UAS SOE graduates will be informed, reflective, and responsive
teachers within diverse classroom, school, and community contexts
All education programs through the School of Education at University of Alaska Southeast
are accredited by the National Council for the Accreditation of Teacher Education, a
performance-based teacher accrediting body for schools, colleges, and departments of
education recognized by the Alaska Department of Education and Early Development, the
U.S. Department of Education, and
the Council for Higher Education Accreditation.
Course:
ED 655 Geometry and Measurement: Content and Pedagogy for K-8 Teachers
Instructor:
Dr. Virgil G. Fredenberg
Mode of Instruction: Distance via Elluminate Live!
Class Hours:
Wednesday, 4:15 – 7:30 PM
Office Hours:
Tuesday, Thursday 10:00 – 11:00 AM
Monday, Tuesday, Wednesday 1:30 – 3:30 PM
I.
Catalog Course Description and Credit Hours of Course:
Provides K-8 teachers with the underlying principles of geometric and spatial sense and the levels of
geometric learning with practice developing a variety of physical models, manipulatives, and software
appropriate to K-8 classrooms. Examines current instructional and assessment practices in geometry that
are research and standards based and that lead to visualization and spatial reasoning for K-8 students.
II.
Prerequisite(s):
ED 614
III.
Textbook and/or Required Readings:
Aichele, D. B., Wolfe, J. (2008). Geometric Structures. Pearson/Prentice Hall. Upper Saddle River, NJ.
www.prenhall.com. ISBN: 978-0-13-148392-7
IV.
Technology Needed
You will need headphones with a microphone for your computer. It will make working with Elluminate
Live! much easier.
V.
Alignment Matrix
1,2, 3,
4, 5, 6
Assessment ensuring that
the objective has been met
1.1, 1.2, 1, 2, 3,
3.1, 3.2, 4, 5, 8, 2.c, 5.a
3.3, 3.5 9, 10
1.1, 1.2,
3.1, 3.2,
3.3, 3.5
1.1, 1.2,
1, 2, 3, 1.3, 3.1,
4, 5, 6 3.2, 3.3,
3.5
1, 4
ACEI
Standard
Met
Demonstrate the ability to integrate geometry
and measurement into the K-8 mathematics
curriculum with accommodations for special
needs students
1, 4
NCTM
Standard
Met
Demonstrate understanding of the underlying
concepts of geometry and measurement as
evidenced by perseverance, ability to select
appropriate strategies to solve problems, and
ability to justify and defend their solutions
Demonstrate the ability to convert problem
situations so geometry and measurement can be
employed to find solutions
Demonstrate the ability to challenge students to
construct, analyze, and support tasks and criteria
for solving problems using geometry and
measurement
Review, synthesize, and evaluate research on
geometry and measurement in the K-8
mathematics curriculum, and the best practices
for teaching algebra and functions
Graduate
Competencies
The candidate will:
SOE
Goal Met
Course Objective
1, 2, 3,
4, 5, 8, 2.c, 5.a
9, 10
1, 2.c,
1, 2, 3,
3.b, 3.c,
4, 5, 8,
3.d, 4,
9, 10
5.a
1.1, 1.2,
1, 2.c,
1, 2, 3,
1.3, 3.1,
3.b, 3.c,
4, 5, 8,
3.2, 3.3,
3.d, 4,
9, 10
3.5
5.a
1.1, 1.2,
1, 2.c,
1, 2, 3,
1, 2, 3, 1.3, 2.2,
3.b, 3.c,
4, 5, 8,
4, 5, 6 3.1, 3.2,
3.d, 4,
9, 10
3.3, 3.5
5.a
Participation
Exercises
Community problems
Lesson Plan
Community problems
Lesson Plan
Community problems
Concept Description and
Reflections
Web Site Description and
Reflections
Lesson Plan
Community problems
Lesson Plan
V.
Relationship of the Conceptual Framework to Standards
An increasing emphasis on professional standards for educators reinforces the relevance of the School of
Education’s vision of an informed, reflective and responsive professional educator as the grounding
tenants of our Conceptual Framework. As the lists of expected achievement indicators, competencies,
and dispositions issued by government and professional groups become more extensive, only an informed
professional who actively reflects on his/her teaching and is responsive to student, family and community
needs will be capable of meeting the intent of those standards. The general theme of our vision is that
each of these areas strives to nurture and prepare professional educators so that they can meet the needs of
diverse learners. Efforts include continuous endeavors to creatively incorporate technology throughout
individual subject area fields, promoting understanding and appreciation for diversity, and support of the
development of literacy skills needed in an increasingly complex society.
VI.
