Longwood University
Department of Mathematics & Computer Science
MATH 657 - 01 (Fall 2011)
Geometry and Measurement for K-8 Teachers
Instructor:
Email:
Phone:
Office Hours:
Dr. Maria Timmerman
timmermanma@longwood.edu
Office: 434.395.2890
4:00 – 5:00 pm, Tuesday
1:30 – 2:30 pm Wednesday; 10:00
Course Location: Ruffner 350
Time: Tuesday, 6:00 – 8:45 pm
Home: 434.978.7184
Office location: 339 Ruffner
– 12 noon Thursday; or, by appointment
Texts:
Bass, A. (2008). Geometry: Fundamental concepts and applications. Boston, MA: Pearson.
ISBN: 0321473310, or, 9780321473318
Schifter, D., Bastable, V., & Russel, S. (2002). Geometry: Measuring space in one, two, and three
dimensions. Parsippany, NJ: Dale Seymour Publications. ISBN:
Schifter, D., Bastable, V., & Russel, S. (2002). Geometry: Examining features of shape. Parsippany,
NJ: Dale Seymour Publications. ISBN:
Other Required or Suggested Materials:
 Notebook/sprial notebook for notes, calculator (any type), ruler, protractor, graph paper, string, and
colored pencils (optional) and measuring tape (optional)
 CDs or jump-drives to save course material & computer files
 Turn cell phones to Vibrate during class. Cell phones may NOT be used as a calculator during exam.
Other Information: Students are responsible for checking the ANNOUNCEMENTS, COURSE DOCUMENTS,
and EXTERNAL LINKS in Blackboard in advance of each class period. See http://blackboard.longwood.edu.
Also, students are responsible for downloading all needed course documents from Blackboard, printing them if
hardcopies are desired, and knowing the information contained in these documents. NOTE: All students
should receive a letter from Longwood stating your user ID and directions for logging on to Blackboard. Please
contact the Help Desk (434.395.4357) if you need instructions for logging on, or have other IT questions.
Course Description: 3 Graduate Credit Hours
Geometry and Measurement for K-8 Teachers is one of the core mathematics courses for the K – 8
Mathematics Specialist Programs developed through a cooperative arrangement of James Madison University,
Longwood University, Norfolk State University, University of Mary Washington, University of Virginia, and Virginia
Commonwealth University. The course explores the foundation of informal measurement and geometry in one,
two, and three dimensions. The van Hiele model for geometric learning is used as a framework for how children
build their understanding of length, area, volume, angles, and geometric relationships. Visualization, spatial
reasoning, and geometric modeling are stressed.
Course Objectives:
This course is designed to engage participants in the following: (a) constructing a deeper understanding of the
fundamental K-8 content of measurement and geometry, (b) examining students’ ways of reasoning
mathematically about measurement, spatial relationships, and geometry, and (c) developing pedagogical content
knowledge of measurement and geometry (appropriate for K-8 Mathematics Teacher Specialists.).
Participants will define and select mathematical objectives for their students, reflect and analyze their thoughts as
they learn the course content, and ask questions that will help students deepen their understanding of
measurement and geometry concepts and skills.
MATH 657 – Fall 2011
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M. Timmerman
Course Competencies:
By the completion of this Math 657 course, students should be able to demonstrate:

Problem Solving: Know, understand and apply the process of mathematical problem solving

Reasoning and Proof: Reason, construct, and evaluate mathematical arguments and develop an
appreciation for mathematical rigor and inquiry (Longwood K-8 Mathematics Specialist Content
(Longwood K-8 Mathematics Specialist Content Portfolio).
Portfolio).

Mathematical Communication: Communicate their mathematical thinking orally and in writing to
peers, faculty, and others (Longwood K-8 Mathematics Specialist Content Portfolio).

Mathematical Connections: Recognize, use, and make connections between and among
mathematical ideas and in contexts outside mathematics to build mathematical understanding
(Longwood K-8 Mathematics Specialist Content Portfolio).

Mathematical Representation: Use varied representations of mathematical ideas to support and
deepen their own and their students’ mathematical understanding (Longwood K-8 Mathematics
Specialist Content Portfolio).

