Teaching Dossier
Sergio Chaves
Updated: Oct 2023.
If reading a PDF version of this Teaching Dossier, it is recommended to visit its online version, available in my personal website here
Contents
- Brief Biography
- Teaching Philosophy
- Teaching Experience
- Teaching Effectiveness
- Curriculum Development
- Professional Development
- Diversity, Equity and Inclusion Statement
- Additional Documents
1. Brief Biography
Teaching has always been a driving force behind my academic journey. After completing my Master's degree in Mathematics in 2013, I seized the opportunity to instruct introductory courses in Mathematics, which ignited my passion for teaching and inspired me to pursue a Ph.D. in Mathematics at the University of Western Ontario in 2015. Throughout my doctoral studies, I continued to expand my teaching experience by working as a teaching assistant for a diverse range of courses and actively contributing to the support of undergraduate while widening my teaching and professional portafolio. Since 2021, I've been a Visiting Assistant Professor at the University of Rochester, where I've had the privilege of teaching a variety of courses, including higher level courses. My passion for teaching is evident throughout this dossier, and I am committed to fostering the learning process of my students as I continue to advance in my academic career.
2. Teaching Philosophy
"What is mathematics?" is a question I always begin my undergraduate first-day class with. While some students may hold positive perceptions of mathematics, biases, negative images, and misconceptions remain common among undergraduates. These misconceptions include beliefs such as "Mathematics is a hard, challenging, and boring subject", "It is solely about finding and using formulas", "It's just a required course for my program", or "It's only about solving problems."
My teaching philosophy is rooted in raising awareness about the importance of mathematics, highlighting the valuable skills acquired through its study, and dispelling stereotypes and misconceptions. My approach centers on inspiring and motivating students to engage in activities such as estimation, verification, interpretation, articulation of results, and the ability to connect with others' ideas. These principles form the foundation of my teaching career. Moreover, sharing my passion for the subject and witnessing the transformation of students' answers to the question "What is mathematics?" into more positive perspectives has shaped me into the educator I am today.
I view teaching as a comprehensive process that extends well beyond the confines of the classroom. It encompasses a spectrum of elements, including preparation, practical experience, motivation, and a guiding educational philosophy. These factors collectively shape a student's perspective on the subject matter, both within and outside the classroom. In my perspective, teaching represents a crucial phase in the journey of learning and character development, one that should be adapted to align with the current advantages and requirements of the contemporary world.
A more detailed Teaching Philosophy Statement can be accesed through the additional files section
3. Teaching Experience
University of Rochester: Assistant Professor
Western University: Teaching Assistant and Teaching Fellow (2015- 2020)
While pursuing my doctorate degree at Western University I was a teaching assistant for both graduate and undergraduate courses. After completing my Ph.D. in July 2020, I was appointed as a Teaching Fellow supporting the implementation of online teaching due to the COVID-19 limitations for on-site classrooms.
Universidad de los Andes: Instructor and Teaching Assistant (2011-2015)
I instructed at Universidad de los Andes , a top-10 private university in Colombia with a diverse student body representing the top 1% of high school graduates. The university provides robust financial support to students in need. In terms of teaching, I led first-year courses with over 200 students, divided into groups of about 35, each assigned to an instructor. Course coordination, scheduling, and exams were handled by the course coordinator, with instructors meeting two weeks before exams to discuss topics and suggest potential test problems. Typically, I taught 1.5-hour classes twice a week for 16 weeks to these smaller groups.
I was responsible for all the preparation of the lecture material, assignments, quizzes and assessment of the following courses.
I served as a teaching assistant in several first-year courses (pre-calculus, differential calculus, linear algebra) when I was pursuing my Master’s degree providing support to the main instructor by grading quizzes, assignments, exams and running tutorial sessions. I also had a major assistant role in the following course.
Instructors and Teaching Assistant provide help in any course in mathematics to any student that attends the Pentagon (Mathematics Help Centre) which runs Monday to Friday from 8am to 4pm. Every instructor/teaching assistant stays in average 4 hours/week in this help space.
Universidad del Rosario: Instructor (2013)
During 2013 I served as an instructor at Universidad del Rosario in the growing department of mathematics at that institution. Universidad del Rosario is a private university in Colombia known for its strong programs in business, administration and economics; therefore, the direction of the courses was driven towards that area.
Universidad Central de Colombia: Instructor (2013)
During 2013 I served as an instructor at the Universidad Central de Colombia in the department of engineering and mathematics. My responsibilites were tailored around working professionals studying during nights and weekends. These dedicated students pursued undergraduate degrees in engineering while juggling their full-time jobs. Classes were scheduled from Monday to Friday, 6 pm - 10 pm, and on Saturdays from 9 am - 5 pm, spanning 16 weeks. Each term, I instructed two courses with approximately 30 students in each class. The program's unique challenge lay in accommodating the students' demanding schedules, and the evaluation methods included midterms, exams and bi-weekly assignments with carefully selected problems. This rigorous approach aimed to ensure students' success and learning while facing the challenges of a full-time job.
