Project Abstract
Albert Einstein is widely known as one of the most influential thinkers of all time. But what did he discover? In this project students learn the basics of Special Relativity. Students research, prove, and present their findings of this counterintuitive reality.
What did you teach and how did you teach it?
I taught this from a formal mathematical model. We began with assumptions, and drew conclusions from those assumptions. Then we looked at the consequences of the conclusions and experimental evidence that verifies their truth.
More specifically, we began with a discussion of Galilean relativity. Students solved basic algebra problems that built the basic terminology of frame of reference. From there we researched the Michelson Morley experiment. Students read three different descriptions of the experiment, and mathematically modeled it using algebra and trigonometry. They then grappled with the failure of this experiment to produce results, and looked at Einstein's explanation, that the speed of light is invariant.
The next step was to examine a thought experiment, the light clock. Using Einstein's hypothesis, they were able to model the behavior of a clock on a moving space ship from the perspective of a passenger, and a stationary observer. From this, they derived the Lorentz factor for the special case of time dilation.
At this point, we took a few days to look at the consequences of what had been shown. Students solved a series of conceptual problems that illustrate the counterintuitive nature of these findings, including a specific example of a "Twin Trip", where one identical twin travels into space and returns at a different age than his twin who remains on Earth.
From here we delved deeper into the equations, viewing length contraction, mass increase, and tentatively linking to e=mc2. Our mathematical proofs became more limited as the concepts became more challenging, but students did get a chance to grapple with some very complex ideas. Students were divided into teams that researched not only proofs of these topics, but actual experiments that demonstrate the concepts.
The final step was to present our learning in order to teach the basics of the concept to an intelligent but uninformed audience. Students chose from our in class examples a series of examples to explain.
What concepts and skills did the students gain in this class through this project?
The main goal of this project was to show how using basic math skills we could prove the existence of very interesting ideas. While algebra may not be the most exiting subject to many students, time travel and the fourth dimension are. In many ways, the goal of this project is to convince students of the power of basic math to describe the world around us.
As far as specific skills, the primary one was mathematical logic and proof. Students were always challenged to answer the question of why a step they proved was valid. The focus was on a chain of logic that began with a simple observation, namely that the speed of light is constant, and ended with the idea that time, length, and mass are not constant, and can be manipulated.
Mathematically, the skills used were algebra and geometry. In the course of their proofs, students had to solve complex algebra using the Pythagorean Theorem, factoring, rational expressions, and quadratics. Students had most of the skills, but this served as a good start of the year refresher.
How is the curriculum for this project academically rich and grade-level challenging?
While the technical math skills required for this project were well within the reach of twelfth grade students, the conceptual framework is extremely challenging, and presented the most difficulty for my students. When they walked through an example, they were able to understand. However, when asked to recreate an explanation, they struggled. It took many iterations for their explanations to become precise and correct. The concept is so abstract and complex, that this was to be expected. However, the high theoretical level also made the work engaging.
To what extent was there integration across disciplines in your class through this project?
This project has a clear connection between math and physics. Ultimately theoretical physics is in many ways simply math, and this project is essentially theoretical physics. However, by requiring students to teach the content, I brought in a technical writing and presentation component. While I did not focus on this, the act of explaining to an outside audience required a much deeper understanding of the concepts. In this way the integration of subjects enriched their learning in the primary discipline.
Which Habits of Heart and Mind (HoHM) and Design Principles were utilized in this project?
From a literal sense, the habit of perspective is the essence of this project. Ultimately, the whole idea of relativity is that viewing physical properties that we view as unchanging from different perspectives leads to changes. This emphasizes the literal significance of taking into account alternative views from a purely physical sense.
As a math project, there was a substantial emphasis on evidence. As each conclusion is ultimately unbelievable, each required a strong mathematical proof with it. This is the purest form of evidence in the academic world, and something that can be applied across disciplines.
The actual production of our presentation was done in groups, and required a great deal of effort. Students were challenged to explain concepts to each other and to revise their work multiple times. Given the level of conceptual difficulty, it also required a great deal of perseverance for the students to put all the pieces together.
How did you incorporate refinement through this project?
Early in the project as we studied the concepts, students turned in written work. If the work did not demonstrate an understanding of the concept, it was returned for revision and resubmission.
Once we began the presentation process, students gave three talks. The first was to their classmates, the second was to juniors, and the final one was to a panel of teachers. Each experience gave them feedback to prepare them for creating their presentation. Each group created drafts to be shared with the class that were then updated with feedback, resulting in a final product.