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.

Faith how would you then state that Lehrer's work was influenced by Hazen and Trefil or by Galileo ?

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