As a mathematics educator, I strongly encourage and welcome change into my philosophy of teaching. I strive to evolve and adapt in order to meet the increasing needs of students and provide a productive educational environment. From this perspective, the building blocks of my teaching philosophy follow.
Promote Active learning. I emphasize to students that the key to learning math is to do math. One cannot learn math by memorization of formulas and theorems alone. For example, it would be unreasonable to think you can learn to play like a concert pianist by simply listening to piano concertos. Only through tedious practice do your fingers and mind learn to work together. The same is true for math. The brain must be trained and exercised in order to effectively solve problems and apply sophisticated theorems. Therefore, I provide students with numerous opportunities to practice math and receive feedback on their work. I achieve this by giving students the opportunity to work on problems in groups so that they can learn from each other. I then facilitate each group as they focus on their assignments. In addition, I selectively assign homework designed to ensure students practice the most important skills in each lesson and give short in-class quizzes allowing students to practice doing math in an exam format.
Give math context. One of the most difficult challenges with motivating math is making it relevant to students. A common question I encounter from students is “When will I ever use this?” Some topics are easier to motivate towards students’ everyday lives or future careers, such as explaining optimization to engineering students and cost/revenue functions to business students. However, topics such as tedious row reduction problems in Linear Algebra and series convergence tests in Calculus II are often seen as irrelevant to them beyond the present course. Although in some instances this may be true, I always stress that learning to work through tedious problems or abstract topics trains us to be better problem solvers and is an important skill to have in any field. Moreover, practicing these types of problems often prepares us to apply them to new or more intricate problems that do have significant relevance or application in the future.
Engage Students. Although active learning is vital to the education process, it is also crucial to effectively relay important information to students. I present math in a manner that is dynamic, relatable, and understandable. I recognize that some topics in math are challenging for students to understand. However, explaining these challenging topics can always be overcome by relating the main ideas to something more identifiable to students. The use of illustrations and concrete examples often shed light on any confusion, allowing students to grasp even the most abstract concepts. I also engage students using technology. In the classroom, WolframAlpha and Desmos provide excellent tools to demonstrate, animate, and simulate a variety of topics. I also implement Campuswire in my classes, which is an online discussion board geared towards the STEM subjects. Piazza allows students to engage with each other and myself outside the classroom by posting questions that anyone can answer and discuss.