Longwood University
Department of Mathematics & Computer Science
MATH 430, Teaching Mathematics in the Middle School (Spring 2011)
Professor:
Office Location:
Phone/Voicemail:
Math Office:
E-mail:
Office Hours:
Dr. Maria Timmerman
340 Ruffner
434.395.2890 (w), 434.978.7184 (h)
434.395.2194 (Gale Moss)
timmermanma@longwood.edu
3:30 – 4:30 pm, Tuesday; 1:00 – 2:00 pm Wednesday;
10:00 – 12 noon, Thursday
Class Times:
Tuesday: 5:30 – 8:15 pm, 354 Ruffner
Texts:
Fosnot, C.T. & Jacob, B. (2010). Young mathematicians at work: Constructing algebra. Portsmouth,
NH: Heinemann. ISBN-13: 978-0-325-02841-5, OR, ISBN-10: 325-02841-9.
Lamon, S.J. (2005). Teaching fractions and ratios for understanding: Essential content knowledge
and instructional strategies for teachers (2nd Edition). Mahwah, NJ: Lawrence Erlbaum
Associates. ISBN: 978-0-8058-5210-3.
Small, Marian. (2009). Good questions: Great ways to differentiate mathematics instruction. Reston,
VA: National Council of Teachers of Mathematics. ISBN: 978-0-8077-4978-4
Other Required or Suggested Materials:
 Notebook, graphing calculator, ¼ inch graph paper, ruler, colored pencils, and scissors
 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
tests.
Additional Information: Students are responsible for checking the ANNOUNCEMENTS and
ASSIGNMENTS in Blackboard in advance of each class period. See http://blackboard.longwood.edu. Also,
students are responsible for downloading the syllabus, online articles, and all other needed course
documents from Blackboard, printing them if hardcopies are desired, and knowing the information
contained in these documents. All academic regulations in the current Longwood Catalog will be
followed.
Course Description:
A study of current practices in middle-school mathematics teaching with emphasis on principles,
techniques, and materials. Required for those planning to teach middle school mathematics. 3 credits
Course Objectives:
This course is designed specifically for students who plan to pursue teacher licensure in middle school
mathematics. Thus, a major goal of the course is to re-examine the mathematics content
knowledge you will teach, as well as develop pedagogical ideas for teaching middle school
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mathematics, and how students learn mathematics developmentally. Given that mathematical
reasoning develops as a result of problem solving, the course will provide you with many
opportunities to solve problems, and examine how students develop ways to reason mathematically
as a result of problem solving.
This course is designed to engage you in the following: (a) constructing a deeper understanding of the
essential content of the K-8 strands of rational numbers, proportional reasoning, and algebra: (b)
examining students’ ways of reasoning mathematically, and (c) developing pedagogical content
knowledge related to the strands of rational numbers, proportional reasoning, and algebra.
Course Competencies:
By the completion of this Math 430 course, students should be able to:
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Solve rational number, proportional reasoning, and algebra problems/tasks in multiple ways
through the perspective of a teacher of middle school mathematics.
Know, understand, and apply the process of mathematical problem solving in the context of
rational number, proportional reasoning, and algebra problems.
Use hands-on activities, a variety of representations, and various pedagogical tools to solve
mathematics problems related to the teaching and learning of middle school mathematics.
Communicate mathematical ideas orally and in writing.
Identify the strands of mathematical proficiency and describe how they are interwoven.
Know mathematical concepts that can help students learn meanings of essential big ideas,
strategies, and models for middle school mathematics.
Develop differentiated lessons for the teaching of middle school mathematics.
Examine and analyze national and state standards for the teaching of mathematics.
Develop their professional competence, confidence, and enthusiasm for learning and teaching middle
school mathematics.
