I began my teaching career as a graduate student at Virginia Tech, and the culture there has made an indelible impact on my outlook. As has always been the case, there is a long-standing deal between society and academics. We academics are (or at least supposed to be) given the ability to chase the questions that excite us, while we also agree to educate our fellow citizens in our area of expertise. Every year middle class people come to our university to be educated and help create an educated populace. During this education, I genuinely believe that whether they know it or not a student’s ability to think and reason and even their thoughts on the utility of thinking and reasoning can be massively shaped by their instruction. Gaining the ability to effectively think through problems is of immeasurable importance to an individual, and grants them access to a whole world of understanding that can truly enrich their life. The impact I have as a teacher to guide students to this world is the reason I come back to teaching year after year.
Logic, truth tables, deductive reasoning, proof forms, modular arithmetic, irrationals, direct proof, contradiction, contrapositive, induction, set theory, functions, etc.
Related to the challenges above, discrete math students struggle most when they are asked to solve problems independently. I believe this comes from two sources. One, they are unmotivated to fully justify why their conclusions are true. Two, they have not been taught the necessity of trying and failing when doing mathematics.
My main goal is to teach students how to think. Beyond just how to have thoughts, but how to differentiate between supported and unsupported ones. I tackle this by working to engage students with these problems on as deep a level as possible. One simple approach is to design relevant examples which matter to them more than tired textbook problems about even and odds. I also make sure to model trial and error in my lectures to normalize the messiness of real world problem solving early.
Class Size - 40
Modality - In-person lecture
Effectiveness Score - 5.75
Class Size - 70
Modality - In-person lecture
Effectiveness Score - 5.87
Class Size - 40
Modality - Online Asynchronous
Effectiveness Score - 5.89 out of 6 vs university average of 4.72
Class Size - 70
Modality - In-person lecture
Effectiveness Score - 5.93 out of 6 vs 4.99 out of 6
Class Size - 70
Modality - Flipped Classroom
Effectiveness Score - 5.73 out of 6 vs university average of 4.99
Class Size - 30
Modality - In-person lecture
Effectiveness Score - 5.52 out of 6 vs university average of 4.71 out of 6
Class Size - 70
Modality - In-person lecture
Effectiveness Score - 5.42 out of 6 vs university average of 4.33 out of 6
Class Size - 70
Modality - Online Asynchronous
Effectiveness Score - Data unavailable
Limits, continuity, explicit differentiation, implicit differentiation, optimization, related rates, fundamental theorem of calculus, Riemann sums, integration, u-substitution, integration by parts, partial fraction decomposition, trig sub, sequences/series convergence, improper integrals, etc
Most students enter college conditioned to think that math is just about copying the procedures from class. Therefore, they attempt to feel their way through problems they should be thinking through. This hinders their ability to solve novel problems, not directly covered in class.
First, it is important in any foundational course to make sure the students actually get through the material. Even if this requires a more repetitive, less theoretical approach it is my main priority. However, along the way, I take any opportunity to expose my students to the captivating parts of these mathematical problems that we all enjoy. This can be done by using engaging real world examples, or posing mathematical problems as mysteries or puzzles. If I can spark their curiosity, I can fuel their motivation to be independent problem solvers.
Class Size - 40
Modality - In-person lecture until March and then suddenly online synchronous
Effectiveness Score - 5.68 out of 6 vs university average of 5.04 out of 6
Class Size - 40
Modality - In-person lecture
Effectiveness Score - 5.33 out of 6 vs university average of 4.81 out of 6
Many students have developed the feeling that they are not capable of understanding mathematical problems, so they do not even make the attempt. While teaching, I go above and beyond to try and engage these students socially in the classroom in an attempt to lower the intangible barriers preventing them from participating in the first place.
While engaging my students, I also practice a wonderful technique I picked up from my mentor Andy Norton, which is to meet students where they are. The goal when I discuss a problem with a student is to understand the procedure they used to reach their answer. Only through this understanding can I explain to them not just why the actual solution is valid, but also why their solution is invalid.
In many settings it is crucial that the student be the one doing the explaining. In office hours for example, seeing me solve a problem yet again is not nearly as instructive as them being forced to face the ideas themselves, with me as a guide.