Basis for Student Evaluation:
Assignment
Attendance and Participation
Exercises
Community problems
Concept Description and Reflections
Web Site Description and Reflections
Lesson Plan
Points
Due Date
39 points total
12 @ 3 each, drop lowest
33 points total
6 @ 3 each, drop lowest
15 points total
6 @ 3 each, drop lowest
15 points total
2 @ 3 each
6 points total
4 parts @ 3 each
12 points total
ongoing
see schedule
see schedule
see schedule
see schedule
see schedule
VIII.
1.
2.
3.
4.
5.
6.
IX.
Explanation of Assignments
Attendance and Participation – attend and participate in all class sessions. Your peers will be learning from your
contributions and discussion just as you will be learning from them.
Assigned exercises – will be assigned for each session.
Community problems – Share six problems created employing geometry topics or concepts that connect geometry to
the local community. These may be referred to as place-based problems.
Geometry concept descriptions and reflections – you will read and report on six geometry topics or concepts. A
brief written description of what you found and your reflection on it. You may choose from the following topics or
propose your own.
a. Van Hiele levels
e. The Pythagorean theorem
i. Congruent figures
b. Teaching geometry
f. Circles
j. Application of similar triangles
c. Geometry in the real world
g. Symmetry
k. Cultural geometry
d. History of geometry
h. Transformations
l. Technology and geometry
Web site description and reflection – description of web site that has useful strategies for teaching two of the topics
found in item 4 above. Along with your comments, describe what you found there and how you might use it. Be
sure to include the host of the web site or the copyright, when it was last updated, and its web address. These will be
shared with the rest of the class.
Lesson plan – turn in plan of the lesson created for your class that utilizes one of the shared community problems or
an adaptation of one of the shared problems you created.
a. Clear understandable title and objectives
b. Clear and understandable procedures and activities
c. Clear and understandable connections to community/culture/real-world.
d. Quality of lesson plan – remember to edit your work for spelling, grammar and presentation. The overall look is
important.
Schedule (This schedule may be subject to change or update due to unforeseen circumstances)
Date
Session topics
Assignments
Introduction; Review procedures for online course; Exercise 1
Jan. 12
Chapter 1: Polygons and Angle Relationships
Concept Des & Ref 1
Exercise 2
Jan. 19 Chapter 2: Quadrilaterals and their definitions
Community problem 1
Chapter 3 & 10: Constructions …
Exercise 3
Jan. 26
Van Hiele Levels
Concept Des & Ref 2
Exercise 4
Feb. 2 Chapter 4: Explorations in three dimensions
Community problem 2
Exercise 5
Feb. 9 Chapter 5: Area
Web Site Des & Ref 1
Concept Des & Ref 3
Feb. 16 Chapter 6: Explorations with geoboard areas
Feb. 23 Chapter 7: Similarity and slope
Mar. 2 Chapter 8: Pythagorean theorem and perimeter
Mar. 9
Spring Break
Mar. 16 Chapter 9: Geometry of circles
Mar. 23
Chapter 11: Congruence conditions and reasoning
from definitions to properties
Mar. 30 Chapter 13 Computer Explorations
Apr. 6
Apr. 13
State Testing Week
Chapter 14: Mira Constructions and other
constructions
Chapter 15: Symmetry
Chapter 16: The four symmetries
Apr. 27 Chapters 17 & 18: Symmetry examples
Apr. 20
Exercise 6
Community problem 3
Exercise 7
Concept Des & Ref 4
Exercise 8
Community problem 4
No School
Exercise 9
Concept Des & Ref 5
Exercise 10
Web Site Des & Ref 2
Exercise 11
Community problem 5
Lesson Plan
No Class
Exercise 12
Concept Des & Ref 6
Community problem 6
Due Dates
Exercise 1
Concept Des & Ref 1
Exercise 2
Community problem 1
Exercise 3
Concept Des & Ref 2
Exercise 4
Community problem 2
Exercise 5
Web Site Des & Ref 1
Concept Des & Ref 3
Exercise 6
Community problem 3
Exercise 7
Concept Des & Ref 4
No School
Exercise 8
Community problem 4
Exercise 9
Concept Des & Ref 5
Exercise 10
Web Site Des & Ref 2
No Class
Exercise 11
Community problem 5
Lesson Plan
Exercise 12
Concept Des & Ref 6
Community problem 6
X.
Grading Scale
Item
Attendance and participation
Assigned exercises
Community problems
Concept descriptions and reflections
Web Site descriptions and reflections
Lesson Plan
Points
Grade
XI.
