The Shoulders of a Giant
Updated: Jun 4, 2020
Read about our founder, Rich Dlin's perspective on math and on the heavy responsibility of teaching to help each student realize their potential
Throughout my decades of teaching one thing has guided my teaching philosophy at every stage of its ongoing development: I must have the shoulders of a Giant. Not in the literal sense of course but springing from Sir Isaac Newton’s famous quote.
Newton could not have made the advancements he did had it not been for his predecessors – the mathematicians he studied, and the teachers he learned from. His Giants. What a responsibility they had! And what a profound contribution they made to the progress of mathematics through to modern times. One wonders, did they know? I believe they did, because I feel it every time I prepare a lesson and then step into a classroom or lecture hall. I may or may not be teaching the next Isaac Newton, but every student has the potential to achieve a greatness unique to themselves, and whether explicitly or implicitly, they are trusting me to help them realize it. I must provide the shoulders to stand on. The shoulders of a Giant. This, along with my passion for mathematics, and my love of learning and thought, informs every single lesson I teach.
…every student has the potential to achieve a greatness unique to themselves, and whether explicitly or implicitly, they are trusting me to help them realize it.
Why I Teach Mathematics
Many high school students often ask the purpose of studying mathematics. In the later years of high school and early university, some have found their own answer, while many more are still looking for the answer or looking to confirm what they believe. Some know they are “good at math” but may be uncertain as to how that can help them in the bigger picture of life. Others feel that math is a mystery to them and often conclude that it is not important to them. As an educator, one of the ways I provide to them the shoulders of a Giant is to show that the study of mathematics offers so much more than a surface inspection reveals, and is certainly not limited to a tool for engineers, scientists, and analysts. To me these applications are “happy side-effects” more than a “raison d'être”.
“What is this good for anyway, and when am I ever going to use it?”
Math is not just about “getting the right answer”. It is about proving that a result is correct. This emphasis on proof is critical. In the real world, being right is rarely enough if you cannot convince others. Clear, methodical, audience-appropriate explanations are invaluable in this regard. Developing and presenting proof is as much an art form as it is a science (perhaps even more so), and this informs every explanation I craft, at every level. When a student has the foundation looking for the “why” of things, the “how” follows easily. This proof-based approach ultimately improves students’ ability to construct arguments or explanations in all facets of life. It has a profound impact on their communication skills, as well as their approach to confrontation. Arguably, most every interaction with others is some form of proof, so that proof dominates all good communication.
How I Teach Mathematics
The threefold essence of a strong teacher is passion for learning, for students, and for the subject matter. It is important to teach and model all three of these, along with a good dose of humour to establish humanity. The depth of experience and introspection available through the study of mathematics is profound, and this, coupled with a constant scrutiny of my ability to communicate it to a range of personalities, learning styles, and innate interest and ability levels, informs my approach as an educator.
When I work with students, whether one-on-one or in a class, I am simultaneously aware of many things. With respect to content: What specific math skills am teaching? What appreciation is inherent in this topic? What further reflection can be spawned from this material? With respect to pedagogy, there is the constant flow of non-mathematical problem solving that happens in the preparation stage, and often even more so in the real-time delivery: Who am I teaching? How do they learn? If it is a group, what is the multi-celled organism we call a “class” telling me as we progress through the lesson? Some students ask thoughtful questions. Some stare defiantly, wondering what use this could possibly be to them. Some want to ask but don’t know how, and so stay silent. Some don’t know what questions to ask. Some shift uncomfortably at key moments. Some turn and whisper to a neighbor. Some just look bored. All of them deserve my attention – my shoulders. So, I process all this information, and it informs the progression of my lessons. My experience enables me to both prepare learning-style comprehensive lessons and allows me to adjust in real time based on what I am hearing, seeing, and feeling from the student(s). Students often remark that I seem to answer questions they were only thinking they would like to ask. It is because while I teach, I listen with all my senses. And I am aware that students learn with all of theirs.
Technology as a Teaching Tool
It is a joy to teach in modern times, with tools provided by technology that Newton could not have dreamed we might have. With technology, my guiding principle is also informed by the notion of standing on the shoulders of Giants. I use technology extensively when I teach, but also carefully. Technology is “cool” but should only be used in teaching if it is useful. That is, it too can be a Giant. To this end I am always thinking “If older mathematicians had access to this technology, how could they have used it to go further, or think more deeply?” For example, how much more might Newton have discovered if he had graphing software, capable at a minimum of graphing any function we can think of in an instant? How much more could Archimedes have accomplished if he had been able to investigate the properties of geometric shapes and solids virtually, with the ability to impose certain parameter restrictions and then investigate infinite combinations in seconds? These and so much more are available to us now, and these too are Giants on whose shoulders our students stand. This is why so many of my lessons incorporate demonstrations and investigations that use technology like graphing software, computerized algebra systems, and spreadsheets (always and only after we earn the right to use it by looking at and practicing how to do it manually). Anything that frees our brains from the tedium of calculation or careful sketching, thus allowing us to explore combinations and configurations that would otherwise be virtually insurmountable, finds its way into my class.
Teaching is an honour and a heavy responsibility. Each student counts on me to help them realize their potential. Consistency, passion, reflection and refinement are how I continue to improve each year. Passion for mathematics, for the multi-dimensional people who are my students, and a good sense of humour are my tools of the trade. I am a Teacher. I could not imagine being anything else.