The courses that I taught at this institution are the following.
➢ Multivariate Calculus - Instructor
➢ Mathematical Logic - Instructor
➢ Linear Algebra - Instructor
I also was a suppoprting instructor providing independent tutorial sessions for reviewing lectures and problem-
solving to full-time students in the morning and afternoon programs in the following courses.
➢ Integral Calculus
➢ Differential Calculus
The activities and participation on these tutorial sessions were 15% of the final grade.
Mentoring Students
Summer projects and Undergraduate dissertation
During the Summer 2023, I worked with some of the students from my Abstract Algebra class from the Spring 2022 in applications of group theory to combinatorics problems. An extension of the connection between counting colored neckalces and Lyndown words was explored from a mathematical and computational prespective.
In particular, one of the directions explored included the relationship of these combinatorial problems with Cohomology of certain polyhedral product actions. The project is serving as a dissertation project for one students aiming to graduate by Summer 2024.
Directed Reading Programs
The directed reading program (DRP) is an educational initiative that allows students to engage in independent, guided study of advanced mathematical topics under the supervision and mentorship of a faculty member or graduate student. The primary goal of a DRP is to provide undergraduate students with the opportunity to explore mathematics beyond their regular coursework and develop their mathematical skills and understanding. I have participated in the following directed reading programs:
Pares Ordenados Program - Spring 2023 (Website in Spanish) . Pares Ordenados (ordered pairs in Spanish) it is a recently developed directed reading program targeted to foster mathematical learning to latin-american students that identify themselves as a minority. The program is run in an online format, conducted in Spanish, connecting undergraduate students from underrepresented groups in mathematics in the region with Faculty and graduate students across the world. My mentee was a student from Universidad del Valle, Colombia, intersted in learning algebraic topology. He faced challenges accessing to qualify faculty in their home university and the program was a fit for him. Topics such as the fundamental group, homotopy theory and homology where explored during the program and a project on the applications of algebraic topology tools into solving mathematical problems was developed. The project was selected in the poster session at the Colombian Congress of Mathematics in the same year.
University of Western Ontario DRP - Fall 2019 (Website) . I had the opportunity to work with an engineering student passionate about mathematics, yet unsure about pursing a math major. My mentee and I worked on a geometrical approach to the Poincaré-Hopf theorem for surfaces in the 3-dimensional space. The followed reference was Firby, Peter A., and Cyril F. Gardiner. Surface topology. Elsevier, 2001. By the end of the term, my mentee was able to understand and explain the Euler Characteristic and the proof of the index theorem using a geometrical approach; moreover, he decided to completely dedicate to pursue his Major in mathematics after the program, ended up transferring to UBC next Fall. On Winter 2020 we continued working on a reading course in Topological Manifolds following the classical book of Lie, extending the material from the DRP project.
Other relevant Teaching and Training experience
Visiting Fellowship in Assessment in AP Precalculus
In Fall 2023, I was invited by the AP Higher Education College Board (USA) to serve as a Visiting Faculty member. My role was to contribute valuable insights and feedback on the Advanced Placement (AP) Precalculus program. This collaborative effort aimed to ensure that the program maintains alignment with college-level courses while preserving the essential value of the AP Program for institutions and students. AP courses serve as a means for high-school students to engage with advanced coursework prior to college entry.
The high academic standards mantained by AP courses are reflected in their effectiveness in preparing students for success in subsequent college-level courses. This preparation often translates into students excelling in their college studies, with a higher likelihood of pursuing majors related to the respective AP subjects, particularly in the STEM field.
My contributions to the program involved revising its content and assessments, driven by my experience and the expectations I hold for undergraduate students enrolling at a Precalculus class in my institution. This collaborative effort between institutions, educators and the College Board ensures that the AP Precalculus program continues to provide students with a robust foundation for their academic journey, helping them excel in their higher education journey.
Training Teaching Assistants
At the University of Rochester, I have had a trainer role for both undergraduate and graduate teaching assistants in the methodologies and practices of the department. This includes workshops on essential tasks such as navigating Webwork, Gradescope, and Blackboard, using their interfaces, customizing settings, uploading and grading student work, and sending emails, among other features. These workshops have not only benefitted teaching assistants but have also been valuable to colleagues within the department.
In 2019-2020 as a Senior graduate student, I was also tasked the supervision and training of recent graduate students in the use of the online grading systems used by the deparment: CrowdMark, GradeScope and WebWork.
I have authored comprehensive documentation on creating problems within Webwork, which includes companion files to facilitate problem creation within the platform. This documentation also covers the basics of the PERL programming language, which I self-learned while working with Webwork. This tutorial has proven to be a valuable resource for the mathematical community at various universities.
