Content Area

"Teachers know and understand the content area for which they have instructional responsibility."

Reflection on the Standard:

It is imperative for teachers to have a thorough understanding of the content they teach. With an in-depth knowledge of their content, teachers are able to present the same material in different ways to ensure that all students comprehend it. A thorough understanding of the content also prepares teachers to answer any questions their students have about the material. Moreover, when teachers fully understand the content that they teach, they will be better able to help students make meaningful connections with the content by identifying applications to areas outside of the classroom.

Artifact:

To illustrate this standard, I have selected a mathematical proof in which I show by contradiction that the square root of 2 is irrational. Please click the artifact icon below to view this proof:
solver.pdf

Explanation of Artifact in Relation to the Standard:

The mathematics classes that I have taken thus far have not only exposed me to a wide variety of abstract mathematical ideas, but have also increased my understanding of the reasons why basic properties in high school mathematics occur. The concept of different number systems can be confusing and overwhelming to high school students when first presented. Having an in-depth understanding of irrational numbers, I can present this number system in a basic way with diagrams, definitions, and simple applications, but would also be prepared to go more in-depth and discuss more abstract examples and applications if necessary to help students fully understand the concept.

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