EDEE 643

Elementary School Mathematics:

Process and Implementation

Spring 2003

 

Dr. Ann Wallace

7 College Way, #305

953-7372

wallaceah@cofc.edu

http://www.cofc.edu/~annw/

Office hours: After class and by appointment

 

Text: Mathematics for Elementary School Teachers, Second Edition, by Bassarear

Class time:     Monday  4:00-6:45 PM

Class supplies: South Carolina Math Curriculum Standards K-8 (from web-www.state.sc.us/sde), NCTM Principles and Standards for School Mathematics Chapters 1-6 (from web-www.nctm.org)

 

Course Objectives and Description

 

EDEE 643 is designed for certified (K-8) teachers who have completed a bachelorÕs degree in education. There are two main goals for this course:

 

  1. To help masters candidates make sense of mathematics and to develop a strong understanding of the fundamental ideas of mathematics education.
  2. To equip masters candidates with appropriate methodology and instructional strategies to teach mathematics contentK-8, as well as a working knowledge of the standards for teaching and assessment endorsed by the National Council of Teachers of Mathematics and the content and process standards of South Carolina.

 

This course will help you develop a form of instructional practice in mathematics in which students develop what the National Council of Teachers of Mathematics (NCTM) calls Òmathematical powerÓ. Mathematical power includes the ability to reason mathematically, to make conjectures, to develop mathematical arguments, and to communicate about mathematics. It also includes an attitude towards mathematics as one of inquiry, exploration, and sense making. Students should feel self-confident in their ability to think about and reason about mathematical ideas. In this course you will learn to look at mathematics teaching as facilitating studentsÕ mathematical conceptual development rather than as presenting content for students to learn.

 

Specifically, masters candidates will:

 

1.      examine and articulate the major topics, processes and patterns of mathematics content of elementary and middle grades as presented in the South Carolina Frameworks and Standards, NCTM Standards, and the course text. (Standard II)

2.      develop an understanding and appreciation of diversity among learners in its multiple forms, and methodology to differentiate instruction and assessment to meet the needs of all children. (Standards I, II, VI, VII)

3.      use problem solving as the overriding approach to the development of studentsÕ understanding of the content of an appropriate mathematics curriculum. (Standards I, II)

4.      explore a broad mathematical curriculum and appropriate assessment which includes numeration and number theory; computation and estimation with whole numbers, decimals and fractions; patterns and relationships; data analysis, statistics and probability; geometry and measurement; and algebra. (Standards II, VI)

5.      be able to structure classroom activities around conjecturing, organizing, discovering, evidence gathering, and support building so that students learn to reason mathematically and communicate logically. Candidates will be able to choose materials that foster this learning environment and justify their choices to other teachers. (Standards IV, V, VII)

6.      use technology tools for computation, for investigating and solving problems and for exploring concepts. (Standard III)

7.      reflect on the professional nature of teaching and the obligation of teachers to be articulate communicators concerning the goals and purposes of effective mathematics education. (Standard VII)

 

 

Assignments

 

  1. Class assignments (20 points).  There will be several class assignments in which you explore various aspects of teaching and learning. The following is a tentative list of assignments:

 

-         Videotape analysis of an inquiry-based classroom segment

-         Instructional task sequence

-         Analysis of studentsÕ work

-         Investigating teaching using a CD-ROM

-         Using technology to develop understanding

-         Investigating a unit from a reform-oriented curriculum

 

  1. Text assignments (10 points).  Masters candidates are expected to attempt the items assigned from the text. As a general policy, we will discuss the items and opportunities will be provided to complete or adjust items during the discussions.

 

  1. Assigned Readings.  There are several types of readings: selected chapters from the NCTM Principles and Standards and SC Standards, and library readings from the list provided. Some readings are required and others you will select. Hard copies of all readings may be found under my name on reserve in the library. Electronic copies may be accessed from http://www.cofc.edu/~annw/.

 

-         NCTM and SC Standards readings- Some chapters are assigned as a complete unit. Other chapters are assigned by topic. You are to read the relevant material from each of these chapters as a unit, as indicated on the daily plan.

-         Required library readings (10 points)- There are two major readings, each of which will be discussed in class. You will hand in reflections for these readings as indicated on the daily plan. Each reading reflection is to be two to three typed pages and should include a discussion of the major points of the article along with your understanding of how it relates to our class activity and your classroom experiences.

-         Short library readings (5 points)- You are to read 10 articles from the short readings list and write a reflection (NOT a summary) of approximately one-half page for each. All of the articles from the list are from the NCTM journals Teaching Children Mathematics, the Arithmetic Teacher, and Mathematics Teaching in the Middle School.

