# Teaching Portfolio

Table of Contents:

## Teaching Philosophy

Introduction

I enjoy teaching mathematics! I enjoy teaching college students the way of mathematics and to teach how to think like a mathematician. I like seeing my students gradually becoming independent and active learners and seeing them getting confident to reason through new problems. As a math teacher one of my goals is to make my students independent and active learners who are confident in the subject. My teaching career began at University of Colombo (UoC), Sri Lanka, as a recitation instructor then I was a graduate teaching assistant at Ohio University (OU). There I worked in the capacity of instructor of record and as a recitation instructor. I have also worked as a teaching assistant at the Center for Talented Youth (CTY) in Johns Hopkins University (JHU). However, it is at Michigan State University (MSU) where the bulk of my teaching philosophy was developed. At MSU I held leading TA positions and mentoring positions as well as instructional positions. I have taught a wide range of courses throughout my teaching career ranging from entry level math courses like "college algebra" to calculus sequences and to transitional and flipped-classroom courses such as "transitions to proofs". I have worked hard, observed, learned from, and mentored by inspirational teachers to develop my teaching practice. My teaching practice was recognized through the GTA Award for Excellence in Teaching in 2021. Below is a summary of my current teaching philosophy, aspects of who I am as a teacher.

Personal Philosophy and Practice

Among many aspects of teaching, below are some of the most important things for me as a teacher. These are developed from my own experience as a student, through feedback from students in my role as an instructor and through other inspirational math instructors.

Enthusiasm leads to motivation:

Experience have taught me that students are motivated when the instructor is enthusiastic. Enthusiasm of the instructor carries over to students and make the class more enjoyable and students more engaged. I have been inspired by teachers who are more enthusiastic in the subject no matter how simple the subject is for them compared to the level of their expertise. It is inspiring to come to the class where the instructor is enthusiastic from beginning to end. I have made a point of actively channeling my enthusiasm to make my student more engaged. Enthusiastically delivering new content to my students have made them more eager to learn, ask more questions and actively participate in the class discussion.

Clear and prompt communication

I believe that another vital key for students' academic success is clear communication of what do we, as instructors, expect from our students and what resources are available for the students to help them to meet these expectations. Especially with some hybrid or online modalities where the assignments are sometimes done online through a particular platform or where the assignments are submitted in a specific way, it is important to establish these requirements clearly and in the beginning of the semester. It is also vital that the students are aware of the resources such as textbooks, office hours, free tutoring help, web apps, video notes, etc. from the first day of the class for them to succeed. First few minutes of each of my classes are spent on reminding my students these information.

Understanding takes precedent over taking down notes

I have noticed that some focus on writing down notes instead of trying to actively learn the new content. I, myself, am a victim of this situation whenever I have taken a particularly tough class. This could be perhaps in the hopes of having notes may help them to understand the content ``later on" even if they do not understand it at the time. I however think actively listening and learning take precedent over taking down notes. But most students are afraid of forgetting things without notes. To counter this, I started writing my own skeleton style notes and fill them in the classroom. Once the class ends for the day, students can expect to find the filled-in notes on the official online platform (d2l for MSU). Providing these skeleton notes and a copy of the completed notes after the class help students to focus on actively listening and participating in the classroom discussion.

Practice... practice and practice

Students in most standard calculus courses are evaluated through exams and quizzes. A typical student is expected to spend 2 to 4 hours per week per each credit of college level math. Students are expected not only to complete the homework questions but also to practice questions on their own. With practice students learn to solve math questions more accurately and further practice helps them to do math questions more efficiently. I always encourage my students to do beyond what is in their homework. Sometimes I encourage them to attempt certain questions from the textbook. For more demanding areas that require a lot of practice such as concepts of limits and chain rule in differentiation. I have created my own "workbooks" for students to practice with. These workbooks have been a great success with students and students have pointed that in their evaluations of the course.

Do not leave the classroom with questions in mind

When I am teaching a math course one of my "rules" in the classroom is that students are not allowed to walk out of the class if they have any unanswered questions or unclear ideas. As means to achieve this I try to schedule office hours immediately after the class and not to deliver new content in the last 5-10 minutes of the lecture. Granted that it is not always possible for student to attend office hours immediately after the class the idea is to let the instructor know that there was something unclear before leaving the classroom. Most of the time it is the case that there are more than one student who had the same question(s). Knowing that, the instructor can address the questions before the class ends or, if the time doesn't permit, ask students to keep a mental note of these questions and address them in the beginning of the next class. To achieve this goal, it is important that students are given plenty of chances for questions and are prompt for questions in an inviting manner. Instead of asking students if they have any questions I find it is more inviting to ask: "what question do you have about … ?”.

Mid-semester teaching/learning evaluations

While the instructor does get students’ feedback at the end of the semester it is important to get feedback from students during the semester. These evaluations should be both critical (in terms of how effective the teaching is) and reflective (in terms of how the students can improve on). I typically take these evaluations at least twice during the semester, depending on the course modality (more evaluations if the course is online). These feedback forms contain about 4 questions targeting: things that are going well in the class, things that the instructor can improve on, things you as a student have done to positively contribute towards your learning experience and what can you as a student improve upon.

