MTE 550 - Geometry and Measurement

 

Course Instructors:        Dr. Kimberly Childs, childs@math.sfasu.edu

                                                Dr. Debbie Pace, pace@math.sfasu.edu

 

 

Course Facilitators/Mentors:

                                                Dr. Lesa Beverly, lbeverly@math.uttyl.edu

                                                Ms. Jennie Freeman, jfree@lufkinisd.org

                                                Ms. Mary Ann Williford, mawilliford@hotmail.com

 

Office:                                NM 304, (936) 468-3805

                                                Ms. Linda Boozer, Dept Secretary

boozer@math.sfasu.edu

Textbooks: 

                        Serra, Michael (2000), Discovering Geometry.  Key Curriculum Press.

                       

Long, Calvin T. & DeTemple, Duane W. (2000).  Mathematical

Reasoning for Elementary Teachers.  New York, N.Y.:  Addison Wesley Longman.

                        Van DeWalle, John A. (2001). Elementary and Middle School

Mathematics:  Teaching Developmentally. New York, N.Y.: Addison Wesley Longman.

Principles and Standards for School Mathematics, National Council of Teachers of Mathematics, 2000.

Bassarear, Tom (2001).  Mathematics for Elementary Teachers

(Explorations manual). Boston, MA.:  Houghton Mifflin.

 

 

Course Description: Concepts of Euclidean and non-Euclidean geometry with emphasis on deductive and inductive reasoning, discovery and proof, congruence and similarity, and creative thinking about quantitative, spatial, and logical situations.  Special attention will be given to the implementation of geometry and measurement into the middle level (4 - 8) curriculum.  

 

 

Course Goals and Objectives:  The goals of the Geometry and Measurement course include providing mathematics content and pedagogy necessary for teaching geometry and measurement in grades 4-8. Specific course content, goals, and objectives are consistent with the NCTM Principles and Standards for School Mathematics, the SBEC Standards, the Master Mathematics Teacher Certification Standards, and with the Texas Essential Knowledge and Skills.

 

Specific goals and objectives include:

 

• To use spatial reasoning to investigate concepts such as direction, orientation, perspective, shape, and structure;
• To use mathematical reasoning to develop, generalize, justify, and prove geometric relationships;
• To make connections among geometric and measurement ideas, number concepts, and algebraic structures;
• To analyze the properties of two- and three-dimensional figures;
• To understand transformational geometry and relate algebra to geometry and trigonometry using the Cartesian coordinate system;
• To understand the geometric relationships and axiomatic structure of Euclidean geometry.

 

Course Evaluation

 

• Activities (30%)

Assigned work includes daily assignments, short quizzes, class participation in various activities and discussions, and written responses on various assigned readings.

 

• Tests (50%)

Two major tests covering material discussed in weeks one and two.

 

• Performance Assessment (20%)

The performance assessment will be based on course content and pedagogy. It will measure how well you have met course and MMT objectives.

 

Course Syllabus  (Class:  July 15 - 26)

 

GEOMETRIC FIGURES:  DEFINITIONS, PROPERTIES, AND RELATIONSHIPS

 

·        Build Basic Vocabulary of Geometric Figures

·        Analyze Properties of Two and Three Dimensional Figures; Euler’s Formula

·        Classify Figures According to Properties

·        Explore Relationships Between Lines, Planes, Polygons, and Solids

·        Strengthen Spatial Visualization Skills

 

GEOMETRY AND MEASUREMENT

 

·        Explore Standard and Nonstandard Units of Measurement

·        Explore Linear Measurement: Perimeter, Circumference

·        Explore Area Measures of Polygonal and Circular

·        Explore Area Measures of Oddly Shaped Regions

·        Investigate and Prove the Pythagorean Theorem

·        Explore Measures of Surface Area and Volume: Lateral Surface Area, Base, Height, Slant Height

·        Use the Geometer’s Sketchpad to explore perimeter and area

 

GEOMETRY OF CONGRUENCE, SIMILARITY, AND  TRANSFORMATIONS

 

·        Investigate Properties of Congruent Figures including Congruence Properties of Triangles:  SSS, SAS, ASA, AAS

·        Investigate Properties of Similar Figures including Similarity Properties of Triangles:  AA, SSS, SAS

·        Conjecture About and Justify Geometric Relationships

·        Explore Ratio and Proportion Applied to Geometric Figures

·        Perform Basic Constructions Using Mira, Paper Folding, Compass and Straightedge, and Technology

·        Use the Geometer’s Sketchpad to perform basic constructions

·        Perform Rigid and Similarity Transformations on a Variety of Figures

·        Explore Properties of Rigid Transformations: Translations, Reflections, Glide Reflections, Rotations, Line Of Reflection

·        Explore Types of Symmetry: Line, Rotation, and Point Symmetry; Identify the Center of Rotation

 

GEOMETRY AND MEASUREMENT CONCEPTS IN THE ELEMENTARY CURRICULUM

 

·        Trace geometry and measurement content strands through the elementary school curriculum

·        Review nationally recognized project materials involving geometry and measurement