Here is the summary of my teaching method (This page is not complete and more content is coming soon!)
How I teach in class (my teaching methodology)
I begin each session by reviewing the previous class to connect prior material to the current topic. This approach reinforces foundational knowledge and shows how new concepts can be built upon existing ideas. Throughout the lecture, I verbalize my thought process while working through proofs or examples, explaining why certain methods are chosen and how to anticipate and correct potential errors. When introducing a new topic, I start with a brief overview, discussing its history and
objectives. Additionally, I incorporate technology to support note-taking and create visualizations of key concepts, which helps students better grasp my thought process and the overall structure of the subject matter.
In analytical courses such as Real Analysis, Algebra, and Linear Algebra, I emphasize the importance of understanding theorems by addressing three key aspects: why the theorem is essential, its future applications within the course, and its real-world significance and historical context. To facilitate understanding, I start by presenting an example related to the main theorem or concept. Together with the students, we analyze the example, paying particular attention to the details of the theorem’s hypotheses. This sets the stage for me to formally state the theorem, highlighting the connections to the initial example. Next, I present a second example, often from a different perspective, or one where the theorem’s hypotheses fail to hold. This helps students deepen their understanding of the theorem’s scope and limitations. Once I am confident that students grasp the theorem’s statement, I guide them through the proof process step by step, actively engaging them by asking for their suggestions to proceed. For complex or longer theorems, I often break the proof into smaller, manageable parts by introducing intermediate lemmas. These lemmas are proven first, allowing students to build their understanding incrementally before tackling the main theorem. While I am writing on the board, I emphasize on mathematical writing and communication through mathematical notations.
Students’ evaluation in Real Analysis Fall 2024 ( Washington and Lee University )
Question: Please describe the most significant skills/knowledge that you gained or developed further in this course.
” I learned how to approach math in a more logic way and this class really makes me see Cal theorems from different perspectives.”
” I became a better proof writer, as well as a more confident mathematician, especially regarding what is possible when solving analysis problems.”
” I have furthered developed my mathematical thinking ability.”
” Think in detail and step by step. “
In my teaching, I am committed to fostering a deep understanding of mathematics while encouraging critical thinking in a motivating, engaging, and supportive learning environment.
Students’ Evaluation Fall 2024 Calculus II ( Washington and Lee University )
“Sometimes the clarity of the notes and lectures made the material difficult to understand, but by asking a question, she was always happy to help you better understand the topic and
clarify .““ The professor was really kind overall. She was inclusive of all students and asked if we understood the concepts. Sometimes it would be too lecture focused though, which makes the class monotonous and not interesting. I would’ve appreciated more activities in class to learn and test our knowledge.“
“The professor answered many of the questions in class and had many office hours which I would attend regularly. She often asked students to solve problems on the board or work on the problem ourselves before she showed us the answer. The environment was inclusive.”
making complex concepts more accessible to a diverse range of learners is my highest priority as in liberal arts colleges, this is a big challenge. Therefore, I found some teaching methods and ways more useful based on my experience and attending teaching workshops and courses.
- I integrate the think-aloud method in my teaching to explain and model my thought process for solving problems. I encourage my students to explain their thinking loudly in group work and board presentations. In this way, students learn different ways for a single problem and gradually learn the way of solving mathematical problems on their own.
- I employ backward design to design my courses to ensure that my course materials are structured with clear learning outcomes in mind. I have successfully adapted these strategies for both face-to-face and online learning environments, ensuring that all students, regardless of their background, can engage meaningfully with the material and develop their mathematical thinking
Critical and creative thinking
Critical and creative thinking are essential skills to be applied across the curriculum and beyond the classroom. These skills encourage students to think purposefully and work effectively. I foster critical thinking by incorporating brainstorming into each topic. I begin by posing thought-provoking questions, allowing students time to reflect and respond. This process helps them explore the best possible solutions to problems, encouraging them to provide logical reasoning to support their answers.
Student’s Evaluation from Real Analysis Fall 2024 ( Washington and Lee University )
“Prof Ahsani posted HWs that really stimulate me to go beyond what we’ve went over in the class.”
“I have furthered developed my mathematical thinking ability.”
Group activities and class discussion
Another part of the learning process in mathematics is the discussion. I always encourage my students to collaborate and discuss their work with each other either through in-class group activities, board presentations, or outside of the class because it develops more ideas and improves productivity. I encourage students to adopt the think-aloud technique during group activities and individual work. By vocalizing their reasoning, students develop stronger metacognitive skills1enabling them to critically evaluate their approaches and improve their problem-solving abilities.
Student’s Evaluation from Calculus II Fall 2024 ( Washington and Lee University )
“She was always very kind and eager to have students participate in class by solving problems on the board. She always encouraged questions or people to challenge her thinking which I think cultivated a really inclusive and vibrant learning environment.”
“My interaction in class was good, my classmates were approachable, and they created a safe space for me in class to ask questions and the professor was always available and approachable. “
How I assist my students outside of the classroom
I believe teachers have a key role in facilitating and supporting students in their academic lives. I
am available and approachable for my students outside the classroom via email, during office
hours, and via Zoom when I am not on campus. To ensure that cultural, diversity, and equity
awareness are promoted in my classes, I know that I should understand each student. Therefore,
I encourage my students to use office hours to introduce themselves and make a good connection
with their teacher. I ask my students to discuss a problem instead of seeking a solution. I do
not give ready answers; instead, I encourage them to come up with a solution in an interactive
process during office hours. I have made more effort to encourage my students to use office hours
regularly in recent years. I started by providing a worksheet (usually one problem with multiple
connected parts) at the end of some lectures and asked students to work on it and ask their questions
during office hours. This strategy was more successful, and surprisingly, my office hours were very
productive, and I created better relationships with my students.