Hazen and Trefil (2009) describe the beginning of modern science by describing creation and application of Newton’s laws. Newton’s use of the scientific method and the generalizability and simplicity of his laws made them unique in the study of the natural world to that point.
Leher (2009) looks at modeling as a way for students to both gain and demonstrate knowledge. Creation of a good model requires students to determine the most important factors and make decisions about what makes a good model. Students can use representative models and microcosms to investigate.
Galileo (1638) defined uniform acceleration through careful experiments and manufactured observations. He did this refuting common knowledge and establishing a simple mathematical model for acceleration.
A few of the ideas the resonated most with me from the readings were:
· The importance of taking time to really address misunderstandings (Galileo 1638)
· The value of background knowledge in forming new ideas for Newton (Hazen and Trefil 2009)
· The value of multiple models for explaining new ideas (Galileo 1238)
Last week in class, each group developed a slightly different model for understanding and explaining acceleration. We recognized that to know and to show others that acceleration was happening, we would need models, not just explanations using words, even for this very intuitive concept. Galileo used models in his experimental design. He needed a way to slow the effects of gravity, so he created a representative world for his study that would make accurate measurement possible: he “diluted” gravity with incline planes. These same models which allowed him to know that acceleration was uniform allowed him to explain that knowledge to others. Later, when Newton united the heavenly and terrestrial conceptions of gravity, he was able verify his laws using both Galileo’s and Kepler’s models. If the greatest scientific understandings of history came through accurate use and application of models, then we can clearly see the benefit of using models to help our students gain new understandings.