Teaching Statement

Diversity fosters learning. Surrounding ourselves with varied individuals let's us learn new ideas and new ways to think. As teachers, we are expected to facilitate the learning of a diverse group of students whether we realize it or not. They may come from different socio-economic backgrounds, follow different fields of study, have different learning styles, etc. It is our job to both bridge this diversity to help them learn a subject and use this diversity to their learning advantage. Often we can only focus on the former as we get stretched thin by so many obligations. But through my career I have learned that both are necessary to become a successful teacher.

We all struggle to at one point or another to reach every student in the classroom. Class sizes at a large university can be upwards of 400 students. And even in smaller seminar classes it can be hard to tailor your lesson to students with different learning styles, let alone different backgrounds. In my first year as a graduate student I saw how difficult it was teaching a math class to students who came from varied backgrounds and diverse interests. In a graduate stochastic modeling class we had some students who knew the material like the back of their hand, and some students who had barely taken probability. It seems impossible in these situations to be able to engage, reach, and challenge every student. And it is! But I've learned that in order to maximize learning, the traditional teaching style should be flipped.

Traditionally the classroom is focused on the instructor, creating a teaching-centric environment. This turns diversity in the classroom into a barrier rather than a benefit. A key benefit of a learning-centric environment is the incorporation of active learning. The up and coming strategy to employ this style of learning is the flipped classroom, where lecture-style learning is done by the student outside of class time and interactive learning is done inside the classroom. Although early case studies of flipped classrooms show promising results, they can be difficult to implement with few resources or help. But we can take the idea of incorporating more student centered learning during class time. This is where diversity acts as a strong suit in the classroom. For example, crafting smaller group activities where students of different backgrounds can work together are key. And many teachers already employ these techniques, but having this style of interactive learning rather than just a lecture is necessary for addressing a heterogenous group of students.

An an educator we often want to pack as much information as possible into our students. This can result in hurried lectures and confused students. It is worth taking the time to assess students backgrounds, allowing for a flexible syllabus, and focusing more on group learning. As a teacher we are torn many directions, and we need to use all of the resources that are available. Especially for large classes, your right hand is the TA. Giving students memorable learning experiences is more valuable than packing them with information. And to accomplish this, TAs can help understand where students stand on their understanding of the material, as well as be a useful link between the teacher and the students for what is confusing. This may seem like an idealistic goal, but effective lessons take a lot of work.

Overall, as a current and future educator I plan to use diversity and a tool for learning by focusing on student-centered learning. Reaching a diverse set of students with tough material at times seems impossible, but with hard work and key use of teaching techniques we can give them a memorable and lasting learning experience.

Teaching History

UCLA

• EEB C119A/C219A - Mathematical and Computational Modeling in Ecology
  My time as a TA for this class was both challenging and greatly rewarding. Students in this class came from varied backgrounds (mathematical, computational, biological, etc.) and were both graduate and undergraduate. I was the sole assistant and in charge of teaching coding in R during discussion sections. Even though this class had been offered before, we overhauled it, and I was able to create my own lab sections from scratch. Overall it was a great experience similar to creating my own short-course as an introduction to the basics of coding.

  • 26 undergraduate, 5 graduate students
  • Two-75 minute lectures, two-50 minute lab sections (~15 students each) per week
  • Topics include: formulation and analysis of mathematical models, basic techniques of scientific programming, probability and stochastic modeling, and methods to relate models to data
  • Group project during second half of course focusing on novel model creation and analysis
  • Weekly alternating quizzes and homework
  • Responsibilities
    • Create weekly lectures and lab assignments with practice problems for students.
    • Work with professor to create quizzes, homework assignments
    • Weekly meetings with professor to go over student progress and evaluations.
    • Hold office hours 2x each week to help with homework, group projects, and studying for quizzes.
    • Grade all assignments, quizzes, and final project presentation and paper.

• LS30A - Mathematics for Life Sciences
  The TA experience for this class was more of a challenge due to the large class size. With over 300 students total it was hard to for the professor to help every student and the assistants became the key point-people for questions. I was able to develop tools for addressing large groups of students, especially during office hours, like being able to point students in the correct direction and having them work together rather than walking them through each step. It was necessary for students to work together to build teamwork skills and properly understand each assignment.

  • 331 undergraduate students (87% first years)
  • Three-50 minute lectures, two-2 hour lab sections (~20 students each) per week
  • Topics include: mathematical modeling as a tool for understanding the dynamics of biological systems, single- and multi-variable differential equation models of dynamical processes in ecology, physiology, etc.
  • Discussion topics include: Sage for problem-solving, plotting and dynamical simulation, basic programming concepts and skills, such as program flow control and data structures
  • Responsibilities
    • Bi-weekly office hours (3+ hours) to help with lab and homework assignment.
    • Grade weekly problem sets, Sage coding assignments, and two exams.
    • Weekly meetings with professor and TAs.