Recommendation Letters
I am always delighted to provide recommendation letters for students who have interacted with me in various capacities, whether through coursework, teaching assistant roles, or collaborative reading projects. I have received requests from undergraduate students at all levels, seeking recommendations for purposes such as transferring schools, pursuing graduate studies, or applying for scholarships and internships.
Volunteering and Commmunity Service
During 2015 I volunteered as instructor of conversational basic Spanish for students travelling to Central and South America Spanish-speaking countries under the program Impact Experience Program at Western. Students are part of projects that impacts a community abroad. Impact Experience offers all students at Western and its affiliates access to unique co-curricular opportunities to support community projects around the world.
I have also been a tutor for High-school and College students supporting their learning experience in most of the courses in Mathematics and Statistics. I provide my help both in-person or online to students around the world. I started the MathForce project; a group providing math support to students in the London, ON. community by connecting high-school students and graduate math students.
4. Teaching Effectiveness
Formal Teaching Evaluations
Student Evaluations at the University of Rochester
Summary (average out of 5) of teaching evaluations at the University of Rochester. This questionary assesses instructor stance and accomodations due to the COVID-19 pandemic.
Fall 2021 - Spring 2022
| Category | MATH 142 2 | MATH 235 3 | MATH 162 2 | MATH 240H 2 | MATH 141 1 |
|---|---|---|---|---|---|
| The exams/assignments covered important aspects of the course. | 4.6 | 4.7 | 4.1 | 4.8 | 4.2 |
| The assignments were helpful in understanding the material. | 4.2 | 4.6 | 3.8 | 4.7 | 3.9 |
| The exams/assignments were clearly worded. | 4.2 | 4.4 | 4.2 | 3.3 | 3.9 |
| Lectures / class discussions were well organized or well managed. | 3.9 | 4.6 | 4.4 | 4.7 | 4.1 |
| Classes tended to stay appropriately on topic. | 4.8 | 4.8 | 4.8 | 4.8 | 4.6 |
| I feel this class was valuable. | 4.1 | 4.4 | 4.0 | 4.5 | 3.3 |
| What overall rating would you give this course? | 3.8 | 4.3 | 3.9 | 4.5 | 3.4 |
| Under the current COVID-related instructional conditions, I was able to access course materials (lectures, readings, discussion boards, etc.) when needed. | 4.7 | 4.9 | 4.7 | 5.0 | 4.6 |
| How would you evaluate your educational experience in this course under the current COVID-related instructional conditions? | 4.2 | 4.5 | 4.5 | 4.8 | 4.6 |
| The instructor explained and emphasized important points clearly and effectively. | 4.1 | 4.3 | 4.5 | 4.5 | 4.1 |
| The instructor used examples that helped with understanding the material. | 4.4 | 4.2 | 4.5 | 4.7 | 4.0 |
| The instructor noticed when students did not understand and adjusted accordingly. | 3.7 | 4.1 | 4.3 | 4.3 | 3.3 |
| The instructor demonstrated sincere respect for students. | 4.9 | 4.9 | 4.8 | 5.0 | 4.7 |
| The instructor was willing to listen to student questions and/or opinions. | 4.6 | 4.9 | 4.7 | 4.5 | 4.7 |
| The instructor made himself/herself available for extra help. | 4.8 | 4.9 | 4.6 | 4.8 | 4.7 |
| The instructor tended to be well prepared for class. | 4.8 | 4.9 | 4.7 | 4.8 | 4.7 |
| The instructor provided clear academic honesty guidelines for this course. | 4.9 | 4.9 | 4.6 | 4.8 | 4.7 |
| I have a stronger interest in the subject because of the instructor. | 3.1 | 3.9 | 3.8 | 4.7 | 2.6 |
| What overall rating would you give this instructor? | 3.9 | 4.5 | 4.4 | 4.5 | 4.0 |
| Under the current COVID-related instructional conditions, the instructor clearly articulated course expectations to students. | 4.9 | 4.8 | 4.7 | 4.8 | 4.9 |
| Under the current COVID-related instructional conditions, the instructor used distance learning technology (Blackboard, Zoom, discussion boards, etc.) effectively to communicate course material. | 4.6 | 4.7 | 4.7 | 4.8 | 4.9 |
| Under the current COVID-related instructional conditions, the instructor noticed when students did not understand course material and adjusted accordingly. | 4.3 | 4.7 | 4.6 | 4.8 | 4.3 |
Fall 2022 - Spring 2023
| Category | MATH 150 1 | MATH 165 3 | MATH 236 1 | MATH 150 2 |
|---|---|---|---|---|
| What overall rating would you give this instructor? | 4.1 | 4.3 | 4.7 | 4.4 |
| What overall rating, would you give this course? | 3.6 | 4.0 | 3.7 | 4.2 |
| The exams/assignments covered important aspects of the course. | 4.4 | 4.4 | 4.6 | 4.4 |
| The assignments were helpful in understanding the material. | 4.2 | 4.5 | 4.4 | 4.6 |
| The exams/assignments were clearly worded. | 4.4 | 4.5 | 4.6 | 4.3 |
| Lectures / class discussions were well organized or well managed. | 4.4 | 4.2 | 5.0 | 4.6 |
