Downloads: Student Evaluations || Lectures: #1 #2 || Syllabus Syllabus_2025 || Homework #1 #2 #3
y experiences as a student, TA, and teacher over the last decade have shaped my views of what makes a good educator. I have had a diversity of teaching experiences, from teaching courses in linear algebra, multivariable calculus, and calculus in grad school, to creating a graduate-level algorithms course for the Department of Electrical and Computer Engineering at Duke, to teaching courses in algorithms, introductory functional programming, and mid-level discrete structures at Grinnell. At Grinnell I created a special topics course “Computational Methods in Industry” and also created a first-semester tutorial titled “Can Machines Think?” Outside of the classroom, I mentored a team of research students in Duke's Data+ program for two summers. At Grinnell I have mentored students assisting me with my social justice research and writing across four semesters and two summers. Throughout, I’ve assessed a variety of teaching approaches while managing small discussions, large lectures, one-on-one mentoring, and designing new courses.
Through teaching I have learned that good teaching utilizes manifold techniques and methodologies. Throughout my career I have used my own form of interactive lecture added to small- and large-scale activities. Also indispensable has been individualized attention in office hours, and strongly intentional assignment design. Meanwhile, the growth mindset is an essential spirit animating my teaching. Finally, in my choice of language and of material, in my use of diverse teaching modalities, and most of all to my commitment to meeting each student on their own terms in a safe space, I am always striving to create an inclusive learning environment.
Student Engagement In Lecture
For me, an essential pillar of good teaching is student engagement, such as, participating in class activities, or paying close attention during lecture. Over the years I have developed a teaching style that mixes in-class activities, such as group worksheets or think-pair-share questions, with more standard lectures where I present in an animated style while facing my students and use standard public speaking methods for maintaining attention: movement, gesticulation, vocal inflection, cadence, and, critically, eye contact.
Worked example problems is an important part of my teaching process. I will often do this live on the board, later providing students with annotated slides of the worked examples. Though when time permits, I will frequently prefer to give students some time to attempt the example themselves, before checking in with the class and going over the example as a group. When working examples for the whole class, I always prompt the students to provide the next step. This promotes student engagement, since they tend to ask more questions during these examples.
. Student engagement is also served when I take a little lecture time to discuss concepts beyond the precise subject of the course. I give the students a glimpse into the complex applications of what they are learning, emphasize the importance of that material, and break up particularly dense or repetitive portions of the course. For example, one time I noticed my algorithms students at Duke were getting lost and not asking questions during our discussion of undecidable problems. This can be a rather dense topic, so I took some time to ask students where they thought humans fit in our hierarchy of computation. We then discussed the implications of the famous Turing test, and how they now had the skills to understand it.
Active Learning Techniques
I have also employed, and continue to add, a variety of active participation techniques in my classes. Most involved a worksheet or a prepared problem set, and a standard approach was to have the students work on the problems in groups. But participation techniques can be ineffective if not done correctly. For example, I was once a TA for a set of courses that tried making very difficult worksheets, with the theory that it would force the students to work as a team to figure them out. In practice, these worksheets just made the students anxious, with only a handful of students able to understand the problems. Therefore, I try to choose problems that are challenging, but can still be worked through on time and provide my students with a sense of accomplishment when they arrive at the answer. I also like choosing fun stories for the problems, to both better engage the students with the material (it can be more fun and less stressful thinking about dragon hunting than array searching) while also reinforcing the idea that the course concepts are widely applicable to many different scenarios.
A form of active participation I have used in small classes involved calling individual students to the board to work through problems in front of the class. This sounds terrifying at first, but the purpose is to have only the students work through the problem. If the student at the board makes a mistake, it is up to the other students to help fix it. The idea is to help the students become more confident in their work, while exposing them to the common pitfalls. I take time to explain this goal before we start, and to remind them of it throughout the process. Meanwhile my role is encouraging the students while they are at the board and when they think they have spotted a mistake. This method worked well, and after a few tries, the students themselves could see its value and warmed up to it. Another variation of this that I like to employ involves assigning small groups of students to each work specific problems on the board simultaneously. I then assign each group to review another group’s work, and report back on it to the full class. This gives them the chance to practice working on the problems, reviewing and assessing the problems, and presenting the problems all in the same activity.
