1.2: Teacher as Learner
Describing the teacher as learner almost feels like putting the cart before the proverbial horse. In business, we do not describe another professional’s ability to perform with such a paradox. Is it important that a doctor be a good patient, a manager be a good employee, a photographer be a good model, or a politician a good citizen? The relevant transfer of roles or experiences to gain perspective through empathy and understanding is obvious, but it is not paramount to the overall performance of most professionals.
What is important is first a commitment to life-long learning. This is vital to any professional in order to maintain expertise. The inability or unwillingness to become familiar, if not fluent with the newest concepts only invites the younger, fresher, more up-to-date underlings to pass you up like you are standing still, when in fact you are regressing. Scientifically, the life pattern of all living things fluctuates between states of growth and decay. If our minds are left without stimulus and not challenged to grow, then knowledge begins to decay. There is no static state in which living organisms can survive. So within all fields, there is a driving force to maintain cutting-edge technology and practices. “If it ain’t broke, don’t fix it,” has not propelled many experts or corporations to the top of their field, at least not for very long.
A second characteristic of a professional is integrity. True professionals develop sincere, trustworthy and reliable relationships and deliver strong results. Their contributions are respected and authoritative, and their behavior is consistent with their beliefs about their field. My wife once had a hair stylist who always had something bad to say about a particular cut, style or person that my wife (or any other client) wanted to emulate, stating the negative effects it would have on the condition of her hair. Now, this stylist’s own hair was always discolored and frizzy. Further, she rarely had a suggestion of a product or slightly altered style to make my wife’s ideas work. We called her the Hair Nazi. Although she gave a great haircut for a good value, she continued to lose credibility and ultimately was not perceived as a very professional stylist.
So what is it about teaching that makes being a good student so critical? I believe the key lies where these two characteristics of professionalism meet specifically in the learning environment, where the teacher is the facilitator of the learning process. As professionals, teachers should commit to life-long learning and epitomize integrity in the classroom. Teachers must be model learners. We must continue to learn for our students, with our students, about our students and from our students.
Teachers Learn for Students: We begin to model learning in our content courses by learning for our students. We study our content area with great interest and passion to become one of the only content experts on our students’ lives. We want to transfer the full depth of our knowledge and lay the most solid foundation for their continuing education. We understand that both content and context will change with time, and we must stay abreast of evolutions in both so that our students are prepared for the challenges in their futures.
As a student and new teacher, we are encouraged to always be reflective, and from that we further develop our skills and talents by learning how to improve our techniques. Our lessons are critiqued, our delivery is observed, our methods are questioned, and our objectives are evaluated for clarity and curriculum. As I prepare micro-lessons for class, I use past feedback from students and instructors alike. For example, Dr. Watt once explained to me that, although my writing on the board is relatively clear, I should reconsider the way I write variables. Suddenly it became clear to me why all of my college math professors writing on the board is virtually indistinguishable. My x, y, and z are becoming x, y, and z; just like theirs. They learned to do this because it is important in transcription to prevent confusion buy differentiating a sloppy x from a y or v on the board.
Geometry is my particular passion, so when I was presented with a Geometer’s Sketchpad software project to construct a congruent triangle, I approached with greater restrictions. The underlying validity in Euclidean Geometry is about the consistency of congruency, and in particular with the collapsible compass. We are accustomed to measuring a distance on the compass then removing the compass and measuring the same distance in another area. The argument is that a collapsible compass may not maintain accurate measurement when it is picked up. The only accurate way to construct congruency is through relating other congruencies. To that end, I set out to try to construct a congruent triangle using a collapsible compass in the Sketchpad. The results are enclosed. Although the instructor’s comments are kind, I was more proud of the validity of my arguments and the fun I had doing the assignment. Most of the other students just copied segments and angles to another space, thus emulating the behavior or a non-collapsible (or locking) compass.
I also feel fortunate that I am entering the teaching field at a time when teachers are coming out of isolation and embracing outside participation in their classrooms. The collaborative efforts teachers are making to engage other disciplines, student/parent potential, and community opportunities are better meeting our students’ needs. A lot of preparation is generally required, and many teachers are stretching beyond the bounds of their subject matter to bring more meaningful experiences to their students. Throughout our careers, we should continue to embrace interdisciplinary tactics and alternative methods that create active and practical learning environments for our students, so they will remain competitive in a shrinking global market.
