Looking at the Ngram results for “teaching and learning” one might expect teaching, and by proxy the teacher, to be less relevant in the future of academia. I think this is a dangerous line of thinking. Effective educators find a way to strike a balance between their own teaching and the importance they place on the students’ ability to be self-sufficient learners. The best of these actually use this balance to ignite a passion for life-long learning among their students. Although I do not think I have mastered such a balance in my own teaching I hold up this harmony between teaching and learning as the goal toward which I strive.
My personal philosophy of teaching and learning revolves around the belief that there are three primary components of a successful approach to striking the balance between teaching and learning.
- Successful teaching and learning are functions of engaging anytime, anywhere content.
- Successful teaching and learning are functions of fostering a Christian community of peer mentoring.
- Successful teaching and learning are functions of rigorous and strategic planning.
Successful teaching and learning are functions of engaging content. When I look at the results of the graph of teaching vs. learning on the previous page my first reaction to the relatively flat importance of teaching compared to learning is to suggest that teaching plays “catch up” far too often. What I mean by this is a new technological advance incites the hunger for learning and traditionally the world of academia is a slow adopter.
Mathematics as much as any subject in academia suffers from the predisposition of students who believe the material to be fundamentally boring, of little practical use, and impractically arduous. There is even a medical term, math anxiety, associated with feelings of anxiety that one cannot perform efficiently in situations involving the use of mathematics. No other subject engenders such a quick response from the student populace.
It’s my belief that students’ perceptions of mathematics can be directly tied to the greater problem of academia playing “catch up” and are symptoms of a problem having absolutely nothing to do with math. If you study mathematics you come to appreciate how wondrous it is. From a Christian perspective, you really do connect with the famous Galileo quote that mathematics is the language with which God wrote the universe. When you know mathematics the way I have come to know it, you cannot help but see a topic that is every bit exciting as it is informing. If in my teaching I do not impart this excitement or invite a sense of wonder, then I do a disservice to my students. For many students the traditional “blackboard” lecture accompanied by the “work 1-50, odds” model for teaching mathematics is all they have known. I would guess in that environment there are few students who can effectively learn mathematics and fewer still that can appreciate it.
Given the wonderful resources available at Abilene Christian University, I have been able to create a massive library of video tutorials (with more being added every semester), set up web content while working toward a fully functional content blog, engage in discussions on course blogs, utilize mobile devices in the classroom, provide students with high quality lecture notes, and conduct a variety of creative assessments. While each of these will be discussed in more detail elsewhere in this portfolio, their importance to, and impact on, my personal philosophy of teaching as a function of engaging content cannot be understated.
While at ACU, I have used and become proficient with LaTeX, Beamer, Excel, Maple, MATLAB, Ti-Smartview, iOS devices, MathStudio, Photoshop, Dreamweaver, Adobe Captivate, Camtasia, WordPress, Turning Point, Prezi, Keynote, Google Forms, etc… and though this list is in no way exhaustive, it serves to illustrate a salient point: creating engaging content for students is impossible without maintaining a commitment to staying current on the latest educational technology.
Use of technology alone is not a recipe for successful, engaging content. When you imagine something that was completely engrossing or riveting, like a great book or a new experience part of what makes the moment so enjoyable is the sense of story that is created. In many ways, I believe a great teacher is a great storyteller. Whenever possible, I try to tell my students a story, to paint a picture of the world where math is a central cog of what was and what is yet to be.
For example, did you know that in the original design of the stealth bomber a simple calculus mistake, one any first year calculus student could find, actually minimized the mile per gallon efficiency of this “long range” bomber? Or did you know that the original proof of the Four Color Theorem consisted of 2000 cases and over 100,000 subcases most of which were checked computationally. The proof of this theorem raised a somewhat philosophical debate regarding the validity of a proof which no man has read, and a larger question of “how do we know computers do not make mistakes”?
The final component of delivering engaging content is that it needs to be available anytime, anywhere. If you look at the graph, which is only through 2010, I would strongly wager that if we look at the same graph ten years from now there will be an even stronger upward trend on learning. The sheer abundance of information at our students’ fingertips is expanding more rapidly than at any other point in human history. The pull to “learn on my own time” is so strong today that teacher’s are not only forced to re-think their classroom experience but embrace the idea of a classroom that extends beyond the 3 hour per week, face time, chairs in rows model that has hardly changed in the last hundred years. Once again, academia is playing “catch up”. As a result, all content delivered in my classes is available on-line across multiple devices (designed precisely for those devices). When I sit down to design content and not restrict myself to the confines of the “traditional classroom experience” I can deliver a product that has more breadth, more depth and has the accessibility that students are demanding from their educations today. I look forward to the opportunity of sharing some of this content with you in this portfolio.
