out to me the most was that calculus I and II are a must go over for this class. Personally, I have not seen pure calculus I and II since Fall of 2018. I say pure calculus because I have taken engineering courses that do in some way relate to calculus, however it is not as numerical and intricate like math courses are with their concepts. Since it has been 3 years, when it comes to identities properties and methods of solving either integration or differentiation, especially of trigonometric or logarithmic functions, it takes a minute for the wheels to start spinning. Going forward, I will be diligently going over my notes from both of my previous calculus classes as well as reading mathematic material online to freshen up my skills in terms of differentiation and integration in order to understand the “under-the-hood” process of the bigger scheme that is differential equations.
Love the idea of “under-the-hood” in the math – it seems to capture the idea of understanding the inner workings, instead of just the user interface, and it can definitely make a huge difference in learning, understanding and retaining math!
The advice that is most relevant to me is how competent you should be in integrals and derivatives before entering the class. Those 2 concepts are what are the foundation of all we’ll be doing in this class. To be honest this is my 4th time taking this because of my struggle of understanding plus some of my lack of motivation when it comes to college these past couple years. I’m hoping I can learn from my errors this semester considering the multiple attempts I took previously to pass this class. The changes I could make right now is being less hesitant to ask my professor or classmates for assistance. I could also put more time aside to dedicate towards this course compared to my previous attempts.
Good luck, you can do it this time! I’m not a great math student and always struggled, had to take Pre-Calculus twice, so I definitely know the struggle of repeating classes. For me personally, what helps, is redoing the same problems over and over til I’m blue in the face, even if I got them right so that it sort of becomes like muscle memory. We should definitely all study together, feel free to reach out if you wanna go over a topic together!
You got this Andrew, jus believe that u can do it and believe that there is hope to pass this class and there shall be hope. No matter how dark of a situation you may find yourself in, there’s always a light because, wherever there is darkness, there is also light. And also never give up, learn from your mistakes and do things differently.
After reading the responses from the previous class I agree that we need to have a strong base for calculus 1 and 2. The reason for this is since the start of the course we have been using methods from both classes to solve the topics learned in this class. One thing I found helpful is many of the previous students who took this class said to spend as much time as possible to understand the topics in this course. Based on the advice given I would approach the topics or problems I may not understand in a different way. For example, if I have a question I would try to ask it right away in order to get a better understanding.
I concur, patience and perseverance is the key to success in this class. The problems may look frightening and perplexing at first, but you must persevere in your efforts and never give up when learning the topics. The most important thing is to take in all the steps and practice executing them.
The advice that seemed most relevant to me personally was relearning/practicing the things/topics u already know coming into this class. The reason why it’s so relevant to me is because before I would come into a math class confident that since I learned it before, I don’t need to relearn it again and don’t need to waste time practicing topics I already am familiar with and that’s the big mistake I would make in the beginning of my semester for some of my old math classes here at city tech. So my advice to the future students of this class is to not get overconfident with how good u may be in the past topics of this course but instead keep practicing and accept that u still have room to improve on in these topics and in your math skills. And take this class seriously and don’t underestimate it thinking since u know calc 1 and 2, that you will do fine if u jus use your previous knowledge and not practice/test your previous knowledge constantly throughout the semester. Because if you do that you will not perform nearly as good as u would had you taken it seriously from the start. Based on my advice, the changes I can make which i already am since my mat 1475 class, to help me succeed in this course is take this class seriously and practice all the topics with the motivation as if I never learned them before.
The advice which seems relevant to me is to find extra problems in the textbook if I’m still not comfortable clear about a topic after doing the hw. I also liked the advice about using youtube when I don’t understand a topic. These two techniques helped me a lot in calculus 2. I do need to find a new youtube channel though because the one I used in the past doesn’t have any videos on diff eq.
The advice that seemed the most relevant to me personally is that if you have trouble integrating at all that differential equations will become somewhat difficult. Because in order to solve differential equations you need to know how to integrate properly. Its relevant to me because I personally sometimes do have a hard time figuring out how to integrate. changes that i can make right now to help me is go over calc 1 and calc 2 notes as well as to ask as many questions as possible to where I understand the material properly.
Reading the advice from past students really put into perspective the most important aspects of learning in general, not just this class. Building a foundation is the key to every success story and it is no different in differential equations. Although there are foreign concepts when you enter the class a foundation of derivatives and integration is crucial for surviving and succeeding in this class. Another thing I would like to mention is the office hours, I’ve been planning on abusing this feature for this class and my other classes this semester because in the past I was foolish and only sought out minimal help… big mistake. It’s clear to me that differential equations are going to take up a lot of my time this semester and using the advice from the spring students is definitely going to help me prioritize correctly and efficiently.
That is very good advice to go back to derivatives and integration to build up that base because it seems everything we do in this class circles back to doing derivatives and integration. Having those concepts down to the wire will make solving these problems a lot faster and easier.
From the answers of previous students, one piece of advise that stuck out the most to me was one given by a student regarding the fact that prior math knowledge of basic algebra, derivatives, and integrals is required. This is important because it is very specific so you’d know where to start when preparing for this class. Also, the changes I would make right now to follow this advice is pretty obvious too but other than that, I know it is critical to persevere and never give up when learning the new topics. The most essential thing is to do things slowly and cautiously.
While it is a math subject and prior math understanding of core algebra, derivatives, and integrals is essential, I will advise the entering students one crucial point. When taking this course, I will encourage students to be patient and perseverant. Although the topics may appear scary and difficult at first, it is critical to persevere and never give up when learning them.
The advice that is most relevant to me is how you should understand integrals and derivatives before entering the class as most if not all of the martials requires the use of knowledge from past classes so base on that advice and as someone rather forgetful I tasked myself with rereading and refamiliarized the concept of the power rule, trig rules and various other concepts from past classes in order to firmly grasp the new concepts.
“The most important prior knowledge that you need in order to succeed in this class is a good understanding of derivatives and integrals.” This statement seems most relevant to me since differential equation is a continuation of calculus, that means that we will continue using stuff that we learn previously. A change i would make is that i would put my best effort to practice and remember those two main topics which are integrals and derivates, that way i can understand the lessons in this class easily.
I would completely agree with all the comments and advice I read from the previous students. Just as us students in Fall ’21 have came to find out that in order to have great success in differential equations, review what we learned in the past is very very key. This is very important also if you’re like me where you took a break from taking a math class and really needed to brush the rust off. Many of the materials mentioned were correct. For example, derivatives, integrations, bernoullis, eulers, etc. These materials are very much essential building blocks or stepping stones in order to better understand the new material such as for example Laplace transforms. So please review, review, and review.