Effective use of Technology: Embrace technology as an essential tool for teaching and learning
mathematics (Longwood K-8 Mathematics Specialist Content Portfolio).

Understanding of the knowledge, skills, and processes of the Virginia Mathematics Standards of
Learning [related to measurement and geometry] and how curriculum may be organized to teach
these standards to learners (VA Mathematics Specialist Endorsement Requirement).

Communicate their mathematical thinking orally and in writing to peers and course instructor

Understanding of and the ability to use the five processes—becoming mathematical problem solvers,
reasoning mathematically, communicating mathematically, making mathematical connections, and
using mathematical representations—at different levels of complexity (VA Mathematics Specialist
(Longwood K-8 Mathematics Specialist Content Portfolio).
Endorsement Requirement).

Understanding of the history of mathematics, including the contributions of different individuals and
cultures toward the development of mathematics and the role of mathematics in culture and society
(VA Mathematics Specialist Endorsement Requirement).

Understanding of the sequential nature of mathematics and the mathematical structures inherent in
the content strands [related to measurement and geometry] (VA Mathematics Specialist
Endorsement Requirement).

Understanding of and the ability to use strategies for managing, assessing, and monitoring student
learning, including diagnosing student errors [related to measurement and geometry] (VA
Mathematics Specialist Endorsement Requirement).

Understanding of and proficiency in grammar, usage, and mechanics and their integration in writing

Understanding of the connections among mathematical concepts and procedures and their practical
applications (VA Mathematics Specialist Endorsement Requirement).

Understanding of a core knowledge base of concepts and procedures within the discipline of
mathematics, including the following strands: geometry and measurement (VA Mathematics
(VA Mathematics Specialist Endorsement Requirement).
Specialist Endorsement Requirement).
MATH 657 – Fall 2011
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M. Timmerman

Understanding of and the ability to select, adapt, evaluate and use instructional materials and
resources, including professional journals and technology (VA Mathematics Specialist Endorsement
Requirement).
Course Grade Assignment
A ~ 90 – 100 %
B ~ 80 – 89 %
C ~ 70 – 79 %
F ~ below 70% or lack of attendance
Plus and minus grades are given at the
discretion of the professor.
Course Requirements and Evaluation:







Attendance, active participation in class
discussions/activities, and mathematics goals,
autobiography, & learning theory paper – 5%
Reflective Focus Questions/Other Assignments– 15%
Problem Sets and Sharing Strategies – 15%
Interview Project (with partner) – 20%
Work Sample Analysis – 10%
Course Portfolio (includes history of mathematics paper and final reflective summary) – 15%
Final Exam – 20%

Attendance and Active Participation: Class activities require communication, interactions, and
discussions with other class members, and these cannot be reproduced. Class attendance is expected,
both for you to learn and so that others may benefit from your input. Missing 4 or more class AM or
PM sessions, excused or unexcused, results in an “F” for the course. Please be sure to arrive on
time for each class session. If you must be absent due to an illness, family emergency, or other
extenuating circumstance, please notify me in advance.

Assignments and Projects: Assignments should be completed and submitted on time. No
assignment will be accepted after the due date. Make-up work will be allowed only if you have a
medical excuse or are absent due to a Longwood University sponsored activity. If you are going to be
absent due to a Longwood University activity, notify me no later than a week in advance of the conflict.

