Longwood University
Department of Mathematics & Computer Science
MAED 623 - 21 (Summer 2011)
Instructional Design for Mathematics in Grades K-8
Instructor:
Email:
Dates:
Phone:
Office Hours:
Dr. Maria Timmerman
Course Location: 356 Ruffner
timmermanma@longwood.edu
Time: 9:00 am – 3:30 pm; Lunch: 11:30 am – 12:30 pm
June 17, 20, 21, 22, 23, 27, 28, 29
Office: 434.395.2890
Home: 434.978.7184
By appointment
Office location: 340 Ruffner
Required Texts:
Johnson, K., & Herr, T. (2001). Problem solving strategies: Crossing the river with dogs (2nd edition).
Emeryville, CA: Key Curriculum Press. ISBN 978-1-55953-370-6
National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through
grade 8 mathematics: A quest for coherence. Reston, VA: Author. ISBN: 0-87353-595-2
Small, M. (2009). Good questions : Great ways to differentiate mathematics instruction. Reston, VA : NCTM.
ISBN : 978-0-8077-4978-4
Other Required or Suggested Materials:
 Notebook/sprial notebook for notes, calculator (any type), 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 exam.
Other Information: Students are responsible for checking the ANNOUNCEMENTS and ASSIGNMENTS in
Blackboard in advance of each class period. The website is 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
The course will focus on a study of the K-8 mathematics curriculum and standards, current studies and
trends in mathematics, strategies to teach mathematics to diverse learners, and the role of technology in
the teaching and learning of mathematics through hands-on activities and the use of professional
resources.
Instructional Design for Mathematics in Grades K-8 is one of the core mathematics leadership 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.
Course Objectives:
This course is designed to engage participants in the following:
 investigate various problem-solving strategies and use these strategies appropriately to solve a variety
of mathematical problems.
 communicate mathematically in writing and orally.
 apply strategies to make mathematics accessible for all students (in particular, open questions and
parallel tasks).
 examine the structure of NCTM Principles and Standards and the Virginia Standards of Learning.
 compare performance of US students compared to students from other countries on international tests.
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M. Timmerman
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examine the coherence of mathematics identified in the NCTM Curriculum Focal Points.
identify the strands of mathematical proficiency and describe how they are interwoven.
examine current trends in teaching and learning mathematics with technology.
examine NCTM’s Professional Standards for Teaching Mathematics to determine how to establish highquality teaching and learning of mathematics. (as appropriate for K-8 Mathematics Teacher Specialists.)
In particular, participants will explore a wide variety of K-8 mathematical problems and activities through
structured tasks designed to develop participants’ depth and flexible understanding of mathematical content,
understand developmental stages of how students learn mathematics, and to consider the following elements
used to effectively differentiate mathematics instruction: (a) What are the big ideas related to fundamental
mathematics principles in a given situation? (b) What is the role of student choice, strategies, and models that can
be used to solve problems? and (c) How does assessment inform levels of mathematical development and starting
points for each student?
Course Competencies:
By the completion of this Math 623 course, students should be able to demonstrate:
 Problem Solving: Know, understand and apply the process of mathematical problem solving
(Longwood K-8 Mathematics Specialist Content Portfolio).
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Reasoning and Proof: Reason, construct, and evaluate mathematical arguments and develop an
appreciation for mathematical rigor and inquiry (Longwood K-8 Mathematics Specialist Content
Portfolio).
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Mathematical Communication: Communicate their mathematical thinking orally and in writing to
peers, faculty, and others (Longwood K-8 Mathematics Specialist Content Portfolio).
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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).
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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).
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Effective use of Technology: Embrace technology as an essential tool for teaching and learning
mathematics (Longwood K-8 Mathematics Specialist Content Portfolio).
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Understanding of the knowledge, skills, and processes of the Virginia Mathematics Standards of
Learning and how curriculum may be organized to teach these standards to [all] learners (VA
Mathematics Specialist Endorsement Requirement).
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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
Endorsement Requirement).
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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).
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Understanding of the sequential nature of mathematics and the mathematical structures inherent in
the content strands (VA Mathematics Specialist Endorsement Requirement).
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Understanding of the connections among mathematical concepts and procedures and their practical
applications (VA Mathematics Specialist Endorsement Requirement).
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Understanding of major current curriculum studies and trends in mathematics (VA Mathematics
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Understanding of and the ability to select, adapt, evaluate and use instructional materials and
resources, including professional journals and technology (VA Mathematics Specialist Endorsement
Specialist Endorsement Requirement).
