Subject Matter Knowledge
Informal and Formal Reasoning
Being a Mathematician it is important to always double check facts. As a mathematics teacher I want to instill the value of confirming ideas and answers to assure precision. I have included a couple of artifacts on how I apply informal and formal reasoning. Below is an Applied Mathematics proof that I solved during a mathematics course. In the proof I showed the rate at which a dripping bucket of water decreases by finding the change in potential energy and the transportation of kinetic energy. I also include a prove I did in geometric systems proving the Side Side Side Theorem for triangles. These artifacts show how I apply informal and formal reasoning in different areas to check facts.
Multiple Representation
The biggest part of mathematics is representing multiple things in different ways to appeal to every type of learner. Most mathematical ideas go hand and hand. Its good to make connections with previously learned topics, so that students will always be current on previously taught information. Below I have included two ways to solve systems, by graphing and solving them using the substitution method.
Natural Phenomenon
Many Natural Phenomena are described using mathematics. For example, electric current produces a magnetic field. This magnetic field can be visualized as a pattern of circular field lines surrounding a wire. One way to explore the direction of a magnetic field is with a compass. The Biot-Savart Law can be used to determine the magnetic field strength from a current segment. The Lenz law can be used to induce current if and only if the magnetic flux through a loop is charging. And last but not least faradays law induces in a conducting loop if the magnetic flux through the loop changes. Current induces magnetism, change in charge gives you magnetism, and change in magnetism gets current. Below is two experiments I did to show how current induced magnetic field changes with current and also with. Connecting Topics in Mathematics
Its very important for teachers to connect past mathematics and future mathematics to current mathematical skills . Incorporating every aspect of life helps the student relate topics and gives them a reason for learning. Below I have include two artifacts that show how I connect mathematics. I have included a clinical interview performed in Knowing and Learning in Mathematics and Science. This interview was performed to pre asses a learners problem solving strategies. Below I also have a knowledge packet that I completed during a course called classroom interactions. The knowledge packet show all the past content I student needs in order to learn how to write equations to lines parallel to each other.
Connecting State Standards
Standards give teachers a guide to follow when educating students. Not only does it help them ensure mastery but standards provide rules for teachers to follow. Below you will find two standards that I deconstructed during a PBL that I created in Project Based Learning class.
Historical Importance
History is often forgotten when teaching mathematics. Mathematics has been around for centuries, and has been discovered by some of the greatest people to every walk earth. To show how I incorporate historical content, I have include an essay that I wrote in Perspectives on the contributions of women in mathematics. I have also include a time line I created in Senior Seminar that shows all the steps leading up to the classification of Finite Simple Groups.
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