Last FallĀ I taught this same course for the first time.Ā Ā 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 2071, to give advice to entering students. Ā Write at least three sentences … describing what you would tell them.

To see the assignment and the studentsā responses,Ā follow this link.

Your assignment, due next Thursday, September 4th, is to:

- Read through ALLĀ the responses (there are 22 of them).
- 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 with this course?

**Extra Credit.Ā **For extra credit, write a response to one of your classmatesā comments. Ā Do you have any advice? Ā *Be kind.*

The advice that related to me personally was Renautha because as I was reading her statement I felt related to her situation in the fact that I am also taking probability and statistics and its good to know that these two courses will be related to one another at some point of the semester. I also like the fact that she encouraged students to do homework and read the chapters from the book. I agree 100 percent that doing homework is beneficial and it gives you practice. I liked how she gave her personal opinion on which topic was challenging because this will make me aware in advance of what I need study and work on if I get into those problems as well. I also liked the advice she gives students about studying algebra and to be careful because you can easily make simple mistakes. My favorite part in reading is when Renautha wrote:

“The only real advice I have is to PRACTICE, PRACTICE, PRACTICE!

Overall, this was a great class and I think you did a great job at teaching the course material. You made it extremely enjoyable and I think thatās what helped me learn the concepts easier. The homework assessments were helpful and didnāt feel as thought they were punishment as they are in other classes. The daily sheets with the topics were definitely helpful and I think they will help in our other classes.”

This inspired me to push myself harder and always practice. It also shows me that I have a good professor who is teaching the class and not those other crappy professors that don’t really teach well or is unable to help students out.

Hi Julia – thanks for being our first-post-er. I agree, some of my best learning experiences have been when multiple classes seem to converge on the same ideas – I hope that happens for you this semester!

-Prof. Reitz

I like what you wrote Juila and I totally agree with you that doing homework is beneficial and it is also a good practice for the course. My advice to you is that I think you should also try to memorize the connotations because it will help you through out the course and it will make the problems easier for you to understand . Good Luck!

Hi Julia, I can honestly agree with you that it shows how great of a Professor Reitz is. He definitely likes to help out his students whenever he can and it is always important to take advantage of his office hours cause it is a great time to ask him questions. I also really like the part where Renautha writes about Practice, and it is true when you say how homework is beneficial, because it is. Homework is the best way to get practice done.

Hey Julia, I definitely agree with practice, PRACTICE AND PRACTICE. The more you attack a problem and figure it out, the easier it becomes when you see it on the exam or especially the final. I also agree with you that the daily sheets is also very helpful because you can always go back to them before or after class to review what you had learned. Also the examples given on those handouts makes it even easier to review your class notes. I have a great time stepping into this classroom because the energy that this professor gives is OUTSTANDING!

When I read all of the responses from your past students I came across 2 pieces of advices that I believe is true and will help me throughout this semester. The first piece of advice I liked was when one student said “each topic is like a ring and in order for you not to fall apart, you need to tie all the rings together to form a necklace.” I felt what this person was saying is highly correct simply because throughout the course, if you don’t understand what’s going on in the beginning of the semester, then when the exam starts you won’t be able to understand what the problem is asking you just because you didn’t fully understand that piece of information that was given to you. I personally believe in that because just like in algebra if you don’t know what a binomial is or a polynomial, then how will you know to factor them or multiply them in the future if you don’t even know the basic steps. The other piece of advice I liked was when one student said you MUST know your algebra, otherwise, while doing proofs you will fail to answer them if you don’t understand the algebra part.

So based on the advices I got from these two students I know what changes I will make right now in order for me to pass and understand this class. From now on I will raise my hand WHENEVER I don’t understand anything, I will not be afraid to make mistakes or even ask questions to my professor. The 2nd change I will make is to review up on my algebra. I recently finished taking Calculus 2, but I never really went all the way back to my algebra. I will review it at least 20 minutes a day just to know for sure that I haven’t forgotten it.

Three cheers for asking questions! For some reason, this is one of the hardest things to do – I found it to be true, even all the way through grad school – but when you can overcome it, you find that it increases what you get out of classes enormously. And asking questions usually helps other students, too – if you are puzzled by something, chances are very good someone else (many others!) are too.

