CI 4030: Teaching Mathematics in the Elementary School
Spring 2007
Block 433, TF 12:00-1:50 ED 214
Block 435, TF 3:00-4:50 ED 224
Instructor: Dr. Kathleen Lynch-Davis
318D Duncan Hall
Office Phone: 262-7247
Home Phone: (336) 977-4812
Email:
Office Hours: Monday- 10:30-12:30
Wednesdays-10:30-12:30
Fridays-10:30-11:30
Please feel free to call anytime. Phone calls and email messages will be returned promptly.
Required Text: Van de Walle, J. A. (2004). Elementary and middle school mathematics: Teaching developmentally. Boston: Pearson Education.
North Carolina Standard Course of Study for Mathematics K-5. http://www.dpi.state.nc.us/curriculum/mathematics/scos/
National Council of Teachers of Mathematics. Curriculum Focal Points. (Grades K-5) http://www.nctm.org/focalpoints/downloads.asp
Other readings: Throughout the semester, readings will be required that will be on reserve in the library or handed out in class.
Supplementary Materials: A TI-15 calculator, a NC Overhead Manipulative Kit , we will use pieces of this kit throughout the semester. I will let you know prior to each class meeting what you will need.
Course Goals
This course will help you think about teaching and learning mathematics in grades K-6. It will not provide a "recipe" for good elementary mathematics teaching. Rather, the course readings, outside assignments, class activities, and discussions will provide opportunities for you to think about the learning and teaching of mathematics in ways that enable you to make good instructional decisions. It is necessary to give careful consideration to the content and methods of mathematics instruction that will help your students be successful in today's world. The discipline of mathematics is growing and changing. Over half of all mathematics has been invented since World War II. It is impossible for any one person to know all there is to know or to be able to predict the specific mathematical content of problems that one might encounter, but it is important for people to be able to make sense of mathematical situations. Success in the 21st century will be available to students who possess more than a large number of facts and computational skills.
Teaching in North Carolina requires that you use the Standard Course of Study to guide your curriculum decisions. There are five math strands with problem solving permeating the entire curriculum: number and operations; measurement; geometry; algebra; and data analysis and probability. At the end of each school year in grades 3-6, students take an end-of-grade (EOG) test. In a single two credit hour course, it is impossible to adequately work with everything that you need to know to be an elementary math teacher and everything you will be responsible for regarding EOG tests and other K-2 assessments. The strand focus for this course is geometry and assessment. You explored three strands in Math 2030 and a fourth strand in CI 3030. Thus by the end of your program, you will have experienced some work with all five of the strands in the Standard Course of Study.
Goals for the course span across several interrelated areas. You will probably notice that they are stated as areas you are "beginning to" learn about since these are areas that you will continue to work on during your elementary education program and ones that teachers work on improving across their careers.
Understanding Mathematics to Teach: You will begin to expand your understanding of mathematics as it relates to geometry and geometric thought and expand your perspective about what mathematics is and what it means to learn mathematics to teach.
Understanding Yourself as a Learner of Mathematics: You will begin to examine yourself as a learner of mathematics. This will enable you to compare and contrast the kinds of instruction you experienced throughout your schooling and the approach to teaching you want to develop across your career. Learning to pay attention to your prior learning experiences as a learner of mathematics will help you articulate, challenge, and revise assumptions about teaching and learning mathematics.
Understanding Children as Learners: You will begin to learn how children's mathematical knowledge, skills, and disposition develop over time. You will learn to think about ways to adapt planning and instructional strategies to the learning needs of diverse individuals and groups.
Developing Knowledge of Curriculum and Planning: You will begin to construct knowledge of mathematics curriculum and how to select and organize content, skills, and strategies. This will include exploring the geometry strand from the North Carolina Standard Course of Study.
Understanding Assessment: You will begin to learn ways to assess students' mathematical understanding. You will examine the various purposes of assessment. You will work closely with one student to assess his/her mathematical understanding.
Establishing and Managing an Equitable Community of Mathematics Learners: You will begin to explore what it means to create a mathematical learning community that fosters mathematical learning for all students, taking into account their gender, race, ethnicity, socioeconomic status, language use, special needs, and personal qualities. You will examine ways in which particular classroom discourse patterns and particular tasks influence diverse learners as they learn mathematics.