 

  1. Practicum (60 points). See attached.

 

  1. Course Notebook (20 points). Each student will prepare a course notebook that includes:

 

-         A table of contents

-         Course assignments, exams and papers

-         Instructional activity materials

-         Reading reflections

-         Class notes

-         Other material as agreed on or assigned in class or of your own choosing

 

  1. Quizzes (15 points each).  There will be unannounced quizzes containing items parallel to the text items assigned for a class session.

 

  1. Final Paper (30 points). You will write a final paper, which synthesizes the entire course, including the practicum, in light of the NCTM and SC Standards. Details will be provided later.

 

Attendance Policy

 

All class sessions are heavily oriented to active student participation and involvement. Therefore, attendance at every session is critical. In the event that you must miss a class meeting, it is expected that you will inform me in advance of the absence, emergencies excepted. Students who miss class are responsible for content covered and for any information and printed material handed out in class. Absences may adversely affect your grade.

 

 

 

SCHOOL OF EDUCATION

 

The mission of the School of Education at the College and University of Charleston is the development of educators and health professionals to lead a diverse community of learners toward an understanding of and active participation in a highly complex world. In pursuit of this mission, faculty and students will demonstrate:

 

  • intellectual curiosity and rigor;
  • reflective, research-based practice;
  • collaboration and consensus building;
  • field-oriented service and community outreach;
  • and cultural sensitivity and understanding.

 

 

 

 

*TEACHING AND LEARNING STANDARDS*

 

Standard I:            Evidence theoretical and practical understanding of the ways learners develop.

 

Standard II:           Demonstrate understanding and application of the critical attributes and pedagogy of the major content area.

 

Standard III:          Evidence a variety of strategies that optimize student learning.

 

Standard IV:         Participate in informed personal and shared decision making that has as its focus the enhancement of schooling and the profession.

 

Standard V:           Communicate effectively with students, parents, colleagues and the community.

 

Standard VI:          Demonstrate an understanding of the continuous nature of assessment and its role in facilitating learning.

 

Standard VII:         Show an understanding of the culture and organization of schools and school systems and their connection to the larger society.

 

 

POLICIES AND PROCEDURES FOR UNDERGRADUATE COURSES

IN THE SCHOOL OF EDUCATION*

 

  1. GRADING CRITERIA: The following criteria are used for the assessment of interim and final grades:

 

Letter Grades

Percentage Range

Grade Points

Interpretation

 

A

93-100%

4.0

Superior

B+

88-92%

3.5

Very Good

B

83-87%

3.0

Good

C+

78-82%

2.5

Fair

C

74-77%

2.0

Acceptable

D

70-73%

1.0

Barely Acceptable

F

³-69%

0.0

Unacceptable

 

  1. ATTENDANCE: Class attendance and punctuality are expected professional behaviors. Students are responsible for all content and assignments for each class. If, for serious personal or medical reasons several classes are missed, the instructor should be informed of the reason. A student may be dropped from a course for excessive absences (i.e. missing two sessions of classes which meet once each week; missing four sessions of classes which meet twice each week; and, missing six sessions of classes which meet three times each week).

 

  1. MAKE-UP EXAMINATIONS AND QUIZZES: If the course instructor determines that a quiz or examination (other than the final examination) was missed for a legitimate reason, a make-up may be administered. It is the responsibility of the student to make arrangements for the make-up. This is to be done as soon as possible after the missed examination/quiz.

 

  1. DUE DATES: Due dates for course assignments, as well as scheduled quizzes and assignments, are listed in the course calendar or are announced in class. Consequences related to late material are determined by the instructor.

 

  1. DEAD WEEK: The week preceding final examination week is one during which instructors concentrate on "closure" activities. Therefore, during that week no quizzes or examinations will be given nor will major papers or projects be due.

 

  1. FINAL EXAMINATIONS: The final examination for each course will be administered during the period scheduled for final examinations. (Undergraduate students who have more than two final examinations scheduled on the same day may arrange for an alternate time for one examination through the Office of the Undergraduate Dean.)

 

  1. RESEARCH PAPERS: Papers will be typewritten (word processed) using the style of the Publication Manual of the American Psychological Association (Fourth Edition, 1994).

 

 

Major Readings

 

Ball, D. (1991). WhatÕs all this talk about discourse? Arithmetic Teacher, 39(3), 44-48.

 

Stigler, J., Fernandez, C., & Yoshida, M. (1996). Traditions of school mathematics in Japanese and American elementary classrooms (pp. 149-175). In L. Steffe, P. Nesher, P. Cobb, G. Goldin, & B. Greer (Eds.), Theories of mathematical learning. Mahwah, NJ: Lawrence Erlbaum Associates.

Reading List for Short Readings

 

Atkins, S. (1999). Listening to students: The power of mathematical conversations. Teaching Children Mathematics, 5, 289-295.

