Teaching
I love teaching and University of Redlands Students are amazing!
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Classes I Teach
Here is the list of courses that I teach. The ones in bold have online content including homework, videos, and lecture notes. Please be patient as I slowly build these sites and fix typos! If you access an active course, some of the content will be hidden as the class progresses. Feel free to email me if you want access to the fill content or if you have suggestions or corrections.
Click on the links below:
Math for Data Science
Introduction to Data Science
Introduction to Programming in Python
Machine Learning
Calculus I
Calculus II
Introduction to Math Modeling
Differential Equations
Topics in Applied Math - Nonlinear Dynamics
Partial Differential Equations
Numerical Analysis
Machine Learning
Senior Seminar
First Year Experience Fall 2021 - Mathematics and Art
Junior's - How to prepare for your Senior Year
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Teaching Philosophy
An excellent teacher makes a big difference in a student's development. As a student, I was fortunate to have motivational teachers who helped me achieve an understanding of the physical world and showed me the beauty and fun of mathematics. Each of these professors had specific and important qualities that had a great impact on my academic career, and defined the type of teacher that I want to be. In lecture they were organized, interesting and thoughtful, leaving room for student questions. Their assignments were difficult but meaningful and they were creative in giving the students new methods for learning the material. They were accessible to students, always willing to listen to comments and they were constantly growing and changing to become better teachers and mentors. In my teaching, I work to demonstrate these qualities and constantly reflect on how I can better teach and motivate my students, like the teachers who shaped my career.
Lectures must be thoughtful and organized in order for the students to get the most out of the experience. When preparing a lecture, I take the time to think of tangible ``real world" examples of how to think about the more abstract mathematical ideas. For example, I tell them to think of ``a vector field as walking through a strong wind" or ``flux as water running off a table". During lecture, I discuss the applications of the new methods or ideas and give examples of how mathematics is used in practical situations such as engineering or research. In class, I give the students the opportunity for comments, questions or discussion by taking occasional breaks from lecture to ensure comprehension. I give students the chance to practice problems in class and often incorporate worksheets or projects into my classes. In my calculus II class, I have the students write a proposal for a new mug design that must be created using a volume of revolution. They have to use integration to calculate the volume, surface area, and mass of their design. It is very fun to see their creativity on the project and to give them an example of a volume of revolution that they can more easily visualize. I encourage in-class dialog in my lectures and find that it leads to a more lively and interactive class. When the students are comfortable asking questions and giving feedback, they take ownership of the class and are more willing to put in the work necessary to learn the material. I think of my lectures as a chance to demonstrate my passion for mathematics and work to stimulate student interest in mathematics. I remember one particularly lively lecture, discussing the fundamental theorem of line integrals, that ended with student exclamations ''wow, that is so cool". I also received an email from a student after another lecture about surface integrals thanking me for the ``extremely helpful lecture" and for making the material ``understandable''. It is vital to capture the student's attention while still carefully explaining each topic. My ultimate goal as a teacher is to make each lecture one that is ``extremely helpful`` and leaves the students with the feeling ``wow, this is so cool".
Mathematics is beautiful, logical and precise, but for students it often seems abstract and inaccessible. As a teacher, I pay careful attention to how I can best assess my students progress and work with them toward a better understanding of mathematics. The best assignment will challenge the students, allow them to practice the methods learned in class, instruct them on good learning methods, and give me as a teacher an accurate measure of their understanding. My favorite assignment combines writing assignments with traditional problem sets. Each week I assign a problem set and a writing assignment, either essay or short answer. I often ask the students to write a one to two page essay explaining how they set up a typical problem, what types of problems use the method, when they might see this again in their engineering future, and what things they need to be careful about in doing the calculations. (See my teaching portfolio for example assignments and student work.) These assignments were helpful to my students and I was surprised at how effective they were in practice. My students told me that they never before read their math books until these assignments and found that reading the book and writing about math was a new and useful study method, even for their other classes. Translating mathematics into English also improved their grasp and retention of the material. I was surprised that by reading the student's essays I could quickly see where there were problems in comprehension and I could address those issues immediately lecture. These assignments allowed me to identify when the students could carry out the calculation but did not understand what they were doing or why they were doing it. Identifying specific comprehension problems early in the course means that each student has the opportunity to succeed in the class. On exams and problems sets I expect the students to write in words what they are doing at each step, this allows me to more easily identify problems in comprehension and forces them to really think about each step in the calculation. One of my favorite student assignments involves the students solving ``math puzzles", in which I write out solutions to problems but the cut up the pieces and jumble them up. I then ask the students to reassemble the problems and write in words why the pieces go together or follow one another. I also ask the students to consider where the problems are similar and where the problems are different, to help see where there are patterns in the solutions. This is particularly helpful in teaching applications of integration. Often the students forget that for each problem they need to first consider a small piece of the problem, after assembling the puzzles they saw that each solution had this type of analysis. I enjoy coming up with new and interesting assignments that stimulate student learning and interest, while giving me useful feedback on their understanding and progress in the course.
The most important quality of a great teacher is the ability to be critically reflective. I consistently work towards being accessible to students and open to their comments and concerns, as a way to inform my critical reflection. My job as a teacher is an ongoing dialogue between my ideas for the class and the needs of the students. By listening to, and addressing, student concerns, I am more likely to encourage a positive learning environment. I often ask the students to fill out mid semester reviews of my teaching. I ask them what is working in the class and what is not. These reviews allow me to address student concerns and change my teaching where necessary. One of my favorite classes to teach is mathematical modeling, this class attracts a wide range of students, from math majors to environmental studies students who have only had calculus I. At the beginning of the class it was hard to find a pace, and a mathematical level, that worked for this wide range of students. However, by talking with the students, by asking for feedback about what they were learning and what they thought I was teaching, and by allowing the students to fill out anonymous surveys about the class, it turned into a successful and enjoyable experience. I was impressed with how advanced their final mathematical modeling projects were and how much time and effort they put into applying the techniques learned in class to research areas, outside of math, that they were passionate about. I also find it very helpful to have my peers and mentors attend my classes and give me feedback about my teaching. The first time a reviewer came to my lecture I was so nervous, I felt that I had to be perfect. After class I sat down with him we talked about the class. We discussed both my strengths and weaknesses in a supportive and constructive way. I realized after this experience that it's not just about a single perfect lecture but about working with mentors and reflecting on my strenghts and weaknesses so that I can become an exceptional teacher. I find that accepting comments from my students and seeking feedback from mentors and peers is the best way to be critically reflective and that it only helps to improve my teaching with every experience I have.
I strive to become more like the excellent teachers who motivated and inspired me. I am an accessible lecturer who listens to student's concerns and encourages a positive learning environment throughout the academic term. I make my lectures thoughtful, organized and lively. I invest my time and energy into making interesting assignments and projects that emphasize unique study methods for learning challenging new material. Most importantly, I seek mentors and critically review my teaching, so I can change and grow with each new teaching experience. - Teaching Evaluations