TEACHING STATEMENT CHENXU HE

My goal in teaching is to present mathematical concepts in the simplest and most transparent way; to ensure students become fluent and confident in their problem-solving skills; to convey the beauty of the subject and the wide applications of the math they learn; and to help students to develop their own mathematical abilities which will benefit them in their futures. I accomplish this by having a breadth of courses I can teach, by making course materials easily accessible to students, and by my encouraging advising. I have experience teaching the entire sequence of Calculus, ordinary differential equations, linear algebra and upper level math courses, e.g. classical analysis. I began teaching Calculus for students of arts and sciences and of engineering in fall 2005 as a Teaching Assistant at the University of Pennsylvania. My most significant teaching experience so far is as a Visiting Scholar at the University of Pennsylvania (2009–2010), as the C. C. Hsiung Visiting Assistant Professor at Lehigh University (2010–2012), as the Visiting Assistant Professor at the University of Oklahoma (2012–2015), and as the Visiting Assistant Professor at the University of California-Riverside since Fall 2015. UC-Riverside is one of the most ethnically diverse college campuses in the nation. Through my career, I have interacted with thousands undergraduate students representing a broad spectrum of demographic diversity, including international students from all around the world with different cultures. I put every effort to ensure that the learning environment is supportive and inclusive, especially for women and the underrepresented groups. As I have done for students over years, I set up my own course sites in the online system, e.g., iLearn and BlackBoard, before the class starts; they contain the syllabus, lecture notes, schedule of lectures, and exams’ schedule. I also include detailed policies for homework assignments and exams. The students could access this at the beginning of the quarter and they knew what they would learn from my class and my expectations for them. Before each lecture, I review the materials and think carefully how to distribute time for each topic and whether there are any particular parts in need of a more elaborate and detailed explanation. For example, in the lecture of iterated integrals, I sketch a very clear picture of the solid in 3d space and identify the cross-sections parallel with different coordinate planes by colors. Then I raise the question of how to find the volume by summing the very thin cross-sections. The students quickly see that one definite integral gives the area of the cross-section and the integral of all cross sections gives the volume of the solid. After the whole class has understood this new formula of the volume, I write down the precise statement of the Fubini theorem and move to examples for practice. For practice problems, I ask their options first. I may ask another one with encouragement if the first response is not quite right. I will give some hint if the problem is challenging to most of them. For the Honors Calculus or upper level math class, I carefully select the topics which I will present in class and leave the others as home reading. The topics I choose cover the essential concepts and results. I also make my plan more flexible and expect questions during the lecture. Finally I write a well designed problem set as a homework assignment. The 1

Chenxu He

Teaching statement

problems test their understanding of the basic concepts and the skills they learn from the class. I occasionally give some extra credit problems so that the best students can discover their full potential in math. For example, one problem in my Honors Calculus class is to use the Frenet frame to study the curves in 3d space. In some of my Calculus classes I use the classroom technology to facilitate the student’s learning. For example, in the study of the Lagrange multiplier method, I motivate my class by an example of functions in two variables. I use Mathematica to prepare a very fine picture of level curves. It then becomes apparent how special the intersection of the curves where the function achieves extreme values is. I write down the system of equations for the extreme values. Instead of providing an immediate solution, I call the students’ names and ask their opinions and let them suggest an approach to the solution; ultimately I may provide help so that they can fully analyze the problem. I strongly believe that the active participation of my students is a very important part of the teaching process. The class gains much more from the questions they raise than the lecture I give. Before I move on to the next topic, I check the class to make sure that all of them understand. For instance, my student Jillian wrote to me “You truly helped me develop a better understanding for the theory behind the numbers. You were very good at thoroughly explaining the concepts to us and making sure we understood the concepts before moving on.” My office hours were never enough for my students and I love to talk with them about math after class. I try to serve as a constant and supportive resource for them. I listen to their thinking before giving any comments. If the approach is not correct, I will show where it leads us and then let them re-think it. If they are on the right track, I will encourage them to continue to work out a complete solution. As an example, my student George wrote to me “Any time I was unsure of the material, you made yourself available even outside of your posted office hours. ...I have the utmost respect for the fact that getting the material across to your students was your number one priority every day.” My love of teaching is rewarded by the consistent and positive feedback from my students such as comments like “[Dr. He] was the best math professor I have ever had. Very effective in engaging the class, and asking questions to get students thinking. He also taught in both visual and verbal forms” from an anonymous evaluation form. My teaching skills are always being improved. I modify my teaching style and keep adding more into my toolkit based on the students’ feedback and that of my colleagues. After leading a wide variety of math courses, I am an experienced and accomplished teacher. I am ready and excited to take on the challenge of inspiring students’ mathematical interest and improving their mathematical ability.

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