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:              387-3842                                                                            e-mail:

Office Hours:   Tuesdays 11 a.m. – noon, and by appointment at other times.



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 studentsŐ 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 laboratory-oriented 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 studentsŐ 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 2nd class)

á          Coursepack for Math 3520 (Grant) available at the bookstore [Coursepack # WMF07-125]. 


(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.


Course Prerequisites

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.


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).



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 task-based 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 well-grounded 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:

In-Class 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 re-read your class notes, and fill in the gaps in order to ensure that they make sense at a later date.

Post-Class 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.




The following is a tentative outline of the required graded assignments and their weights:

á          Midterm                                                                                                         Ĺ 15% of final grade

á          Comprehensive final                                                                            Ĺ 25% of final grade

á          Writing Assignments, Reflections, etc.                                Ĺ 24% of final grade

á          Course Project (3 parts)                                                                    Ĺ 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 make-up 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 e-mail, or by arranging to have it brought in by a classmate). 


Attendance Policy:

This is a laboratory-oriented 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.



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 havenŐt 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); 269387-2116;


E-mail Policy: 

The only email address that I will use to communicate with you is the one associated with a BroncoNet ID.    [Typical form]  You can access this email account or get instructions for obtaining a BroncoNet ID at


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 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




(to be read before this class)

Tentative Assessments

January 8

Teaching Mathematics for Understanding




Teaching Mathematics for Understanding

Coursepack, p. 4 – 11

Teaching Mathematics in the Context of the Reform Movement (portions)

Ň120-Day Free AccessÓ to NCTM

NCTM Principles and Standards website, Process Standards



Teaching Mathematics for Understanding

NCTM Standards

Coursepack, p. 13 – 29

Choices & Challenges

TN: Reasoning and Proof in Math,Pt2



Number Concepts & Counting

Coursepack, p. 30 – 46

  Counting Cases

Writing 1 Due


Issues in Counting & Lesson Analysis




From Counting
to Addition




Meaning of x/Ö

Coursepack, p. 49 – 61

Modeling the Operations Cases




Fluency &
The Basic Facts

 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



Developing Strategies Beyond Counting




Whole Number



Project #1



Whole Number


Coursepack, p. 84 – 96

LynnŐs Cases

TN:  Reasoning & Proof in Mathematics







Tentative Assessments


Whole Number


Coursepack, p. 97 – 105

Harmful Effects of Algorithms

TNs:  Computational Fluency,

Computational Algorithms & Methods



Whole Number


Coursepack, p. 108 – 115

SusannahŐs cases










March 11

Assessing Student Thinking

Coursepack, p. 116 – 124

Building Assessment into Instruction



Assessing Student Thinking




Lesson Planning

Coursepack, p. 125 – 127

Lappan Article



Lesson Planning, Part 2


Project #2



Analyzing Tasks

Coursepack, p. 128 – 136

Van de Walle (Teaching through problem solving, a Three-Part Lesson Format)



Exploring Representations:

Base-Ten Blocks

Coursepack, p. 137 – 141

TN: Representations & Contexts for Mathematical Work


April 1

Base-Ten Blocks




Manipulatives for

Coursepack, p. 145 – 150

Magical Hopes



Manipulatives for
Fractions, cont.




Student-Generated Representations


Project #3



Creating a Learning Environment

 Coursepack, p. 151 – 172

 Teaching Problems & the Problems of Teaching



Planning to Teach

Coursepack, p. 173 – 179

What I Learned From Teaching Second Grade; & Maintaining Our Integrity


April 21

8:00 a.m.
– 10:00 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 1-2 days.


Investigations in Number, Data, and Space, Second Edition

One of the new K-5 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: ]

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 K-6

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.

Welchman-Tischler, R.  (1992).  How to use childrenŐs literature to teach mathematics.   Reston, VA:  NCTM.

Whitin, D. J. & Wilde, S.  (1992).  Read any good math lately?  ChildrenŐs books for mathematical learning, K-6.  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]