MATH 3520:
Teaching Elementary School Mathematics
Spring 2008
T Th 9:30 a.m. – 10:45 a.m.
Instructor: Dr. Theresa J. Grant Office: 4427 Everett Tower
Phone: 3873842 email: terry.grant@wmich.edu
Office Hours: Tuesdays 11 a.m. – noon, and by appointment at
other times.
COURSE DESCRIPTION
This course is designed to give prospective elementary teachers an understanding of what it takes to teach mathematics successfully to children. It is extremely challenging to teach mathematics well and we will be working on several aspects of what it takes to do this. First, it is important that you understand the content well that you will be teaching to children. Beyond understanding the content, you must also have the wherewithal to anticipate the ways children might think about the content and the kinds of strategies they might use to solve various problems. As a teacher, how do you make decisions about how to help students who are struggling with the material? What will support them to gain an understanding of what they are learning so that they will have the confidence to move forward? How do you make decisions about how to extend students who might have a solid understanding of the material at hand? And perhaps one of the most critical questions is how you determine whether a child has a solid understanding of mathematics in the first place.
All of these decisions impact what teachers do in the classroom to create an environment where students are challenged to think, to learn mathematics with understanding (rather than rote memorization), and to make connections among mathematical ideas. You will be challenged to think about how the culture you set in the classroom shapes what students will do to learn mathematics and what they will learn to value. We will focus on what kinds of lessons produce what kinds of thinking and work on developing your own lessons to promote understanding.
The focus of this course will be on knowing
mathematics for teaching. What does
that entail? First, you will
consider what is important for your students to learn. In other words, what kinds of
understanding, skill, and practices do you want to develop in your
students? Second, you will think
about what it is you need to know in order to support their learning. Teaching depends on particular kinds of
mathematical understanding and skill different from what it takes to do well in
a math course as a student yourself.
In preparing to teach, a teacher should prepare mathematically for what
might happen as a lesson unfolds, prepare good questions to elicit thinking,
and think carefully about the amount and kind of information you provide to
students to support their work.
We will focus this semester, then, on developing
mathematical knowledge that is useful in teaching. Our focus on the mathematical content will be on number work,
particularly whole numbers and fractions, with some work on other topics. Within these topics, we will also work
on mathematical teaching practices, focusing on what teachers must do to
support their studentsÕ understanding.
These foci have been selected because they are central to so much of the
elementary school curriculum and because teaching them well is not easy.
This is a laboratoryoriented course where you will experience many different activities for teaching children. You will learn from doing the activities what you cannot possibly learn from reading about them or copying notes from another student in class. Therefore, attendance is essential. [See attendance policy on the next page.] A semester is also a short time to learn about these complex ideas about teaching mathematics. However, if you work hard and attentively this term, you will learn mathematics for teaching. You will develop skills of watching and listening that enable you to make sense of how others think mathematically and express themselves in multiple ways. You will develop practices that enable you to create a classroom environment for learning mathematics, to attend and respond to studentsÕ mathematical ideas and ways of thinking, and to plan, teach and analyze mathematics lessons. You will have enhanced your knowledge of mathematics in ways that will prepare you for the specific work of teaching. By the end of the semester, you should have developed an understanding of the process required to continue to learn how to teach so that you can continue to grow throughout your career.
Course Materials (available at the
bookstore in Bernhard – purchase before 2^{nd} class)
á
Coursepack for Math 3520 (Grant) available at the bookstore
[Coursepack # WMF07125].
IF THE BOOKSTORE RUNS OUT OF COPIES, YOU MUST:
(1) Fill out an MTO (Made To Order) form at the
Information Desk of the bookstore,
(2) PAY for the order at that time, and then (3) pick it up after 10:00