I view homework as the sandbox where students can try their hand at solving problems for themselves. To this end, I design each of my homework problems with an explicit purpose. Most are designed to force students to come to grips with an often misunderstood topic from class, leading them to a deeper understanding.
To emphasize the importance of trying and failing to learning, I allow students some amount of homework corrections. That way, they have a grade incentive to learn from their mistakes, as well as lowered consequences for trying in the first place.
"He always goes above and beyond to answer questions. He truly loves teaching and it's extremely apparent. Whenever I had a question, he would explain the concept, but also manage to come up with examples on the fly (which is extremely impressive)."
"The first and most important thing I noticed about Valvo is his enthusiasm, which was a most welcomed change from former math professors I've had here. Each and every class, he comes with a very positive attitude and is excited to teach our class. He also leaves constructive and specific feedback on homework, which is just exactly what I want in any professor. In addition to the above, the lecture content was very useful and going to class definitely helped to learn the material, followed by reasonable homework assignments that all helped prepare for the test."
"Even if the class was quiet for a lot of time you made me chuckle a lot and your over the top attitude made class easy to follow, because of this I went to class every day. "
"Favorite class, taught me that math can be fun!! "
"His lectures were the best I've had at this institution. He made everything engaging, didn't speed through material , and made the course content digestible(which is saying something because Discrete Math is highly conceptual). "
"Excellent professor who is very engaged in the material. I thoroughly enjoyed this course and I felt like Valvo's teaching was a large part of that. I also very much enjoyed the different conjectures and applications of mathematics presented throughout the course."
"Valvo is super engaging during class and genuinely excited about the content he teaches. He is always willing to help, and genuinely wants to understand how students think through the problems. This was the best math class I have ever taken."
"Great overall professor. Really knows the content he's teaching to us and I can tell he actually enjoys teaching"
"Seriously one of the best if not the best professor that I have had in my 2 years at VT. Thought his grade policy was fair and you could just tell that he was incredibly passionate about the material and cares so much about his students. I wish that I could have him for all of my math courses while at VT, amazing."
"He was very dynamic teacher, so it was hard to become disengaged"
"Enthusiasm and passion for math was infectious. Great at explaining things and allowing for mistakes to be made without penalty. Created an great learning environment."
"Professor Valvo's energy, passion for the work, deep communication skills and understanding of the work made him the best teacher by far I had this year. He is a wonderful man, and I am truly glad I was able to take his class. I hope that his career here is long and prosperous, he is a brilliant man."
"Valvo is probably one of the best instructors I have had at VT he is super passionate about teaching and cares about his students success. He gives many opportunities to bring your grade up and his feedback actually helps you improve. He is very approachable and his teaching style is unmatched"
"He explained all topics very well and down to earth. From funny jokes to real world examples. He has been my best professor since high school. He had a structure to the entire course and the topics that we learned that day. Even while teaching he makes sure to give the definition give an example and then will purposefully do a question wrong as if he were a student on a test and then show us other method to do if we got stuck like that. then he will go on to give even more examples with every case and scenario possible that we might encounter. While explaining each step and his reasoning along the way. Then he will give the method or topic a general use case, general form, and tie it in to other concepts of the course. This is very unlike all of my other teachers who are way less prepared and just go through pre made notes on power point pointing out what equations we need and maybe just barely telling us how to do them. Another good reason vavlo is a great professor is that he engages with the class and takes questions which he will use in the future to better teach the topic next time. Lastly Vavlo was very well spoken and you could tell he enjoyed teaching and his students."
"I loved eveything about the class and valvo's energy was what I really liked"
"Great instructor. Really cares about his students' success and would take the class again"
"Best professor I've had at VT! Explains discrete math really well and has this energy about him where you sense he cares for his students and their ability to learn the material."
"The in-person lectures were fantastic, and I surely would have failed the class without them. Mr. Valvo made sure every class was engaging, made lecture material easy to understand, and gave plenty of in-depth examples of exactly how to approach the types of problems that could appear on exams and homework."
