Teaching Philosophy
“ Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.” - Paul Lockhart, A mathematician’s Lament.
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This quote resonates deeply with my teaching philosophy, which prioritizes student engagement, active learning, and inclusivity. I believe that students bring valuable knowledge, diverse experiences, and unique perspectives into the classroom, and my role as an instructor is to create an environment where these contributions are recognized, connected to broader mathematical ideas, and used to foster a collaborative learning experience.
Active Learning and Student-Centered Instruction
My teaching approach emphasizes active learning, especially through collaborative problem-solving and peer interaction. Beginning in 2016, I introduced active learning strategies in Calculus I and have since refined these methods across Calculus II and upper-level mathematics courses. My dissertation research specifically explored the equity of group testing in an accelerated Calculus I summer course, where I used collaborative assessments to create an inclusive environment that encourages peer support. Teaching Calculus I at three different universities, including one in the North and two in the South, has allowed me to implement and observe the effectiveness of these methods with diverse student groups, with consistently positive results. One student, for instance, reflected, “You never doubted my ability to improve,” highlighting the impact of a supportive and inclusive approach.
In expanding these active learning techniques, I incorporated group work into Calculus II to encourage student collaboration further. By facilitating peer problem-solving, I helped students deepen their understanding and engagement. This approach was well-received; one student remarked, “Dr. Quinn is amazing and truly the best math teacher I have ever had… I love the idea of putting us in groups, giving us the opportunity to know each other and work together.” Such feedback underscores the value of a collaborative learning environment where students actively participate in their learning journey.
Mentorship and Undergraduate Research
Mentorship is integral to my teaching philosophy, and I am dedicated to supporting students in exploring research and professional opportunities. At the University of North Alabama, I have developed a robust undergraduate research program in mathematics education, where I primarily mentor female math education majors. My mentorship projects span several areas, including research on mathematical mindsets in undergraduate classrooms, the integration of technology into math projects for Intermediate Algebra and Calculus III, and a unique study examining non-math majors' perceptions of mathematics through personification. These projects give students hands-on experience in research design, qualitative analysis, and professional presentation, empowering them with skills they can carry into their teaching careers or further studies.
Working with pre-service secondary math education majors, I guide students in developing their pedagogical approaches while fostering their passion for mathematics. I encourage them to implement active learning and inquiry-based methods, helping them understand how to make math accessible and engaging for their future students. Through my role as Co-PI on the LIONS Bridge Program, which supports historically excluded groups in STEM, I also mentor students in confidence-building strategies and inclusivity in the classroom, preparing them to create their own inclusive educational environments.
Fostering Equity, Diversity, and Inclusion in the Classroom
Equity, diversity, and inclusion are central to my teaching philosophy. I strive to create a classroom where all students, regardless of background or identity, feel welcome, capable, and valued. As one post I read expressed, “Accessibility is being able to get in the building. Diversity is being invited to the table. Inclusion is having a voice at the table. Belonging is having your voice heard.” This captures my commitment to not only ensuring that all students have access to my classroom but also that they feel their contributions are meaningful and respected.
My personal experiences have profoundly influenced this commitment. In high school, I was discouraged from pursuing higher education. This experience shapes my dedication to encouraging students, especially those who might doubt themselves or face barriers, to persist and pursue their academic and career goals. My work with NSF-funded initiatives such as LSAMP, Operation STEM, and the LIONS Bridge has reinforced my belief that a sense of belonging significantly impacts student success. Developing bridge programs, peer mentoring, and tutoring systems has shown me that students who feel supported and connected are more likely to succeed.
Inquiry-Based Learning and Conceptual Understanding
I believe students should develop a strong conceptual understanding before honing procedural fluency. In my MA 325: Foundations of Mathematics course, I structured the class around students' discovery of proof techniques, using materials developed by Dr. James Hart of MTSU. This inquiry-based approach encouraged students to build proofs from first principles, which deepened their critical thinking and problem-solving abilities. Teaching this course over two consecutive semesters allowed me to refine my methods, and students responded positively. One remarked, “The class flowed a lot better the second time around and seemed to click more when it came to the core content.” Another student, from this course, remains in contact, expressing gratitude for the course as his introduction to higher mathematics.
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Through mentorship, peer support, and inclusive instructional strategies, I am committed to creating learning spaces where all students feel empowered to excel in mathematics. My journey in education has shown me that when students are encouraged to find their voice, connect with their peers, and engage deeply with mathematical ideas, they not only succeed academically but also develop a genuine appreciation for the beauty and depth of mathematics.
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The above picture was created with my interpretation of the 10 needs for learning mathematics as describe in:
Sfard, A. (2003). Balancing the unbalanceable: The NCTM standards in light of theories of learning mathematics. A research companion to principles and standards for school mathematics, 353-392. My research strives to connect these needs of the students with instructional techniques in undergraduate mathematics classrooms.
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A published and in depth description of the figure above and each of the 10 needs placement in this picture can be found in the conceptual framework in my dissertation here: https://www.proquest.com/docview/2572610024?pq-origsite=gscholar&fromopenview=true