Teachers Learn with Students: We further model learning by modeling not-knowing. Teachers must remove the intimidation of ignorance (unawareness) from the classroom, and the best way to dissolve that fear is to display our own incapacities as teachers—our humanity. Surely I am the content expert, but I do not claim to understand all of the applications and implications of my subject matter in every field. And I will be the last one to recall a formula from memory.
My father is a NFL official, and he is often asked for his position on Instant Replay. While he believes it provides a higher level of precision, it also removes the human element from the game. Players as well as officials are highly trained, but alas are human, and a need not be subject to constant scrutiny. Instant Replay statistics will verify the fact that these men officiate with amazingly high accuracy. I always thought this was a wise perspective.
I believe that there is a human element to mathematics as well, and we will learn from the mistakes we make. I also believe that there is a human element to learning. We all strive for knowledge, yet we can never know everything. At times we may even come to the same solution through different means. We can explore together their similarities and validity. These philosophies should be embraced in the mathematics classroom.
My students and I are on a journey together, and questions will be explored to find sensible answers. I don’t want to be a hand-waving teacher that responds, “That’s not important until you get to Calculus.” The answer may be more appropriately explained at that level, but a high school mathematics student should have the foundation to withstand a reasonable algebraic and/or geometric explanation or demonstration. Their experience will be richer, preparation more thorough, and knowledge more fully inculcated through mutual discovery. As the teacher, I anticipate being stretched outside my comfort zone as unfamiliar applications and new technological developments pose fresh, thought-provoking questions from my students, and I am committed to learning alongside them.
Teachers Learn about Students: Another technique I am working on is strictly non-math related. Dr. Phil Summers is known for learning more than just names and faces in his large Psychology lectures at Indiana University and Vincennes University. This phenomenon not only impresses students, but it is an important exercise in demonstrating his willingness and capacity to learn, and his sincere interest in knowing his students. He can call any one of them by name at anytime, anywhere on campus, and they respond with a higher level of accountability to his efforts.
Students also learn information in different ways, so we must have an acute sensitivity to the students’ personal needs and learning styles. Resources such as Performance Learning Systems’ Kaleidoscope, True Colors, and The Alert Scale of Cognitive Style activities may be used to evaluate the learning styles of the students. Being able to direct a lesson in a way that reaches out to one or more students in a specific manner without distracting from the other students’ experience enhances the learning environment for all students.
Socially, we strive to be accepted into our students’ lives so that we can more effectively communicate with them. We must learn about their goals, language, pastimes, etc. in order to more effectively meet them in their world. We are trying to build a professional relationship and a rapport with them so that we can deliver our message in ways that will be meaningful and understandable to them.
Teachers Learn from Students: I believe there is a role for students to lead in the classroom, and as teachers, we learn so much from observing them by carefully watching how they communicate and draw interest to the subject matter.
Students have brilliant insights. During a recent observation, the teacher was lecturing on the types of angles that are formed when certain lines intersect. When he explained alternate interior angles then moved on, a girl raised her hand and asked, “Is there a such thing as alternate exterior angles?”
Immediately I thought to myself, “Ask her back!” I would have said, “What do you think? Where might they be? Do you think they are congruent? Why? How can we prove or disprove it?” Then when we were finished, I would have said, “Now, your book doesn’t cover them specifically since it’s relatively intuitive from the definition of the other angles we discussed, as you have all just proven. Since it’s not in the book, we can claim this discovery of new knowledge as our own. From this day forward in this class, these angles we just defined will be called [insert girl’s name here] Angles, and you can use them by name in any proof.”
Instead, the teacher said, “Yes, there is such a thing. Some books cover them; others do not because it’s relatively easy to see from these other angles.” Boo! This was a huge missed opportunity for a student to deliver a peer-level, intuitive observation.
As professionals we commit to life-long learning for the benefit of ourselves, our employers, and those we serve—the students. We should look for opportunities as common yet external as continuing our own education as well as within the walls of our own classrooms. We balance this commitment by understanding our natural limitations and openly asking for assistance from a variety of resources that includes the students themselves.