| Classes tended to stay appropriately on topic. | 4.8 | 4.6 | 4.7 | 4.7 |
| I feel this class was valuable. | 3.6 | 4.0 | 4.1 | 4.2 |
| The instructor explained and emphasized important points clearly and effectively. | 3.9 | 4.0 | 4.9 | 4.5 |
| The instructor used examples that helped with understanding the material. | 4.1 | 4.2 | 4.6 | 4.5 |
| The instructor noticed when students did not understand and adjusted accordingly. | 3.5 | 3.5 | 4.4 | 4.1 |
| The instructor demonstrated sincere respect for students. | 4.6 | 4.7 | 5.0 | 4.6 |
| The instructor was willing to listen to student questions and/or opinions. | 4.6 | 4.6 | 4.9 | 4.6 |
| The instructor made himself/herself available for extra help. | 4.6 | 4.4 | 5.0 | 4.4 |
| The instructor tended to be well prepared for class. | 4.7 | 4.6 | 5.0 | 4.8 |
| The instructor provided clear academic honesty guidelines for this course. | 4.7 | 4.6 | 4.7 | 4.6 |
| I have a stronger interest in the subject because of the instructor. | 3.1 | 3.4 | 4.0 | 4.0 |
Some Comments written in these evaluations are the following
Student Evaluations at Universidad de Los Andes
At the Universidad de los Andes, instructor performance is evaluated by the students under the following categories. Scored discretely from 1 to 4, representing strongly disagree, disagree, agree and strongly agree respectively. Students have also a space for provide comments on positive or negative aspects of the instructor performance.
For example, in a class of 14 students in the course of Integral Calculus and Differential Equations the obtained student evaluations are as follows:
| Category | Course Average (out of 4) |
|---|---|
| The course meets the established learning objectives. | 3.93 |
| The development of the course foster student’s commitment to studying this subject. | 3.79 |
| The instructor implements effective activities (presentations, discussions, projects, assignment, etc) to enhance student’s learning. | 3.79 |
| The textbook, lecture materials or any other teaching tools used both inside and outside of the classroom are adequate for the course objectives. | 3.86 |
| The assessment methods are clearly established from the beginning of the course. | 3.86 |
| The exams, assignments and graded activities are appropriate and consistent with the course objectives. | 3.93 |
| The grades are returned accordingly to the university policies. | 3.79 |
| The instructor is respectful with the students. | 3.93 |
| The instructor arrives promptly to the course lectures. | 3.93 |
| The instructor promptly assists students in both inside of the classroom and outside of it (office hours, email, e-learning platform, etc) | 3.93 |
Comments written in these evaluations are the following
For a class of 25 students in the course of Integral Calculus and Differential Equations the obtained results are as follows
| Category | Course Average (out of 4) |
|---|---|
| The course meets the established learning objectives. | 3.84 |
| The development of the course foster student’s commitment to studying this subject. | 3.72 |
| The instructor implements effective activities (presentations, discussions, projects, assignment, etc) to enhance student’s learning. | 3.72 |
| The textbook, lecture materials or any other teaching tools used both inside and outside of the classroom are adequate for the course objectives. | 3.84 |
| The assessment methods are clearly established from the beginning of the course. | 3.80 |
| The exams, assignments and graded activities are appropriate and consistent with the course objectives. | 3.76 |
| The grades are returned accordingly to the university policies. | 3.96 |
| The instructor is respectful with the students. | 3.96 |
| The instructor arrives promptly to the course lectures. | 3.84 |
| The instructor promptly assists students in both inside of the classroom and outside of it (office hours, email, e-learning platform, etc) | 3.72 |
Comments written from these evaluations are the following.
Teaching Assistant evaluations
Most of the teaching assistant evaluations at the University of Western Ontario are in charge of the instructor of the course. The aspects of assessment for teaching assistant and the respective average (out of 10 instructor’s evaluation forms) obtained are the following.
| Category | Category Average (out of 5) |
|---|---|
| Assessment on Teaching Assistant’s Marking performance. | 4.7 |
| Assessment on Teaching Assistant’s Teaching Performance | 4.5 |
| Assessment on Teaching Assistant’s effectiveness in completing assigned tasks | 4.9 |
| Assessment on Teaching Assistant’s promptness on arriving to the classroom, exams, office hours, etc. | 4.5 |
A compendium of some teaching assistant evaluations during my time at Western can be found in the additional files section here.