"In part of being enthusiastic in his teachings, he went out his way to give relations to other parts of the class as well as common examples that related to the problems"
"This is the REALEST instructor. His class is fun and engaging and during a pandemic, Professor Valvo still manages to keep a smile on his face. This is the only live lecture I attended because there is no better place to learn Discrete math than learning it from Professor Valvo. He used real world examples to help his students understand the concept, then he goes over the technicalities and shows his students everything the proper way. Shifting from small scale to big scale really helped me understand the theory of the sections. Virginia Tech this is your best professor so treat him right. Also you should give Professor Valvo a raise, I'm telling you, he's not just the best discrete math professor, he's single-handedly THE BEST PROFESSOR. Professor Valvo genuinely enjoys what he does and you can ask any of the students that have had him, they all see that from a mile away. I had a blast taking this course although at some times it was difficult and it really challenged me to think. Obviously there were days where I didn't want want to do any sort of math, but looking back I'm glad I was able to power through and overcome the challenges I faced. I love the way Professor Valvo structured his course and I can definitely agree it's a fair structure. The course isn't easy and at the same time the course isn't impossible. If you take time to learn the concepts taught in this class, you should do just fine at least to pass anyways. Also, I'm the last person in the room that will say they enjoy math, but I can confidently say that I enjoy DISCRETE math and that's only because of Professor Valvo. Out of all the math courses I've taken in my life, this is the only class where I will always remember certain concepts that blew my mind and this is the only math class where I truly think I've mastered most of the concepts."
"Awesome professor! One of the best math professors I have ever had. Stay golden!"
"Professor Valvo is easily one of the best professors at this university. Incredible passion for math that gets everyone excited, always gives his all, and actually cares about students. So refreshing to have had this professor."
"His charismatic teaching style always kept my attention, but his comments on submitted work always helped to clear up misconceptions. Any time he saw widespread misconceptions in the class, he addressed it to make sure everyone properly understood everything before continuing on with new topics.
"Daniel Valvo is a fantastic instructor and is exactly what the VT math department needs. He is young and passionate about math, which influences us students to give our all. He uses modern examples and stimulates discussion which makes discrete math not only easier to comprehend, but more enjoyable. His grading policy is really good and shows that he cares about his student's understanding over just covering course material. He is my favorite instructor in the VT math department and brings a fresh perspective that I think lots of older instructors would benefit from adapting"
"Valvo was extremely friendly in class and made the learning environment so much more fun. I genuinely enjoyed coming to class and learning the material, which is not something I have felt about any other math class. He was very encouraging as well, and made the material easy to understand. I really enjoyed all the humor both in class and in the written assignments, it made me look forward to completing them."
"I really enjoyed how he taught this course. He always had so much energy and enthusiasm which made the lectures more interesting. He incorporated fun ways of teaching material, and I found that it would simplify my understanding of things. His lectures were logical, and his office hours were super helpful as well. He answered our questions in ways that challenged our line of thinking, and he also always encouraged people to ask questions."
"My favorite teacher right here. I had him for two semester for MATH 1225 and MATH 1226. Daniel Valvo has an energetic personality and it was very fun to be in his class. I wish I could have him for many more semesters because he could explain the subject very well. He really cared about his students and enjoyed talking about math. He had a passion for teaching and math that made me want to continue learning. Although the subject was difficult, he made an amazing job at teaching the material necessary. I can not explain how much I enjoyed being in his class, but it was an experience I would never forget. Thank you Professor Valvo, you have helped everyone learn math in the most positive and enjoyable way. Being in this class boosted my interest in math. Thank you."
"There are very few teachers who have helped my learning as much as Mr. Valvo. He is extremely enthusiastic about his material and loves explaining the material in easy-to-understand ways. When Mr. Valvo was teaching, I felt like he truly cared about my learning and wanted to help me understand the material. Mr. Valvo would spend many hours in review sessions or in office hours because he knew his students would understand the material better. He truly was putting in 110% effort when he was teaching the material. I used to think that I did not like math. But after being taught by Mr. Valvo, I realized I actually just don't like not understanding the material and I really do like solving math problems. Mr. Valvo's enthusiasm for his subject is inspiring and has made me more enthusiastic about calculus as well. I hope when I am older I am like him and am extremely passionate about my work/research/whatever I end up doing. This class was taught extremely well and if Mr. Valvo was teaching Multi-variable Calculus I would request for him to be my teacher. If I had to rate his teaching on a 10 point scale, I would give him an 11 :)"
"He is one of the best calculus teachers I have had. The amount of enthusiasm made calculus fun and more rewarding. He is also very easy to approach and gives very helpful advice and has many openings to contact if there are issues."