MATH 7413 Ð Geometry for Inservice Teachers
Spring 2007
Dr. Janie Cates
jcates@westga.edu
Purpose: PSC Standards Ð2 ii, iv, v, vii, viii, 3, 4, 5, 6, 7, 8 v, viii, 9, 10, 11, 12, and 13
This course focuses on preparing P5 mathematics specialist candidates to:
a) Broaden understanding of fundamental concepts of geometry with particular attention given to specific methods and materials of instruction.
b) Solve measurement and geometry problems using multiple strategies, manipulatives, and technological tools.
c) Construct and justify arguments as well as interpret solutions; and determine reasonableness of answers and efficiency of methods.
d) Nurture collaboration, critical thinking, handson exploration, manipulative use, problembased inquiry, technology utilization, and activity implementation addressing various learning styles.
e) Select and use a variety of formative and summative assessment techniques to monitor student progress, gauge studentsÕ mathematical understanding, and interpret schoolbased progress.
The principle geometry topics to be taught in this course are: introductory geometry, constructions, congruence, and similarity, concepts of measurement, motion geometry, and tessellations.
Learning Outcomes: PSC Standards Ð 2 ii, iv, v, vii, viii, x, xi, 5, 7, 8 iv, v, vii, and 14
All students course will learn to:
1) Analyze characteristics and properties of two and threedimensional geometric shapes and develop mathematical arguments about geometric relationships.
2) Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
3) Apply transformations and use symmetry to analyze mathematical situations.
4) Use visualization, spatial reasoning, and geometric modeling to solve problems.
5) Understand measurable attributes of objects and the units, systems, and processes of measurement.
6) Apply appropriate techniques, tools, and formulas to determine measurements.
7) Demonstrate a deep understanding of how P5 students learn mathematics and of the pedagogical content knowledge appropriate to P5 mathematics teaching.
Course Objectives: PSC Standards Ð 2 ii, iv, v, vii, viii, x, xi, 5, 7, 8 iv, v, vii, and 14
All students will be able to demonstrate:
1) an understanding of standard vocabulary and symbols of elementary mathematics.
2) an ability identify, describe, visualize, classify and compare one, two, and threedimensional shapes.
3) a confidence, desire, and ability to use estimation to facilitate solving geometric and measurement problems.
4) an ability to use geometry in realworld problem solving.
5) a welldeveloped spatial sense including both two and threedimensional figures (tessellations, symmetry, congruence, similarity, polygons and other curves, polyhedra).
6) an understanding of geometry and measurement from a historical perspective.
7) an ability to apply the process of measurement to one, two, and threedimensional objects using nonstandard and customary geometric units.
8) an ability to solve measurement problems involving perimeter, circumference, area, volume, temperature, and mass.
9) an understanding of coordinate, and transformational geometry with an emphasis on problem solving.
10) an understanding of the uses of a variety of manipulatives, technology, and other materials for the P5 level.
11) an understanding of the vision of mathematics education as put forth in NCTM's Principles and Standards (2000).
12) an understanding of the scope and sequence of elementary school mathematics programs.
13) a knowledge of current professional literature in the field of mathematics education.
Pedagogy and Professional Development Objectives:
1) Select and use appropriate concrete materials and technological tools for learning mathematics.
2) Select, use, and determine the suitability of the wide variety of available mathematics curricula and teaching materials.
3) 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.
4) Demonstrate knowledge of different types of mathematical instructional strategies.
5) Use multiple strategies to assess studentsÕ mathematical knowledge.
6) Identify professional mathematics organizations and describe their contributions to the teaching of mathematics and the professional development of teachers.
Technology: PSC Standard Ð 5
The GeometerÕs Sketchpad; Calculators: TI73 Explorer, TI83 Plus SE, Voyage 700
Manipulative Materials: PSC Standard Ð 8 iv, v, and vii
Compasses, pentominoes, geoboards, rulers, protractors, polydrons, patty papers, metric and standard weight systems, polyhedras, miras, thermometers, tangrams, pattern blocks, cubic centimeters and cubic inches, scales.
Text: Mathematics for Elementary Teachers, AddisonWesley Publishing Co., Author: Beckman, 2005.
Instructional Methods: PSC Standards Ð 10, 11, 12, and 13
Teaching methods for this course will include small and large group projects, individual, small group and whole class problem solving, student presentations, teacher led discussion, and some lecture.
Evaluation Methods: PSC Standards Ð 2 ix, x, xi, 3, 4, 5, 6 i, ii, iii, 7, 8 iv ,v, vii, 9, 10, 11, 12, and 13
Student performance will be evaluated through the use of projects, inclass presentations, tests, reflective logs, computer work, 5day geometry instructional unit, peer and selfassessment, and content and pedagogical proficiency demonstrations.
Assignments: All assignments, with the exception of the partner projects, are individual assignments and must be in a typed, doublespaced format with Times/Times New Roman font, size 12, and 1inch margins unless otherwise indicated. Assignments are due at the BEGINNING OF CLASS on the designated date. Failure to meet deadlines and/or follow directions will result in a grade reduction of at least 10% per assignment. Technical/computer problems are not an acceptable excuse for a late assignment. Rubrics are provided for each assignment and must be turned in with the corresponding assignment. Assignments submitted without the rubric will counted as late submissions. If you are absent, it is your responsibility to get any missed work and turn in any assignments that are due. An absence DOES NOT change an assignmentÕs due date. Remember: Assignments are not negotiable, however, due dates are. Contact the instructor to make arrangements if necessary BEFORE the assignment is due.
1. Partner Project Ð Create a vertical progression for your grade levelÕs (K2, 35 or 68) GPS Geometry and Measurement standards. How do these align with NCTMÕs goals for
grades K2, 35, and 68?
2. Partner Presentations Ð Select one of the class activities for each chapter (4 chapters Ð 8, 9, 10, and 11) that you and your partner would like to be in charge of leading. During that class, you and your partner will lead the activity for the rest of the class. You may choose to do the presentations individually.
3. Glossary Ð Develop a geometry and measurement glossary. Words can be found in the margins of your text. You may also add your own words. Each word should be on a separate page. For each word, complete a Frayer model Ð see sample. (Examples should include picture representations if appropriate.)
4. Geometry Problem Sets Ð You will have 2 geometry problem sets to complete outside of class.
5. Journal Entries Ð You will have 8 Geometry/Measurement journal ÒpromptsÓ to respond to in your reflective journal. Begin each entry on a new page.
6. Geometry Unit Ð Create a geometry unit (510 days) that you can use in your classroom. Use the GPS for your grade level.
7. GeometerÕs Sketchpad Activities Ð You will have several activities to complete using GeometerÕs Sketchpad. When you complete the activity, you will need to print out a copy of it to submit. Some of these will be done in class. Others will be outofclass assignments.
8. Chapter Tests Ð At the end of each chapter, you will take a test based on the materials
and information we have worked on in class.
Grading
Assignment 
Points Possible 
Evaluation Method 
Partner Project 
50 
Rubric 
Partner Presentations (4@25 points) 
100 
Rubric 
Glossary 
75 
Rubric 
Geometry Problem Sets 
50 
Rubric 
Reflective Journal 
50 
Rubric 
Geometry Unit 
75 
Rubric 
GeometerÕs Sketchpad Activities 
50 
Rubric 
Tests (4@100 points) 
400 
Exam 
Total Points 
850 