Graduate Credit: For each hour you attend class, you should plan to spend 2 to 3 hours on
coursework. Thus, for a 3-credit graduate course, on a weekly basis, you will need to spend a
minimum of 6 to 9 hours preparing for each class meeting – reading, studying, and completing
assignments. Major assignments will require more time.
Additional Information
Students are expected to purchase all required materials, attend all class sessions, complete all assignments as
given, and participate in all class activities. All academic regulations in the current Longwood Catalog will be
followed.
Weekly chapter readings and online articles: Weekly readings should be completed prior to the class
session date as they are listed in the course outline. You are expected to analyze and reflect on all readings
and come to class prepared to contribute to discussion. The quality of the class will depend on the extent of
your participation. Each participant should be prepared to lead class discussions of the readings.
Reflective Focus Writings/Assignments: During the semester, you will be asked to reflect on focus
questions related to the assigned chapter readings and posted articles on Blackboard. Take-away
statements and specific quotes will often provide the framework for these written reflections completed in a
word-processed format. Other specific projects and written assignments may occur during the semester.
Problem Sets: Problems will be assigned related to the course readings. When requested, solutions should
be detailed with work shown using Polya’s problem-solving process structure, Driscoll’s geometry framework,
or connections to the van Hiele model of geometric thinking. You may use your book, other references, and
MATH 657 – Fall 2011
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M. Timmerman
discussion with other class members when completing these problems. However, the final product
submitted for a grade must be your own work. Problems will be graded on the problem-solving process,
effort, and use of a variety of strategies. Problems will not be graded entirely for accuracy of the final result.
These problems may be shared and discussed the next class session, and problem sets will be turned in on a
random basis throughout the semester.
Interview Project: With another class participant, conduct a measurement or geometry interview with two
different K-8 students, preferably at the same grade level. If possible, video tape or digitally record the
interviews so that you can analyze each interview. Further details will be discussed early in the semester.
Work Sample Analysis: Work samples will be analyzed during the semester. In your classroom or from a
‘borrowed’ classroom, collect measurement or geometry work samples from three students: one whose work
you think is strong, the other two whose work is not strong. Further details will be discussed concerning the
written analysis and learning goals for each student.
Course Portfolio: Each participant will complete a course portfolio that will serve as an assignment for this
course as well as part of the “program portfolio” for the K-8 Mathematics Specialist program. Further details
will be provided early in the semester.
Final Exam: Consists of K-8 mathematics content, how students think about and learn mathematics, and
pedagogy examined in the course from the entire semester including mathematical concepts, processes,
and discussion information based on assignments, in-class activities, powerpoints, and class notes.
Notebook: Each participant should keep a notebook that contains activities, ideas for discussion,
assignments, and class notes to encourage your development of mathematical and pedagogical ideas. The
notebook is NON-GRADED but will help you with several assignments.
Suggested items in Notebook:




Daily notes related to mathematics problems and discussions (both during class and while you
are completing out-of-class chapter readings, focus questions, and assignments)
Copies of class activities
Individual ideas that can help develop the basis for final reflection in the course portfolio
Copies of reflective writings
Longwood’s Honor System
A strong tradition of honor is fundamental to the quality of living and learning in the Longwood community.
Longwood affirms the value and necessity of integrity in all intellectual community endeavors. Students are
expected to assume full responsibility for their actions and to refrain from lying, cheating, stealing, and
plagiarism.
The Longwood Honor Code applies to all work for the course as follows:
 Any out-of-class assignments and projects can include using text information properly cited, discussion
with other class members, and/or discussion with professor. However, the final product submitted
for a grade must be the student’s own work.

Any in-class activities that involve teamwork allows for discussion within your team (unless otherwise
noted in directions from professor).

