Evidence-based teaching practices
Since 2012, I’ve taught over 10 different courses and nearly 10,000 students. Over the years, I’ve enjoyed experimenting with pedagogies rooted in both well-established teaching literature and my own data-driven insights. Below, I’ll summarize how I currently structure the main course I teach, Numerical Methods. Details about the rationale behind some of these methodologies are described in the Research page.
Flipped Classroom
Since Fall 2020, I’ve been running my course in a flipped format, which is as much about flipping the script on traditional lectures as it is about flipping the responsibility onto students (in a good way). Here is how the course is organized:
- Pre-lectures: twice a week, students complete pre-lectures consisting of short videos (5-7 minutes) and checkpoint questions (see slides), which they are required to finish before the following Tuesday’s class. They also have the option to explore the lecture content through our online textbook, either as a supplement to or replacement for the videos. This structure allows students to engage with foundational material at their own pace prior to class. Pre-lectures contribute to 4% of the course grade.
- In-class group activity: during Tuesday classes, students collaborate in small groups (2-3 members) to solve real-world problems using IPython notebooks. These problems are scaffolded to provide step-by-step guidance, ensuring students can navigate complex concepts effectively with little to no-guidance from course staff. Additionally, PrairieLearn’s autograder offers immediate and constructive feedback, enabling students to refine their understanding in real-time. My entire course staff is present to support these activities. Group activities contribute to 11% of the course grade.
- Clicker-based review and whiteboard discussions: Thursday classes focus on approximately eight multiple-choice questions, which students answer using an online clicker system. Initially, students respond individually, without peer discussion, and then discuss their responses with those around them. After each question, I provide the correct answer, sometimes with a brief explanation. Once all questions are covered, the last 30 minutes of class are dedicated to targeted problem-solving. Each multiple-choice question is assigned to a course staff member who explains the solution on one of the classroom’s 12 whiteboards. Students can move between boards to seek assistance for the specific problems they need help with. This approach creates an open, forum-like environment where students actively engage in discussions and focus on the areas they find most challenging.
This flipped style transforms class time into an interactive and collaborative learning environment, prioritizing active problem-solving over passive content delivery.
Formative assessments: unlimited attempts and immediate feedback
During the semester, I provide students with several opportunities for learning via formative assessments. In these, students are not penalized for making mistakes. Instead, they are encouraged to attempt problems repeatedly, with immediate feedback, to achieve 100% credit through effort. Each week, students have two small homework assignments, each with an average of ten questions. These homework assignments cover the concepts from the two weekly pre-lectures. Students also complete five longer programming assignments during the semester, each focused on a different application. Combined, they contribute to 35% of the course grade.
Together, pre-lectures, group activities, and homework/programming assignments make up 50% of the course grade. These formative assessments ensure that students are not penalized for mistakes and can achieve full credit through consistent effort.
Summative assessments: low-stakes with adoption of frequent testing
Research in engineering education shows that frequent assessments help with long-term retention of course content. Based on the literature and my own research findings, students in my class complete six 50-minutes quizzes during the semester, each covering content taught in the previous two weeks. These quizzes are administered asynchronously during a 3-day period at a computer-based testing center, where students do not have access to external online resources, such as ChatGPT, beyond what is provided within the quiz itself. To support students, I make the online textbook available during the quizzes, so they don’t need to memorize concepts but instead focus on applying them to solve problems. Unlike formative assessments, quizzes do not allow unlimited attempts on questions, except for a couple of coding questions, emphasizing accurate application and understanding of the material. Each quiz contributes to 35% of the course grade. The final exam contributes to the remaining 15% of the course grade. It is cumulative, has the same format as the quizzes, but is twice as long, giving students 1 hour and 50 minutes to complete it.
You can check this page on computer-based assessments for details on the grading differences between homework and quizzes, along with example questions.
Practice exams
To help students prepare for the quizzes, they have access to unlimited practice quiz instances starting one week before each quiz date. These practice quizzes use the same question generators as the official quizzes, both structured as a series of “slots,” with each slot linked to a pool of question generators of similar difficulty and concept coverage. When a quiz (or practice quiz) is generated, each slot is randomly populated with a question from its pool. Typically, a quiz consists of 9-12 slots, with each slot containing 2-5 question generators, resulting in an average of about 40 question generators per quiz. With unlimited practice opportunities, students can encounter variations of all question generators that may appear on the official quiz.