Final grades will be distributed according to the following scale:
A 
= 
765 < x < 850 
B 
= 
680 < x < 765 
C 
= 
595 < x < 680 
F 
= 
x < 595 
The final letter grade of ÒAÓ will be reserved for those students who demonstrate excellence in all of their work and contributions to class.
Class Outline (Tentative)
Date 
Topic 
Class Activities 
Assignments Due 

January 
9 
Syllabus 


11 
Chapter 8 
8.2 Ð I, J, K 8.3 Ð T, U, V 


16 
Chapter 8 
8.4 Ð X, Y, Z, AA, CC 


18 
Chapter 8 
8.5 Ð DD, EE, GG, HH 


23 
GeometerÕs Sketchpad 
8.5 Ð FF, II, KK 


25 
Chapter 8 
8.6 Ð MM, NN 8.7 Ð OO, SS, UU 


30 
Chapter 8 Ð Test Chapter 9 Ð Geometry of Motion and Change 
9.1 Ð D, E, F 9.2 Ð G, H, L 


February 
1 
Chapter 9 
9.3 Ð M, N, O 9.4 Ð P, Q, R, U 

6 
Chapter 9 Ð Test 



8 
Field Assignment 

Problem Set #1 

13 
Chapter 10  Measurement 
10.1 Ð A, C, D; 10.2 Ð E 10.3 Ð F; 
Glossary Ð Ch. 8 Partner Project 

15 
Chapter 10 
10.4 Ð G, I, J 10.5 Ð K, L 10.6 Ð M, N, O 
Journal #14 

20 
Chapter 10 Ð Test 

Glossary Ð Ch. 9 

22 
Chapter 11 Ð More About Area and Volume 
11.1 Ð A, B, C 11.2 Ð D, E, F 11.3 Ð G 
Sketchpad Activities 

27 
Chapter 11 
11.5 Ð L, M 11.6 Ð N 
Problem Set #2 

March 
1 
Chapter 11 
11.7 Ð O, P, Q, R 11.8 Ð S, T 
Glossary Ð Ch. 10 
6 
Chapter 11 
11.10 Ð W, X, Y, Z, AA 11.11 Ð CC, DD, EE 


8 
Chapter 11 Ð Test 

Journal #58 

13 
Probability and Statistics begins!!! 
Glossary Ð Ch. 11 

15 


Geometry Unit 