I agree with you, Jonas. Asking questions is one of the best way to study mathematics, especially to stop the professor right there when you start getting confused. It does help a lot students who are so shy to ask.

I agree, asking questions is good because the professor will be able to help you out with the material you don’t understand and it’s good to have it explained more then once. Asking questions also helps break out of your comfort zone because usually people are afraid of asking questions. The more questions you ask the better it is to understand the topic.

I agree that asking questions is very helpful and important to understand the problem that you are finding difficulties. I think it also builds confidence and encourages people to ask more questions next time.

understanding what we need to gain a better handle on is the most important step. The methods and practices of algebra are still with us after advanced calculus classes. Basic arithmetic errors are made at all levels and understanding how to work through roadblocks helps us learn the building blocks of math which algebra is always the foundation.

I totally agree! Asking questions will definitely help you understand better. Not only does it encourage active learning in class but also a method to develop thinking skills. This is also an addition to some of the changes that I like to make.

Thanks to you!

Yes, totally 100% agree to raise your hand whenever you do not understand. It is important that you do because it makes it easier to make sure you understand the concept complete and not just half of it. Reviewing your algebra would be a great thing to do because we will be using a lot of algebra when doing proofs; that is where it becomes crucial to know and understand algebra.

I feel like ibrahimadam193’s comment was the most helpful for me because it breaks the class down and gives me a warning on what I should expect from the class. The part that I can relate to the most would be the section that tells me “Donāt treat this class like your other math classes”. I feel like I would do everything last minute but I it really takes a hour or two I’m glad I found this out before I got use to doing the work last minute. I also tend to skip that part where I should double check the answer but the class is about proofs so I will start getting use to that too

as most of student did mention in their comments, this class is about mathematical and logical proofs. this class is an introduction to abstract mathematics meaning students will need to be more creative than it is required in calculus or algebra . student will be dealing with qualitative math as logical reasoning, method of direct proof or proof by induction not always obvious to figure out. student will need to perform as many proofs as he or she can in order to get used with this new field of math(take it as advice).

I like that you bring up creativity – that will definitely be important here, more so than in many math classes!

Any response to the second part of the question? (“Based on this advice, what changes can you make right now to help you with this course?”)

Yes that is why it is important to practice, take notes, ask questions, do homework, listen to professor and study. Although it sounds like alot you are able to understand the material and pass the class.

If I had to speak to a 2071 Math class I would tell them to open their mind. That solving problems through repetition is no longer the focus of doing well in class but understanding the thought process of coming up with formulas and all the numbers. I would say to definitely put on your thinking cap and not to focus on what you learned before but be able to see the proofs and logic behind the math.

As a person who is guilty of thinking of math as “just tell me what to do and let me do it”, this class will be a change of pace for me. I have a history of writing out as many steps as I can to solve a problem, but doing so does not show I understand the math except as a linear step-by-step progression. As a future teacher, I’m going to eventually be asked “why?” and justify different steps in different terms than I have already come to understand them. I’d like to assume that’s why some of us are here.

The trend I see in the advice from last years’ class is “beware of proofs”. Induction proofs, contradiction proofs, etc… I will do no such thing. Of course, this can change over the course of a semester or if Professor Reitz pulls a Yoda, and tells me “you will be (afraid).”

I also notice that there are statements to the effect of “get help from your classmates.” Getting help from the professor is a given, but his hours are limited. Our classmates are a network you can go to to get help. Sure they might not have the level of expertise Prof. Reitz has, but some will understand the material in their own way and explain it in a manner you can understand if the professor’s explanations go over your head. It helps that a sizable portion of the class is in math education (with one or two outliers), so we will have to see each other in other classes.

Feel free to ask me questions (provided I seem like I know what I’m doing), but I will expect some reciprocation if I am in a similar predicament.

Sometimes we learn best from our peers rather our teachers – students often have a good sense of which part of the material is confusing, something that is harder to figure out when you’re standing in front of the classroom!

I think the most relevant advice for me personally was Albina’s advice because she gave a lot of information about the course and how I should master this course by doing my homework and reading the chapters. Also, she gave a good advice which was that I have to memorize all the connotations to be able to deal with all the problems and understand the questions easily. Also, I like how she advised the students about not reading materials that will not be used because it will get us confused. The best advice that I liked about Albina was repeating the word Practice which made it very clear to me that practicing for this course will make things easier for me. In addition, I think I can make a lot of changes right now since I am still at the beginning of the semester. I can focus more in doing homework and practice many problems. I also should read the lessons to understand more and memorize everything from the beginning so it would be easier for me to understand everything that comes after

I like this advice a lot – Humans are creatures of habit, and the start of something new is the right moment to begin the habits you want to keep. Good luck!

