I believe learning works best when students build on what they already know rather than memorizing disconnected ideas. In my courses, I emphasize the connections between topics - showing students how new concepts emerge naturally from familiar ones. I use tools like "Syllabus Map", "Warm-up Problems", and open-ended problem-solving to help students see the structure of mathematics and develop confidence in their own reasoning. 

Every lecture begins with a "Warm-up Problem", which is a worksheet that starts with something students already know how to do and guides them, step by step, toward the new idea. For example, on the day I introduce linear approximation, students find the equation of a tangent line, then rearrange it to estimate a nearby value of the function. During the lecture, after I formally introduce linear approximation, I refer back to what they just did, making the connection explicit. This approach helps students see mathematics as a connected discipline rather than a sequence of isolated techniques. 

Over the past six years, I have taught undergraduates from diverse backgrounds in Sri Lanka and the United States, ranging from algebra and precalculus through the calculus sequence, to upper-level courses including real analysis, differential equations, functional analysis, and predictive analytics. At Pitt, I have served as instructor of record, teaching fellow, and teaching assistant across multiple courses, and I have been invited twice to teach in the Swanson School of Engineering's Summer Engineering Academy for incoming freshmen.