In addition to supporting learning, practice quizzes help reduce anxiety by familiarizing students with the quiz format and content. This transparency also diminishes the incentive for cheating during asynchronous exams, as students have already had ample exposure to the quiz material.
Flexible formative assessment deadlines
One way to encourage students to stay on track with course content is by implementing frequent and strict deadlines for formative assessments. However, strict deadline policies can increase students’ stress, lead to rushed or poor-quality submissions, and even incentivize cheating. From one of my research studies, I found that removing deadlines entirely can result in a significant number of students procrastinating and submitting formative assignments late, which negatively impacts their performance on summative assessments. To balance these challenges, I have adopted a flexible deadline policy for all formative assessments.
This policy allows students to earn full credit (100%) if they submit assignments within one week of their release, encouraging them to stay on track with the course schedule. For assignments submitted after this initial period but before the corresponding quiz date, students can still earn 96% credit. This approach provides flexibility for students who may need extra time while maintaining an incentive to engage with the material promptly, ultimately promoting better learning outcomes.
Online and in-person offerings
Teaching large classes comes with the challenge of securing adequate spaces for class meetings. Moreover, students benefit from different learning environments, with some preferring classroom interactions and others thriving in more flexible modalities. Previously, I offered two in-person sections to accommodate over 400 students, but attendance often dropped to less than half. To address this, since 2021, I have been offering one in-person section and one online section of my course.
The primary difference between the two sections lies in how students complete the “in-class” group activities:
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In-person section: Students attend class during the scheduled lecture time and work in teams to complete computer-based activities. Teaching assistants are available in the classroom to provide support, maintaining a 20:1 student-to-instructor ratio. Attendance is required.
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Online section: Students have no attendance requirement and can complete the same in-class activities asynchronously with their groups. During lecture time, they have the option to join a Zoom meeting supported by teaching assistants (also maintaining a 20:1 student-to-instructor ratio). Within Zoom, students can collaborate in breakout rooms and request help from the course staff as needed. Alternatively, they can work with their groups at a time of their choosing during the lecture day, either remotely or in person.
A research study I conducted revealed that this flexible approach, which accommodates varying student preferences and simplifies class scheduling, did not lead to statistically significant differences in the overall performance of students who chose the online section compared to those in the in-person section. This indicates that offering both modalities effectively meets diverse student needs without compromising learning outcomes.
Teaching experience
| Course name | Term taught |
|---|---|
| Numerical Methods 1 | Spring 2018, Fall 2018, Spring 2019, Fall 2019, Spring 2020, Fall 2020, Spring 2021, Fall 2021, Spring 2022, Fall 2022, Spring 2023, Fall 2023, Spring 2024, Fall 2024 |
| Intro to Computing: Eng & Sci | Fall 2024 (co-instructor) |
| Current Topics in Computing Education Research | Fall 2024 (co-instructor) |
| Applied Linear Algebra | Fall 2020 |
| Computational Tools for Linear Algebra | Spring 2020 |
| Brushing up Linear Algebra and Programming Fundamentals using Python | Fall 2019 |
| Python for Data | Fall 2019, Spring 2020 - Pot A, Spring 2020 - Pot B |
| Real World Cases in Scientific Computing | Fall 2018 |
| Introduction to Online Learning Systems | Fall 2017 |
| Finite Element Analysis | Spring 2016, Spring 2017 |
| Introductory Solid Mechanics | Spring 2012, Fall 2012, Spring 2013, Fall 2013, Spring 2014, Fall 2015, Fall 2016, Fall 2017 |
| Statics | Fall 2014, Spring 2015, Spring 2017 |
Teaching awards
- Rose Award for Teaching Excellence, 2022, Grainger College of Engineering, University of Illinois at Urbana-Champaign
- Scott H. Fisher Computer Science Teaching Award, 2022, Computer Science, University of Illinois at Urbana-Champaign
Past Highlights
Over the years, I have explored various teaching innovations and course development projects that have shaped my approach to education. Below is a collection of key resources and activities that reflect these efforts.