The Final Exam will be completed INDIVIDUALLY (unless otherwise noted in directions from professor).
Please write and sign the honor code on the final exam indicating that: “I have neither given nor
received help on this work, nor am I aware of any infraction of the Honor Code.”
MATH 657 – Fall 2011
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
Any student that violates the Honor Code will receive a zero on graded assignments and
will be reported to the Longwood University Honor Board.
Statement of Compliance with Americans with Disabilities
Any student who feels s/he may need an accommodation based on the impact of a physical, psychological,
medical, or learning disability should contact the instructor privately. If you have not already done so, please
contact the Office for Disability Services (103 Graham Building, 395-2391) to register for services.
Inclement Weather Policy
Information concerning cancellation of classes due to inclement weather is available at www.longwood.edu, on the
campus radio, WMLU 91.3 FM, or by calling 434.395.2000. In addition, I will post an announcement on Blackboard
if the weather prevents travel to Longwood. The website is http://blackboard.longwood.edu.
Important Notice: No more than nine Longwood non-degree graduate hours may be counted towards a
degree, certificate or licensure program. Students are expected to apply to a Longwood graduate program
prior to enrolling in classes. At the latest, all applications materials should be received by the Graduate and
Extended Studies Office before the completion of six hours.
Tentative Course Schedule – schedule may be changed as needed
Class
Sessions
Class 1
August 23
Class 2
August 30
Class 3
September 6
MATH 657 – Fall 2011
Assignment: Chapter Readings Before Class Session
Course Introductions: Community of Learners
NCTM and VA Content and Process Standards
The “Unit” and Different Dimensions
Ordering Rectangles Activity
Van Hiele Model of Geometric Thinking
Composing and Decomposing in 1, 2, and 3-Dimensions
Spatial Visualization: Quick Images
Crazy Cakes and video
Polya’s problem-solving process
Read Measurement (brown): Chapter 1
Write 2 ‘take-away’ statements for Chapter 1
Due: Mathematics autobiography, goals, and theory of how
students learn measurement or geometry paper
Bring VDOE K-3 VA SOL vertical alignment document
Geometric Habits of Mind Framework (Driscoll)
How Big is a Foot?
1-Dimensional Measurement: Perimeter (Length)
2-Dimensional Measurement: Area
Read Measurement (brown): Chapters 2 and 3
Write 2 ‘take-away’ statements for Chapter 2
Due: Focus Questions (measurement): Chapter 3, cases 1217
Due: Using 2 different strategies, measure the perimeter of your
right hand, and record your work. Next, using 2 different strategies,
measure the area of your left foot, and record your work. Use
Polya’s process, and write out how you used Polya’s 4 phases to
solve each problem. Be creative and be ready to share your
strategies and models, which will be collected
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M. Timmerman
Class 4
September 13
History of Geometry
Angles and video
Strands of Mathematical Proficiency
Read Bass: Preface, History, and Section 1
Problem Set: pp. 13-15, #24-29, 30, 32, 59, 61, 67, 68
Read: James Otto and Pi Man: A Constructivist Tale article
Write 2 ‘take-away’ statements for this article
Class 5
September 20
Triangles
Pythagorean Theorem
Read Bass: Section 2
Problem Set: pp. 30-33, #11, 15, 17, 22, 23, 52-61, 71-76
Read Shapes (green): Chapter 3
Due: Focus Questions (shape): Chapter 3, cases 12-17
Class 6
September 27
Quadrilaterals
2-Dimensional Measurement: Area of Rectangles
Read Bass: Section 3
Problem Set: pp. 48-50, #27-32, 34, 61-65
Read Measurement (brown): Chapter 5 (not chapter 4)
Read Shapes (green): Chapter 4
Write 2 ‘take-away’ statements for each chapter
Class 7
October 4
More on Quadrilaterals
2-Dimensional Measurement: Area of Many Quadrilaterals
Read Bass: Section 5 (not Section 4)
Problem Set: pp. 77-79, #17-21, 22-28, 29-34, 38, 40, 42,
43
Read Measurement (brown): Chapter 4
Due: Focus Questions (measurement): Chapter 4, cases 1821
No Class
October 11
Class 8
October 18
No Class - Longwood Reading Days: Oct. 10-11
PCTM Conference, October 11th, 9:00 – 3:00 pm
Completing Work Sample Analysis Project
See NCTM Illuminations technology websites for geometry and
measurement: http://illuminations.nctm.org/
Different Measures, Same Shape
Transformations, Symmetry, Congruence, and Similarity
Read Bass: Section 7
Problem Set: pp. 103-107, #25, 32, 34, 36-39, 44, 54, 61
Read Measurement (brown): Chapter 7, only cases 29-30
Read Shapes (green): Chapter 5
Write 2 ‘take-away’ statements for each chapter
* Share notes on at least 2 different Illuminations Activities
Due: Presentation and Work Sample Analysis
MATH 657 – Fall 2011
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Class 9