While meaningful for small classes, these board-based active learning techniques were infeasible for very large classes like my algorithms course at Duke. In that class, I utilized a think-pair-share approach which I continue to employ at Grinnell. I provide students with a prompt. They then have a few minutes to talk about it with their neighbors while I wander the room, listen in, and sometimes join discussions. When enough time has passed that a few groups have started to hit on the important concepts, I bring the class back together and have some of the students share what their group discussed.
One of my favorite activities in my algorithms course at Grinnell has been “Interview Days,” and idea that I got from one of my colleagues who taught the course previously. The activity involves pairing the students and having one member of each pair leave the room. I then present a problem and solution for the remaining students, providing them with detailed instructions, hints to give, and follow-up questions to ask. When we bring their partners back into the room, the students interview each other. After half of the class session passes, we switch sides and repeat the activity with a new problem. I find that students really enjoy these days, and some of them even role play as they interview each other. I believe that these activities not only give students good practice at thinking through a new problem, but also provide them with the opportunity to assess each other’s work while seeing how other students approach new problems. Meanwhile, it also simulates at least some of the stress of a real interview setting, and can help act as a bit of preparation for future interviews. I also encourage them to find groups of friends to practice these types of activities outside of class as a great way to practice these skills.
Going Beyond The Subject
Student engagement is also served when I take a little lecture time to discuss concepts beyond the precise subject of the course. I give the students a glimpse into the complex applications of what they are learning, emphasize the importance of that material, and break up particularly dense or repetitive portions of the course. For example, when introducing the dry subject of Riemann sums in single variable calculus, I have students think about how a computer might evaluate an integral, and how the different endpoint rules and other methods we discussed relate directly to numerical integration techniques used in my research. In another recent example, I noticed my algorithms students were getting lost and not asking questions during our discussion of undecidable problems. This is a rather dense topic, so this year I used an interlude to ask students where they thought humans fit in our hierarchy of computation. We then discussed the implications of the famous Turing test, and how they now had the skills to understand it.
Office Hours and Individualized Support
I utilize all of these techniques to help promote in-class student engagement. But while student engagement starts in the classroom, it should not end there. Office hours are a major part of my approach because they give me the chance to work one-on-one or in small groups with my students. I try to take a Socratic approach during office hours so that the students end up answering the questions themselves, and feel an ownership over their solutions.
Because I believe that office hours are so important, and because they have received such positive feedback from my students over the years, I try to encourage students to attend. I tell my students that if they are willing to put in the effort to seek me out and ask questions, then I am willing to work with them for as long as it takes to understand the answers. For me, these are not just words: I follow through. I have often extended office hours to help a couple struggling students, have scheduled individual meetings with students who have asked, have checked in with specific students falling behind to set up extra meetings, and have sometimes made myself available to answer questions after hours and over weekends through email or a course forum during the more difficult weeks of the semester. At Grinnell, I have even implemented a weekend math review early in the semester whenever I have taught algorithms to help students who were struggling with some of the more foundational mathematical concepts.
Individualized attention also allows me to directly engage with the students in the most inclusive way I know: letting them know that everyone has special needs sometimes and I am here to accommodate whatever they might need. For example, at Grinnell recently I had a black woman student who had arrived very late to several class sessions, and had missed much of the material. I reached out to her and encouraged her to see me during office hours. She clearly felt out of her depth when it came to the mathematical content of the course. She told me that she had failed multiple math courses at Grinnell in the past, and that she was “bad at math.” There was nobody in line for office hours that day, so I took over an hour to work through a private, one-on-one lecture with her to cover the material. As we worked together, it became evident that she recalled a lot of the material from the class, and actually had an impressive level of intuition for many of the key algorithmic concepts of the course. Her mathematical technique was perhaps slow, but given the time, she was able to complete all of the problems with little guidance. She just needed the patience and space to work through it herself: to recall the information and put it together. I gave her that support, and she walked away not only understanding the material, but having gained a newfound confidence in her own intuition. She does still insist that she is not great with the technical side of the course. But I have heard her rightfully bragging to her friends about her fantastic algorithmic intuition. She just needed someone to have the patience to actually listen to what she had to say and recognize the skills she could demonstrate when given the chance.
Thoughtful Assignment Design
I also work to engage my students through the thoughtful design of my homework assignments and projects. My homework assignments typically have a handful of easy, more standard problems, but also include a couple difficult, complex, and hopefully fun problems that force my students to really think about the material and extend their understanding. While this is not something that works for the limited time in-class active learning techniques, these problems fit much better for longer-term homework assignments where the students have plenty of time to ask questions and seek help at my office hours. For projects, I like designing complex problems that can be broken down into a series of relatively easy tasks. This gives the students a clearly defined objective, while also providing them with that sense of satisfaction at having completed a rather complex task by the end of the assignment.