Informal Teaching Evaluations
These are some email communications sent by students directly to me after the course is over
These comments are obtained from the Facebook group “Courses that you should take” for students at the
Universidad de Los Andes:
This comments was sent by a students when working with them in regular one-to-one tutoring meetings.
Peer Evaluations from Class Observations
The following are comments from observer Graduate students attending one of my lectures during the Teaching Mentor Program (2019) at Western University.
“Excellent usage of Audio-Visual aids to facilitate learning. Superior Enthusiasm displayed in delivering the lecture content. Effective usage of whiteboard around the classroom. Higher comfort level experienced between the attendees and the instructor leading to better understanding of the subject content, distribution of worksheets that helped the attendees understand the subject better. Overall, you practices an outstanding university teaching style and incorporates many teaching strategies that makes learning experience worthwhile.” Glen DSouza. Research Assistant. Department of Chemical and Biochemical Engineering. (2019).
“You had an astute ability to explain complex concepts to your audience by deconstructing big ideas into smaller ones. When introducing the topic, you began by asking your students very simple questions, such as “what is a polygon?” and subsequently asking students to identify the correct polygons out of a variety of mixed shapes. This provided students with not only a clear definition but an opportunity to practice applying their knowledge. You continuously utilized interactive exercises with the class with handouts and gave the class adequate time to practice on their own. By taking up the worksheets after with the class, students were able to identify their own knowledge gaps and develop a clearer understanding of the content.” Hanna Roberts. MSc. Candidate, Clinical Anatomy. Dept. of Anatomy and Cell Biology (2019).
The complete review letter can be accessed in the Additional Files section here
5. Curriculum Development
Teaching Methods and style
My lectures and teaching style are designed to provide a structured and engaging learning experience for students. Here's how my lectures typically unfold:
Course Organization
- I provide a clear course schedule with sections and suggested problems on the syllabus, ensuring that students have a roadmap for their learning journey. This organization promotes a sense of direction and purpose in the course.
Preparation
- Before each lecture, I share reading notes with students. These notes give them an overview of what will be covered and highlight the learning outcomes of the day, allowing students to follow along more effectively. This pre-lecture preparation is like a compass, guiding students through the lecture content.
Technology Integration
- To accommodate remote students, I use tools like Zoom for live sessions and provide lecture recordings. I also use a microphone to ensure that everyone can hear me clearly. In the age of technology, this integration enables seamless access to knowledge.
Engagement and Interaction
- I start each lecture by checking if students have any questions or need clarification on previous topics. This immediate interaction empowers students to voice their concerns and fosters a sense of inclusivity in the learning process.
- Throughout the lecture, I incorporate concept-check questions to encourage student participation. I use technological tools like Poll Everywhere to make it easy for students to interact and provide their responses. This real-time engagement transforms passive listeners into active learners.
Balance Between Theory and Practice
- My lectures are carefully balanced between theoretical concepts and practical applications. I engage students with active learning strategies and sprinkle in a bit of humor to keep the atmosphere lively and enjoyable. This balance not only equips students with knowledge but also the ability to apply that knowledge in real-world scenarios.
Assessment and Follow-up
- At the end of the lecture, I suggest concept-check questions to reinforce learning. I allocate some time for students to answer final questions and encourage them to follow up during office hours or reach out to the Teaching Assistant (TA) for further assistance. This assessment and follow-up ensure that students don't just learn in class but also retain and apply what they've learned.
Resources for Reference
- For students' convenience, I post clear lecture notes and recordings of the lecture for future reference. This ensures that they have access to the material whenever they need it. These resources are like a library of knowledge, available 24/7.
Guiding the Learning Journey
- During the lecture, my role as a professor is crucial. I serve as the navigator of the learning journey. I guide students through the curriculum, helping them connect the dots between different concepts. I provide context, explain complex ideas, and ensure that students grasp the material.
- My real-time feedback and interaction with students offer them the opportunity to seek clarification, voice their concerns, and engage in discussions. This open dialogue fosters a dynamic learning environment where students actively participate in their education.
Facilitating Learning with Technology
- The integration of technology, including Zoom and Poll Everywhere, enhances the learning experience. It breaks down barriers between physical and virtual students, making education accessible to all. It also makes learning more engaging, as students can actively participate using their devices.
Cultivating a Lifelong Learning Mindset
- Through balanced lectures that blend theory and practice, I instill a lifelong learning mindset in students. They not only acquire knowledge but also the skills and confidence to keep learning beyond the classroom. They understand that education is not limited to a specific course but a continuous journey.
Empowering Students
- Ultimately, my goal is to empower students. By providing clear organization, engaging lectures, and accessible resources, I enable students to take control of their education. I equip them with the knowledge and tools they need to succeed, both in the course and in their future endeavors.