Strategies and Experience

Introductory Courses:

I have taught the introductory level courses: College Algebra (at OU) and Survey of Calculus (at MSU). In my experiences the students in these classes have the highest level of mathematics anxiety. So, my main goal in these classes is to build students confided in their own math skills and get rid of their misconceptions about mathematics. It is my duty to convince these students that: it is not necessary to memorize different methods for each type of questions and try to solve it in a mechanical way but to understand the concepts behind each of the questions then the methods flow naturally.

Calculus Courses

Typically, students in calculus courses have more math background than those who take introductory courses. I have taught Calculus 2 in capacity of the instructor and as a recitation instructor at MSU. I was also the TA in charge of Piazza forum in one of the semesters for Calculus 2. I was also a recitation instructor for calculus 1 at OU. These courses typically follow a uniform syllabus and thus has limited freedom for instructors. For these classes I break the class into two parts. First part is the theory part, and the second part is the practice part. After a class discussion about the theory involved, I move to solve questions which are prepared ahead of time by going through their homework and textbook. The entire class starts a problem, and we solve them together, often students help me to solve the question from the theories they just learned. This helps students to get familiar with the content and to face questions confidently.

Transitional Courses:

These courses are targeted towards student who are planning to take proof-based math courses such as undergraduate analysis or algebra. In MSU I have taught MTH 299 - Transitions to Proof, which trains the students in proof writing. Since students are transitioning from more calculation-based math to logical reasoning it is important that they practice writing proofs. This class is a flipped-style classroom in the sense that only a fraction of the class is spent on introduction of proof techniques and then all then the proofs for all example statements are sourced from the students. Students then are split into groups and are asked to prove statements together with their group. During these groupwork sessions, my goal is to help them to logically construct an argument to prove their claims. Then the proofs are presented and discussed with the entire class. For this class it was also important to let the students know that it is okay to feel frustrated at a proof, most time spent on math research is like that, but to "follow their nose", the proof might be closer to completion than you think. The ε-n proof involving limits of the sequences were particularly difficult for students to first grasp. But with many practice questions most of the students were able to write-up complete proofs for such limits by the end of the semester.

Online Teaching

Another increasingly popular aspect of teaching is online teaching. I have taught Survey of Calculus online in the capacity of an instructor and I have conducted recitations for Calculus 2 online. Teaching online has its own set of hurdles. One main hurdle is keeping students focused and engaged. To achieve this, I like to create online polls ahead of the lesson and to launch them during certain parts of the lesson. It is also important that the work-shown during online lessons are done thoroughly and clearly so that all students can follow the lesson easily. As a method to give students a similar chance for questions (compared to an in-person class students have the option to use the chat (private or public) and also to use the raise hand emoji (on zoom).

## Example Material

## Teaching Evaluations

*MSU uses a scale of 1 - 5, with 1 being the best and 5 the worst.

*Detailed full student evaluations with comments can be made available by request

## Teaching Leadership & Mentoring

Leadership and Mentoring:

I have been a lead teaching assistant and a teaching mentor in the Center of Instructional Mentoring (CIM) at MSU. As a teaching mentor I have mentored new graduate teaching assistants and as a lead teaching assistant I have observed and provided feedback on undergraduate learning assistants and new graduate teaching assistants. When mentoring new TAs, they first observe my classes and then get to teach a part of the class on their own. For most of the new TAs this is the first time they are teaching at a college. I help them to prepare for the class and after the class we discuss on our differences in teaching methods. As a lead TA I provide non evaluative feedback describing the good practice I saw and what I think they can improve upon. I try to draw examples from my own experience and encourage them to try new techniques.

## Diversity, Equity & Inclusion

DEI Statement:

As a person within a higher education institution in the United States of America sometimes I feel like everyone should understand what concepts of diversity, equity, and inclusion (DEI) mean. Nevertheless, the challenges to diversity persist especially for students and researchers coming from underrepresented racial and ethnic groups. As a person of color from a "developing country", and an international student in the Unites States I am constantly aware that I am a minority. As a student, instructor and a researcher, I have faced challenges and have felt the need to assert myself more strongly than some of my peers. Not only that I have personally experienced challenges in academia but also witnessed my spouse, who is also pursuing a doctoral degree in mathematics, facing and overcoming challenges. Therefore I have always been committed to DEI and recognize the barriers formed not only by the cultural differences, socioeconomics but also differences in race, gender and sexual orientation.

During my time as a graduate student I had the privilege to be elected as a graduate student representative in the Graduate Studies Committee (GSC) in the department of mathematics in Michigan State University for the academic year 2021-2022. There I had a pleasure of getting involved in the strategic plans in the department involving graduate studies. As a minority graduate student I shared my experiences and made suggestions for policies at the department level. I also helped fellow international students in the department to navigate through bureaucratic hurdles related to visa status, taxes and cultural differences that they faced. Even after my tenure as a graduate student representative at GSC I helped the new committee members in various activities related to graduate studies in the math department.