The mention of the emphasis on group work was the most relevant to myself. Group work is the common factor to some of the hardest classes i have yet to take in college. Group work forces you to create common language in a group of individuals that process things differently. This difference can help us as peers to explain concepts in different vocabulary and helps us have broader understanding of the concepts. In wanting to become a teacher, this many roads leading to the answer is most important for me to absorb to learn how to always offer an alternate route to the answer with my students in the future.

The best advice that seemed most relevant to me personally was Ms. Desir’s. I find her advice very sincere and ideal for students who wish to do well in this class. The key ingredient as she mentioned is to utilize the time and resources given productively. A couple of ways is by paying attention to what is taught in class and working with classmates to improve the learning experience. Studying with peers is a great way to learn. As she mentioned it is one way to help understand complex areas because the classmates might be able to phrase it an easier manner. Most often this is true and it has also helped me in the past esp. in physics and calculus. The second part of the advice is something that we hear most of the time but least followed that is, to practice. This is absolutely true because if we make practice as a habit it will make a lot easier to prepare for the final. I personally have to stick to this advice right now and be consistent with it because lately I’ve been doing homework in the last minute so I find very little time to practice.

I think I should pay heed to these valuable advises more and implement these changes to help me with this course. One additional change that I would like to make is to stop procrastinating. I find this like a “drug” because it is easier said than done. But hopefully I will try to get this rid of my system so that I can organize my work in a timely fashion and do my best by implementing the advises and studying well for this course.

after reading all the responses about this course, i saw that many of the past students emphasize in understanding the concept of algebra. i feel that this is very important since many of the past students have mention that if one doesn’t understand algebra with ease, one will make common mistakes. i also feel that if one practice and does all the hw’s one will be able to understand the material, day by day. i feel that these two things i mention are relevant to me because i am the kind of person that doesn’t take practice into consideration,i am a person that waits two days before an exam to “study”. i also am a person that thinks i don’t need to review my algebra because “it’s easy”.

with the advice from the past students i would try tochange my personality and put more emphasis in practice and take every thing i learn in my past math courses serious, especially algebra, i will retouch this material.

You have great self-awareness, which is half the battle!

In my opinion, the most relevant advice was from Albina Yevdayeva. I find it most relevant because she’s shares her experience’s from day one of the class to the end. From what she said, I believe that the best way to pass this course is to take the time to memorize all the connotations and take my time when i do the homework. I can relate to her experience because in my second day of class I did found myself looking back at my notes just to understand the question; due to the fact that I didn’t know the connotation. Also from her statement, “each topic is like a ring, which at the end can give you a nice necklace,” tells me that it best to have a complete understanding of the subjects taught early on because it will be the basis of answering future. Unlike other math course i’ve taken in the past where i just had to memorize things, I plan to take the time to try to get a clear understanding of each topic that is taught in this course by taking my time doing the homework, asking questions, and forming study groups when I need to.

I liked Albina’s necklace quote also – and the fact that it stands out makes me think about the power of a simple image in helping people remember an idea. This is something for me (and you all!) to think about in our teaching, when we are trying to find ways to get ideas to stick in peoples’ heads.

this is sidney sao

I agree with the student from last year called ibrahimadam193 saying that getting tons of practice is needed. Because learning math cannot become success without doing problems by oneās own. Understanding about what professors said during the class and reading the textbook are only the first step of studying math courses. When people start doing problems their own, questions will come up. And solving questions is the most important part of studying mathematics.