a.m. the next day.
á
Completion of Math 1500, 1510 and 2650 with grades of C or
better is required. Those not meeting the course prerequisites will be automatically
dropped from the course by the Mathematics Department. Finally, if you are pursuing the
Elementary Mathematics Minor, you must maintain a grade of B or better in all
courses in this minor.
á
YOU MUST HAVE BEEN ADMITTED TO THE ELEMENTARY EDUCATION
PROGRAM.
In addition, it is highly recommended that you do not take
this course until after you have taken educational psychology (either ED 3090 or ED 3100).
Projects:
The
projects will
give you the opportunity to work with peers to experience the kinds of
activities necessary for developing your ability to teach mathematics
effectively. The first two projects will focus on number and operations. In the first project, you will analyze one
particular lesson from a reform curriculum and one particular lesson from a
traditional curriculum on the same topic, and think about how each lesson does
or does not encourage children to learn the content with understanding. In the second project, you will
implement and analyze a taskbased interview with an elementary student to
explore the range of important mathematical ideas relevant to number and operations. The third project will involve the
analysis of several related tasks within a different mathematical topic (e.g.,
data analysis, geometry). You will be given detailed descriptions of each
project during the semester, including specific grading rubrics.
Class Participation:
Class
participation is absolutely critical for all of you to get the most out of the
activities we do and discussions we have in class. As you work on formulating your personal philosophy about
teaching mathematics, it is imperative that you consider ideas other than your
own and weigh the advantages and disadvantages of specific instructional
approaches. Therefore, effort will
be made to elicit various beliefs about teaching so that as a group we can
consider each option. By the end
of the semester, your ideas about teaching will be informed by perspectives
from other students, from mathematics educators, from authors of articles and
case studies, and from watching real students in real classrooms. The extent to which you make an effort
to participate during small group time (and take advantage of this time to work
through ideas) as well as participate during whole group time will impact your
ability to formulate a wellgrounded philosophy about teaching mathematics. Consistent and productive participation
in class will be considered in determining final grades in borderline cases,
assuming the student has a solid passing grade in the class.
Course Notebook:
Students typically have difficulty taking notes in this class, and
so we have specific suggestions for how to organize your ideas from this course
so that they will be useful to you when doing assignments and preparing for
exams, as well as for when you begin to teach. Your notebook should include the following different types
of entries:
InClass Notes:
These should capture what we do in class by listing
activities, drawing any representations we discuss, and jotting down ideas that
are discussed. After every class
you should also set aside about 5 minutes to reread your class notes, and fill
in the gaps in order to ensure that they make sense at a later date.
PostClass Notes:
These should include the following: 1) a summary of the important issues/points from class; and 2) your reactions to these points where you discuss which ideas/issues surprised you, which ideas you are
continuing to think about and in what way, and 3) what connections you are
noticing across classes, and which
ideas you would still like to learn more about.
Reading Notes:
For every individual reading that is assigned,
your reading notes should include:
1) a summary of
important ideas/arguments made in the reading, 2) your reactions to these ideas/arguments, where you discuss which ideas/issues you agree with,
and which ideas you are questioning and in what way, and 3) what connections
you are noticing, across readings
and/or between this reading and class activities. In some cases, you may be given
specific questions to help you reflect on a set of readings.
COURSE REQUIREMENTS AND GRADING POLICY
The following is a tentative outline of
the required graded assignments and their weights:
á
Midterm Å
15% of final grade
á
Comprehensive final Å
25% of final grade
á
Writing Assignments, Reflections, etc. Å
24% of final grade
á
Course Project (3 parts) Å
36% of final grade
IF ALL course requirements have been met, grades will
be assigned according to the scale:
A Outstanding, exceptional, extraordinary 93% – 100%
BA 88%
–92%
B Very
Good, High pass 82%
– 87%
CB 77%
– 81%
