MATHEMATICS 655-94
FUNCTIONS AND ALGEBRA
Fall 2008
Instructor: Dr. Sharon Emerson-Stonnell
Office Hours: MTWRF 10 – 11am and 1 - 2 pm
E-mail: emersonstonnellss@longwood.edu
Telephone: 434-395-2197
Text:
Russell, S. J., Schifter, D., & Bastable, V. (2008). Reasoning Algebraically about
Operations. Dale Seymour.
Russell, S. J., Schifter, D., & Bastable, V. (2008). Patterns functions and Change. Dale
Seymour.
Recommended Supplies: Graphing paper and colored pencils
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.
Course Description: This course will examine representing and analyzing mathematical
situations and structures using generalization, algebraic symbols, and reasoning.
Attention will be given to the transition from arithmetic to algebra, working with
quantitative change, and the description of and prediction of change.
1. Represent functions in different ways (TC4).
2. Describe relations using algebraic symbols (TC4).
3. Demonstrate algebraic reasoning (TC4).
4. Use algebraic reasoning in problem solving (TC4).
5. Describe age-appropriate algebraic concepts (TC4).
6. Demonstrate understanding of ways in which children learn mathematics (TC4).
Longwood University Conceptual Framework: The Educator as Reflective Citizen
Leader
Professional Teacher Outcomes:
V1 – Educators as Reflective Citizen Leaders
TC 1 – Plan for Instruction
TC 2 – Implementation and Management of Instruction
TC 3 – Evaluation and Assessment
TC 4 – Knowledge of Subject
TC 5 – Classroom Behavior Management
TC 6 – Communication Skills
TC 7 – Professional Responsibilities
TC 8 – Technology
TC 9 – Diversity
Course Requirements:
1. There will be a take-home midterm worth 20% of your final grade. The exam will be given on
October 15 and is due on October 22.
2. Attendance is mandatory. Each student is expected to actively participate in all group work and
class discussions.
3. Daily class assignments will constitute 15% of your final grade.
4. A curriculum materials analysis will be required. You will need to examine and analyze three
different activities in probability or statistics from the NCTM Navigation Series. The paper
should be double spaced, 12 font with 1 inch margins. The analysis paper will constitute 10% of
your final grade. The analysis paper will be due on November 19.
5. A mathematics history self reflection paper is required. The paper should reflect your growth in
understanding number sense and algebra history and their effect on content and education during
this course. The paper should be 2-3 pages, double spaced, 12 font with 1 inch margins. The
self reflection paper will constitute 10% of your final grade and is due on November 12.
6. A written analysis of your students’ work is required. The analysis should be double spaced, 12
font with 1 inch margins. The analysis paper will constitute 15% of your final grade and is due
on October 29.
7. A course portfolio is required. The paper should reflect your mathematical knowledge and
growth in mathematical understanding during this course. The essays should be typed, double
spaced, and 12 font with 1 inch margins. The course portfolio will constitute 10% of your final
grade and is due on December 10.
8. There will be a comprehensive final exam for this course. The exam will be worth 20% of your
final grade and will be given on December 10.
9. Absences are excused only for illness, college sponsored activities, and recognizable
emergencies. You must assume full responsibility for all material covered during your absence.
A grade of "0" will be assigned for all work missed due to unexcused absences.
10. Make-up tests will be given only when the reason for missing the test meets the criteria for an
excused absence. Make-up tests will always be more difficult then regularly scheduled tests.
11. I expect you to conform to the Longwood College Honor Code as contained in the Student
Handbook. All assignments and tests must be pledged.
Feel free to come by my office at any time during office hours for help. If you are unable to come
during office hours call and make an appointment for another time period.
Class Schedule:
August 27
Virginia SOL and NCTM Standards
Homework:
Read the Introduction and RAO Chapter 1 and answer Focus Questions
September 3
Dicovering Rules for Odds and Evens
Homework:
Read RAO Chapter 2 and answer Focus Questions
Even and Odds Homework
September 10
Finding Relations in Addition and Subtraction
Homework:
Read RAO Chapter 3 and answer Focus Questions 1-4 and 6
Addition and Subtraction Homework
September 17
Reordering Terms and Factors
Homework:
Read RAO Chapter 4 and answer Focus Questions
Integer Addition Homework
Try first activity with your students
September 24
Expanding the Number System
Homework:
Read Chapter 5
Multiple Operations Homework
October 1
Doing and Undoing, Staying the Same
Homework:
Flower Problem
Read Chapter 6 and answer Focus Questions 3, 4, and 6
Integer Subtraction Homework
October 8
Multiplying in Clumps
Homework:
Read Chapter 7 and answer Focus Questions 4-7
Multiplication Homework
Try second activity with your students
October 15
Exploring Rules for Factors
Homework:
Midterm take-home
Read PFC Chapter 1 and answer Focus Questions
October 22
Using Patterns to Determine What’s Ahead
Midterm take-home due
Homework:
Read PFC Chapter 2
Exploring with Houses and Building with Toothpicks homework
October 29
Representing Situations with Tables, Diagrams, and Graphs
Student Work Analysis Paper due
Homework:
Read PFC Chapter 3 and answer Focus Questions
Formulas Homework
November 5
Finding Formulas
Homework:
Read PFC Chapter 4
Exploring Linear Relations
November 12
Comparing Linear Functions
Math History Reflection paper due
Homework:
Read PFC Chapter 5 and answer Focus Questions
Systems of Equations Homework
Complete NCTM Curriculum Analysis Paper
November 19
Does Doubling Work?
