|Course Syllabus for Math 6110 Informal Geometry 8:00am – 4:00pm on June 28th – July 7th Room 207 and 210 (NOC)|
Catalog Description Topics include plane figures, polygons and tessellations, space figures, symmetric figures, systems of measurement, area and perimeter,
volume and surface area, congruence and similarity mappings, and topological mappings. In addition, an individual, independent unit is included.
Course Rationale The purpose of this course is to prepare prospective P-8 teachers to become effective facilators in the teaching of mathematics. The intent of
the course is to insure that prospective teachers have a solid understanding of geometry and acquire a range of methods for facilitating the learning of geometric
concepts. Mathematics instruction today needs to focus on the development of mathematical thinking that entails helping students to construct their own
understanding of what it means to know and do mathematics. In order to accomplish this goal, teachers must be confident in their own ability to know and do
mathematics, as well as, to be prepared to teach all children.
Required Textbooks and Resources*
We will be using 3 primary resources in class, which are all available at the NGCSU bookstore. Please bring all these materials to class each day.
Geometer’s Sketchpad Student Edition Version 4
The Student Edition comes with the Sketchpad software (for Windows or Macintosh), a Learning Guide, 101 Projects Ideas, and a Quick
Exploring Geometry with The Geometer's Sketchpad® Version 4
By Dan Bennett
Rethinking Proof with The Geometer's Sketchpad® Version 4
By Michael de Villiers
* More information and resources at Key Curriculum Press http://www.keycollege.com
Supplementary Materials and Resources
Although I have enough materials for everyone to use to use in class, feel free (and encouraged) to bring a ruler, protractor, compass, and a calculator to class.
We will use these tools often and students often find it helpful to work with their own materials in class.
Course Goals Students in Math 6110 will have the opportunity to...
Content Objectives Students in Math 6110 will have the opportunity to study the following topics:
Points, Lines and Planes
· Solve problems involving properties and concepts of points, lines and planes in a two-dimensional setting
· Classify lines as parallel, perpendicular, intersecting and skewed
· Solve problems involving properties and concepts of circles such as area, circumference, diameter, sector, angles, arcs, radius, equation of a circle
· Classify quadrilaterals as squares, rectangles, parallelograms, trapezoids, or rhombi
· Solve problems involving properties of quadrilaterals such as parallel lines, diagonals, midpoints, length, width, area, perimeter
· Explore what happens to the area and perimeter of a quadrilateral as the dimensions are modified
· Classify triangles as acute, obtuse, right, equilateral, equiangular, isosceles, and scalene
· Explore triangle properties and triangle centers such as medians, altitudes, angle bisectors, centroid, orthocenter, circumcenter, incenter, etc.
· Solve triangle problems involving change of dimensions, perimeter, area, and the Pythagorean Theorem
· Classify polygons as regular, convex, and congruent
· Construct polygons in GSP; determine which can create tessellations
· Explore problems involving properties of polygons such as vertex angles, interior angles, exterior angles, area, perimeter, apothem, lines of symmetry, diagonals
· Solve problems involving volume and surface area of cubes, cylinders, rectangular solids, spheres, cones, and pyramids
· Explore the properties of vertices, edges, faces, and dimensions of solids
In order to demonstrate the ability to
· Select and use appropriate technological software to explore, analyze, and represent geometry problems
· Communicate mathematical understanding of a variety of geometric concepts
· Communicate mathematical thinking by expressing their reasoning, analysis, and extensions of the mathematical concepts associated with an investigation in written, verbal, and visual forms
· Modify geometric investigations for appropriate use in the middle school classroom
· Incorporate technology into the learning and teaching of geometric concepts
· Make connections between course experiences and standards-based reform documents, such as the NCTM standards
Students will be assessed with the following methods
· (50%) An online portfolio of investigations and solutions
Participants will be assessed on the content and quality of their online portfolios. Feedback and suggested modifications for a select number of write-
ups will be provided throughout the course. Assessment will be based on use of representation, analysis, appropriate selection and use of technological
tools, creation of extensions, and accuracy of mathematics. (Due Monday, July 26th no later than 3:00pm)
· (15%) In addition to the investigation write-ups, the participants will plan middle school instructional activities and mathematics lessons that
demonstrate the ability to integrate technology and geometry for use in their own classroom. (1 lesson plan due on July 7th and 1 lesson plan due on July
26th with portfolio)
· (15%) A content based, one hour exam will be given on the last day of class (July 7th)
· (20%) Daily class participation and homework assignments
Course Grade will be assigned base on the percentage of total possible points a student earns during the semester.
Because of the unique nature of our course, daily attendance is mandatory. Please note that according to the policies of North Georgia College & State University,
students that miss more than 14% of the scheduled class meeting times may be dropped from the course.
Metacognitive Model & Teacher Education Program Competencies
The NGCSU Mathematics Education Program prepares teachers to assume within the school community the roles of Decision-Maker, Facilitator, and Leader as
identified in the metacognitive model. Twelve Teacher Education Program competencies reflecting the model are aligned to a specific role. Overlap into more than
one role and mathematics course may occur. Current research and professional standards identify these competencies as important for effective teaching (NBPTS
and ASCD Framework).
Subject Matter Knowledge
Methods, Materials, Resources
Research & Evaluation
The integrity code will be upheld in this course. The NGCSU catalog states:
North Georgia College & State University is dedicated to providing an educational climate characterized by integrity. Academic integrity, in particular,
must be the cornerstone of an institution of higher learning and must pervade all segments of the NGCSU community. Furthermore, academic integrity is
the mutual responsibility of the various constituencies (students, faculty, staff, and administration) which comprise the university. The integrity code, "On
my honor, I will not lie, cheat, steal, plagiarize, evade the truth or tolerate those who do," reflects NGCSU's commitment to academic integrity.
Time Outside of Class
You cannot expect to accomplish or gain what you should from this course without spending time (in addition to the time we have in class) working on assignments,
including time on the computers. The usual expectation of 2 hours study outside of class for every hour in class is probably a minimum. If you are spending more
than 6 hours a week, please let me know so I can help you with managing you time and/or assignments or so that I can make adjustments accordingly There are 33
computer laboratories available on campus if you do not have internet access or Geometer's Sketchpad at home.