C Satisfactory, acceptable, adequate 71% – 76%
DC 66%
– 70%
D Poor 60%
– 65%
E Failing Below 60%
NOTES: You must attain at least a C (71% or higher)
in this course in order to take the Math & Science Practicum (ED402). In order to pursue the Elementary
Mathematics Minor, you must attain at least a B (82% or higher) in all
elementary mathematics courses.
The exams
will cover the content of class discussions and assigned readings. [Not all the things discussed in class
will be in the readings, and not all readings will be discussed in class.] No makeup exams or quizzes will be given. NOTE: the last exam is during Finals Week. The assignments will be
handed out in class and must be turned in by the specified due date (and time). Only one late assignment will be
accepted per semester as long as it is turned in before the assignment has been
discussed in class, or the graded assignments have been returned; the grade of
a late assignment will be automatically lowered by one letter grade per day
(24 hour period). If you are absent the
day an assignment is due, you are still required to submit the assignment on
time (either by email, or by arranging to have it brought in by a
classmate).
Attendance Policy:
This is a laboratoryoriented course
where you will experience many different activities for teaching children. You will learn from doing and
discussing the activities what you cannot possibly learn from reading about
them or from copying notes from another student in class. Therefore attendance and participation
are essential. Not only do
excessive absences suggest a lack of professionalism and commitment, but they
guarantee that you will not attain the objectives of this course. Your final grade will be lowered by
one letter if you have more than two absences, excused or unexcused. If you have excessive absences (more
than 4 for the semester), you will not receive higher than a grade of C
regardless of your performance on assignments and exams. Attendance will be taken at the
beginning of class. If you are late,
it is your responsibility to notify the instructor (after class) of your
presence. [Each late
arrival or early leave will count as half an absence if you are late/leave
early more than twice.]
In
the event that you must be absent from class, it is your responsibility
to:
(1)
let me know before the missed section, if at all possible;
(2)
obtain the notes and handouts for missed class from a peer;
(3)
reflect on these notes;
(4)
read the required readings before the next class;
(5)
after you have reviewed all of the material above, make an
appointment with me to discuss any questions you have about the material.
Policy on Incompletes:
Three conditions must be met for an
incomplete:
(1) you must have completed most of the
coursework;
(2)
your current grade is DC or better; and
(3)
circumstances beyond your control prevent the completion of the
coursework on time.
All incomplete grades
must be approved by the Chair of the Mathematics Department.
Accommodations
Any student with a documented disability (e.g., physical,
learning, psychiatric, vision, hearing, etc.) who needs to arrange reasonable
accommodations must contact the professor and the appropriate Disability
Services office at the beginning of the semester. If you believe you need some
type of accommodation due to a disability and havenÕt yet talked with the
Disabled Student Resources and Services office, here is their contact
information: 2210 Wilbur Ave (across from Rood before the Health Center, above
the Day Care Center); 269‑3872116; http://www.dsrs.wmich.edu.
Email Policy:
The only email address that I will use to communicate with you is the one associated with a BroncoNet ID. [Typical form firstname.lastname@wmich.edu.] You can access this email account or get instructions for obtaining a BroncoNet ID at GoWMU.wmich.edu.
Academic Integrity
You are responsible for making yourself aware of and
understanding the policies and procedures in the Undergraduate and Graduate
Catalogs that pertain to Academic Honesty. These policies include cheating,
fabrication, falsification and forgery, multiple submission, plagiarism,
complicity and computer misuse. [The policies can be found at
www.www.wmich.edu/catalog under Academic Policies, Student Rights and
Responsibilities.] If there is reason to believe you have been involved in
academic dishonesty, you will be referred to the Office of Student Conduct. You
will be given the opportunity to review the charge(s). If you believe you are
not responsible, you will have the opportunity for a hearing. You should
consult with me if you are uncertain about an issue of academic honesty prior
to the submission of an assignment or test.
Tentative Schedule
DATE 
TOPIC 
READINGS 
Tentative Assessments 
January 8 
Teaching Mathematics for Understanding 