Course Content Outline and Methodology:
The course will cover mathematics topics from all 3 course texts. Class sessions will engage you in
student-centered learning environments with hands-on explorations, collaborative small-group work
and discussion, pairs engaged in problem-solving tasks and communication, and whole-class
discussions that model the instructional practices that are advocated in the Curriculum and Evaluation
Standards (NCTM, 1989), the Professional Standards for Teaching Mathematics (NCTM, 1991), the
Assessment Standards for School Mathematics (NCTM, 1995), the Principles and Standards for School
Mathematics (NCTM, 2000), and the Curriculum Focal Points (NCTM, 2006). Specifically, these reform
documents support a constructivist perspective for the teaching and learning of mathematics.
Mathematics teaching and learning are problem-solving activities. For each hour you attend
class, you should plan to spend 2 to 3 hours on coursework. Thus, for a 3-credit 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. To succeed as a
mathematics student and teacher it is essential to know mathematics vocabulary. As you read each
section, you may want to write each mathematics word on a 3x5 note card, along with its definition,
symbol (if any) and examples. Not only will this make studying for tests and quizzes much easier, it
will also be a useful resource in your future teaching career.
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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.
Course Requirements and Evaluation:
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Attendance, active participation in class
discussions, in-class assignments, and
initial mathematics paper – 15%
Problem Sets – 15%
Interview Project (with partner #1) – 10%
Chapter Readings & take-away statements – 10%
Midterm Exam – 15%
Mathematics Trail Project (with partner #2) – 10%
Lesson Differentiation Plan (with partner #3)– 10%
Final Exam – 15%
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.
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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 3
or more classes, 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, emergency, or
other extenuating circumstance, please notify me in advance.
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Assignments will be given in-class that focus on mathematics concepts and pedagogy. Many
of these assignments will be group assignments that require a group to work together to
complete an assignment to be handed in during class, or, the next class session. Note: Any
student not in attendance when a class assignment is started or completed can
receive at most half-credit for a completed assignment.
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Assignments and Projects: Assignments should be completed and submitted on time. Late
work will result in significant grade reductions according to the following scale: 1 day late, 10
percent reduction; 2 days late, 25 percent reduction; 3 days late, 40 percent reduction; 4 days
late, 60 percent reduction; more than 4 days late, grade of zero will be assigned. Students
who have extenuating circumstances may be allowed extensions on a case-by-case basis, but
such extensions must be requested prior to the date the assignment or project is due.
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: During the semester, readings will be assigned to
be completed prior to the next class session 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. It would
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be useful to write down key mathematical ideas as you complete readings. These are called ‘takeaway’ statements as you synthesize ideas from the readings. Work to articulate the meaning of the
idea in your own words. For each idea, give a reference in the readings or your own experiences
during the week. The quality of the class will depend on the extent of your participation. Each
student should be prepared to lead class discussions of the readings.
Problem Sets (Problem Solving Journal): Each week there will be problems assigned related to
the course readings. When requested, solutions must be detailed with work shown using Polya’s
problem-solving process structure. You may use your book, other references, and discussion with
other class members when completing these problems. However, the final product submitted
for a grade must be the student’s own work. Problems will be graded on the problem-solving
process, effort, and in some cases, using at least two different strategies or models. Problems will not
be graded entirely for accuracy of the final result. These problems may be shared and discussed the
next class meeting, and problem sets will be turned in on a random basis throughout the semester.
Mathematics Trail Project – Working with partner #1, you will create a “Math Trail” to engage
middle school students in exploring the mathematics that surrounds them. Your project will be to
select sixth, seventh, or eighth grade as your focus and create a mathematics trail on the Longwood
campus that could be used by local students. The problems on the trail must use the mathematics
included in the 2009 Virginia Standards of Learning in a way that is consistent with the NCTM (2000)
Principles and Standards for School Mathematics. More details will be shared early in the semester.
Interview Project: Working with partner #2, conduct a rational number or algebra-based interview
with two different middle school students, preferably at the same grade level. If possible, videotape
or digitally record the interviews so that you can analyze each interview. Further details will be
discussed in class.
