Longwood University
Department of Mathematics & Computer Science
MATH 651 - 01 (Spring 2010)
Numbers and Operations for K-8 Teachers
Instructor:
Email:
Phone:
Office Hours:
Dr. Maria Timmerman
Course Location: Ruffner 354
timmermanma@longwood.edu
Time: Saturday, 9:00 - 12:00, 1:00 – 4:00 pm
Office: 434.395.2890
Home: 434.978.7184
Cell: 434.962.4579
3:30 – 4:30 pm, Tuesday
Office location: 340 Ruffner
2:00 – 5:00 pm Wednesday (or by appointment)
Texts:
Schifter, D., Bastable, V., & Russel, S. (1999). Number and operations, part 1: Building a system of
tens. Parsippany, NJ: Dale Seymour Publications. ISBN: 0769001696.
Schifter, D., Bastable, V., & Russel, S. (1999). Number and operations, part 2: Making meaning for
operation. Parsippany, NJ: Dale Seymour Publications. ISBN: 0769001726.
Other Required or Suggested Materials:
 Notebook/sprial notebook for notes, calculator (any type), and colored pencils (optional)
 Computer disks, 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
Number and Operations 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 will focus on the content and processes that support the number & number
sense and computation & estimation strands of the Virginia K-8 Mathematics Standards of Learning. The five
NCTM and Virginia process standards—problem solving, reasoning and proof, connections, communication, and
representation—will be emphasized throughout the course. While participants learn how students confront these
mathematical concepts and processes, they will also be exploring the mathematics for themselves. Participants will
read cases about K-8 mathematics in classroom settings, view videos, explore mathematical concepts and a
variety of representations, analyze student work, and read current research about these issues.
Course Objectives:
This course is designed to engage participants in the following: (a) constructing a deeper understanding of the
essential content of the base ten structure of the number system, (b) examining students’ ways of reasoning
mathematically about place value representations, number and operations, and (c) developing pedagogical
content knowledge of number and operations (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 the
structure of the base ten number system and computational procedures.
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Course Competencies:
By the completion of this Math 651 course, students should be able to:

Solve multi-digit computations for whole number operations (addition, subtraction, multiplication,
and division) in multiple ways using invented (not standard) algorithms, mental mathematics, and
computational estimation (Longwood K-8 Mathematics Specialist Content Portfolio).

Know, understand and apply the process of mathematical problem solving in the context of whole
number and some rational number problems (Longwood K-8 Mathematics Specialist Content
Portfolio).

Develop the meaning of addition, subtraction, multiplication, and division, and provide multiple
models for whole number operations and their applications (Longwood K-8 Mathematics Specialist
Content Portfolio).

Demonstrate computational proficiency, including conceptual understanding of numbers, ways of
representing number, relationships among number and number systems, and the meaning of
operations (Longwood K-8 Mathematics Specialist Content Portfolio).

[Demonstrate an] Understanding of the knowledge, skills, and processes of the Virginia Mathematics
Standards of Learning [related to number sense and operation sense] and how curriculum may be
organized to teach these standards to learners (VA Mathematics Specialist Endorsement
Requirement).

Recognize the meaning and use of place value in representing whole numbers and finite decimals,
comparing and ordering numbers, and understanding the relative magnitude of numbers (Longwood
K-8 Mathematics Specialist Content Portfolio).

Analyze integers and rational numbers, their relative size, and how operations with whole numbers
extend to integers and rational numbers (Longwood K-8 Mathematics Specialist Content Portfolio).

Demonstrate knowledge of the historical development of number and number systems including the
contributions of diverse cultures (Longwood K-8 Mathematics Specialist Content Portfolio).

Communicate their mathematical thinking orally and in writing to peers and course instructor

[Demonstrate an] 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
(Longwood K-8 Mathematics Specialist Content Portfolio).
(VA Mathematics Specialist Endorsement Requirement).

[Demonstrate an] 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).

[Demonstrate an] Understanding of the sequential nature of mathematics and the mathematical
structures inherent in the content strands [related to number & number sense and computation &
estimation] (VA Mathematics Specialist Endorsement Requirement).