Again, even in assignment design one must always be thinking of inclusivity issues. For example, overreliance on sports examples can alienate those groups who tend to be less concerned with sports. And, of course, many international students are largely unfamiliar with popular American pastimes like baseball and football. While I do not tend to use sports in my problems, there is no need to banish them altogether, for some groups do relate well to sports. The key is to embrace the diversity of people by reflecting it in the sorts of problems you use, while also keeping the problems fresh and engaging. One of my favorites used dragons to illustrate how to search for a moving target in a sorted array. At the urging of a colleague I looked into whether this would be a turn-off to many women who, in older studies, were less likely to be engaged with such fantasy tropes. Looking into it revealed that women nowadays are now much more likely to engage with such fantasy worlds. Also, I realized that for many of my Asian students dragons are a welcome part of their mainstream culture. In the end, I kept the dragons and the students love them. But I had to look into it, and make a careful judgment call, because inclusivity doesn’t just happen. It takes thought and work.
Growth Mindset & Mastery Grading
Another essential pillar underpinning my approach to teaching is the growth mindset: learning is best accomplished when we give ourselves space to make mistakes and grow from them. Encountering new subjects and grappling with new ideas can be challenging and can feel like a struggle at times. But if we lean into the struggle and embrace it, we can pursue improvement without the fear of failure. The struggling means we are learning! The challenge leads to growth! I have this discussion directly with students at the beginning of each semester, and remind them of this important fact at times throughout my courses. My approach to teaching - including mastery grading, interactive classwork, and personalized attention - is intentionally designed to champion this growth mindset. In my classroom, mastery grading is essentially the idea that allowing students to resubmit or reattempt their work can lead to better reflection on their mistakes and help them improve their understanding. There are a variety of studies showing how such policies can lead to better outcomes for students, can help them engage in new ways with their own education, and can help them feel supported and less anxious when encountering new and challenging material
Teaching Is Learning
My years, including the infamous COVID year of remote and hybrid teaching, have reaffirmed that teaching is, itself, a learning process. I will continue to experiment and seek out new techniques to create an engaging course environment for my students as I grow as an educator. I myself have adopted the growth mindset in my teaching: I research, I try out new ideas, I evaluate effectiveness.
Through teaching I have learned that good teaching utilizes manifold techniques and methodologies. Throughout my career I have used my own form of interactive lecture added to small- and large-scale activities. Also indispensable has been individualized attention in office hours, and strongly intentional assignment design. Meanwhile, the growth mindset is an essential spirit animating my teaching. Finally, in my choice of language and of material, in my use of diverse teaching modalities, and most of all to my commitment to meeting each student on their own terms in a safe space, I am always striving to create an inclusive learning environment.
Student Engagement In Lecture
For me, an essential pillar of good teaching is student engagement, such as, participating in class activities, or paying close attention during lecture. Over the years I have developed a teaching style that mixes in-class activities, such as group worksheets or think-pair-share questions, with more standard lectures where I present in an animated style while facing my students and use standard public speaking methods for maintaining attention: movement, gesticulation, vocal inflection, cadence, and, critically, eye contact.
Worked example problems is an important part of my teaching process. I will often do this live on the board, later providing students with annotated slides of the worked examples. Though when time permits, I will frequently prefer to give students some time to attempt the example themselves, before checking in with the class and going over the example as a group. When working examples for the whole class, I always prompt the students to provide the next step. This promotes student engagement, since they tend to ask more questions during these examples.
. Student engagement is also served when I take a little lecture time to discuss concepts beyond the precise subject of the course. I give the students a glimpse into the complex applications of what they are learning, emphasize the importance of that material, and break up particularly dense or repetitive portions of the course. For example, one time I noticed my algorithms students at Duke were getting lost and not asking questions during our discussion of undecidable problems. This can be a rather dense topic, so I took some time to ask students where they thought humans fit in our hierarchy of computation. We then discussed the implications of the famous Turing test, and how they now had the skills to understand it.
