What is good teaching? In the first years of my teaching, I thought of my role in the classroom primarily as being able to explain the material to students well, so I spent much preparation time with organizing the material in order to present it to students effectively. My review sessions – where I presented a concise overview of the material, example problems, and tips and tricks – seemed to have been very successful. But were they really?
Active learning. Over time, my view of what it means to be successful in teaching has changed considerably. As far as student satisfaction is concerned, I got very good feedback, but this does not automatically mean that student learning was also optimal. In fact, considering the wide body of education research on the benefits of active learning over passive listening, a lecture-style review is almost certainly not the best in terms of retention or conceptual understanding. Interestingly, however, when I incorporated elements of group work and peer learning into my review sessions, students were much less enthusiastic and satisfied. In fact, a student explicitly told me that reviewing like this was a waste of time.
Of course, my activities may not have been designed perfectly, but this is likely not the only factor responsible for students’ resistance to non-traditional ways of learning. Active learning methods such as group work create anxiety on two fronts: on one hand, students have to interact with each other, which does not come easily or comfortably to many of them. On the other hand, they are also asked to perform tasks that they have not seen before, such as meaning-making and argumentation. It is not hard to see why this creates more anxiety than simply having to sit and listen.
I found that one key step to overcoming these anxieties is to share the theory and evidence behind using active learning methods instead of traditional lectures with the students, especially in teacher education classes. Not only does this provide an opportunity for students to reflect on the nature of their own learning, it also allows them to provide me with more elaborate and thoughtful feedback, on which I greatly rely in my teaching.
"I'm not a math person." Students’ anxiety towards math, however, often has a source much older and much deeper than new learning methods. Likely stemming from their previous experiences, they arrive to college math classes with the idea that math is something to fear, something extremely boring, or both. This hinders students’ development and success. Therefore, I make it a priority to teach the content in a way that is also fun and enjoyable.
Making math fun. As an example, I have created quests out of worksheets, where each correctly solved problem told the students which problem to solve next, and the answer to the last problem answered a fun fact multiple choice question (e.g., “Which of the following five weird foods does not exist?”). Other examples include the use of cross products and scalar products of vectors in Angry Birds and first-person shooter video games or the illustration of the so-called Alternating Series Test by the story of a crazy bee flying back and forth between two batches of ice cream, turning around more and more often, unable to choose one.
Student-teacher relationships. Another important lesson I have learned was the unintended consequence of an otherwise not too pleasant event: an ankle fracture during my first winter in Madison. I had to miss the first two weeks of the semester, and I was teaching on crutches for more than a month after that. At first I thought it was going to be a disaster, but my students were really understanding. Suddenly I was not only the usual powerful and distant authority figure in the eyes of the students, but a human being with human issues. They saw me struggling to walk, and not only were they happy to help out when needed, but they also appreciated that I was there to teach them despite my condition. This made me much more empathetic towards students as I started to see how they also have many things to juggle in their lives. Things happen to them unexpectedly, as well, and they sometimes struggle with the class, not unlike how I was struggling to get to class and stand on my feet.
Technology. In order to broaden my repertoire as a teacher, I frequently chose to teach classes I have not taught before and got involved with special programs like WES (Wisconsin Emerging Scholars) for Calculus or WisCEL (Wisconsin Collaboratory for Enhanced Learning) for Algebra. Teaching Math 112 in WisCEL was an especially influential experience for me. This was my first course that heavily relied on technology: the textbook, homework, quizzes and tests were all provided by commercial learning software. I learned how technology in the classroom is a double-edged sword depending on how and when its being used. I think it was certainly beneficial for students to receive immediate feedback on their homework, which allowed them to reflect on their progress and understanding right away. However, the software only offered a series of lower-level problems very similar to each other. My impression was that solely doing repetitive practice of problems did not result in more than surface-level understanding, only a short-term ability to solve specific kinds of problems.
Students need to tackle more complex problems requiring higher level thinking to reach a deeper understanding of concepts, allowing them to use their skills in different contexts. Technology can be an asset to accomplish this goal, as well: for example, open-ended questions (e.g., “Explain the geometric meaning of the gradient.”) can be asked in an online homework, with a follow-up question asking to rank a list of possible answers to the same question. This ranking is graded by the computer and allows students to reflect on their thinking.
Learning as a teacher. Lastly, I realized that to become a good teacher it is not enough to develop a certain set of skills and methods. The key to remaining a good teacher is being attentive, open-minded and flexible in this fast-changing world. Generations of students, technologies and educational paradigms change in quick succession, and I need to be ready to constantly adjust and update my teaching with the changing circumstances.