MTED 2250: TEACHING MATH IN ELEMENTARY SCHOOLS
MTED 2250: TEACHING MATH IN ELEMENTARY SCHOOLS
Instructor: Carrie Altman
Contact Information: [email protected]
Office Hours: By appointment
The goal for this class is to prepare you to teach mathematics by exploring mathematics teaching strategies and
philosophies. We will explore the state of mathematics education today and use that knowledge to discuss
teaching methods that might be more effective. I hope to give you the skills and tools to start teaching
mathematics with confidence so that you can give your students a toolkit for success in math.
Please obtain a copy of Writing in Math Class by Marilyn Burns (see below for complete source). This is not in
the university bookstore. The cheapest place I have found it is on amazon.com for under $17. You will need
this book by the beginning of October; please do not delay in ordering it. All other readings will be on e-
reserve or handed out in class. A guideline of readings is on the syllabus; readings may be adjusted depending
on the pace or needs of the class.
A primary goal for this class is for students to sort through their own beliefs about mathematics education and
to refine their philosophies of mathematics education. For this reason, it is essential that all students participate
in class discussions on a weekly basis. Students are expected to come to class every week, prepared to learn.
Assignments are given well in advance; for this reason, there is no excuse for coming to class without reading
the assigned material. Please come with a comment to share about each reading and do not be surprised if I ask
your view of a particular excerpt. It is expected that all students will be respectful of each other’s comments. I
expect your undivided attention during class; there is a lot of material to cover in two hours. Cell phones must
be turned off before students enter the classroom.
Since this class only meets once a week, it is imperative that students come to class unless there is an
emergency. Students may miss one class without penalty or excuse. Each subsequent absence will lower a
student’s class participation grade by twenty points. Repeated tardiness will also affect a student’s class
There will be two opportunities for group work in this class. It is expected that all students share the weight of
these projects. Please be aware of all students’ schedules and meet at a time that is convenient for all members
of the group. It is expected that all students participate in the presentation of the material. Please be respectful
of your classmates.
All assignments are due at the beginning of class on their due date (unless specified otherwise in class) and will
be considered late if not handed in at that time. Late assignments will be penalized by 10 points per day late. If
your assignment is late, please email it to me when it is finished and bring a hard copy to the next class.
Collaboration and sharing of ideas is important during class time; however, please do not use other students’
ideas for your own assignments. I will also be thrilled for you to use outside resources when getting ideas for
lessons; however, please cite any ideas that are not your own. If you have a question about using someone
else’s work, please feel free to email me.
Assignment #1: 6 Journal Entries (60 pts.)
Assignment #2: Writing in Math Class (40 pts.)
Assignment #3: 3 Lessons to be Taught in Practicum Placement (90 pts.)
Assignment #4: Student Interview Assignment (90 pts.)
Assignment #5: Philosophy of Mathematics Education (150 pts.)
Class Participation (60 pts.)
This class is about refining your definition of mathematics education. For this reason, it will be
important for you to reflect on what you are learning and applying in and out of class. You must complete 6
journal assignments throughout the semester. Each one should be at least one page in length, long enough to
develop your reasoning. You may choose when to complete these assignments but please date them; I want to
know when you were thinking these things. These journals are due in groups of three; see calendar for due
dates. Do NOT put these off until the last minute, but please allow some time between them for growth.
Please choose from the following topics; you may use each topic no more than once and may have one
journal that is on a topic of your own choosing. I am looking for all of these to be in light of our classroom
readings and discussions.
Observe another teacher giving a math lesson for children. What went well? Would could be
done differently? How else might this topic be approached? How does this relate to our
readings and discussions? (This must be a different lesson from your student interview
Reflect on one of the readings for our homework. What was new to you? Do you agree or
disagree with the author? Why? How does this change your view of mathematics education?
Reflect on our class discussion. What did you learn? What does this make you want to learn?
What do you want to try in the classroom?
Describe an experience you had teaching math. What went well? What would you do
differently next time?
Describe a particular student during a math class, either taught by you or another teacher. What
did he or she understand or misunderstand? Did the light bulb go on? What could be done to
follow up with this student?
Reflect on your experience taking math classes as a child or young adult. What strategies did
you use? What teaching strategies were employed? What did you understand or misunderstand?
Informally interview another teacher about teaching math. What did you learn? What strategies
does he or she use?
