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Learning Objectives of the Algebra throughout the Curriculum linking course:
In addition to and in coordination with the general goals of the M302 courses, students in M302: Algebra will...
- Learn how to pose conceptually focused problems in high school algebra.
- Connect concepts between high school algebra and high school geometry.
- Develop insights about teaching the relationships between equations and their graphs.
- Conceptualize matrices as linear functions from one Euclidean space to another. In particular, students should be able to conceptualize graphs in the Euclidean plane as linear maps from one copy of the real line to another.
- Visualize how group theory can be applied to geometric transformations and how groups are abstracted from symmetries of 3D objects.
- Understand the historical development of number systems, like the rational numbers and the complex plane, as it relates to the secondary school curriculum.
- Examine ways to help students justify and explain algebraic ideas, like “why is a negative times a negative a positive?”
- Design thought-provoking high school tasks related to number theory, such as divisibility rules.
- Understand how the Fundamental Theorem of Algebra relates to ideas in high school algebra.
- Connect ideas of matrices, linear transformations, systems of equations, transformational geometry, and group/ring theory.
- Recognize how theoretical ideas from linear algebra and modern algebra are connected to Indiana Standards.
- Apply linear algebra to cryptography and networking problems suitable (but challenging) for secondary school students.
- Explore purposes of determinants in terms of secondary school curricula.
- Learn how to use various technologies effectively to represent mathematical ideas.
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Summary of Objectives:
The learning objectives listed above center on two main ideas about connecting Linear and Modern Algebra to teaching and secondary school curriculum. First, you should understand matrices as linear transformations of Euclidean spaces (lines, planes, space, etc.) and be able to relate this to secondary school topics such as graphing linear equations and solving systems of equations. Second, you should be able to use your understanding modern algebraic structures (such as groups, rings, and fields) to facilitate students’ understandings of algebraic relationships, including the “why’s” of mathematics.
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