MATH 7413 – Geometry for Inservice Teachers

Spring 2007

Dr. Janie Cates


Purpose: PSC Standards –2 ii, iv, v, vii, viii, 3, 4, 5, 6, 7, 8 v, viii, 9, 10, 11, 12, and 13

This course focuses on preparing P-5 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, hands-on exploration, manipulative use, problem-based 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 students’ mathematical understanding, and interpret school-based 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 – 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 three-dimensional 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 P-5 students learn mathematics and of the pedagogical content knowledge appropriate to P-5 mathematics teaching.


Course Objectives: PSC Standards – 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 three-dimensional shapes.

3)    a confidence, desire, and ability to use estimation to facilitate solving geometric and measurement problems.

4)    an ability to use geometry in real-world problem solving.

5)    a well-developed spatial sense including both two- and three-dimensional 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 three-dimensional 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 P-5 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 students’ 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 – 5                

The Geometer’s Sketchpad; Calculators: TI-73 Explorer, TI-83 Plus SE, Voyage 700


Manipulative Materials: PSC Standard – 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.


Instructional Materials: PSC Standard – 9

Text: Mathematics for Elementary Teachers, Addison-Wesley Publishing Co., Author: Beckman, 2005.


Instructional Methods: PSC Standards – 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 – 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, in-class presentations, tests, reflective logs, computer work, 5-day geometry instructional unit, peer and self-assessment, 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, double-spaced format with Times/Times New Roman font, size 12, and 1-inch 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 assignment’s 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 – Create a vertical progression for your grade level’s (K-2, 3-5 or 6-8)        GPS Geometry and Measurement standards. How do these align with NCTM’s goals for

           grades K-2, 3-5, and 6-8?


2.        Partner Presentations – Select one of the class activities for each chapter (4 chapters –      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 – 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 – see sample. (Examples should    include picture representations if appropriate.)


4.        Geometry Problem Sets – You will have 2 geometry problem sets to complete outside        of class.


5.        Journal Entries – You will have 8 Geometry/Measurement journal “prompts” to        respond to in your reflective journal. Begin each entry on a new page.


6.       Geometry Unit – Create a geometry unit (5-10 days) that you can use in your classroom.     Use the GPS for your grade level.


7.        Geometer’s Sketchpad Activities – You will have several activities to complete using           Geometer’s 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 out-of-class     assignments.


8.        Chapter Tests – At the end of each chapter, you will take a test based on the materials

and information we have worked on in class.





Points Possible

Evaluation Method

Partner Project



Partner Presentations (4@25 points)






Geometry Problem Sets



Reflective Journal



Geometry Unit



Geometer’s Sketchpad Activities



Tests (4@100 points)



Total Points




Final grades will be distributed according to the following scale:




765 < x < 850



680 < x < 765



595 < x < 680



x < 595


The final letter grade of “A” will be reserved for those students who demonstrate excellence in all of their work and contributions to class.


Class Outline (Tentative)



Class Activities

Assignments Due







Chapter 8

8.2 – I, J, K

8.3 – T, U, V



Chapter 8

8.4 – X, Y, Z, AA, CC



Chapter 8

8.5 – DD, EE, GG, HH



Geometer’s Sketchpad

8.5 – FF, II, KK



Chapter 8

8.6 – MM, NN

8.7 – OO, SS, UU



Chapter 8 – Test

Chapter 9 – Geometry of Motion and Change

9.1 – D, E, F

9.2 – G, H, L




Chapter 9

9.3 – M, N, O

9.4 – P, Q, R, U



Chapter 9 – Test




Field Assignment


Problem Set #1


Chapter 10 - Measurement

10.1 – A, C, D;

10.2 – E

10.3 – F;

Glossary – Ch. 8 Partner Project


Chapter 10

10.4 – G, I, J

10.5 – K, L

10.6 – M, N, O

Journal #1-4


Chapter 10 – Test



Glossary – Ch. 9


Chapter 11 – More About Area and Volume

11.1 – A, B, C

11.2 – D, E, F

11.3 – G

Sketchpad Activities


Chapter 11

11.5 – L, M

11.6 – N

Problem Set #2



Chapter 11

11.7 – O, P, Q, R

11.8 – S, T

Glossary – Ch. 10


Chapter 11

11.10 – W, X, Y, Z, AA

11.11 – CC, DD, EE



Chapter 11 – Test



Journal #5-8


Probability and Statistics begins!!!

Glossary – Ch. 11




Geometry Unit