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