Understanding Yourself as a Colleague: You will have many opportunities to work with peers throughout this course. Collaborating in a variety of professional activities and reflecting on your participation will initiate you in collaboration with colleagues across your career.
Course Themes and Central Questions
In the contexts of teaching and learning mathematics, we will explore three major themes to help us work toward the course goals.
MYSELF AS A LEARNER: How did/do I learn mathematics? How do my own past and present experiences compare with what I want for learners in my own classroom? What kind of learning in mathematics will I need to continue to pursue across my career?
SOCIAL CONSTRUCTIVISM: How do diverse students learn mathematics? What role does social interaction play in their learning? How do learners construct understanding? In what ways am I similar to or different from the learners I will teach (e.g., race, ethnicity, culture, socio-economic, ability linguistic, gender)? What implications do these comparisons have for my teaching and my students’ learning?
ALTERNATIVE IMAGES OF PRACTICE: What do classroom practices that draw on recent research and theories look like? How can I create the kind of classroom I envision? What goals, materials, discourse patterns, and tasks will facilitate learning in mathematics? How should I plan for the kind of instruction I envision?
NCDPI Standards
Consequently, your instruction and experiences in this course will help you begin to meet several of the North Carolina Department of Instruction standards for elementary education teachers.
NCDPI Standard 2: Elementary teachers have a broad knowledge and understanding of the major concepts in mathematics.
NCDPI Standard 7: Elementary teachers use developmentally appropriate strategies to design and deliver instruction in all areas of the elementary curriculum.
NCDPI Standard 9: Elementary teachers understand and use the processes of problem solving, reasoning and proof, communication, connection, and representation as a foundation for the teaching and learning of mathematics.
NCDPI Standard 15: Elementary teachers encourage underrepresented groups to engage in the schooling process, especially math and science.
Grading Policies and Assignments
Grading: Grading expectations will be made clear prior to the due date for each assignment. You are strongly encouraged to meet with me to discuss questions about the assignments. Your final grade for the semester will be based on a series of written assignments, a test, class attendance and participation. Specific guidelines and grading criteria will be given over the course of the semester. I reserve the right to reduce the grade on late assignments. Your final grade will be determined as follows:
Weekly Assignments, Participation 10%
POW 5%
Article Critiques 10%
Investigating Resources 5%
Field Assignments
· Case Study Project 20%
· Lesson Plan Project 20%
Professional Development 5%
Tests (1 or 2)* 25%
TOTAL 100%
*You must receive at least a C on the tests to pass the course. You must complete all assignments to pass the course, this includes the field experience assignments.
Your participation in our class activities and discussions is important not only for your learning but also the learning of others. You are strongly encouraged to be prompt for each class. Two tardies will be treated as an absence. You are allowed one absence in this class. Every absence beyond this will result in your grade being decreased by one letter, for example an A will go to an B.
Grading Scale:
A = 94-100%
A- = 90-93%
B+ = 87-89%
B = 83-86%
B- = 80-82%
C+ = 78-79%
C = 76-77%
C- = 74-75%
D = 69-73%
Academic Integrity Code:
The Appalachian State University Integrity Code will be followed in all cases of academic misconduct. The Code may be viewed at:
http://www.academicaffairs.appstate.edu/academic_integrity_index.htm
Violations of this code by teacher education candidates are regarded as particularly serious and may result in removal from the program.
Weekly Assignments and Participation: These assignments could include but are not limited to in-class activities, homework problems, responses to class readings, and lesson plans. You will read and/or complete reading responses as scheduled. You also will be asked to write reflections about the work we do during class. Writing can help you to clarify and stretch your thinking about teaching. Throughout the semester, I will collect your writing and reflections. Reflections consist of more than descriptions and involve in-depth analysis. In addition, you will be asked to do short (almost) weekly assignments. These assignments will range in difficulty.
The learning that I aim for in this course (clarifying, testing, and justifying ideas) depends largely on your attendance and active participation. Prompt attendance is expected at all class and field experiences. This class will involve much student participation. Your attendance and participation in our class activities and discussions is important not only for your learning but also for the learning of others.
