Course Number: MATH 3110
Course Title: Informal Geometry
Credit Hours:  3 semester hours

Instructor: Margaret Poitevint (mpoitevint@ngcsu.edu)
Oakes Center 227
Office: (706) 867-2722
http://radar.ngcsu.edu/~mpoitevint/index.htm

Office Hours:  See website or my office door.

Description: This course is designed for K-8 pre-service teachers and focuses on topics such as plane figures, polygons and tessellations, space figures, symmetric figures, systems of measurement, area and perimeter, volume and surface area, and congruence and similarity mappings. This course may not be used to fulfill the academic concentration requirement for graduate secondary mathematics education students.

Prerequisites: Six hours of college-level mathematics to include Math 2400 - Statistics; Math 2008 or Math 3100.

Purpose: This course supports the philosophy that today’s K-8 mathematics teachers must be able to nurture collaboration, critical thinking, hands-on exploration, appropriate use of manipulatives, problem-based inquiry, incorporation of multiple forms of technology, and activities that acknowledge multiple intelligences and learning styles. The focus of this course is on providing rich opportunities to synthesize and enact key concepts of geometry. Exploring new ideas; solving problems using multiple strategies, manipulatives, graphing calculators, software, and other available technologies; and interpreting solutions, reasonableness of answers, and efficiency of various methods form the foundation for increasing the pre-service teacher’s awareness of how to bring students of diverse backgrounds to high levels of achievement.

Course Content:
Inductive and Deductive Reasoning
Angles, Triangles, Polygons, and Circles
Visualization and Spatial Reasoning
Constructions, Congruence, Similarity, and the Pythagorean Relationships
Concepts of Measurement
Motion Geometry and Tessellations
Technology Investigations and Applications of Geometry

Course Objectives: Students will be able to:

1) apply standard notation and terminology related to points, lines, planes, segments, rays, lines, angles, polygons, curves, two-dimensional transformations, and coordinate geometry;
2) identify and apply characteristics and properties of symmetry, geometric figures in the plane, transformations in the plane, and coordinate geometry;
3) build and manipulate representations of two- and three- dimensional objects and visualize objects from different perspectives;
4) specify locations and describe spatial relationships using coordinate geometry and other representational systems;
5) apply properties of customary, metric, and non-standard measurement systems to solve problems involving one-, two-, and three-dimensional objects;
6) perform constructions using tools such as compass, straightedge, Mira, paper folding, and dynamic geometry software;
7) use concrete models, drawings, and dynamic geometric software to explore geometric ideas and their applications in real-world contexts;
8) apply transformations and use symmetry, similarity, and congruence to analyze mathematical situations;
9) select and use a variety of tools, models, technologies, strategies, and methods for investigating geometry concepts appropriate for use in the elementary and middle grades;
10) demonstrate the ability to develop mathematical arguments relating arithmetic and geometric properties;
11) select, use, and determine the suitability of the wide variety of available mathematics curricula and teaching materials;
12) recognize the role of national, state, and local level mathematics standards and legislation in developing local curriculum and planning instruction that addresses the needs of diverse student populations; and
13) identify professional mathematics organizations and describe their contributions to the teaching of mathematics and the professional development of teachers.

Text/Materials:  Mathematics for Elementary Teachers, A Conceptual Approach, Seventh edition, Bennett and Nelson, McGraw-Hill, 2007
Activity packet available from the instructor or Print Services

Instructional
Components: This course will develop a mathematical and pedagogical knowledge base that fosters the development of the pre-service teacher as a facilitator, decision maker, and leader through the use of a variety of:
1) instructional strategies and methods including lecture, guided discussion, modeling, collaborative learning groups, hands-on activities that actively engage students in the learning process; and
2) instructional materials, assessment techniques, and scoring rubrics that reflect the spirit of the NCTM Principles and Standards (2000) and the National Board for Professional Teaching Standards (1998); diverse learning styles; multiple intelligences; and multicultural components.

Manipulatives
and Technology: Using manipulatives and technology as tools for learning and doing mathematics are important components of this course. Tools include pattern blocks, tangrams, geoboards, snap cubes, attribute blocks, Miras, protractors, compasses, rulers, patty paper, TI-73 Explorer, and The Geometer’s Sketchpad (GSP) software.

Computer Usage: Due to the emphasis placed on learning geometry in a computer-based interactive environment, access to a computer with GSP and the World Wide Web outside of the regular class meeting times is essential to your success in this course. GSP is available in labs throughout campus, but you may wish to consider purchasing the student edition of GSP for $39.95 at www.keymath.com/store/software/gsp.html.