NCTM Curriculum Analysis Paper due
Homework:
Read PFC Chapter 6 and 7
Pine Sports Complex Manager Homework
December 3
Examining Non-Constant Rates of Change
Functions without Formulas
Homework:
Complete Math 659 Portfolio
Study for final exam
December 10
Final Exam
Math 655 Portfolio due
Attendance Policy: Students are expected to attend all classes. Work missed because of illness
or other excused absences may be made up. Work missed because of unexcused absences
receives a grade of 0. If you miss an exam or are late with an assignment you may be asked to
provide proof that you had a legitimate reason (such as illness, certain college-sponsored
activities or recognized emergencies). When possible, you should
notify the instructor in advance of assignments you expect to miss because of legitimate absences.
Honor Code: Students are expected to abide by the Longwood College Honor Code.
Assignments should be pledged, but the provisions of the Honor Code are assumed to apply to all
work, pledged or not. Students are encouraged to study together and to seek help from the
instructor or tutors when needed, but receiving unauthorized help or copying will be graded is a
violation of the Honor Code.
REFERENCES/BIBLIOGRAPHY
Mathematics Teaching in the Middle School
Mathematics Teacher
School Science and Mathematics
Teaching Children Mathematics
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Cangelosi, J. S. (1992). Teaching mathematics in secondary and middle school:
Research-based approaches. New York, NY: Macmillan.
Carpenter, T. P., Franke, M. L., &Levi, L. (2003). Thinking Mathematically.
Portsmouth, NH: Heinemann.
Clark, C. H., & Nelson, M. N. (1991). Evaluation: Be more than a scorekeeper.
Arithmetic teacher, 38(9), 15-17.
Cooney, T. J. (Ed.), 1990). Teaching and learning mathematics in the 1990s: 1990
Yearbook. Reston, VA: National Council of Teachers of Mathematics.
Countryman, J. (1992). Writing to learn mathematics: Strategies that work, K-12.
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Cuevas, Gilbert J. & Yeatts, Karol. (2001). Navigating through Algebra in Grades 3-5.
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Davidson, N. (Ed.), (1990). Cooperative learning in mathematics: A handbook for
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Davis, R. B., Maher, C. A., &Noddings, N. (Eds.), (1990). Constructivist views on the
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Driscoll, Mark, (1999). Fostering Algebraic Thinking. Portsmouth, NH: Heinemann.
Friel, Susan, et. al. (2001). Navigating through Algebra in Grades 6-8. Reston, VA:
National Council of Teachers of Mathematics.
Grouws, D. A. (Ed.), (1992). Handbook of research on mathematics teaching and
learning. Reston, VA: National Council of Teachers of Mathematics.
Johnson, D. R., (1994). Motivation counts. Palo Alto, CA: Dale Seymour.
K-8 Building Blocks for Algebra. Eisenhower Regional Consortium for Matematics and
Science Education at AEL.
Lesh, R., & Lamon, S. J., (Eds.), (1992). Assessment of authentic performance in school
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National Council of Teachers (1995). Assessment standards for school mathematics.
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National Council of Teachers (2000). Principles and Standards for School Mathematics.
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Patterns, Functions, and Algebra. Virginia Department of Education.
Reimer, Wilbert. (1996). What’s Next? A Pattern Discovery Approach to Problem
Solving. Fresno, CA: AIMS Education Foundation.
Romberg, T. A., & Wilson, L. D. (1992). Alignment of tests with the standards.
Arithmetic teacher, 40(1), 18-22.
Sammons, K. B., Kobett, B., Heiss, J., & Fennell, F. (1992). Linking instruction and
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Thornton, S.J. (2001). New Approaches to Algebra: Have We Missed the Point?
Mathematics Teaching in the Middle School, 6(7), 388-392.
Webb, N. L. (Ed.), (1993). Assessment in the mathematics classroom: 1993 yearbook.
Reston, VA: National Council of Teachers of Mathematics.
Wiebe, A., Youngs, M., & Erickson, S., (2001). Multiplication the Algebra Way.
Fresno, CA: AIMS Education Foundation.