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Mathematics 235

MATH 235: Fundamentals of Geometry

Prerequisites: Mathematics major, Interdisciplinary Studies- Middle School Education major, Interdisciplinary Studies- Elementary major or permission of instructor.

Credit hours (3)

The course introduces core concepts and principles of Euclidean geometry. Emphases are placed on the use of spatial visualization and geometric modeling using software and/or physical models to explore and analyze geometric structures and their properties both from formal and informal perspectives. Course content adheres to the current National Council of Teachers of Mathematics Standards and may include the Virginia Standards of Learning where they can appropriately be applied.

Note: Students who have earned credit for MATH 335 may not subsequently earn credit for MATH 235. It is recommended that Elementary Education majors take MATH 122 prior to MATH 235.

Detailed Description of Course

Course content includes:

1.Using deductive axiomatic methods of proof and inductive reasoning

2.Geometric Constructions

3.Angles

4.Coordinate Geometry

5.Parallel and Perpendicular Lines

6.Geometric figures, their properties, relationships, and the Pythagorean Theorem

7.Tessellations

8.Trigonometric relationships

9.Measurements of perimeter and area of two-dimensional figures

10.Measurements surface area and volume of three-dimensional figures

11.Transformational Geometry

12.Special Topics

Detailed Description of Conduct of Course

Course instructors will emphasize building conceptual understanding within and between concepts discussed in class and on improving deductive reasoning skills. This may be completed with the use of various instructional methods such as cooperative/group learning activities, student presentations, small group and whole class discussions and questioning, and student explorations of geometric concepts using manipulatives and technology.

Goals and Objectives of the Course

The primary goal is to build a foundational knowledge of geometry that is necessary for students pursuing a career in K-12 education. In addition, this course will emphasize preparing students to improve their problem-solving strategies by helping them think critically and creatively about ideas, issues, and problems within geometry. Upon successful completion of this course, students will:
   1) Perform investigations of geometry using appropriate software and/or physical models
   2) Construct direct and indirect geometric proofs related to the concepts of the course
   3) Develop a deeper understanding of axiomatic reasoning and its role in developing mathematical concepts
   4) Understand the connections between the geometric concepts, procedures, and applications taught within the course
   5) Construct logical and persuasive arguments of geometric concepts

Assessment Measures

Graded tasks may include homework, quizzes, and written exams. They may also include writing assignments, self or peer assessments, individual or group projects or presentations, and class participation.

Other Course Information

None

Review and Approval

November 7, 2017
April 26, 2017
October 10, 2016
June 20, 2015