EDEE 431 Elementary School Mathematics and Its Instruction

Fall 2002

 

Dr. Ann Wallace

7 College Way, #305

953-7372

wallaceah@cofc.edu

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

Office hours: Mondays and Wednesdays 10:00-11:00 and 1:00-2:00, or by appointment

 

Text: Today’s Mathematics, Parts I and II by Heddens and Speer, 10th edition

Class times: Section I    M, W       2:00-3:15

Section III   M, W, F  11:00-11:50

Class supplies: SC 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) ruler, calculator, scissors, glue stick, 3-ring binder (notebook paper and dividers).

 

Final Exam:   Section I - Wednesday, December 11, 12:00-3:00 P.M.

                        Section II - Saturday, December 7, 12:00-3:00 P.M.

 

Course Objectives and Description

 

The general objective for this course is for you to develop a form of instructional practice in mathematics in which students develop what the National Council of Teachers of Mathematics (NCTM) calls “mathematical power”. Mathematical power includes the ability to reason mathematically, to make conjectures, to develop mathematical arguments, and to communicate about mathematics (Standards I, III, V). 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 students’ mathematical conceptual development rather than as presenting content for students to learn.

 

In addition, a teacher of mathematics should not only be proficient in how to teach mathematical concepts and skills, but should also have a working knowledge of the interrelatedness of those concepts and skills. In this course we will explore current research and innovative teaching methods that will go a long way toward giving math a new image- one that shines with relevance, usefulness, and a sense of connection with other disciplines as well as with real life (Standards III, VII).

 

Specifically, we will focus on three areas that lead to teaching that is consistent with the NCTM professional and curriculum standards: 1) students’ learning, 2) the role of the teacher, and 3) worthwhile mathematical tasks.

 

 

·      Understanding the mathematical learning of students:

 

In order to understand and investigate how your students learn a mathematical concept it is important to know the content yourself. To this end, we will take class time investigating mathematical concepts for our own learning. Additionally, we will reflect on our own learning and anticipate how students might understand the same concept in different ways (Standards I, III).

 

·      Re-defining the teacher’s role:

 

Our own experience in mathematics tells us that the role of the teacher is to impart mathematical knowledge to our students through lecture format and guide students to use the correct math skill for solving problems. In this class we will redefine the role of the teacher in an inquiry classroom. Class time will be devoted to investigating the role of the teacher in facilitating meaningful discourse, using formal and informal notations to support learning, and guiding the development of supportive learning environments (Standards II, III, V, VI).

 

·      Envisioning and creating worthwhile tasks:

 

As we redefine our students’ role and our own role as teachers in an inquiry classroom it becomes apparent that most traditional textbooks are insufficient for creating and maintaining an inquiry spirit. Thus, we will learn what constitutes a worthwhile mathematical task by discussing several instructional design principles of Realistic Mathematics Education (RME). Additionally, we will investigate the supports and constraints associated with using technology and manipulatives in mathematics instruction (Standards I, IV).

 

Assignments

 

  1. Class Assignments (20 points each).  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 students’ work

-       Textbook assignments

-       Investigating teaching using a CD-ROM

-       Using technology to develop understanding

-       Investigating a unit from a reform-oriented curriculum

 

  1. Assigned Readings.  There are several types of readings: selected chapters from the NCTM Principles and Standards and SC Standards, two major library readings and five short library readings that you select from the list provided. Hard copies of all readings may be found under my name and this course 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.

-       Major library readings (10 points each)- 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 at least 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 each)- You are to read 5 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. Problem Solving Lesson Plan (30 points). Students will develop a problem solving lesson plan. The lesson plan should be constructed similar to the Japanese lesson plan included in this packet (I will provide samples as well). The purpose of the lesson plan is to develop an instructional sequence for a specific grade level and mathematical content area.

 

  1. Student Interviews (30 points). For this assignment each of you will interview one K-8 student to document a variety of students’ cognitive understanding on a range of mathematical tasks. The tasks do not assess a student’s skill level but rather elicit responses that indicate their cognitive development. A list of mathematical problems that are appropriate for interviewing will be provided and depend on the grade level and mathematical understanding of each student.

 

  1. Course Notebook (35 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. Mid-term and Final Exam (40 points each).  These exams will be based on class activities, discussions, readings, and the NCTM and SC Standards. The mid-term will be a take home exam.

 

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. Tardiness is not tolerated and will be counted as an absence.

 

 

Daily Plan

 

The daily plan at the end of this syllabus indicates the mathematical content and text chapter to be covered each week. Additionally you will find corresponding NCTM and SC Standard pages and/or chapters. You are responsible for the text and Standard readings prior to each class. Topics that are integrated throughout the course include:

 

·      The role of imagery

·      The role of manipulatives

·      The role of symbolization and pedagogical notation

·      The role of algorithms

·      The role of technology

·      Classroom discourse

·      Assessment

·      Equity and diversity

·      Teaching approaches, such as collaborative and small group

 

 

 

 

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:

 

 

 

 

 

*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

≥-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).

 

 

Lesson Plan

 

Grade level:

 

Mathematical Intent (what you hope to accomplish):

 

 

 

Rationale (why you are doing this):

 

 

 

 

Context of the lesson:

 

            Previous Lesson                      Today’s Lesson                       Next Lesson

 

 

 

 

 

 

 

Overall Lesson Objectives:

 

 

Details of the lesson:

 

Steps

Activities

Anticipated Student Thinking

Time

Guidance/Advice

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Important points to consider (social norms, small groups, notation, etc.):

 

 

 

 

 

 

 

 

 

Materials:

 

 

Major Readings

 

Ball, D. (1991). What’s 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). What’s 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). Children’s 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). Children’s right to be wrong. Arithmetic Teacher, 35, 107.

 

Lawson, D. (1997). A teacher’s 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 student’s 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 O’Brien, 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 who’s 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). “Image maker”: Developing spatial sense. Teaching Children Mathematics, 5, 374-378.

 

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