Requirement).
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Understanding of and the ability to use strategies to teach mathematics to diverse learners (VA
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Understanding of major current curriculum studies and trends in mathematics (VA Mathematics
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Understanding of leadership skills needed to improve mathematics programs at the school and
division levels, including the needs of high and low-achieving students and of strategies to challenge
them at appropriate levels (VA Mathematics Specialist Endorsement Requirement).
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Understanding of and proficiency in grammar, usage, and mechanics and their integration in writing
Mathematics Specialist Endorsement Requirement).
Specialist Endorsement Requirement).
(VA Mathematics Specialist Endorsement Requirement).
Course Requirements and Evaluation:
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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.
Attendance, active participation in class
discussions/activities, and mathematics goals,
autobiography, & learning theory paper – 10%
Problem Sets – 20%
Reflective Focus Writings/Assignments – 15%
Lesson Differentiation – 20%
Course Portfolio (includes history of curriculum paper and final reflective summary) – 15%
Final Exam – 20%
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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,
at both morning and afternoon sessions, for you to learn and so that others may benefit from your
input. Missing 4 or more class sessions (AM or PM), 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.
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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 unique extenuating
circumstances may be allowed extensions on a case-by-case basis, but such extensions must be
requested prior to the date the assignment is due.
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Graduate Credit: For each daily class, you should plan to spend 2 to 3 hours nightly on coursework.
This will include preparing for each class session – reading, studying, and completing assignments.
Major assignments will require more time on 3-day weekends built into the course.
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.
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M. Timmerman
Chapter readings and online articles should be completed prior to the class session day as they are listed
in the course outline and announced as postings on Blackboard. 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 and
problem sets.
Problem Sets (Problem Solving Journal): Each day there will be problems assigned using a different
strategy 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 your own work. Problems will be graded on the problem-solving process, effort, use of the
assigned strategy, and at least one alternative strategy (may not exist for every problem). 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 course.
Reflective Focus Writings and Assignments: During the course, you will be asked to reflect on focus
questions related to assigned chapter readings and posted articles on Blackboard. Take-away statements and
specific quotes will often provide the framework for these reflections completed in a word-processed format.
In addition, a few small projects/papers that synthesize readings and websites will be assigned.
Lesson Differentiation: This project will involve revising an existing lesson to incorporate various strategies
to make mathematics accessible for students of varying ability levels. Specific details will be discussed in class.
Course Portfolio: Each student enrolled in this course will complete a course portfolio that will serve as an
assignment for this course, and part of the ‘program portfolio’ for the K-8 Mathematics Specialist Degree
Program. Further guidelines will be provided in class. Due: Friday, July 15th.
Final Exam: A cumulative, closed book in-class exam that focuses on content from the entire course including
but not limited to the following: K-8 mathematics curriculum and standards, mathematics curriculum studies
and trends, focal points, problem-solving strategies, strands of mathematics proficiency, and issues related to
teaching mathematics to all students (e.g., special needs, gifted students, etc.)
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
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:
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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. 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).
ALL TESTS ARE TO BE COMPLETED INDIVIDUALLY.
Please write and sign the honor code on all exams 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
Class
Sessions
Class 1
June 17 AM
Class 2
June 17 PM
Class 3
June 20 AM
Course Content
Assignment: Chapter/Online Readings Before Class Session
Course Introductions
Community of Learners
Mathematizing
History of Mathematics Education
Polya’s Problem-Solving Process and Metacognition
NCTM Principles and Standards
Due: Mathematics autobiography, goals, and theory of how
students learn mathematics paper
TIMSS
VA Content and Process Standards
Unpack the Standards
Strategy: Draw a Diagram, Systematic Lists
PISA
Curriculum Focal Points
Assignment completed before Monday:
Read online articles: see Blackboard postings
Class 4
June 20 PM
Class 5
June 21 AM
Read Johnson & Herr: Chapters 0 (Introduction), 1, and 2;
NOTE: Stop and work the problems in the reading BEFORE reading
the students’ solutions.
Due: Problem Set A, pp. 24-27, #1, 2, 6, 9, 10, 11; Problem
Set A, pp. 44-46, #1, 3, 7
Also, for each assigned problem set, identify and list: (a) Big
Ideas, (b) connections to specific new VA SOL, and (c) attempt 2
different strategies (focus for specific chapter, and an alternate)
In addition: For 1 problem, explicitly identify how you are
using each of Polya’s 4 phases of problem solving.