Active Learning Techniques
I have also employed, and continue to add, a variety of active participation techniques in my classes. Most involved a worksheet or a prepared problem set, and a standard approach was to have the students work on the problems in groups. But participation techniques can be ineffective if not done correctly. For example, I was once a TA for a set of courses that tried making very difficult worksheets, with the theory that it would force the students to work as a team to figure them out. In practice, these worksheets just made the students anxious, with only a handful of students able to understand the problems. Therefore, I try to choose problems that are challenging, but can still be worked through on time and provide my students with a sense of accomplishment when they arrive at the answer. I also like choosing fun stories for the problems, to both better engage the students with the material (it can be more fun and less stressful thinking about dragon hunting than array searching) while also reinforcing the idea that the course concepts are widely applicable to many different scenarios.
A form of active participation I have used in small classes involved calling individual students to the board to work through problems in front of the class. This sounds terrifying at first, but the purpose is to have only the students work through the problem. If the student at the board makes a mistake, it is up to the other students to help fix it. The idea is to help the students become more confident in their work, while exposing them to the common pitfalls. I take time to explain this goal before we start, and to remind them of it throughout the process. Meanwhile my role is encouraging the students while they are at the board and when they think they have spotted a mistake. This method worked well, and after a few tries, the students themselves could see its value and warmed up to it. Another variation of this that I like to employ involves assigning small groups of students to each work specific problems on the board simultaneously. I then assign each group to review another group’s work, and report back on it to the full class. This gives them the chance to practice working on the problems, reviewing and assessing the problems, and presenting the problems all in the same activity.
While meaningful for small classes, these board-based active learning techniques were infeasible for very large classes like my algorithms course at Duke. In that class, I utilized a think-pair-share approach which I continue to employ at Grinnell. I provide students with a prompt. They then have a few minutes to talk about it with their neighbors while I wander the room, listen in, and sometimes join discussions. When enough time has passed that a few groups have started to hit on the important concepts, I bring the class back together and have some of the students share what their group discussed.
One of my favorite activities in my algorithms course at Grinnell has been “Interview Days,” and idea that I got from one of my colleagues who taught the course previously. The activity involves pairing the students and having one member of each pair leave the room. I then present a problem and solution for the remaining students, providing them with detailed instructions, hints to give, and follow-up questions to ask. When we bring their partners back into the room, the students interview each other. After half of the class session passes, we switch sides and repeat the activity with a new problem. I find that students really enjoy these days, and some of them even role play as they interview each other. I believe that these activities not only give students good practice at thinking through a new problem, but also provide them with the opportunity to assess each other’s work while seeing how other students approach new problems. Meanwhile, it also simulates at least some of the stress of a real interview setting, and can help act as a bit of preparation for future interviews. I also encourage them to find groups of friends to practice these types of activities outside of class as a great way to practice these skills.
Going Beyond The Subject
Student engagement is also served when I take a little lecture time to discuss concepts beyond the precise subject of the course. I give the students a glimpse into the complex applications of what they are learning, emphasize the importance of that material, and break up particularly dense or repetitive portions of the course. For example, when introducing the dry subject of Riemann sums in single variable calculus, I have students think about how a computer might evaluate an integral, and how the different endpoint rules and other methods we discussed relate directly to numerical integration techniques used in my research. In another recent example, I noticed my algorithms students were getting lost and not asking questions during our discussion of undecidable problems. This is a rather dense topic, so this year I used an interlude to ask students where they thought humans fit in our hierarchy of computation. We then discussed the implications of the famous Turing test, and how they now had the skills to understand it.
Office Hours and Individualized Support
I utilize all of these techniques to help promote in-class student engagement. But while student engagement starts in the classroom, it should not end there. Office hours are a major part of my approach because they give me the chance to work one-on-one or in small groups with my students. I try to take a Socratic approach during office hours so that the students end up answering the questions themselves, and feel an ownership over their solutions.
Because I believe that office hours are so important, and because they have received such positive feedback from my students over the years, I try to encourage students to attend. I tell my students that if they are willing to put in the effort to seek me out and ask questions, then I am willing to work with them for as long as it takes to understand the answers. For me, these are not just words: I follow through. I have often extended office hours to help a couple struggling students, have scheduled individual meetings with students who have asked, have checked in with specific students falling behind to set up extra meetings, and have sometimes made myself available to answer questions after hours and over weekends through email or a course forum during the more difficult weeks of the semester. At Grinnell, I have even implemented a weekend math review early in the semester whenever I have taught algorithms to help students who were struggling with some of the more foundational mathematical concepts.
