Mathematics is a subject rich with ideas and concepts. The understanding of concepts begins with the building up of a mental network of connections. The more connections there are within such a network, the deeper the learning. As our thinking becomes more sophisticated, new concepts develop more easily and naturally as a result of already existing constructs. With no such network in place, even the tiniest step forward from one concept to the next can be overwhelmingly difficult for our students. The development of this mental network forms the basis for what I call deep learning. It should be our goal to incorporate deep learning appropriately in our mathematics curriculum. All too often, we as educators employ a surface level approach to teaching. This may happen as a result of feeling the constraints of time in the classroom. Surface learning is quick and compartmentalized while deep learning requires patience and is holistic in nature. I am a firm believer that students can develop the deep learning needed to learn even the most difficult mathematics given enough time, nurture, and guidance.
We are all born with an innate desire to learn. We often see this desire manifest in small children by the curiosity and inquisitiveness they exhibit. These two characteristics are a natural part of being human. Satisfying our curiosity and engaging in free inquiry brings satisfaction and pleasure into our lives. One of the aims of a college education is to promote lifelong learning. Students who gain a deep inward satisfaction from learning something substantial and challenging will more likely be able to learn independently and grow intellectually throughout their lives. It is my belief that learning mathematics can and should be a pleasurable experience for our students. We need to help our students rediscover their childlike passion and joy for learning that all too often lies dormant under layers of prior educational conditioning.
Social dimensions are essential for creating an effective model of mathematical pedagogy. We can accomplish this by continually encouraging our students and acknowledging their efforts. Students inwardly desire the approval and encouragement of their teachers. They seek appreciation and admiration from their peers in solving difficult problems. The intrinsic pleasure embedded in the learning process depends, in part, on how we respond to our students’ social needs and wants. By satisfying these needs, we create a supportive and inclusive classroom atmosphere. Such an environment is crucial for students to take risk and thereby grow. This allows for the peeling away of prior educational conditioning.
One of the easiest and yet most effective ways for a teacher to more readily create an inclusive environment is by exposing their true being and authentic self. An authentic person has a certain aura of realness about them. With it, there is an influential presence that even a child can discern. By being authentic, a teacher can establish a human connection with a student. This connection is the real heart of the teaching process. Indeed, I agree with the adage that teaching is not so much a science as it is an art; the bottom of which is the ability to tune into another person’s wavelength. The teachers whom I have a fond memory of are the ones who gave of themselves freely. They have made a lasting impression throughout my life. It is this kind of teacher I want to be remembered as by my students.
Kurt H. Overhiser