Teaching Innovations and Course Design
My stand on teaching innovation and course design revolves around flexibility, adaptability, and a student-centered approach. By carefully selecting materials, customizing content, diversifying assessment methods, leveraging technology, and maintaining a focus on the individual needs of each student, I aim to create a dynamic and effective learning environment that empowers students to reach their full potential while also providing accessible grading options to support their diverse learning journeys.
- Curated Learning Materials: I believe in choosing appropriate textbooks and secondary materials for each course. These resources should align with the course's objectives and the needs of the students. Furthermore, I am committed to providing open-source options whenever possible, making education more accessible and affordable. Additionally, I often share archive files from previous homework and exams to help students review and practice.
- Tailored Learning Experiences: No two courses or audiences are the same. To ensure that each student's educational journey is as effective as possible, I focus on tailoring course objectives and content approaches to meet the unique needs of the audience. Getting to know the students prior to the semester is invaluable in this regard, allowing me to adapt my teaching methods and materials to maximize their learning outcomes.
- Diverse Assessment Methods: To assess students' understanding and promote critical thinking, I incorporate various types of exam questions. This includes open-response questions, multiple-choice, true-false, and answer-given problems. Allowing students to bring a page of notes to certain assessments can aid in their comprehension, encouraging them to synthesize key concepts rather than rote memorization.
- Benefits of Oral-examinations: In small group classes, I have found that integrating one-on-one final examinations serves as an effective and valuable assessment method. These assessments not only evaluate a student's knowledge but also encourage active participation, thoughtful discussion, and foster a welcoming and accommodating learning environment. By engaging students individually, this approach enables personalized feedback, in-depth understanding of the subject matter, and the opportunity for students to express their thoughts and ideas with confidence. It also minimizes the risk of academic dishonesty and eases the stress associated with traditional written exams.
- Integrated Technology: I recognize the importance of technology in the modern educational landscape. I actively use and encourage the integration of technology in my lectures and assignments. However, I also emphasize the balance between traditional teaching methods and technological tools. There are both benefits and drawbacks to relying heavily on technology, and I strive to find the optimal blend that enhances the learning experience.
- Accessible Grading: I understand that students may have diverse starting points, and it's crucial to provide options for accessible grading. This can include different calculation methods for the final grade or allowing the option to drop certain homework scores. These strategies ensure that every student feels they have the possibility to excel, regardless of their initial performance.
I also have a proposed Syllabus for a course in Transformation groups that I am looking forward to deliver for graduate students interested in my research areas. This proposed syllabus can be accessed in the Additional Files section.
During most of my time as instructor and teaching assistant, I prepared independently problem sheets, assignments and quizzes considering the topics covered in class and the most beneficial questions for the students to prepare for their exams. In particular, I thrive for using technological tools into math teaching. I advocate for open source projects and the use of interactive blackboards when teaching mathematics.
Online Teaching
Online teaching has evolved into an integral component of modern education, catering to the needs of new generations. The technological advancements that provide accessibility and convenience should be embraced by educational institutions and educators. I firmly believe that students can derive immense benefits from a blend of traditional and online teaching methods, and I work for their continual improvement.
By relying on the power of digital tools such as Desmos, Geogebra, or Wolfram Alpha to illustrate concepts in calculus and linear algebra, or to demonstrate step-by-step problem-solving, students can perceive mathematics as a dynamic subject that evolves alongside humanity's progress. I always seek the opportunity to employ these tools to enrich the learning experience during my lectures.
Moreover, it is essential to engage students actively in both in-person and online settings. Utilizing tools like Poll Everywhere, Gradescope, or Blackboard quizzes during class fosters interactive learning, allowing me to gauge students' understanding and address their queries in real time.
Recognizing the diverse learning styles of students, I ensure accessibility by recording my lectures, making them available for reference at any time. Additionally, I provide clear, concise notes to facilitate independent study, offering comprehensive support for their academic journey.
Having taught both entirely online and blended courses, with over 200 YouTube videos, I have observed that online teaching holds distinct advantages in specific scenarios. However, I also acknowledge the profound legacy of the classical blackboard-and-chalk setup that has served education for centuries. I believe in promoting and preserving this time-tested method, especially when it remains a highly effective teaching approach, so I reserve this method to certain higher-level classes or topics.
Some sample video lectures can be accessed through the Additional Files section of this Dossier.
Technology use for Question Design
My mathematical question creation stance has been marked by a dedication to originality, the effective use of technology, the sharing of resources, and a commitment to improving mathematical education on both a local and national scale. I believe that the art of crafting questions is an integral part of helping students unlock the beauty and power of mathematics
In my commitment to developing quality mathematical questions, I adhere to the following principles:
Originality and Content Alignment
I prioritize originality while ensuring that the questions align with the content delivered in lectures and assignments. This approach keeps the assessment relevant to the course material.
Webwork and Randomization
Webwork is my preferred platform for creating questions due to its ability to introduce layers of randomization and provide immediate feedback. This system enhances both homework and exam experiences, promoting deeper understanding and retention of the subject matter.