Globalization and Education
Strands of Mathematical Proficiency
Strategy: Eliminate Possibilities, Matrix Logic
NAEP: Mathematics in the US
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Assignment completed before Tuesday:
Class 6
June 21 PM
Class 7
June 22 AM
Read Johnson & Herr: Chapters 3 and 4
Read Curriculum Focal Points: pp. 1-20
Read online: see Blackboard postings
Due: Problem Set A, pp. 68-71, #2, 6, 8, 10; Problem Set A,
pp. 112-116, #2, 6
Due: TIMSS and Dare-to-Compare Assignment
NCLB and IDEA
Strategy: Look for a Pattern, Guess-and-Check
Differentiate Mathematics Instruction
Core Strategies: Open and Follow-up Questions, Parallel Tasks
Assignment completed before Wednesday:
Class 8
June 22 PM
Class 9
June 23 AM
Read Johnson & Herr: Chapters 5 and 6
Read online: see Blackboard postings
Read Small: Chapter 1
Read Curriculum Focal Points: Appendix, pp. 21-41
Due: Problem Set A, pp. 149-155, #2a, c, f, i, j; 4, 5, 10, 13,
14, 15, 17; Problem Set A, pp. 185-189, #4, 6, 10, 12
Worthwhile Tasks
Classroom-Based Inquiry
Strategy: Subproblems, Unit Analysis
Problem-Based Lesson Planning
Assignment completed before Thursday:
Class 10
June 23 PM
Class 11
June 27 AM
Read Johnson & Herr: Chapters 7 and 8
Read Small: Chapter 2
Read online: see Blackboard postings
Due: Problem Set A, pp. 209-211, #1, 5, 9, 11; Problem Set
A, pp. 257-261, #1, 6, 7, 16
Learning Theories
Accessible Mathematics: Equity an High Expectations
Strategy:Solve an Easier Related Problem, Physical Representations
Access Strategies: Tiering and Scaffolding
Removing Barriers for Struggling Learners
Entry Points for All Students
Assignment completed before Monday:
Class 12
June 27 PM
Read Johnson & Herr: Chapters 9 and 10
Read Small: Chapters 3 and 4
Read online: see Blackboard postings
Due: Problem Set A, pp. 296-298, #1, 3, 4, 5; Problem Set
A1, pp. 304-305, #1, 3, 5, draw representations for ‘acting
it out;’ pp. 319-321, Problem Set A-2, #11, 12, 14, 15
Due: Curriculum Focal Point Assignment
Developing Mathematically Promising Students
Differentiating for Gifted Students
Class 13
June 28 AM
MATH 623 – Summer 2011
Strategy: Work Backwards, Venn Diagrams
Mathematics and Culture
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Family Mathematics Nights
Assignment completed before Tuesday:
Class 14
June 28 PM
Class 15
June 29 AM
Read Johnson & Herr: Chapters 11 and 12
Read Small: Chapters 5 and 6
Read online: see Blackboard postings
Due: Problem Set A, pp. 346-350, #1, 3, 6, 12, 14; Due:
Problem Set A, pp. 377-381, #3, 4, 6, 8
Assessment: Inform Instructional Decisions
and Improve Student Achievement
Opportunities for Teaching with Technology
Assignment completed before Wednesday:
Read online: see Blackboard postings
Read Small: Conclusions
Class 16
June 29 PM
Due: Lesson Differentiation Project
Do Final Exam (in-class)
Due - Friday, July 15th: Course Portfolio
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.
_____. Perspectives on the teaching of mathematics: Sixty-sixth yearbook (2004). R. N. Rubenstein and G. W.
Bright (Eds.). Reston, VA: Author.
_____. Mathematics curriculum: Issues, trends, and future directions: Seventy-second yearbook (2010). B.J.
Reys, R.E. Reys, and R. Rubenstein (Eds.). 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.
Senk, S. L., & Thompson, D. R. (2003). Standards-Based school mathematics curricula: What are they? What
do students learn? Mahwah, NJ: Lawrence Erlbaum Associates.
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
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.
Description of 1st written paper:
Mathematics Autobiography, Individual Goals, and Theory of Students’ Learning of Mathematics:
Due Class Session #1, June 17th.
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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 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:
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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 a separate paragraph, describe your theory of how students learn mathematics in 3rd 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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