As fun as the Arithmetic Derivative is, I wanted to finally publish my first post in a series of tutoring/educational blog posts. I want to introduce this category by talking about my philosophy on tutoring...but how hard is that??
Tutoring is such a dynamic activity between a tutor and a tutee - to put this relationship into words would depend on exactly who the two people working together are - their existing knowledge, their desired knowledge, their learning/thinking patterns, and their teaching patterns. As much as mathematicians love to generalize, trying to generalize in this situation would be VERY detrimental to both the tutee and the tutor. The details are incredibly important here and can't be generalized away.
General Philosophy
In a sense, this dynamic act between tutor and tutee is my general philosophy on tutoring. A tutor should help their tutee learn in the most understandable, enjoyable, and productive way possible to the tutee. To be able to do this, the tutor needs to be well-versed in the many different types of tutees they could work with. They need to be able to quickly adapt to the best teaching method in the moment.
One of the many things that could affect the tutor's teaching method is the tutee's learning/thinking style. If you're reading this right now and are hearing a voice read it to you in your head, you are a verbal thinker. This means that you, like myself, have an internal monologue. If you're a verbal thinker, you might understand verbal instructions or explanations easier.
However, it's possible to have no internal monologue at all! Someone who has no internal monologue will instead formulate thoughts and ideas either through patterns, connections, and feelings (a pattern thinker), or through images, objects, places, or colors (a visual thinker).
Additionally, it's possible (and likely) that you learn best through some combination of these thinking styles. I find that while I have an internal monologue and can reason through certain arguments in my head, everything becomes much clearer when I can see the argument written out. Further, I find things stick in my head for the longterm if I can find a way to organize my new knowledge into a pattern that "makes sense". Then the pattern is stuck without me even having to think about it!
And this way of learning is one of the first things we DO learn! Remember learning the alphabet? A, B, C, D, E, F, G,... Even now, did you read that in the tune of twinkle-twinkle-little-star? It's a long-established fact that if you can associate a piece of information to music, then you're much more likely to remember it - simply because we find it easier to remember music. For a slightly higher-level example, who learned the quadratic equation song to the tune of pop-goes-the-weasel?
For more visual learners, sometimes attaching concepts to objects in the room could make remembering those concepts easier. If you can associate a mathematical formula with a picture on the wall - then when you find yourself struggling to remember all the letters and symbols and signs, you came look up at the picture and your brain will fill in the gaps.
While I was a grad student at the University of Michigan, one of my office-mates and I would talk about how how many of our classes "felt" differently, in terms of both color and music. Complex Analysis was like a smooth jazz and for me was always green. If my notebook for the class wasn't a green cover, it just didn't feel right. Differential Geometry always had a blue feel - Real Analysis was definitely heavy metal and red. And the crazy thing is that I found myself more in the right head-space for my classes when I was listening to the music that I naturally associated with that subject.
Next time, I'll talk about the benefit of asking leading questions, the very-related Socratic method, and other aspects of my tutoring philosophy.
Thank you for reading!
Jonathan Gerhard