Question Pool and Tutorial Documents
I maintain an extensive pool of questions in Webwork, creating over 500 questions in various mathematical areas. These questions have led to the development of tutorial documents that have proven invaluable to fellow instructors interested in utilizing the system.
Collaboration and Outreach
I am dedicated to helping colleagues from other institutions adopt Webwork, guiding them through system installation and question creation. Notably, I supported the Colombian group "Lema" in their efforts to implement Webwork in the Spanish language.
ICFES Mathematical Question Bank
Additionally, I served as a designer and reviewer for the bank of mathematical questions at the Colombian Institute for the Assessment of Education (ICFES). This institution is responsible for developing standardized exams used for assessing students in Colombia. I contributed by creating innovative questions and evaluating previously created questions to ensure they met high standards of versatility, reliability, and validity, aligning with the rigorous requirements of the ICFES exams.
I am currently working on the joint use of WeBWork with other open source projects as GeoGebra, SageMath, PreText and Rederly . as well as fostering the use of these tools in Colombia by helping with demonstrating the use of the software and with their translations together with the Grupo Lema. I am currently have a tutorial (both in English and Spanish) in progress on WeBWork question creation providing some templates and macros on how to effectively type new questions in WeBWork and integrating with other software. A preliminary version can be accessed here .
Reflection on Teaching Proofs in Mathematics
Teaching mathematical proofs for undergraduate students is a challenge for both instructors and students. Proof is an essential part on learning as it develops reasoning skills, improves problem solving aptitudes and it is also a fundamental basis for future researchers. This reflection is focused on studying the difficulties experienced in the learning and teaching process of formal mathematical proofs, and discuss whether the traditional "definition-theorem-example" lecture method is the most appropriate for the students to success in mathematical courses.
The full reflection can be accessed in the Additional Files section here.
6. Professional Development
Certificates, Courses and Programs on Teaching
Anti-Racism Foundations Certificate (2023)
Program that examines the ongoing impact of racism in the Canadian context, focusing on equity-deserving groups including Indigenous Peoples and Black people. The main objectives are the following:
- Recognize the relevance of the history of racism in Canada and its impact on equity-deserving groups.
- Examine the invisibility of Whiteness and microaggressions, and the harmful impact that both can have on racialized individuals.
- Identify strategies to address implicit bias and prevent microaggressions.
- Implement strategies and actions to begin or continue an anti-racist journey to create a more equitable and inclusive community.
Microcredential in Inclusive Teaching For Equitable Learning (2022)
Partner program between the Association of College and University Educators (ACUE) and the University of Rochester It is Faculty program for instructional excellence and student success. Over the an aacademic year, faculty across have the opportunity to participate in a micro-courses focused on learning and implementing research-based teaching practices to address issues of bias and inequity in learning environments.
The program provides proven strategies to create more equitable and just learning environments. Faculty will learn practices from the following modules:
- Managing the Impact of Bias
- Reducing Microaggressions in Learning Environments
- Addressing Imposter Phenomenon and Stereotype Threat
- Creating Inclusive Learning Environments
- Designing Equity-Centered Courses
- Developing Self-Directed Online Learners
Western Certificate in University Teaching (2020)
The program objective is to enhance the quality of teaching by graduate students and postdoctoral scholars, and to prepare them for a future faculty or professional career. It is a program that explores several components of Teaching in courses, workshops and different activities. The program is completed in a span of two years. More information can be accesed here . A completion certificate is posted in the Additional Documents section.
Advanced Teaching Program (Winter 2019) - Western University
The Advanced Teaching Program (ATP) is a 20-hour short course designed for advanced graduate students
who would like to develop practical teaching skills for current and future teaching roles. Topics include
course design strategies, active learning, authentic assessment of student learning, and maintaining a culture
of respect and community in the classroom. Participants gain hands-on experience by practicing
instructional techniques in microteaching sessions where they receive constructive feedback from peers and
an experienced team of instructors.
Teaching Mentor Program (Winter 2019) - Western University
The Teaching Mentor Program is a unique opportunity for graduate students and postdoctoral scholars to
receive feedback on their teaching and classroom management approaches from peers in their own teaching
environment. Four to five participants will work together and visit each other’s classes, tutorials or labs
over the course of the semester. I was part of a group of 5 Graduate Student from a diverse range of
backgrounds (Engineering, Medical Sciences, Humanities and Science).
An example of one of the feedback letter that I provided to my peers can be found here .
TA Day: Graduate Student Conference on Teaching (Sep 2015, 2016, 2017) - Western University
This one-day yearly conference introduces graduate students to teaching at Western and helps prepare them
for their roles as Teaching Assistants. TA Day has welcomed new graduate students to Western for over 30
years.
