“Mathematics is much more than a language for dealing with the physical world.
It is a source of models and abstractions which will enable us to obtain amazing new insights into the way in which nature operates.”
― Melvin Schwartz
I wonder, is insight the bridge between knowledge and understanding? As a teacher I feel sometimes as if I am spending a lifetime trying to actually understand everything I learned in high school. I currently teach high school physics – and I love it. I don’t have a degree in physics but it is the content I enjoy the most. The point of this post concerns a MOOC I enrolled in just for fun – Physics I with Labs taught by Dr. Michael Schatz from the Georgia Institute of Technology.
The interesting part of this course is in the way Dr. Schatz uses technology in instruction. In the class we combine theory, experiment, and computational modeling – all using technology. The course uses video to deliver content; there’s not much new there, although the videos are very well done. He uses stop motion and color creatively to engage the viewer. This is nice, but at some level a lecture is still a lecture.
We collect video of specific types of motion and analyze the motion with free software. I found this to be very engaging. First, it is interesting because I have control over the video capture. I get to capture the motion of something that is interesting to me – from my surroundings. It is genius because from a pedagogical standpoint it is “cheat proof.” No two students will capture the same video. Video analysis is great because we can leverage the power of the computer to generate graphs and data from the video. This has the effect of making math “real.” I began using video with my freshman in IPC and saw immediate engagement and improved understanding of concepts like the slope of a line and parabolas.
The BEST part of the class is the computational modeling. I wanted to learn coding and I thought this would be a great introduction. In the course we use VPython to model the motion we captured and observed in the video. I never could have anticipated the effect this has had on my understanding of physics.
Seymour Papert has advocated teaching kids coding, not for its own sake, but to carry powerful ideas. I now know what that means. In this class we take simple, fundamental principles – Newton’s three laws – and apply them in the code. Many of us are familiar with Newton’s second law: F=m*a. We learn it in high school, work a few problems and then move on. We are not in awe of this equation. Most students find it simple and perhaps even boring. The magic happens when we use a computational model and a loop to reveal the wonder of such a simple mathematical expression.
The computational modeling has granted me insight. I have been able to see the beauty in the math. I have seen the power of such a simple formula to explain seemingly complex behaviors like planetary motion. Like Bruno, I have seen the world in a new and wonderful way. I have seen content that I thought I understood from a new and exciting perspective.
From the standpoint of pedagogy there is much to learn from this experience. My insight came as a result of my deep involvement in the content. I took the video myself – it wasn’t handed to me. I analyzed the video and collected the data – it didn’t come from a textbook. I wrote the code. I inserted the formulas and relevant information – I didn’t use an app or software written by someone else. In short, I did the work – it wasn’t done for me.
Perhaps that’s the point of this post. Do we rob students of understanding by doing too much work for them? In the name of covering content do we tell too much? The longer I teach, the more I realize students have to do the heavy lifting to truly learn anything. We look too often to technology hoping to make learning more “fun” – more palatable. I am reminded we shouldn’t expect technology to engage the student. We shouldn’t expect technology to deliver the knowledge in an exciting way. We should expect the student to use technology and the content to reveal powerful ideas. They need to do and create using technology - as well as consume. We need to create opportunities for students to achieve insight. We must remember insight is something they earn – not something we can give them.