Successful teaching and learning are functions of fostering a Christian community of peer mentoring. Quick question. What separates ACU faculty from those at other degree-giving, four year institutions? Faculty knowledge? Yes, our faculty are skilled professionals, but I think you can find top notch scholars at a variety of institutions. Degree offerings and programs? I think the answer to this is clearly no as much larger universities are able to offer a wider range of academic programs and resources. In my opinion the thing that separates ACU from its peers in higher education is the intentional focus on Christian mentoring. When I first started teaching at ACU I was so focused on making sure the student experience from a content perspective was perfect. Lecture notes carefully and meticulously planned, challenging homework assignments with carefully scripted opportunities to see connections with in-class observations, and while these are a necessity of good teaching and part of the first and last points I will make in this narrative, I found that my teaching did not radically improve until I embraced the idea that my role as a teacher is first and foremost as a Christian mentor.
So what does a Christian community of peer mentoring even look like? While I’m sure this means different things for different faculty, for me it looks like an office full of students that stop by to ask a quick question about an assignment but wind up staying for another hour just to talk and know they are being heard. It looks like a classroom full of students enjoying the food you prepared for them for class that day. It looks like the late night Sunday study sessions you attend with your students before a Monday exam. And best of all, it looks like the header at the top of this page. That is the ACU difference. That is MY difference. Ten years from now will my students remember the decoupling method for LTI systems? Probably not, but they will probably remember me being at their wedding and the genuine interest I take in their lives.
Successful mentoring requires time. Having time to make mistakes and correct them, time to seek advice and give it, time to reform policies and refine them, and time to reflect on the outcomes of the student learning process is a necessity in good mentoring. Time to make changes and evolve does not imply that a teacher or student will. Some people are stubborn in their ways, refusing to adapt to the ever changing educational landscape. On many occasions I have given a lecture, or assigned a project that did not go as expected. If I then assign the same project without taking time to remedy the disconnect my students are experiencing, that is not being a good mentor. Not only have I deprived my students of a better experience, but I’ve also deprived myself of an opportunity for growth.
I believe students learn more from their mistakes than from the problem they get right without much difficulty. Mistakes force us to learn. After five years of teaching students plotted in every quadrant of the ability and motivation scale, I have changed the way I view my contribution to the learning process from the academic side as well. While I still consider my self a primary reference for the student and lecture from that perspective, I now focus a great deal of effort on modeling how a mathematician thinks and learns. I am after all a mathematician and that is a valuable part of my contribution to the students in a mentoring role.
I look forward to the lessons that new years of experiences will bring, but I am blessed to be in the position of not being on an academic island. I have wonderful colleagues whose wealth of knowledge and experience has served to bolster my own walk in the profession and my perceptions of what it means to be a Christian mentor. I’m not ashamed to admit when I do not know something, because there is room for growth in all of us. I try to pass on this perspective to my students, so they will actively seek help and not be afraid to ask for help.
So whether it is writing recommendation letters for a student, guiding a student through a research project culminating in a transformative experience of presenting their work, or simply sitting with a student who is the midst of a life crisis my personal philosophy of teaching is that I am first a Christian and second a mentor and then an academic. I’ve found that this commitment to Christian mentoring has not only transformed my teaching, but myself also, and I look forward to many more full offices and equally full hearts in the future.
Successful teaching and learning are a function of rigorous and strategic planning. I pride myself on being a detail oriented person. I value excellence in all things. As Colin Powell said,
If you are going to achieve excellence in big things, you develop the habit in little matters. Excellence is not an exception, it is a prevailing attitude.
– Colin Powell
Many of my students have commented on how easy to understand and clear my lecture notes are. I believe that giving my students a clear outline of topics to be covered and how the pieces fit together helps make the semester long journey progress more smoothly and adds purpose to each step along the way. In this way the educational experience is less like a disjointed collage of learning experiences.
I plan the pace of the learning experience so that students are given ample feedback in the form of homework, quizzes, mini-projects, and are afforded the opportunity to ask questions so that they may evaluate their understanding. Such an approach requires a constant attention to planning. Every lecture must have a purpose. Every assignment must be more than a grade. Planning a sequence of questions that culminate in that “ah ha” moment requires a teacher to put themselves in their students’ shoes. To take in things and plan things according to how you would feel if you were taking the course.
In mathematics more so than other disciplines the dependence of future material lies squarely on students’ mastery of previous concepts. This places a large portion of the responsibility for learning on the student, but the teacher has a vital role in this process: planned guidance. Directing students in such a way that it fosters early successes and leads to future triumphs is an integral step in the planning and implementing of a successful educational experience. Because I expect so much out of myself I am not afraid to expect the same out of my students. Prodding your students to the same level of personal responsibility in their own work and demanding they take ownership of their work should be a primary goal of any educational experience.
This narrative reflects my commitment to, and love for, teaching. I believe my growth in each of these areas has helped transform my view of teaching and learning, made me a more effective teacher, and will bring me closer to a prevailing attitude of excellence in teaching.