10 
Teaching Mathematics for Understanding 
Coursepack, p. 4 – 11 Teaching Mathematics in the Context of the Reform Movement
(portions) Ò120Day Free AccessÓ to NCTM NCTM
Principles and
Standards website, Process
Standards 

15 
Teaching Mathematics for Understanding NCTM Standards 
Coursepack, p. 13 – 29 Choices
& Challenges TN:
Reasoning and Proof in Math,Pt2 

17 
Number Concepts & Counting 
Coursepack, p. 30 – 46 Counting Cases 
Writing 1 Due 
22 
Issues in Counting & Lesson Analysis 


24 
From Counting 


29 
Meaning of x/Ö 
Coursepack, p. 49 – 61 Modeling the Operations Cases 

31 
Fluency & 
Coursepack, p.
64 – 67 Models of Problem Solving DB: Introducing
Problems with Unknown Change 

February 5 
Developing Strategies Beyond Counting 
Coursepack, p. 73 – 83 Thinking in Units Stickers: A
Context for Place Value Place Value in Grade 2 

7 
Developing Strategies Beyond Counting 


12 
Whole Number Computation 

Project #1 DUE 
14 
Whole Number Computation 
Coursepack, p. 84 – 96 LynnÕs Cases TN: Reasoning & Proof in
Mathematics 

DATE 
TOPIC 
READINGS 
Tentative Assessments 
19 
Whole Number Computation 
Coursepack, p. 97 – 105 Harmful Effects of Algorithms TNs:
Computational Fluency, Computational Algorithms & Methods 

21 
Whole Number Computation 
Coursepack, p. 108 – 115 SusannahÕs cases 

26 
Interviewing 


28 
MIDTERM 


WMU SPRING BREAK 

March 11 
Assessing Student Thinking 
Coursepack, p. 116 – 124 Building
Assessment into Instruction


13 
Assessing Student Thinking 


18 
Lesson Planning 
Coursepack, p. 125 – 127 Lappan Article 

20 
Lesson Planning, Part 2 

Project #2 DUE 
25 
Analyzing Tasks 
Coursepack, p. 128 – 136 Van de Walle (Teaching through problem solving, a ThreePart
Lesson Format) 

27 
Exploring Representations: BaseTen Blocks 
Coursepack, p. 137 – 141 TN:
Representations & Contexts for Mathematical Work 

April 1 
BaseTen Blocks 


3 
Manipulatives for 
Coursepack, p. 145 – 150 Magical
Hopes 

8 
Manipulatives for 


10 
StudentGenerated Representations 

Project #3 DUE 
15 
Creating a Learning Environment 
Coursepack, p. 151 – 172 Teaching Problems & the
Problems of Teaching 

17 
Planning to Teach 
Coursepack,
p. 173 – 179 What I
Learned From Teaching Second Grade; & Maintaining Our Integrity 

April 21 
8:00 a.m. 
Final Exam


Resource
Books On Reserve In Sangren Library
The following books are on reserve at Sangren Library, under the
course number M3520 and the names Terry Grant and Kate Kline. Most of the books are on
"closed" reserve, can be checked out for a few hours, or in some
cases 12 days.
Investigations in Number, Data, and Space, Second Edition
One of the new
K5 mathematics curricula based on the NCTM Standards. Each grade level has
between 9 books on different topics, except Kindergarten which has 7
books. Choose any one of the
books for a particular grade level, open to the first page and you will see a
list of the titles and topics for every book at that grade level. DO NOT TEAR PAGES OUT OF THESE
BOOKS.
The NCTM Standards Documents
NCTM (2000). Principles
and standards for school mathematics.
Reston, VA: NCTM.
[Available on
line at: http://standards.nctm.org
]
NCTM (1989) Curriculum & evaluation standards for school
mathematics. Reston,VA: NCTM.
NCTM (1991). Professional
standards for teaching mathematics. Reston, VA: NCTM.
NCTM (1995). Assesment
standards for school mathematics.
Reston, VA: NCTM.
NCTM Addenda to the Curriculum
& Evaluation Standards for K6
Burton, G. M.
(1993). Number Sense and
Operations. Reston, VA: NCTM.
Del Grande, J. J.
(1993). Geometry and
Spatial Sense. Reston,
VA: NCTM.
Lindquist, M. M.
(1992). Making Sense of
Data. Reston, VA: NCTM.
Coburn, T. G.
(1992). Patterns. Reston, VA: NCTM.
Using Literature
Theissen,
D. & Matthias, M. (1992). The wonderful world of mathematics. Reston, VA: NCTM.
WelchmanTischler,
R. (1992). How to use childrenÕs literature to
teach mathematics.
Reston, VA: NCTM.
Whitin,
D. J. & Wilde, S. (1992). Read any good math lately? ChildrenÕs books for mathematical
learning, K6. Portsmouth,
NH: Heinemann.
Multicultural Connection
Zaslavsky,
C. (1996). The Multicultural Math Classroom:
Bringing in the World.
Portsmouth, NH: Heinemann.
[not on reserve]
Zaslavsky,
C. (1973). Africa Counts: Number and Pattern in
African Culture.
Boston: Prindle, Weber
& Schmidt. [not on reserve]