[Demonstrate an] Understanding of and the ability to use strategies for managing, assessing, and
monitoring student learning, including diagnosing student errors [related to number & number sense
and computation & estimation] (VA Mathematics Specialist Endorsement Requirement).

Use a variety of representations and strategies to model problem situations dealing with whole
numbers and some rational numbers in order to support and deepen their own and their students’
mathematical understanding (Longwood K-8 Mathematics Specialist Content Portfolio).
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
[Demonstrate an] Understanding of and proficiency in grammar, usage, and mechanics and their
integration in writing (VA Mathematics Specialist Endorsement Requirement).

[Demonstrate an] Understanding of the connections among mathematical concepts and procedures
and their practical applications (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:






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Attendance, active participation in class
discussions/activities, and mathematics goals,
autobiography, & learning theory paper – 10%
Reflective Focus Writings/Assignments– 10%
Interview Project (with partner) – 20%
Work Sample Analysis – 10%
Written Classroom Case Study – 10%
Course Portfolio (includes history of mathematics paper and final reflective summary) – 20%
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 wordprocessed format.
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Interview Project: With another class participant, conduct a numbers and operations-based 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 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.
Written Classroom Case Study: Based on your own classroom experiences, write a case study. The format
will be similar to the cases presented in the textbooks, and further details will be provided in class.
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:
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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.”

Any student that violates the Honor Code will receive a zero on graded assignments and
will be reported to the Longwood University Honor Board.
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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 AM
January 23
Class 2 PM
Class 3 AM
January 30
Class 4 PM
Class 5 AM
February 6
Class 6 PM
Class 7 AM
February 20
Class 8 PM
Assignment: Chapter Readings Before Class Session
Course Introductions
Community of Learners
Early Counting
Set and Measurement Models
Place Value Process
XMANIA
Number Combinations
Place Value
CGI Word Problems
Read MMO (purple): Chapters 1 and 2
Due: Mathematics autobiography, goals, and theory of how
students learn mathematics paper
Place Value
Mental Mathematics
Read BST (blue): Chapters 2 and 3
Strands of Mathematical Proficiency
Addition and Subtraction Invented Algorithms
Read BST (blue): Chapters 1 and 4
Read online: see Blackboard postings
Concepts of Multiplication
Multiplication Invented Algorithms
Read MMO (purple): Chapter 3
Read BST (blue): Chapter 5
Concepts of Division
Division Invented Algorithms
Read BST (blue): Chapter 6
Highlights of Research
Read BST (blue): Chapter 8 (omit section 5)
Read MMO (purple): Chapter 8 (omit sections 5, 6, and 7)
Due: Presentation and Work Sample Analysis
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Class 9 AM
March 6
Class 10 PM
Class 11 AM
March 27
Class 12 PM
Globalization and Education
Early Fraction Number Sense
Read MMO (purple): Chapter 4
Read online: see Blackboard postings
Fractions: Addition and Subtraction
Read MMO (purple): Chapter 5
Due: Presentation and Written Classroom Case Study
Operation Sense: Fraction Multiplication
Read MMO (purple): Chapter 6
Operation Sense: Fraction Division
Read MMO: Chapter 7
Due: Presentation and Analysis of Student Interview
Projects
Class 13 AM
April 17
Fractions, Decimals, and Percents
Read BST (blue): Chapter 7
Class 14 PM
Highlights of Research
Read BST (blue): Chapter 8, section 5
Read MMO (purple): Chapter 8, sections 5, 6, and 7
Final Thoughts
Due: Course Portfolio
Do Final Exam (in-class): Cumulative, Closed Book
Class 15 AM
April 24
Reference Books of Interest:
Leinward, S. (2009). Accessible mathematics: 10 instructional shifts that raise student achievement.
Portsmouth, NH: Heinemann.
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.
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
Description of 1st written paper:
Mathematics Autobiography, Individual Goals, and Theory of Students’ Learning of Mathematics.
Due Class Session #3, January 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?
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• 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 mathematics in 2nd
grade and 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.
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