Harvey Mudd College
Attending a small undergraduate college meant that most tutoring and teaching assistant positions were filled by other undergraduate students. This gave me many opportunities to teach starting my sophomore year. Most TA positions were the classic weekly tutoring and grading for a single small class. These experiences were necessary building blocks that helped me understand the basic tutoring process and gain confidence in being a teaching assistant.
The two most important teaching experiences were teaching summer math and being a part of Academic Excellence at Harvey Mudd. The former was a 3 week intensive summer math class that fit two semester long math classes (Linear Algebra 2 and Multivariable Calculus) during the beginning of summer. I took this session my first summer and subsequently TAed the following 3 summers. This class was very stressful for students, and consequently for the small group of TAs for the course. Most waking hours were filled with grading the daily quizzes, homework assignments, and tutoring students. But seeing your students succeed in this environment was incredibly rewarding.
The second important teaching experience was being a member of Academic Excellence, a group of 10 tutors that held tutoring hours 6 nights a week for all math classes offered on campus. This experience was both extremely humbling and gratifying. Each night you held tutoring hours, you had to be ready to field questions from any field of math, and work together with students to help them complete their assignments. We also held review sessions for specific classes, and met with professors as liaisons to see if we met the needs of the instructors.

Teaching Evaluation

2015-2016 Certificate of Distinction in Teaching. "The Certificate of Distinction in Teaching honors your mastery of the course subject matter, skill in the classroom, and commitment to your students. With this award, the Division of Life Sciences recognizes your special contribution to the quality of the student experience in the College of Letters and Science."

Evaluation of Instruction Report Summary

Selected Quotes from Evaluations

• "Christian was extremely proactive in ensuring students understood the labs and class content, holding and extending office hours for students if necessary. His ability to explain concepts is extremely good. He responds promptly to email questions and overall was extremely knowledgeable about the topic." -LS30A Student

• "The discussion section really complimented the course very well. Christian was an A+ TA! He was such a great resource when learning R and completing homework assignments. I felt that he was always prepared to teach discussion and tried to ensure that all students were learning what they needed to. He made himself available whenever students had questions and I witnessed him have a lot of patience when teaching me and other students. I personally feel like his assistance helped with my success in the course. Thanks for a great quarter." -EEB C219A Student

• "Christian is a dedicated TA that goes above and beyond to help his students understand the course material. C119A was challenging for many students, but Christian always came prepared and promptly responded to all emails and concerns to make sure each student was able to succeed. I truly envy those who will get to have him as a TA in the future, and I hope I get the chance to as well." -EEB C219A Student

• "I feel that Christian is the best TA I've had during my time at UCLA. He was very effective at teaching us tools in R during discussion and I felt that his input greatly expanded the scope of the class. If I use R again in the future, I will definitely be referring back to his well made printed lab manuals when starting my projects. In addition to R concepts, I felt that Christian was an effective communicator when explaining model concepts. His office hours were very useful especially for work on the final project and he was always very helpful/insightful. Overall, I had a great experience going to discussion and felt that Christian contributed a lot to making the class fun and reasonable." -EEB C219A Student

Novel Class Syllabus

Probability and Stochastic Modeling for Biology

Description
This class is meant to introduce biologists to the concept of using probabilistic and stochastic models in their own research. More and more classes exist on the line between mathematics and biology focusing mainly on deterministic or statistical modeling. This class aims to get students comfortable with random processes and understand how to implement them in a biological system. Students will be taught basic principles of computer programming in R to practically implement these techniques. Although the target group for this class is biologists, students working on projects with stochastic components from all backgrounds are welcome.

Background
No programming experience is required. This class also assumes that students have no background in probability theory or stochastic modeling. Students should have taken a basic calculus class and be comfortable with topics like algebra, differentiation, and integration. Classes in modeling would be helpful but by no means necessary.

Learning Goals
By the end of the course students will:

• Feel comfortable coding in R.

• Be able to examine a system and design an appropriate model.

• Learn how to analyze and further develop existing models.

• Improve their presentation and scientific writing skills.

Course Structure
This course consists of weekly lectures and lab sections. During lecture students will learn about topics in probability and stochastic modeling (detailed below). Lab sections will focus on learning and improving coding skills. Both sections will reinforce new concepts using realistic biological systems as examples. The latter half of the course will include a group project where students (in groups of 3) pick a system of interest and analyze the system by designing a stochastic model. The ``final exam'' for the course is a paper and oral presentation on their findings.

Grading
Grading is broken into 4 components: quizzes, homework, participation, and project. There will be short weekly problem sets due on [Monday] covering the material taught in the previous week. There will also be weekly 20 minute quizzes on the day the homework is due. These quizzes are designed to test the students on the material from the previous week, but students should not worry about studying if they have completed the homework. Also the 2 lowest scores of each will be dropped (2 lowest quizzes AND 2 lowest problem sets).

Participation is also key to performing well in class. Students should feel free to ask questions during class or answer questions from the professor. But participation is even more important during the smaller lab sections, where students get to work together on lab coding assignments.

Finally, the majority of the grade will be on the final project. This should be the culmination of everything the students have learned in the course.

Textbooks
There are no required textbooks for this course, but the following books are useful!

• Applied Probability by Kenneth Lange

• A Primer of Ecology with R by M. Henry Stevens

Course Outline
Topics for a 10 week quarter

1. Basic Notations of Probability Theory

2. Distributions

3. Calculating Expectations

4. Poisson Process

5. Discrete Time Markov Chains

6. Continuous Time Markov Chains

7. Diffusion Process

8. Branching Process

9. Catch up week

10. Project Presentations