Conference highlights include a keynote presentation by an award-winning faculty member and a panel of
experienced Teaching Assistants from across the disciplines. Participants choose from a variety concurrent
workshops that focus on different teaching topics including: facilitating discussions, managing difficult
situations, communication strategies, and more. Graduate students also have the opportunity to hear from
key campus partners including Western Libraries, the Writing Support Centre, Learning Skills Services,
the Wellness Education Centre, the Teaching Assistants Union, and the Society of Graduate Students
Teaching Workshops and Conferences
University of Rochester Fall 2023 Workshop Series
These workshops included
- Evaluating group work. Oct 2023.
- Scaffolding Writing Assignments. Oct 2023
- Designing effective group work. Oct 2023.
- Using movement to Enhance Learning. Sep 2023
University of Rochester Spring 2022 Workshop Series
These workshops included
- Transparent Assignment Design. Apr 2022
- Asking and Answering classroom questions. Mar 2022
- Anti-Racist Feedback and Messaging. Mar 2022
- Writing Good Multiple Choice Questions. Mar 2022.
- Evaluating Group Assignments. Feb 2022
- Designing Group Assignments. Feb 2022.
- Effective Management and Mentoring of TAs. Jan 2022
Western Fall Perspectives on Teaching Workshop (Aug 2019)
Perspectives on Teaching is a full-day conference designed to showcase
teaching innovations at Western University, and introduce instructors to best practices in student-centered instruction
which can enhance the student experience. The conference program typically includes a keynote address
and 6-9 concurrent sessions.
Own Your Future: May conference on Teaching (May 2019) - Western University
The Own Your Future: May Conference on Teaching is a special one-day event for doctoral students at
Western. Participants are invite to join one or more conference sessions to enhance skill areas related to
teaching, set personal goals for growth as instructors, and connect teaching experiences to their overall
professional development as graduate students.
Western University: Workshop Series 2019
- Writing Teaching Philosophy Statements. Oct 2019.
- Tried and True Strategies to Address Common Assessment Conundrums. Aug 2019.
- Effective Practices for Peer Review of Teaching: Moving Beyond the Student Perspective. Aug 2019.
- Flexible Assessment: Designing Effective Assessments that Support Student Wellness. Aug 2019.
- New Policies for Student Absence and Accommodation -- Is Your Syllabus Ready? Aug 2019.
- Assessing and Articulating your Teaching Skills for Future Careers. May 2019.
- How Can Teaching Help Me Get a Job? May 2019.
- Case Studies on Teaching. May 2019.
- Writing Diversity Statements. May 2019.
- Constructing Your Teaching Dossier. Mar 2019.
- Strategies to Help Students Learn How to Learn. Mar 2019.
- Increasing the Power of PowerPoint. Feb 2019.
- How to Care For and Use Your Teaching Voice. Feb 2019.
7. Diversity, Equity and Inclusion Statement
Throughout my personal and professional experience, I recognize the importance of fostering diversity, equity, and inclusion within the academic community. As a first-generation college graduate, studying in a private-university under a full-scholarship, and pursuing a doctorate in a culturally diverse country yet still a visible minority, I understand the challenges faced by individuals from underrepresented socioeconomic, cultural, ethnic and academic backgrounds. I have been dedicated to promoting diversity in education, STEM field and mathematics where all students should be given equal opportunities regardless of their race, ethnicity, gender, age, religion, language, abilities, sexual orientation, socioeconomic status or country of origin.
Mathematics, as served historically as a universal language, transcends the boundaries of personal backgrounds, and as a powerful means of communication that unites ideas and promote knowledge. However, it is essential to acknowledge that mathematics and other STEM fields have also been portrayed as careers predominantly tailored for men and individuals perceived as exceptionally intelligent. My role in academia and the community is to foster a perspective where Mathematics is seen as a welcoming, inclusive and diverse field accessible to anyone.
A full statement on my Diversity, Equity and Inclusion stance can be accessed here
8. Additional documents
Teaching Samples
Syllabus Samples:
- Syllabus for Discrete Mathematics and Topology courses taught at the University of Rochester
- Syllabus for a proposed course in Transformation groups at Western University
Projects and Reflection Questions:
Lecture Notes
- Clean notes on Differential Equations shared before the lecture
- Annotated lecture on Integral Calculus shared after the lecture
Lecture Recordings
- Lecture on Lines (Precalculus - UofR)
- Lecture on Graph Theory (Discrete Mathematics - UofR)
- Lecture on Linear Differential Equations (Methods of Calculus - WesternU)
Homework and Exams Samples
- Written Homework on Discrete Mathematics
- Final Exam on Integral Calculus
- Final Exam on Discrete Mathematics (implemented in Webwork, each student had a different version).
Teaching Certificates
- Microcredential in Inclusive Teaching for Equitable Learning
- Western Certificate in University Teaching
Teaching Evaluations
- Complete Evaluations from the University of Rochester
- Complete Teaching Assistant evaluation from Western University
- Peer-review Observations