 

Battista, M., & Clements, D. H. (1998). Finding the number of cubes in rectangular cube buildings. Teaching Children Mathematics, 4, 258-264.

 

Billstein, R. (1998). The STEM model. Mathematics Teaching in the Middle School, 3(4), 282-286, 294-296.

 

Bird, E. (1999). WhatÕs in the box? A problem-solving lesson and a discussion about teaching. Teaching Children Mathematics, 5, 504-507.

 

Bishop, A.J. (2001). What values do you teach when you teach mathematics? Teaching Children Mathematics, 7, (346-349).

 

Burns, M. (1991). Introducing division through problem-solving experiences. Arithmetic Teacher, 38, 14-18.

 

Burns, M. (1995). In my opinion: Timed tests. Teaching Children Mathematics, 1, 408-409.

 

Burns, M. (1996). What I learned from teaching second grade. Teaching Children Mathematics, 3, 124-127.

 

Burrill, G. (1997). Choices and challenges. Teaching Children Mathematics, 4, 58-63.

 

Cai, J. & Kenney, P.A. (2000). Fostering mathematical thinking through multiple solutions. Mathematics Teaching in the Middle School, 5(8), 534-539.

 

Campbell, P. (1997). Connecting instructional practice to student thinking. Teaching Children Mathematics, 4, 106-110.

 

Clements, D. H. (1997). (Mis?)constructing constructivism. Teaching Children Mathematics, 4, 198-200.

 

Clements, D. H.(1999). Subitizing: What is it? Why teach it? Teaching Children Mathematics, 5, 400-405.

 

Falkner,K., Levi, L. & Carpenter, T. (1999). ChildrenÕs understanding of equality: A foundation for algebra. Teaching Children Mathematics, 6, 232-237.

 

Graeber, A. O., & Campbell, P. F. (1993). Misconceptions about multiplication and division. Arithmetic Teacher, 40, 408-411.

 

Kazemi, E. (1998). Discourse that promotes conceptual understanding. Teaching Children Mathematics, 4, 410-414.

 

Keiser, J. (2000). The role of definition. Mathematics Teaching in the Middle School, 5(8), 506-511.

 

Kliman, M. (1999). Parents and children doing mathematics at home. Teaching Children Mathematics, 6, 140-146.

 

Labinowicz, E. (1987). ChildrenÕs right to be wrong. Arithmetic Teacher, 35, 107.

 

Lawson, D. (1997). A teacherÕs journal: From caterpillar to butterfly. Teaching Children Mathematics, 4, 140-143.

 

Lehrer, R. & Curtis, C. (1999). Why are some solids perfect? Conjectures and experiments by third graders. Teaching Children Mathematics, 6(5), 324-329.

 

McClain, K., McGatha, M., & Hodge, L. (2000). Improving data analysis through discourse. Mathematics Teaching in the Middle School, 5(8), 548-553.

 

Nickerson, S., Nydam, C., & Bowers, J. (2000). Linking algebraic concepts and contexts: Every picture tells a story. Mathematics Teaching in the Middle School, 6(2), 92-125.

 

Philipp. R. A. (1996). Multicultural mathematics and alternative algorithms. Teaching Children Mathematics, 3, 128-133.

 

Reynolds, A., & Wheatley, G. (1997). A studentÕs imaging in solving a nonroutine task. Teaching Children Mathematics, 4, 166-170.

 

Rowan, T.E. & Robles, J. (1998). Using Questions to Help Children Build Mathematical Power. Teaching Children Mathematics, 504-509.

 

Russell, S. J., & Mokros, J. (1996). What do children understand about average? Teaching Children Mathematics, 2, 360-364.

 

Schifter, D. E., & Carey OÕBrien, D. (1997). Interpreting the Standards: Translating principles into practice. Teaching Children Mathematics, 4, 202-205.

 

Smith, M. S., & Stein, M. K. (1998). Mathematics Teaching in the Middle School, 3, 344-350.

 

Steele, D. F. (1998). Look whoÕs talking: Discourse in a fourth-grade class. Teaching Children Mathematics, 4, 286-292.

 

Steele, D. (2000). Enthusiastic voices from young mathematicians. Teaching Children Mathematics, 6.

 

Warrington, M. A., & Kamii, C. (1998). Multiplication with fractions: A Piagetian, constructivist approach. Mathematics Teaching in the Middle School, 3, 339-343.

 

Weissglass, J. (1998). Maintaining our integrity amidst controversy and attacks. Teaching Children Mathematics, 4, 438-440.

 

Wheatley, G. H., & Reynolds, A. (1999). ÒImage makerÓ: Developing spatial sense. Teaching Children Mathematics, 5, 374-378.

 

Zaslavsky, C. (1998). Ethnomathematics and multicultural mathematics education. Teaching Children Mathematics, 4, 502-503.