The advice that I felt that is and will be most relevant would have to be to practice and practice the information that we will be taught in proofs and logic. Majority of my past fellow classmates kept stating that practice is necessary and it is, I believe practicing is key in order to understand the concepts throughly. I honestly agree when Adam states “one is learning a new way of thinking and interpreting mathematical structures and statements in addition to a completely new language”. Proof and logic is like learning a new language because we go more in deep and into detail about stuff that we already know. The other most important advice is when Loudia mention that we should listen to Professor Reitz, I can agree 100% on this, not only because Professor Reitz is a logistic, but the way he examples things make each concept seem easier and he is always their to help. Which is why whenever one has a question, just ask it cause it’s better to ask the question then not to ask it. Like Loudia said “Someone once said to me math is not a spectator sports”. As long as you work hard, do A LOT of PRACTICE problems and do the work and effort, their should be no reason to not understanding the concepts. The changes that I can make right now is to make sure I always do my homework on time and that I listen in class during lecture, because I know that if I do not listen in class I might even miss something that is crucial to learning a concept. Most of all to tend to practice a lot of problems.

Reading through all 22 posts helped me understand the class more clearly than before. I think the advices that seems more relevant to me are, what Ibrahimadam193 said āDo not be afraid to make mistakes,ā as I often feel like I could solve a problem or know how to do it but then again scared of making mistakes. His other advice which also seemed relevant was āDonāt treat this class like your other math class,ā well itās also quite obvious to me now after taking few class and also what Prof. Reitz mentioned in class that this course is also a writing intensive class and now it helped me to approach the class differently. The other relevant advice was Alphatronās where he talks more about proofs and how to overcome a problem like āif you get stuck on a step and not know where to goā he advices to work in a group and also what Ms. Desir she says āa lot of time where I did not fully understand an idea or concept and by working with one of my classmates in class I understood the material a bit more. Sometimes itās easier to learn from a classmate, they may phrase things in a way thatās easier to understand allowing you to grasp a concept betterā which I totally agree and also that Prof. Reitz encouraging us to solve some problems in groups which is even a plus point for this class, I think. Lastly, I would like to remind myself that almost every single of the 22 post advices to practice and practice and which is so important for us to succeed in math and also in any other class.

Advice from the Past

As reading through all the advice from the students who have taken this course, I have a mixed feeling. It seems that this course requires a solid foundation of algebra, a strong ability of abstract thinking and a well prepared attitude of self-discipline. All these give an impression that it might be a very challenging course. Haunted by this feeling, I feel an unnamed pressure since there is still a long way to go, especially, since yesterday was the every first day of this battle of proofs and logic. However, all the essays from the previous students give me insightful advice that will help me to make learning this course easier and more effective.

First of all, more than two ex-students mentioned that proofs by induction are quite hard for them. They do not see the connection between P (k) => P (k+1) easily. To cope with this problem, some of them suggest thinking outside of the box. I think that is very important for me. Personally, I believe that everyone has a relatively fixed thinking pattern. For example, every time when I open a door, I will instinctively choose to turn to the right side. Similarly, when I deal with math problems, I can say with certainty that I have my own preference of so-called strategies or techniques. These accustomed/ habitual thinking patterns sometimes do lead me to a chaotic situation which prevents me from being efficient. At this point, I appreciate Alanās advice. I will keep in my mind that with regard to the way of proofs, there are a lot of alternatives as if when flying to oneās destination we can take off from different places of the earth, therefore, while trying to break my own habit of thinking, I may see different beautiful views along the road are destined to be proven.

Secondly, I agree with all the ex-students who have addressed the importance of doing homework. Personally, I think I am a beneficiary of doing homework. Usually, students are used to falsely thinking that they are able to completely master the materials just because they followed well what their professors taught them during the lecture time. Consequently, they ignore the homework. Through reading all the advice, I can learn that it is essential to do homework in order to reach the goal of achieving this course because homework provides us with the chance to practice what we have learned and shows us where our weak points are. Moreover, the procedure of doing homework is an indisputable process of strengthening prior knowledge. Therefore, I will definitely take this advice and put it into action.

Lastly, learning from prior mistakes is very necessary. Although none of the ex-students mentioned that in their essays, I still feel the need to point it out. As a self āretrospect, I confess that I often ignore the mistakes that I have made in the past papers, homework, or tests as long as I am satisfied with the scores. Consequently, I have become a realist of earning scores and an idealist of gaining knowledge, by which I mean, I pay more attention to the scores than the knowledge I failed to understand. Accumulatively, I feel as if I am standing on a shaking ground and it is very hard to step further.

All in all, all the advice is precious and meaningful, it is like a lighthouse. It serves us to navigate smoothly during the voyage of proofs and logic and keeps us on the right route. I have to say it again that I really appreciate all the advice.