Evaluation Methods:
Student performance will be evaluated through the use of projects, assignments/activities/investigations, reflection papers, tests, and a final exam. If students are text-messaging (or other distracting behavior), in each instance 5 points will be deducted from the participation grade.  Suggested weighting:

18%  Assignments/Activities/Investigations/Readings/Quizzes/Technology projects/Class participation
54%  Major tests (Two tests counting 27% each)
28%  Final Exam

Student grades are reported to the registrar as the letters A, B, C, D, or F based on a rounded final
average as follows:
  A 90-100
  B 80-89
  C 70-79
  D 60-69
  F less than 60

All tests must be taken with pencil - no erasable pens.  There will be no make-up tests.  A test missed with an excuse approved by the instructor will be replaced with the grade made on the final.  Other missed tests will result in a 0.  Being absent is not an excuse for an assignment being turned in late.  "Late" means any time after the beginning of the class on the date due.

Attendance: Attendance is required.  Any student who is absent more than 14% of the scheduled class meetings (2 days) may be dropped with a WF.  Tardiness is unacceptable and excessive tardiness will be counted as an absence.

Academic Integrity:
Students are expected to adhere to the Academic Integrity Policy for the University:  "On my honor, I will not lie, cheat, steal, plagiarize, evade the truth or tolerate those who do." Violations of the Academic Integrity Policy will be reported to the Academic Integrity Council in an incident report. Please refer the to NGCSU’s Undergraduate Bulletin for additional details.

Academic Disabilities:
North Georgia College and State University is committed to equal access to its programs, services and activities for people with disabilities. If you believe that you have a disability requiring an accommodation, reasonable prior notice needs to be given to the instructor and the Office of Student Disability Resources. In this case, contact Elizabeth McIntosh, Coordinator, Student Disability Resources at 122 Barnes Hall, 867-2782, emcintosh@ngcsu.edu

Web-Based Resources:
National Council of Teachers of Mathematics – www.nctm.org
Key Curriculum Press – www.keypress.com
National Library of Virtual Manipulatives for Interactive Mathematics - www.matti.usu.edu
Math Archives – http://archives.math.utk.edu/
The Math Forum – http://forum.swarthmore.edu/
Texas Instruments –www.education.ti.com
Eric Weisstein’s World of Mathematics (Encyclopedia of Mathematics) - http://mathworld.wolfram.com
TEAMS Mathematics Resources - http://teams.lacoe.edu/documentation/places/math.html
Math Nerds – www.mathnerds.com
SOS Mathematics – www.sosmath.com
Transformations - www.utc.edu/~cpmawata
Intermath – www.intermath-uga.gatech.edu/
The Geometry Center - http://www.geom.uiuc.edu
Georgia Learning Connections - www.glc.k12.ga.us
Helping Your Child Learn Math - www.ed.gov/pubs/parents/Math
Project Interactivate - www.shodor.org/interactivate
Multicultural Pavilion - www.edchange.org/multicultural
Women in Mathematics - www.agnesscott.edu/lriddle/women/women.htm
http://www.mathsisfun.com/geometry/index.html

Bibliography and
Supplementary Reading:

Navigating through Geometry PreKindergarten-2 Grades (with CD-ROM) - National Council of Teachers of Mathematics, 2001.  ISBN Number: 0-87353-511-1
Navigating through Geometry Grades 3-5 (with CD-ROM) - National Council of Teachers of Mathematics, 2001.  ISBN Number: 0-87353-512-X
Navigating through Geometry Grades 6-8 (with CD-ROM) - National Council of Teachers of Mathematics, 2002.  ISBN Number: 0-87353-513-8
Geometry Activities for Middle School Students with The Geometer’s Sketchpad (Key Curriculum Press, 1998)
Exploring Geometry with The Geometer’s Sketchpad (Key Curriculum Press, 1999)
Geometry Labs Activities for Grades 8-11 (Key Curriculum Press, 1999)
Teaching Children Mathematics (NCTM)
Mathematics Teaching in the Middle School (NCTM)
Principles and Standards for School Mathematics (NCTM, 2000)
Professional Standards for Teaching Mathematics (NCTM)
Assessment Standards for School Mathematics (NCTM)
Addenda Series Grades K-6 (NCTM)
Addenda Series Grades 5-8 (NCTM)
Addenda Series Grades 9-12 (NCTM)
Mathematics Activities for Elementary School Teachers A Problem-Solving Approach (Addison-Wesley, 2000)
Women, Minorities and Persons with Disabilities in Science and Engineering: 1996 (National Science Foundation, 1997)
Women And Science Celebrating Achievements Charting Challenges (National Science Foundation, 1997)
Mathematics Activities for Teaching (Wheeler and Barnard, Kendall-Hunt Publishers, 2000)

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).

Decision-Maker Facilitator Leader
Assessment Individual Differences Ethical Perspectives
Planning Subject Matter Knowledge Reflection/Metacognition
Problem Solver Communication Professional Leadership
Methods, Materials, Resources Classroom Management Research & Evaluation