Teaching Philosophy

Teaching is a fundamental part of a student’s educational foundation. Without teaching, there is no learning. Historically, teachers have treated their students like machines; only worrying about the outward behaviors of students, without looking at any internal cognitive processes. With more modern research data at hand, there is evidence to believe that the behaviorist, machine-like, teaching of old is not as efficacious as a new method: using internal processes to unlock the potential of all students. This train of thought is called a constructivist viewpoint. As the name implies, students construct their own correct answers through exploration and activity, rather than trying to absorb information through uninteresting lectures. By trying to solve situation, difficult problems, they reconstruct the experiences that iconic scientists and mathematicians have when they discover a new theory. Through this, students grasp a more conceptual understanding of the topics, rather than a procedural understanding which fosters from lecturing. This is important because a conceptual understanding allows students to derive procedures which are too often forced into our heads. However, students who have a procedural understanding will not be able to derive the concepts from the procedure. In addition, harnessing the natural interest in solving culturally relevant problems allows students to start thinking deeply; thinking about real world problem solving is what really matters at the end of the day. This is what teachers should prepare students to do; introducing students to life outside of the schoolyard, where they will really be using problem solving skills every day to impact the world around them, not spitting out facts on tests or worrying about their GPA. What teaching is revolves around more than just the subject matter. More than just “find x” or “find the integral of this function.” Teaching ought to prepare and inform students about the world around them, whether it be about the world in the past, how the world works, how people influence the world, or how people interact with the world. It all comes together to create a citizen that will positively benefit those around them with a wealth of knowledge, and a unique perspective on life.

Moreover, how are we to allow students to learn the most and best they are able, and how are we to assess that knowledge? What we ought to do is use a concept called “activity before content.” This allows students to play and explore before introducing a whole bunch of jargon that may complicate things. This method ties back into the experience of scientists discovering a new theorem. A student could find out how to approximate area under the curve using Riemann Sums through engagement, so they call it their own method. This makes it more memorable to the students and they are less likely to forget it. This method also allows for plenty of formative assessment, where the teacher is constantly assessing how his or her lesson is going by listening in on conversations between students, asking intriguing questions, and guiding the students to new and creative responses through classroom discussions. This does not mean formal assessments like tests cannot be used, but rather, used sparingly to determine actual competence with regards to content.