Lesson Differentiation Plan: Working with partner #3, this project will involve revising an existing
lesson (using middle school curriculum, Mathematics in Context) to incorporate various strategies to
make mathematics accessible for students of varying ability levels. Specific details will be discussed in
class.
Midterm Exam and Final Exam: Closed book in-class exams that focus on middle school
mathematics content, how students think about and learn mathematics, and pedagogy examined in
the course will cover the first half of the course (midterm exam) and the entire semester
(final exam). This includes 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 and problem sets)
Copies of class activities and reflective writings
Individual ideas that can help develop the basis for various course projects
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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 problem sets, assignments, and projects can include using text information
properly cited, discussion with other class members, and/or discussion with professor.
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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).
Both the Midterm Exam and Final Exam will be completed INDIVIDUALLY. Please write and
sign the honor code on each 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.
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.
Tentative Course Schedule – schedule may be changed as needed
Assignment: Chapter Readings Before Class Session
Class
Sessions
Class 1
January 18
What is Mathematizing?
Course Introductions
Community of Learners
Rational Numbers & Polya’s Problem-Solving Process
NCTM and VA Content & Process Standards
Rational Numbers
Proportional Reasoning
Class 2
January 25
Read Lamon: Chapter 1 and Chapter 2
Write 2 ‘take-away’ statements for each chapter
Problem Set: p. 14, #3 – solve 2 different ways; p. 14, #1, 2
(reflection); p. 27-28, #1-5, write word problems here; #1, 3
(reflection); and solve Harry Potter problem (in the classroom); optional
to ask middle school student to solve problem
On-line Article: “Transitions from elementary to middle school
math”
Due: Mathematics autobiography, goals, and theory of how
students learn mathematics paper
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Class 3
February 1
Class 4
February 8
Class 5
February 15
Class 6
February 22
Class 7
March 1
Relative and Absolute Thinking
Differentiate Mathematics Instruction
Strands of Mathematical Proficiency
Read Lamon: Chapter 3
Problem Set: pp. 35-38, #2, 3, 9, 10; #1, 2 (reflection); #2 (in the
classroom)
Read Small: Chapter 1
Write 2 ‘take-away’ statements for the chapter
Algebra Structures
Algebra Landscape: Big Ideas, Strategies, & Models
Theories of Learning Mathematics
Read YMW: Chapter 1 and Chapter 2
Write 2 ‘take-away’ statements for each chapter
Reasoning and Unitizing
Number and Operations
Student Interviews: Analyzing Student Thinking
Read Lamon: Chapter 6 and Chapter 7
Problem Set: pp. 72-75, #2-7, 10-12; pp. 84-86, #1, 3, 4, 6, 7
Read Small: Chapter 2
Write 2 ‘take-away’ statements for the chapter
Part-Whole Comparisons
(1st interpretation of rational numbers)
Early Structuring for Algebra
Worthwhile Tasks: 4 Levels of Cognitive Demand
Read Lamon: Chapter 10 and Chapter 11
Problem Set: pp. 121-123, #1 (do multiples of 3, begin with problem
c), 4-6; in the classroom: write word problems for the 4 operations
using the egg carton (set model) context; optional to ask 3rd/4th
graders; pp. 134-135, #2, 3, 6
Read YMW: Chapter 3
Write 2 ‘take-away’ statements for the chapter
Sharing and Comparing
Partitioning and Quotients
(2nd interpretation of rational numbers)
Grade Estimates
Algebra: Context and Models
Due by noon,
Math Trails
February 28th
(D and F)
Read Lamon: Chapter 8 and Chapter 12
Problem Set: pp. 94-97, #1-8; pp. 147-149, #3, 6, 7, 11, 12
Read YMW: Chapter 4
