The Galileo reading documents the process by which Galileo came up with his theories of the properties of objects in motion. He begins by defining uniform motion, then give four axioms and uses these axioms for formulate theorems. He then uses his theorems for uniform motion and applies them to accelerated motion, and walks the reader through the process by which he uses mathematical models to provide theorems for accelerated motion.
The Hazen and Trefil reading is an anecdotal walk through the early history of science, starting with the independent work of astronomers and artisans working primarily in their respective trades, and then combining these two fields to form the study of mechanics. From here, the authors summarize the findings of Galileo and Kepler, and explain how Newton used the models formed by these two scientists to form his laws of motion, detailing his process of scientific inquiry which became a frame for the modern day scientific method. The authors close by broadening the definition of modern science as an orderly study of many varieties of chaotic natural systems.
The Lehrer (2009) article presents the problem of how to educate students at developmentally appropriate levels while not underestimating their abilities to grasp scientific concepts, and gives many methods for effectively teaching science curriculum. These methods used various methodologies to develop models of scientific systems. The author suggested that physical models could be formed to represent specific ideas, and that representational models, such as mathematical theorems, would be useful to promote conceptual thinking and to build on patterns.
The Lehrer text introduced the idea of forming physical models from observations and then utilizing representational models to apply the concepts to other applications. The Hazen and Trefil text then explained how Newton used this method by taking models from other scientists and building upon them. The Galileo text gave an in depth look at how that particular scientist used observations to create physical models, then observed these physical models to form representational mathematical models. The common theme in all three of these readings was the usefulness of models to explain scientific phenomenon. While these texts were elevated, the idea of using physical models to lead into representational models is a very good method for teaching students of all ages the scientific method and giving them the tools for scientific discovery.