How is your philosophy of mathematics education changed? How does this affect your approach
2) Writing in Math Class:
This assignment will be completed in groups and is a two-part assignment. You will be assigned a
chapter to read in the Marilyn Burns book. You and your group will read the assigned chapter and then present
a summary to the class. You should have a handout copied for the class and all group members should
participate in the presentation. This will be done twice during the semester. Do not make this more
complicated than it is; presentations should be no longer than 10 minutes. Use whatever tools you want to make
your presentation. PowerPoint is not required; just be organized.
3) 3 Lessons to Be Taught in Practicum Placement:
These assignments are to be completed in conjunction with your practicum placement. You may turn
these three assignments as you complete them, but they must be turned in within 1 week of teaching the
lesson. Each will be worth 30 points.
Before teaching each lesson, you will write a detailed lesson plan. The following should be addressed in
your lesson plan: goals, state and NCTM standards, materials needed, time allotted, lesson sequence (hook,
content, and check), and extension activities. I should be able to read your lesson plan and know what you hope
the students will learn, how you will teach it, and what you will do to see if they learned it. Please email me a
copy of your lesson plan (as well as Andrea Henrie) 1 week prior to teaching it. If there is a problem with
this, email me.
After you teach your lesson, you will write a short (1-2 page) reflection on what happened. What went
as planned? What surprised you? What did the students learn? What did they miss? What would you do
differently if you could do it again? No lesson goes perfectly. This is as much about learning from failure as
success; I am interested in your process and thoughts more than thinking you are a magnificent teacher. This is
due within 1 week of teaching it.
4) Student Interview Assignment:
You will use one of your practicum observations to complete this assignment. During your observation,
make note of what strategies the teacher is using. What are the students doing and how are they responding to
the instruction? You will be focusing on individual student learning with respect to the instruction. After the
lesson, interview at least one student independently. Ask the student to complete a similar task to the one
presented in the lesson and to explain his or her thinking. You may use math journals but please also ask the
student to explain verbally. If possible, audio record the interview
Answer the following questions in your assignment: What happened during the lesson (brief synopsis)?
What do students seem to understand and what is the evidence? How did the teacher's instruction support this
understanding? What would be the next logical steps in the development of students' understanding and
instruction to support that development? Relate your observations to the discussions and readings from our
class. This paper should be 4-6 pages.
3) Philosophy of Mathematics Education:
This is a compilation of artifacts that hope will be helpful in clarifying your views on mathematics
education. You will create a series of items to exemplify how you would like to teach math in your classroom
and to help you during your first weeks of teaching. This assignment will include the following:
Your written philosophy of mathematics education and why you feel it supports student learning
Rules for discourse in your classroom
A letter/brochure/video for parents to explain how they can support their child’s mathematical learning
3 Games - ready to use in the classroom or to be sent home
5 Journal prompts to be used in your classroom and what learning you hope they will assess.
While there are no right and wrong philosophies to mathematics education, you must support your conclusions.
Your philosophy should be consistent with your rules, explanation to parents, games, and journal prompts. I am
looking to see that you have really thought about how you want to teach and that you are preparing to do so.
DATE TOPIC READINGS ASSIGNMENTS DUE
9/3/07 Introduction and Course Overview
9/10/07 State of Mathematics Education Stonewater (2005) Come prepared with 3 questions
Today Stigler & Hiebert (1999) on each reading
9/17/07 Mathematical Concepts and Marshall (2006) What are the 3 most confusing
Language Brandy (1999) language terms?
9/24/07 How Do Students Learn Math? Burns & Adams (2000) What do most parents not know
Burns (2000) p.24-42 about math education?
10/1/07 Strategies for Teaching Math Burns (1999) What strategies do you find most
Nicol, Kelleher & effective?
Saundry (2004) 1st Teaching Lesson
10/8/07 What is a Word Problem? Burns (2000) p.15-23 How is this the same/different
Burns (1995) – Part 1 from the way you were taught
10/15/07 Writing in Math Class Burns (1995) – Part 2 First 3 Journals
(to be divided) Writing in Math Class
Stix (1996) Presentation #1
10/29/07 Number Conservation and Place Copeland (1984) How were you taught place
Value Sharma (1993) value?
