TEACHING STATEMENT - Kansas State University

TEACHING STATEMENT

XUAN HIEN NGUYEN

My postdoctoral position gave me the unique opportunity to work in education research while keeping an active mathematical research program. In the past two years, I have been involved in many mathematics educational projects; for example, I taught workshops for in-service teachers, wrote a complete set of Calc 1 problems for an online homework system, and interviewed engineering students as part of an interdepartmental longitudinal study. This work has greatly influenced my teaching views and methods. In the first section of this statement, I describe the main aspects of my teaching philosophy. The second section summarizes my work in mathematics education.

1. Teaching philosophy

The world of mathematics is unfamiliar to students. The very cohesion that comes from pure logic and abstract reasoning is beautiful to us, but students can find it unforgiving. Teaching means guiding students so they can become more familiar and comfortable with mathematics. It should be shaped on one hand by the needs of students and on the other hand by the mathematical concepts at hand. The role of a teacher is to help students build their knowledge of mathematics and acquire the skills they need from it.

Early in my career, my way of helping students connect to the material was through clear lectures. When I taught Calculus, I followed the textbook and tried to present the topics in a way most accessible to students. To help them see the course as a whole, I would draw connections between topics, often explaining how an idea in a subsequent chapter answers questions from a previous one. My teaching was solid, but it felt confined. I wanted to improve but did not how until I started working in education research.

In the past two years, I interviewed engineering students as part of a joint project between the departments of mathematics, physics, and engineering. The work is a longitudinal study investigating how students transfer knowledge through their academic career. My role in this project is to follow a group of students as they move through calculus and differential equations, and track their understanding. The notion of "understanding of mathematics" is vague, so we decided to focus on concepts that were present in mathematics as well as physics and engineering. Taking this very broad point of view, or rather, being forced to take this broad point of view has changed the way I approach teaching. I realized that by explaining different topics without having an overall goal, I was localizing them. A course should be centered around its main concepts, rather than its set of topics.

One of the overarching theme we use in the study is the concept of integration. When it is introduced for the first time in Calculus 1, it is through the use of Riemann sums. From this, students learn that integration is adding up small rectangles to find area. In the study, we have found that students develop a solid understanding of integration using this geometric

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meaning. However, this view is too limited. In their physics courses, students have to be able to find for example the total mass of a body with nonuniform density, or the total magnetic field from electrical charges placed on an arch acting at a given point. In order to set up the integrals for the physics problems, students need to see integration as accumulation (adding up infinitesimal pieces of a quantity to find its total). The next time I teach the calculus courses, I plan to introduce the concept of accumulations in Calc 2 and fully explore it in Calc 3, so that it is available to students when they take physics.

Every introductory math course is part of a larger curriculum. It is often easy to forget this, as our teaching assignment is usually unconnected from one semester to the next. For most students, the math courses they take are requirements for later classes in their field of choice. If we want students to see that math is relevant for their majors, the introductory courses have to be designed to fit the students' needs. Discussions with members of other departments can help us be more informed when we teach these courses.

Determining the central concepts of each course may be a purely academic exercise, if it is not grounded by a concern to adapt the content to the level of the students. Setting goals gives me an important direction for the course, but it is only a first step. The next step is to choose the material of a course so that the students can relate to it. Whether I am considering a homework assignment, a chapter from a textbook, or the use of technology, I try to identify what I expect students to learn from it. While some parts of a course can present a different view of a concept already visited, or confront existing misconceptions, other parts can reinforce computational skills. I select the material keeping in mind the main goals of a course and how students will view it.

The last component of a course is its organization. For a teacher, the content of a course and its organization are mostly independent (with some combinations working better than others). To students, the distinction is irrelevant. If students are unsure about when homework is due, their uncertainty can spread to the content of the course. A poor organization can muddle students' understanding and can result in them learning less than they could otherwise. Therefore, in the first week of class, I explain the structure of the course and the work I expect from the students. I make sure that students can find information easily. While a flexible pace is helpful, allowing more time on difficult concepts, a flexible organization has led to more confusion in my experience. A clear set of rules allows students to concentrate on the material to learn.

Effective instruction

2. Teaching experience

I have taught a wide variety of classes, ranging from College Algebra to a graduate course in Real Analysis. My teaching experience also includes two "introduction to proofs" courses using a modified Moore method, teacher workshops, and a content course for elementary education majors.

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I adapt my teaching to the level of the students and the material they need to learn. For example, in a geometry course for math and secondary education majors, I focus on getting students to write their own proofs. The course is taught as a modified Moore method: students work in groups so they can check their reasoning before presenting the proofs at the board. To help students write clearer proofs, each student grades his/her own midterm, as well as the exams of two classmates. The idea behind this assignment is that recognizing one's mistake is difficult, so reading someone else's work can give them a different point of view. The goal is for students to be aware of their own writing.

Technology

I wrote and coded the set of online homework for Calculus 1 used at Kansas State University. In this online homework system, students get one chance to correct their mistakes on each problem set before it is graded. They can try each assignment as many times as they want before the deadline until they are satisfied with their scores. Moreover, help is provided in the form of full solutions for each problem. The system caters to students with different levels of skills. If a student knows the material well, he or she only has to do just one set of problems. A student who wants more practice can find as many problems as needed, as well as full explanations.

Teacher workshops

In the past two summers, I have co-organized and taught three workshops for teachers, in collaboration with Dr. Andrew Bennett from the math department, and Dr. David Allen and Ms. Melisa Hancock from the education department. We covered varied topics such as "Cryptology","Math by inquiry: rational numbers", and "Geometry and art". Educating in-service teachers presents a different challenge since most teachers have already seen the traditional way of presenting math concepts. They are looking for fresh ideas, and the workshops emphasize differentiated instruction. We present the math content from many different points of view to broaden the teachers knowledge of a subject and draw new connections.

As is evidenced by this statement, my teaching experience is very diverse. My teaching is supported by a broad knowledge of mathematics and shaped by my work in education research. I strive to adapt it to the students and the material of each course. I am flexible in my methods and open to discuss, and sometimes adopt, different opinions. My ideal job would value strong teaching and would give me the opportunity to grow as a teacher.

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