# Jialing Dai

*Associate Professor of Mathematics*

#### Office

Classroom Building Room 101B

#### Education

PhD, Mathematics, University of Arizona, Tucson, AZ, 2000

MS, Mathematics, University of Arizona, Tucson, AZ, 1998

MS, Operational Research, Jilin University of Technology, China, 1987

BS, Mathematics, Southwestern Normal University, China, 1985

**Teaching Philosophy**

I have always wanted to be a teacher. I remember playing games about teaching mini classes to my friends at my parents' house when I was young. When the time came to make a decision on my future career, I chose to go to a Normal University without any hesitation. Attending a Normal University was the very first step toward being a teacher.

Looking back at the teaching foot prints I have left on the road of teaching practice, I find my teaching philosophy consists of the following five principles.

I believe that the ultimate goal of teaching is to teach students how to learn independently and acquire the ability of how to think critically. In particular, as a mathematics teacher, I believe that the essential purpose of learning mathematics is not only to master specific mathematical facts, but also to develop logical reasoning, creative thinking ability, analytical problem-solving, and self-learning skills that can be applied in the future.

I believe that preparation is the key for every well-taught class. To effectively prepare for a class, a teacher (1) must have an understanding of the subject matter being taught as well as an understanding of the pedagogical theory; (2) stay current in the field, engage in research and participate in classes, conferences, and/or mentoring that can improve knowledge in the subject matter; (3) be able to make good selections about what to teach, how to structure and organize the material, and how to help students internalize the material through well designed exercises and/or projects. At the same time it is important to stay abreast of current theory and research in the field of teaching and pedagogy. A teacher must know what to teach as well as how to teach it.

I believe that a learner-centered environment creates opportunities for students to be actively involved in the learning process. In such an environment, I find students are willing to contribute their own ideas to the topics being discussed. I myself, as a facilitator, constantly propose questions to guide students and encourage students' independent thinking. Different answers from students, correct or not, always generate excellent discussions, create a great learning opportunity, and often time lead to the topics I plan to discuss and deepen understanding of the material.

I believe that Technology has the power to transform teaching. I have found the great advantage of integrating technologies in teaching. For instance, in college algebra and lower-level calculus courses, the graphing calculator is a great tool. Students use the calculator daily to help with in-class exercises and homework. I used Excel in Business Mathematics to do simulations and solve projects based upon real business problems. I find that Minitab and Fathom work well in Statistics and Data Analysis classes. When students use these software packages to analyze data and explore the assumptions underlying a statistical procedure, interesting questions are often raised that lead to clarity of thinking and better understanding of statistical concepts. I also used Lingo and Maple to enhance the learning in an advanced linear algebra course.

I believe that a teacher must respect the diversity of students. As teachers, we must respect the goals, needs, and individuality of each student and help students to do their best and to achieve their goals. Instructors nowadays face an enormously diversified student population: students with various ethnic and cultural backgrounds, socioeconomic status, different learning styles and academic backgrounds. As a teacher, I respect the differences among my students; integrate various teaching methods and techniques to create a stimulating learning atmosphere in my class; use various ways (numerically, graphically, algebraically, hands-on activity) to get ideas across. I work to create an environment which supports interactive and independent learning opportunity for each student. Being an effective teacher in this highly diversified classroom means finding a way to challenge the strong students, while still provide a solid learning experience for others in the group. Thus I strive to write assignments such that they contain both challenging problems and basic checking-understanding questions. In addition, I find one-one communication with students after class and during office hours is extremely effective and serves the needs of students with different skill levels. I always encourage the use of my office hours and make myself available at other hours as well.

I have taught a wide variety of courses, from college algebra, pre-calculus, calculus I-III, vector calculus, and introductory statistics to upper division linear algebra, probability, abstract algebra, modern geometry, and real analysis. I have received excellent teaching evaluations all these years in both lower and upper-level courses. As a reward to my devotion to teaching, I was awarded the outstanding teaching assistant in Mathematics Department at the University of Arizona in spring 2000. I also received several prizes for excellence in teaching in China.

Through my twenty years plus teaching practice, I have found a great pleasure and self-fulfillment in teaching. When I stand in front of my students and look into their eager eyes, I am determined to do everything I can to help them achieve their dreams. I found students are more willing to challenge themselves and hence gain deeper understanding of the material when the teacher is more passionate and enthusiastic. As an old Chinese saying states: "teachers are engineers of human souls." My born enthusiasm for teaching is transmitted to my students like a wave, thus it encourages and stimulates them to be more involved in class activities and in active learning.

**Research Interests**

Lie theory and representation theory

Statistics

Linear Algebra

Mathematical Finance

Mathematics Education

General Mathematics

Math 35 Elementary Statistical Inference (2 times)

Math 37 Introduction to Probability and Statistics (9 times)

Math 39 Probability and Its Application in Statistics (for Engineering)(4 times)

Math 41 PreCalculus(6 times)

Math 49 Introduction to Abstract Mathematics (1 time)

Math 51 Calculus I (5 times)

Math 53 Calculus II (2 times)

Math 55 Calculus III (7 times)

Math 131 Mathematical Statistics I (1 time)

Math 141 Linear Algebra (1 time)

Math 143 Abstract Algebra I (2 times)

Math 155 Real Analysis I (3 times)

Math 168 Modern Geometry (3 times)

Math 193A Financial Mathematics (special topic course) (3 times)

Math 191 Independent Study (11 Students)