October 25
Class 10
November 1
Class 11
November 8
Highlights of Research
3-Dimensional: Volume
Student Interviews
Read Bass: Section 4
Problem Set: pp. 67-70, #29, 30, 33, 34
Read Measurement (brown): Chapter 8, only sections 1-3
Read Shapes (green): Chapter 8, only sections 1-4
Write 2 ‘take-away’ statements for each chapter
Surface Area
Read Bass: Section 9
Problem Set: pp. 135-138, #10, 12, 18, 19, 27, 34, 53, 57;
and your choice – select 2 problems from #38-48
Read Measurement (brown): Chapter 6, Chapter 7, cases 31-32
Write 2 ‘take-away’ statements for each chapter
Polygons
5 Teacher Talk Moves
Read Shapes (green): Chapters 1 and 2
Due: Focus Questions (shape): Chapter 1, cases 1-6
Write 2 ‘take-away’ statements for Chapter 2
Read online Chapter 2, “The Tools of Classroom Talk” – see:
http://www.mathsolutions.com/documents/97809413555
37_CH2.pdf
Class 12
November 15
No Class
November 22
Circles
Read Bass: Section 6
Problem Set: pp. 88-89, #9, 15, 16, 18, 19, 21, 23-25, 29,
31, 35, 39, 44
Read Shapes (green): Chapters 6 and 7
Due: Focus Questions (shape): Chapter 6, cases 27-31
For class at home: Your choice: Complete “Geometry Project 4”
(Bass, p. 70), OR, “Geometry Project 9” (Bass, p. 139)
Be sure to complete all parts and write a report based on the last
paragraph, p.70, for either project.
Completing Student Interview Project
Working on Course Portfolio
Class 13
November 29
Highlights of Research
Read Bass: Section 8
Problem Set: pp. 117-121, #24, 26, 35, 37, 38, 59
Read Measurement (brown): Chapter 8, only sections 4-7
Read Shapes (green): Chapter 8, only sections 5-6
Write 2 ‘take-away’ statements for each chapter
Due: Geometry Project 4 or Project 9
Due: Presentation and Analysis of Student Interview
Projects
Class 14
December 6
MATH 657 – Fall 2011
Final Thoughts
Due: Course Portfolio
Do Final Exam (in-class): Cumulative, Closed Book
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M. Timmerman
Reference Books of Interest:
Fuys, D., Geddes, D., & Tischerler, R. (1988). The van Hiele model of thinking in geometry among
adolescents. Journal for Research in Mathematics Education, Monograph No. 3. Reston, VA: National Council of
Teachers of Mathematics.
Leinward, S. (2009). Accessible mathematics: 10 instructional shifts that raise student achievement.
Portsmouth, NH: Heinemann.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of
fundamental mathematics in China and the United States. Mahway, NJ: Lawrence Erlbaum.
National Council of Teachers of Mathematics. (2003). A research companion to the principles and
standards for school mathematics. Reston, VA: Author.
National Research Council (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J.
Swafford, and B. Findell (Eds.). Washington, DC: National Academies Press.
vanHiele, P. (1986). Structure and insight: A theory of mathematics education. Developmental
Psychology Series, Academic Press, Inc.
Reference Journals of Interest:
Teaching Children Mathematics, National Council of Teachers of Mathematics
Mathematics Teaching in the Middle School, National Council of Teachers of Mathematics
Journal for Research in Mathematics Education, National Council of Teachers of Mathematics
School Science and Mathematics, School Science and Mathematics Association
Navigations Series (K-12), National Council of Teachers of Mathematics
Patty Paper Geometry and Geometer’s Sketchpad Labs, Key Curriculum Press
Description of 1st written paper:
Mathematics Autobiography, Individual Goals, and Theory of Students’ Learning of Mathematics.
Due Class Session #2, August 30th.
At the beginning of the course, before completing chapter readings, in a two-to-three page word-processed
essay (double spaced, ~ 1 inch margins, and 12-10 point font), you are asked to write a mathematics
autobiography describing your past experiences in learning mathematics.
FIRST: As you describe your experiences, you may find it useful to answer some (not all) of the following
questions:
• What topics in mathematics did you like, and which did you dislike?
• Who were the people who played a positive role in your mathematical life, and why?
• Who played a negative role, and why?
• Describe your good mathematical experiences and the poor experiences.
• In what environments do you learn best?
• What environments hinder your learning?
SECOND: In a separate paragraph or using bullet statements, identify the individual goals you plan to
pursue during this course.
THIRD: In separate paragraphs, describe your theory of how students learn measurement or
geometry in: (a) 3rd grade, and (b) your own classroom. This will probably be different for each of us
(and that’s OK as we begin learning with each other). Depending on your different experiences, some of you
may have a lot or just a little to say for your beginning theories.
MATH 657 – Fall 2011
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