Individualized attention also allows me to directly engage with the students in the most inclusive way I know: letting them know that everyone has special needs sometimes and I am here to accommodate whatever they might need. For example, at Grinnell recently I had a black woman student who had arrived very late to several class sessions, and had missed much of the material. I reached out to her and encouraged her to see me during office hours. She clearly felt out of her depth when it came to the mathematical content of the course. She told me that she had failed multiple math courses at Grinnell in the past, and that she was “bad at math.” There was nobody in line for office hours that day, so I took over an hour to work through a private, one-on-one lecture with her to cover the material. As we worked together, it became evident that she recalled a lot of the material from the class, and actually had an impressive level of intuition for many of the key algorithmic concepts of the course. Her mathematical technique was perhaps slow, but given the time, she was able to complete all of the problems with little guidance. She just needed the patience and space to work through it herself: to recall the information and put it together. I gave her that support, and she walked away not only understanding the material, but having gained a newfound confidence in her own intuition. She does still insist that she is not great with the technical side of the course. But I have heard her rightfully bragging to her friends about her fantastic algorithmic intuition. She just needed someone to have the patience to actually listen to what she had to say and recognize the skills she could demonstrate when given the chance.
Thoughtful Assignment Design
I also work to engage my students through the thoughtful design of my homework assignments and projects. My homework assignments typically have a handful of easy, more standard problems, but also include a couple difficult, complex, and hopefully fun problems that force my students to really think about the material and extend their understanding. While this is not something that works for the limited time in-class active learning techniques, these problems fit much better for longer-term homework assignments where the students have plenty of time to ask questions and seek help at my office hours. For projects, I like designing complex problems that can be broken down into a series of relatively easy tasks. This gives the students a clearly defined objective, while also providing them with that sense of satisfaction at having completed a rather complex task by the end of the assignment.
Again, even in assignment design one must always be thinking of inclusivity issues. For example, overreliance on sports examples can alienate those groups who tend to be less concerned with sports. And, of course, many international students are largely unfamiliar with popular American pastimes like baseball and football. While I do not tend to use sports in my problems, there is no need to banish them altogether, for some groups do relate well to sports. The key is to embrace the diversity of people by reflecting it in the sorts of problems you use, while also keeping the problems fresh and engaging. One of my favorites used dragons to illustrate how to search for a moving target in a sorted array. At the urging of a colleague I looked into whether this would be a turn-off to many women who, in older studies, were less likely to be engaged with such fantasy tropes. Looking into it revealed that women nowadays are now much more likely to engage with such fantasy worlds. Also, I realized that for many of my Asian students dragons are a welcome part of their mainstream culture. In the end, I kept the dragons and the students love them. But I had to look into it, and make a careful judgment call, because inclusivity doesn’t just happen. It takes thought and work.
Growth Mindset & Mastery Grading
Another essential pillar underpinning my approach to teaching is the growth mindset: learning is best accomplished when we give ourselves space to make mistakes and grow from them. Encountering new subjects and grappling with new ideas can be challenging and can feel like a struggle at times. But if we lean into the struggle and embrace it, we can pursue improvement without the fear of failure. The struggling means we are learning! The challenge leads to growth! I have this discussion directly with students at the beginning of each semester, and remind them of this important fact at times throughout my courses. My approach to teaching - including mastery grading, interactive classwork, and personalized attention - is intentionally designed to champion this growth mindset. In my classroom, mastery grading is essentially the idea that allowing students to resubmit or reattempt their work can lead to better reflection on their mistakes and help them improve their understanding. There are a variety of studies showing how such policies can lead to better outcomes for students, can help them engage in new ways with their own education, and can help them feel supported and less anxious when encountering new and challenging material
Teaching Is Learning
My years, including the infamous COVID year of remote and hybrid teaching, have reaffirmed that teaching is, itself, a learning process. I will continue to experiment and seek out new techniques to create an engaging course environment for my students as I grow as an educator. I myself have adopted the growth mindset in my teaching: I research, I try out new ideas, I evaluate effectiveness.
Course Evaluations:
| |||
Sample Lecture Notes:
| algs_bellmanford_lecture_notes.pdf |
| algs_greed_lecture_notes.pdf |
Sample Course Syllabus:
| algssyllabus.pdf |
| syllabus_301_2025b_fall.pdf |
Sample Homework:
| 590_algshw5.pdf |
| 290_ppimhw6.pdf |
| dwarves.pdf |
| roadmap.pdf |