Write 2 ‘take-away’ statements for the chapter
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Class 8
March 8
Rational Numbers as Operators
(3rd interpretation of rational numbers)
Geometry
Read Lamon: Chapter 13
Problem Set: pp. 164-167, #2-7
Read Small: Chapter 3
Write 2 ‘take-away’ statements for the chapter
In-Class Midterm Exam
VCTM CONFERENCE: March 11 – 12th
SPRING BREAK
March 15th
No Class
Class 9
March 22
Class 10
March 29
Rational Numbers as Measures
(4th interpretation of rational numbers)
Measurement
Lamon Problem Set: pp. 166-167, #9-12, 15-17, 19-20
Read Lamon: Chapter 4 and Chapter 14
Problem Set: pp. 45-48, #1-5, 8, 11-13; pp. 177-180, #2, 5, 6, 8-11
Read Small: Chapter 4
Write 2 ‘take-away’ statements for the chapter
Algebra: Equivalence
Variation versus Variables
Planning Lessons: Teaching in a Standards-based Classroom
Read YMW: Chapter 5 and Chapter 6
Write 2 ‘take-away’ statements for each chapter
Read Small: Chapter 5
Write 2 ‘take-away’ statements for the chapter
Class 11
April 5
Due: Presentation and Analysis of Student Interview Project
Ratios and Rates
(5th interpretation of rational numbers)
Distance-Rate-Time Relationships
Similarity and Percents
Class 12
April 12
Read Lamon: Chapters 15, 16, and 17
Problem Set: pp. 198-200, #2-5, 9; pp. 209-210, 4, 7, 9, 12; pp. 220224, #3-5, 8, 11, 15-17 (be sure to write down your reasoning process)
Algebra: Integers and Equivalence
Systems of Equations
Classroom Discourse: Teacher Talk Moves
Read YMW: Chapter 7 and Chapter 8
Write 2 ‘take-away’ statements for each chapter
Due: Mathematics Trail Project
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Class 13
April 19
Class 14
April 26
Class 15
May 3
Algebraic Strategies: Minilessons
Data Analysis and Probability
Read Small: Chapter 6
Read YMW: Chapter 9
Write 2 ‘take-away’ statements for each chapter
Changing Rational Number Instruction
Developing Proofs
Read Small: Chapter Conclusions (pp. 181 – 184)
Read YMW: Chapter 10
Read Lamon: Chapter 18
Write 2 ‘take-away’ statements for each chapter in the 3 texts
Due: Lesson Differentiation Project
Final Exam: 6:30 – 9:00 pm
(TBD: IF possible for all students & room availability,
3:00 – 5:30 pm)
Reference Books of Interest:
National Council of Teachers of Mathematics (2002). Making sense of fractions, ratios, and
proportions. B. Litwillwer, & G. Bright (Eds.). NCTM Yearbook. 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.
Sowder, J.T., Philipp, R.A., Armstrong, B.E., & Schappelle, B.P. (1998). Middle-grade teachers’
mathematical knowledge and its relationship to instruction: A research monograph. Albany,
NY: State University of New York Press.
Description of 1st written paper:
Mathematics Autobiography, Individual Goals, and Theory of Students’ Learning of
Mathematics: Due: Tuesday, January 25th
At the beginning of the course, before completing chapter readings or problem sets, 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 highlighting your past experiences in learning mathematics.
FIRST: As you describe your experiences, please respond to the following questions:
• What were your successes, failures, frustrations, or confidence builders in mathematics?
• How did teachers play an influential role, either positively or negatively?
• What games, hobbies, jobs, or other interests support your mathematical interests?
SECOND: In a separate paragraph or using bullet statements, identify the individual goals you plan
to pursue during this course.
THIRD: In a separate paragraph, describe your theory of how students learn mathematics in 7th
grade. This will probably be different for each of us (and that’s OK as we begin learning with each
other this semester). Depending on your different classroom teaching experiences, some of you may
have a lot or just a little to say for your beginning theories.
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