≥110
A
107-109 103-106
AB+
Description
Points Totals
14 classes [1 excused absence allowed]
12 exercises assigned for each session [drop lowest]
6 problems [drop low]
6 descriptions and reflections [drop low]
2 descriptions and reflections
3 points each part, four parts
98-102
B
95-97
B-
91-94
C+
86-90
C
83-85
C-
3 each
3 each
3 each
3 each
3 each
3 each
Total
78-82
D
39
33
15
15
6
12
120
<78
F
Academic Policy Statement:
Honesty in academic endeavors is a central tenet of the UAS philosophy. One may feel proud of
accomplishments and success attained honorably through hard work. Knowledge gained in this way often
leads to later success in professional pursuits and in personal life. Unfortunately, academic stress and
anxiety sometimes impact the individual in ways that produce dishonest behavior, or taking an “easier”
route to fulfilling academic responsibilities. Infractions of academic dishonesty can lead to serious
consequences. Refer to the UAS Student Handbook for more details. Programs offered through the
Learning Center and the Student Resource Center address topics such as study skills and time
management to reduce stress and thus help to prevent dishonest behavior.
XII.
Student with Disabilities:
To aid college students who experience a documented physical, cognitive, and/or psychiatric disability.
Disability Support Services are available on all UAS campuses. The University of Alaska Southeast is
committed to equal opportunity and programmatic access for students with disabilities (See University of
Alaska Regents Policy: www.alaska.edu/bor/policy/policy.xml). For further information on disability
support services and guidelines about documentation please visit our website at www.uas.alaska.edu/dss
or:
In Juneau:
(907)796-6000
In Ketchikan:
(907) 228-4505
In Sitka:
(907) 747-7716
Early contact with this program promotes a positive educational experience
XIII. Civility and Harassment
Intellectual honesty, mutual respect and freedom from discrimination, intimidation, harassment and
violence against persons or property are central to the UAS mission. Acts of intolerance and abusive
behaviors which violate these basic values will not go unchallenged without our academic community.
UAS is committed to standards promoting speech and expression that fosters the maximum exchange of
ideas and opinions. Ideally, discourse is open, candid and characterized by mutual respect and dignity. It
is the goal of the university to foster a campus climate which promotes the ideals of civility and
appreciation for the uniqueness of each member of our academic community.
XIV. Dispositions of Professional Educators
1. Abide by a philosophy of education and remain flexible to revising it based on new research and
teaching experience.
2. Appreciate unique thinking processes of learners at different stages of development.
3. Appreciate multiple perspectives and value individual differences.
4. Commit to professional discourse about content knowledge and student learning of content.
5. Value assessment and instruction as integrated processes.
6. Commit to ensuring student well-being and development of self-regulation and group interaction
skills.
7. Recognize the school as an integral part of the community and value parents and guardians as partners
in promoting student learning.
8. Value professional ethics, democratic principles and collaborative learning communities.
9. Value technology as a tool for student and teacher lifelong learning.
XV.
References
Alaska Content and Performance Standards Booklet.
Alaska Native Knowledge Network. Alaska Standards for Culturally Responsive Schools.
http://www.ankn.uaf.edu/pubgraph.html
Bush, W. S., & Leinwand, S. (2000). Mathematics assessment: A practical handbook for grades k-2, 3-5,
6 – 8, 9-12, K-12 series of National Council of Teachers of Mathematics. Reston, VA: National
Council of Teachers of Mathematics.
Clements, D. H., & Battista, M. T. (1992). Geometry and Spatial Reasoning. In D.A. Grouws (Series
Ed.), Handbook of Research on Mathematics Teaching and Learning, pp. 420-464. New York:
Macmillan Publishing Co. and National Council of Teachers of Mathematics.
Great Source Education Group. (2001). Geometry to Go. Houghton Mifflin, Inc. Wilmington, MA.
www.greatsource.com. ISBN: 0-669-48129-7
Great Source Education Group. (2001). Geometry to Go, Teacher’s Resource Book. Houghton Mifflin,
Inc. Wilmington, MA. www.greatsource.com. ISBN: 0-669-48807-0
Huettenmueller, R. (2005). Geometry Demystified. Burr Ridge, IL. McGraw-Hill Professional
Publishing.
National Council of Teachers of Mathematics. Navigating through Geometry. Reston, VA: Author.
National Council of Teachers of Mathematics. Navigating through Measurement. Reston, VA: Author.
National Council of Teachers of Mathematics. (1997). Multicultural and gender equity in the mathematics
classroom: The gift of diversity (1997 Yearbook). Reston, VA: Author.
National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics.
Reston, VA: Author.
National Council of Teachers of Mathematics. (1994). Windows of opportunity: Mathematics for students
with special needs. Reston,VA: Author.
Turnball, R., Turnball., A., & Shank, C. (2000). Exceptional children in inclusive environments. Saddle
River, NJ: Merrill.
Vaugn, S., Bos, C., & Schumm, J.J. (2003). Teaching exceptional, diverse, and at-risk students. Boston,
MA: Allyn & Bacon.