Teaching Philosophy
“ Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.” - Paul Lockhart, A mathematician’s Lament.
This quote aligns not only with my belief about what the nature of mathematics is, but also with my philosophy for teaching and learning mathematics. I believe learning mathematics requires students to acknowledge their own ideas, communicate these ideas, and connect, and reflect between ideas of theirs and others using reason and logic. The first two (i.e., acknowledging and communicating) can occur naturally with most students as they enter the classroom with some knowledge and experience of both mathematics and general communication skills.
When it comes to learning mathematics, I believe it is best for students to gain a conceptual understanding before focusing on procedural fluency. Especially in calculus, I have seen that once a student has a conceptual understanding of functions and their behaviors then the procedures are easier for the students to perform. Nevertheless, I do give my students problems that are harder than they may have seen before. I believe that if a student truly understands the material then more complex problems give students a better learning opportunity and greater sense of accomplishment. The goal of my instructional technique is to encourage productive mathematical conversation. Teachers can support learners by orchestrating productive and mathematically rich discussions about students' ideas. If these conversations center on certain topics, teachers can help students by introducing how to make connections between different ideas. When teaching I try to both explain and exemplify how reasoning skills and logic progress ideas in the mathematics community.
I do not see myself as an instructor but instead as a facilitator of my students learning experience. I plan for each class, in hopes that my plan is not followed through completely, due to student conversations, questions, and mathematical inventions. I encourage my students to talk, think, question, revise, and work together to build their knowledge as much as possible. I love helping students see the interconnectedness of mathematics within itself, and also how mathematics is essential for describing and interpreting the world. One example that always comes to mind is from one of the calculus courses I recently taught. During this course, when the class was introduced to the Fundamental Theorem of Calculus, I explained the need for limits, derivatives, antiderivatives, and summation. One student who was enrolled in the course for the third time loudly exclaimed “Oh my, everything finally makes sense! Why have I never seen this before?” This was a highlight of my years of teaching. Particularly, I enjoy helping students see the usefulness of calculus as a way of understanding and describing the real world. I want mathematics to be challenging for my students, but I also want it to be a fun learning experience.
Another goal of mine in the classroom is to build a community of mathematics learners. What community means is something I have been questioning and refining throughout my years of teaching. I have seen the usefulness of purposely placed groups in my classroom and do utilize group work often especially when teaching undergraduate mathematics to future STEM majors. I have noticed students feel more comfortable with asking questions in small groups, even when in seemingly competitive classrooms such as Calculus. One of my goals in the classroom is to foster and help create an inclusive learning community that is supportive and can help alleviate the competitive nature of many STEM courses.
I believe one main goal of mathematics education is to produce mathematically literate students; with whom some may foster a love, passion, and desire to continue their mathematics education, and add to the mathematical knowledge of this world. I truly believe that everyone can learn mathematics, it just takes time, patience, and a supportive community. The aspect of community is what I try to help create and influence as an undergraduate mathematics instructor.
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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