During my time at MSU I was a Lead Teaching Assistant (TA) for the Center of Instructional Mentoring (CIM). As a lead TA I had the pleasure of mentoring new graduate students who are soon to be graduate teaching assistants and instructors at the department. I have observed their teaching and have given written feedback encouraging on genuinely strong aspects of their teaching and helpful tips and methods that were drawn from my own experience as an educator. As a lead TA I have also supported junior international graduate assistants with their concerns about students interaction in the classroom. I have guided them to make their classroom more inclusive by sharing my own experiences and practice. One of my main suggestions for new graduate assistants is to arrive to the classroom early and interact with students and have set office hours and encourage students to attend office hours often as possible.

As an instructor I always foster a friendly learning environment where each student can express their ideas and answer questions regardless their race, gender sexual orientation, nationality or even if the answers are mathematically incorrect. I like to create a space where all students feel that they are heard and that their contributions to the class discussion matter. We all come from different backgrounds, with that we are exposed to math in different ways, these differences should not hinder someone’s academic success. I believe as educators it is our responsibility to recognize instances of violations of DEI where a particular student or a group of students feel undervalued and unheard. I am sensitive to notice and correct when more privileged students dominate the conversations in groups activities. One such example is when I was an instructor for mth 299 - transitions to proof, a flipped style classroom where the majority of the class is spent on group discussions I noticed that the randomly formed groups sometimes had one student who is not a native English speaker with other members being native speakers or one female student in a group of male students. In such instances I have noticed that sometimes the minority students participate and interact less with their group members due to other members being more dominating. I have actively encouraged these students to contribute more towards the conversation without pressuring them by asking questions from each of the members in the group and commenting on each of their answers. I work hard to make my lessons more accessible and thus to make an equitable "playing field" for all my students.

As a researcher I recognize the challenges and hurdles the underrepresented groups face in STEM fields, specially women. As a husband who is married to an exceptional woman in STEM, a math PhD candidate, I have witnessed some of the challenges they face. I have always done my very best to make my research inviting for everyone. I have actively helped different groups of PhD students in their endeavors. I intend to be fully committed to DEI regardless the institution I am a part of and always will thrive to achieve both institutional and personal DEI goals.

## List of Courses

At Michigan State University

Instructor of Record:

MTH 124 Survey of Calculus (online) - Summer 2020

MTH 299 Transitions - Spring 2020

MTH 124 Survey of Calculus - Summer 2019

MTH 124 Survey of Calculus - Spring 2019

MTH 124 Survey of Calculus - Fall 2018

MTH 133 Calculus II - Summer 2018

Grader:

MTH 829 Complex Analysis - Spring 2021

MTH 828 Real Analysis I - Fall 2020

Teaching Assistant:

MTH 133 Calculus II - Spring 2022

MTH 299 Transitions - Fall 2019

Tutor:

Tutor for Advance Calculus at MLC - Spring 2018, Spring 2020

Tutor for MTH 299 at MLC - Spring 2020

At Ohio University

Instructor of Record:

MATH 1200 College Algebra - Fall 2016

MATH 1200 College Algebra - Spring 2016

MATH 1200 College Algebra - Fall 2016

Teaching Assistant:

MATH 2001 Calculus 1 - Spring 2017

Tutor:

The Morton Hall Tutoring Center - 2015-2017

At Center for Talented Youth (CTY) in JHU

Teaching Assistant for "Logic: Principles of Reasoning" - Summer 2017

Teaching Assistant for "Logic: Principles of Reasoning" - Summer 2016

At University of Colombo

Temporary Assistant Lecturer - August 204 - July 2015

Conducting tutorials (recitations fro) 1st and 2nd year undergraduate students

Temporary Instructor - March 2014 - July 2014

Grading pure and applied math 1sta dn 2nd year undergraduate courses.

## Student Resources

Useful Online Tools

Desmos: An online graphing calculator

Symbolab: Graphing, Matrix Manipulations, Calculus (integrals, double integrals, triple integrals and much more).

Wolfram|Alpha: Similar answer engine like symbolab (based on Mathematica) but more powerful.

OpenStax: Peer-reviewed, openly licensed college textbooks.

Free/Open Source Tools

iLovePDF - PDF editing. Can do most thing Adobe Acrobat Pro (paid version) does.

OpenStax: Peer-reviewed, openly licensed college textbooks

OBS Studio - video/screen recording, live streaming, virtual webcam, etc.

LibreOffice - MS Office (Office 365) alternative.

OpenShot - Video editor

HandBreak - Video transcoder (converts video formats)

GIMP - Photoshop Alternative

Other Resources

Math Learning Center at MSU (MLC)

ARC at MSU (LGBTQIA+ Resource)

RCPD at MSU (Resource center for persons with disabilities)