POW: This is an activity completed through the Math Forum Problem of the Week. In partners you will be trained to respond to elementary students work using a prescribed rubric.
Article Critiques: You will be asked to write two critiques, one related to the teaching and learning of Geometry, the other on assessment from the journal, Teaching Children Mathematics. Each critique will be two to three pages in length. Details pertaining to the completion of these critiques will be given on a separate handout.
Investigating Resources for NC Standard Course of Study: As mentioned earlier, there are five strands in the NC Standard Course of Study. Descriptions of the strands can be found at [http://www.dpi.state.nc.us/curriculum/]. As a teacher you are responsible for helping your students work towards the objectives identified in the NC Standard Course of Study. You need to be familiar with appropriate resources that support learning related to the objectives. You will begin to develop a resource file related to the geometry strand. Extensive details for this assignment are provided in a separate handout.
Lesson Plan Project: During the semester, you will be asked to create and teach a series of three lessons decided by you and your practicum teacher. The lesson plan format will be discussed during the first weeks of class. This project is to be uploaded into taskstream. Failure to teach all three lessons will result in failure.
Case Study: This paper will be a case study of one student of your choice in your field experience associated with this block. You will be asked to write about your student’s knowledge of mathematics given the context of your field experience. The paper should be five to six pages in length. Grading will be based both on your description of the student as well as the quality of writing.
Test: We will explore and develop our understanding about the NC strand: geometry, as well as assessment in elementary mathematics. We also will explore children's understanding about this strand. You will have two tests. The test will include all course readings, activities, & discussions. The test will provide an opportunity for you to demonstrate your understanding about geometry and assessment from a teacher’s perspective.
Professional Development Activities: As part of your grade in this course, you will have to attend professional development activities. This can be done by attending three PTMA sessions, by attending NCCTM State Conference, Greensboro, NC October 11 or 12, or the North Carolina Association of Elementary Educators Annual Conference on Monday, October 8.
Tentative Course Outline:
Week of / Focus / Reading and AssignmentsAugust 20 / Introductions
North Carolina Standard Course of Study
NCTM Standards
Developing understanding and problem solving / Reading: Van de Walle, Chapters 1, 2, and 3
Reading: Making Sense
August 27 / Worthwhile mathematical tasks
Van Hiele levels
Lesson plans
Early Geometry / Reading: Van de Walle Chapter 4 and 20
Reading: Clements, Young Children’s Ideas about Geometric Shapes (on reserve)
Huse, Making connections (on reserve)
September 3 / Same as above / No class 9/7
September 10 / 2D Geometry (points, lines, planes, polygons—triangles) / Reading: Chapin, The tools of classroom talk (on reserve)
Article Critique due
September 17 / 2D Geometry (quadrilaterals and circles) / POW preparation
September 24 / 3D Geometry (Polyhedra—Prisms and Pyramids) / POW preparation
October 1 / 3D Geometry (Cylinders, Cones and Spheres) / Article Critique Due
October 8 / 3D Geometry (Cylinders, Cones and Spheres) / Reading: Lehrer, Why are some solids perfect (on reserve)
No class 10/11
POW
October 15 / Symmetry, Tessellations, Perspective, Location and Technology
Assessment / Reading: Renshaw, Symmetry the trademark way (on reserve)
Reading: Van de Walle Chapter 5
Reading: A New Kind of Assessment (on reserve)
Investigating Resources due
October 22 / Symmetry, Tessellations, Perspective, Location and Technology
Assessment / No class 10/26
POW
October 29 / Final 10/30
November 26 / Case Study 11/26
December 7 / Final Meeting / Planning, Teaching, and Reflecting 12/7
Final Note
I want to help you become the best elementary mathematics teacher that you can be. Activities and assignments that are interesting and informative for one student are not always appropriate for another. Although I try to provide class activities and assignments that are useful to all, let me know if you feel you are not getting as much out of this course or the assignments as you think you should. To the extent that requests for alternative assignments seem appropriate and feasible, I will modify activities and assignments to make them more meaningful for you.