2nd Teaching Lesson
11/5/07 Writing in Math Class Burns (1995) – Part 3 Writing in Math Class
Subtraction and Regrouping (to be divided) Presentation #2
11/12/07 Using Manipulatives for Problem Moyer & Jones (2004) What manipulative do you think
Solving Moyer, Bolyard & is most effective?
Spikell (2001) Student Interview
11/26/07 Examples of Lessons & Problem Meron & Peled (2004) Be prepared to share one of your
Solving Strategies Cowens (2004) teaching lessons.
Gibson (2004) 3rd Teaching Lesson
12/3/07 Using Literature to Enhance Meagher (2005) Bring a book to share (or tell
Mathematics Instruction Burns & Silbey (2000) about it if you must).
Diffily (2001) Last 3 Journals
12/10/07 Wrap Up & Games Day Bring a game to share with the
Philosophy of Mathematics
Assignments in bold will be collected at the beginning of the class period. Those in regular type need
not be turned in and are to help you apply the readings in the context of the course.
Cynthia Nicol, Heather Kelleher & Carole Saundry (2004, July). What a Simple Task Can Show: Teachers
Explore the Complexity of Children’s Thinking. International Group for the Psychology of Mathematics
Education (2004), 3, 145-152.
Deborah Diffily (2001). Using Literature to Teach K-1 Math Concepts. 1-17.
James W. Stigler & James Hiebery (1999). Refining the Images. The Teaching Gap: Best Ideas from the
World’s Teachers for Improving Education in the Classroom. New York, NY: The Free Press, 55-72.
Jerry K Stonewater (2005). Inquiry Teaching and Learning: The Best Math Class Study. School Science and
Mathematics, 105(1), 36-47.
John Cowens (2004, October). Measure a Tree. Teaching Pre K – 8, 35(2), 41,43-44.
John Marshall (2006). Math Wars 2: It’s the Teaching, Stupid! Phi Delta Kappan, 87(5), 356-363.
Kathy Gibson (2004, September). Math Doesn’t Always Have to Be Taught as Math! Technology and Children,
Liping Ma (1999). Subtraction with Regrouping: Approaches to Teaching a Topic. Knowing and Teaching
Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United
States. Mahwah, NJ: Lawrence Erlbaum Associates, 1-27.
Marilyn Burns (1995). Writing in Math Class: A Resource for Grades 2-8. Sausalito, CA: Math Solutions
Marilyn Burns (2000). Beyond Word Problems & Managing the Classroom for Problem Solving. About
Teaching Mathematics: A K-8 Resource. 2nd Ed. Sausalito, CA: Math Solutions Publications. 15-42.
Marilyn Burns (2007, March). Marilyn Burns: Mental Math. Instructor (1999), 116(6), 51-54.
Marilyn Burns and Robyn Silbey (2000). So You Have to Teach Math? Sound Advice for K-6 Teachers.
Sausalito, CA: Math Solutions Publications, 79-91.
Mahesh C. Sharma (1993). Place Value Concept: How Children Learn it and How to Teach it. Math Notebook.
Center for Teaching / Learning of Mathematics, vol. 10.
Mary Burns and Sharon Adams (2000). Using What Learners Know. TAP into Learning, 2(2), 1-8.
Patricia S. Moyer, Johanna J Bolyard & Mark A Spikell. (2001). Virtual Manipulatives in the the K-12
Classroom. In: Proceedings of the International Conference on New Ideas.
Paticia S Moyer, M Gail Jones (2004). Controlling Choice: Teachers, Students, and Manipulatives in
Mathematics Classrooms. School Science and Mathematics, 104(1), 16-31.
Peter Wright (1994). Let’s Not Let the Number of Warthogs Be “X”. In: Recreating the Revolution.
Proceedings of the Annual National Conference.
Richard W. Copeland (1984). Conservation of Number and Place Value. How Children Learn Mathematics:
Teaching Implications of Piaget’s Research. 4th Ed. New York, NY: Macmillan, 105-126.
Ruth Meron and Irit Peled (2004). Situated or Abstract: The Effect of Combining Context and Structure on
Constructing an Additive (Part-Part-Whole) Schema. International Group for the Psychology of Mathematics
Education (2004), 4, 1-8.
Sandy Meagher (2005, Januray). All Around Math. Teaching Pre K – 8, 35(4, 79-80.
Tim Brandy (1999).Watch Your Language. “So What?” Teaching Children What Matters in Math. Portsmouth,
NH: Heinemann, 32-55.
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