ELEMENTARY CURRICULUM AND INSTRUCTION: MATHEMATICS

EDMC 4120 - Section 03 (Wednesday )

Instructor: Elmano M. Costa, Ed. D. Fall, 1999

Office: Prof. Schools Bldg. 334 3 Units

Wednesday-12:45 - 3:41 P-104

Phone: (Dept.) 667-3357 (Office) 667-3638 Email: ecosta@toto.csustan.edu

Office Hours: Mon. 1:00-4:00; Wed. 4:30-5:30. Also, call for any questions, special appointment times, etc. I will be available immediately after class to answer questions/meet with students.

I. Course Description

In this course students will examine the issues and the reform movement shaping mathematics education today. Emphasis will be placed on preparing teachers to work in diverse classrooms, and on using principles from the California Mathematics Framework and California Mathematics Content Standards to inform classroom practice and engage students in purposeful mathematics learning.

Prerequisite: Admission to the Multiple Subjects Credential Program

II. Readings

Required

Burns, Marilyn (1992). About teaching mathematics: A K-8 resource. White Plains, NY: Math Solutions Publications.

Selected Readings from packet given out in class.

Highly Recommended Texts

Baratta-Lorton, Mary (1995). Mathematics Their Way. Palo Alto: Addison-Wesley.

Baratta-Lorton, Robert (1977). Mathematics... A way of thinking. Palo Alto: Addison-Wesley.

Stenmark, Jean Kerr; Thompson, Virginia; & Cossey, Ruth (1986). Family math. UC Berkeley: Lawrence Hall of Science.

III. Other Resources

Ashlock, Robert. B. (1998). Error patterns in computation. Upper Saddle River, New Jersey: Merrill.

Burns, Marilyn (1991). Math by all means: Multiplication, Grade 3. New Rochelle, New York: Cuisenaire Company.

California Department of Education (1991). Seeing fractions: A unit for the upper elementary grades. Sacramento: author.

Johnson, David W. & Johnson, Roger T. (1991). Leaning mathematics and cooperative learning: Lesson plans for teachers. Edina, Minnesota: Interaction Book Company.

Lawrence Hall of Science (1992). Frog math: Predict, ponder, play. Berkeley: Lawrence Hall of Science.

TIMS Curriculum (1997). Math Trailblazers: A mathematical journey using science and language arts. Grades 1-3. Dubuque: Iowa: Kendall/Hunt Publishing Company.

Stein, Marcy; Silbert, Jerry; & Carnine, Douglas (1997). Designing effective mathematics instruction: A direct instruction approach. Upper Saddle River, New Jersey: Merrill.

Van de Walle, John ((1998). Elementary and middle school mathematics. Menlo Park, California: Longman.

Willoughby, Stephen S. (1990). Mathematics education for a changing world. Alexandria, Virginia: ASCD.

IV. Evaluation/Grading

Criteria Used to Evaluate Student Learning
1. Class attendance and punctuality.

2. Meeting due dates for assignments. No tardy/late papers, except in extreme emergencies and only with the permission of the instructor as per policy stated below.

3. All work must be typed.

4. Written work must be of graduate quality. Work that is not will be returned for re-doing.

5. Active and informed participation in classroom discussions and activities.

6. Engaging in out-of-class activities and readings from books, journals, periodicals, etc. and share your learning/discoveries with the class.

7. As this is a 3 unit class, students are expected to spend at least 9 hours per week in preparation.

Assignments/Points Points Due

• Attendance and active, informed participation 14 Ongoing
(1point per day - punctuality is expected)

• Four quizzes on reading OR weekly journal OR midterm 20 Ongoing OR 10-27-99 OR 12-1-99

• Report & reflection of observations (at least 2 10 9-29-99
lessons with one in primary & one in intermediate)

• Lesson Plan, Teaching & Reflection: 10 1 wk. after
Direct Instruction Lesson to peers presentation lesson

• Printout and reflection of math web site 10 10-27-99

• One pg. summary of Framework Section/class present. 6 11-3-99

• Lesson Plan, Teaching & Reflection: 10 11-10-99
Exploration lesson to school students

• Written Problem Solving Lesson Plan 6 11-17-99

• Final exam OR teach prob. solv. lesson to students 10 12-15-99
and submit reflection

• Teaching Problem Solving Lesson to peers 4 12-8-99 or 12-15-99

TOTAL 100

Grading*

95-100 points A

91-94 points A-

88-90 points B+

84-87 points B

80-83 points B -

77-79 points C+

74-76 points C

70-73 points C-

*All written assignments except the quizzes /tests may be revised and resubmitted if a student so chooses.

GRADE CONTRACT

Grading

Students will contract for their own grade. Please submit a written, signed, and dated statement indicating which grade you want to try to achieve This will be due Week 2 of class. Later in the semester, if there are unforeseen events in your life, and the work becomes just too much, you may contract for a lower grade on Week 10. However no one can contract up for a higher grade later in the semester.

Indicate whether you plan to take final exam or teach the problem solving lesson to students in a public school.

Requirements for Each Grade

All students are required to do the minimum. Those who meet the stated criteria and successfully complete the minimum course requirements will receive a C for the class.

"C" Contract (Minimum) - 70 points possible

1. All required readings and activities.

2. Journal or quizzes or midterm

3. Observation of two mathematics lessons and a reflection on the observations

4. Complete a problem solving lesson plan.

5. Teach a problem solving lesson to peers.

6. Final exam OR teach the problem solving lesson in a school classroom.

7. One page summary of reading section from Math Framework and classroom presentation

"B" Contract - 90 points possible

1. Do all the requirements for a "C" Contract.

2. Teach an exploration lesson in a school and turn in reflection on the lesson.

3. Complete web site assignment.

"A" Contract - 100 points possible

1. Do all the requirements for a "C" Contract

2. Do all the requirements for a "B" Contract

3. Teach a lesson to peers using a direct approach and turn in reflection on the lesson.

Policy on late assignments

1) Written assignments (except quizzes and exams) can be turned in late. For each week that an assignment is late (anytime after the due date and up to the next class meeting time), grades are reduced 2 points from what the assignment would have earned. However, no assignment will be accepted that is more than 2 weeks late. Also, no assignment will be accepted after the last day of class.

2) If a student chooses to redo an assignment or is told by the instructor to redo an assignment, the student has two weeks to turn the assignment in from the date it was returned to the class. After that, the assignment will not be accepted. No assignment will be accepted after the last day of class.

3) Assignments due the last two weeks of the semester cannot be turned in late.

V. Course Objectives:

Students will grapple with the dilemmas, the research, and the reform movement currently reshaping mathematics education.

Students will analyze instructional practices and alternative forms of assessment compatible with the goals outlined in the Framework and the Standards

Students will become familiar with a variety of instructional formats including: whole class instruction, cooperative groups, menu activities, and investigations.

Students will be able to teach three types of math lessons: direct instruction, exploration and problem solving

Students will gain experience working with a wide range of mathematics manipulatives used to develop conceptual understanding.

Students will gain practical experience teaching lessons in classrooms.

An underlying focus of this course will be on preparing teachers to work in culturally, linguistically, and academically diverse classrooms.

Not an objective, but most of all.....

I hope in this course that you will come to enjoy mathematics and that you will gain confidence in yourself, both as a mathematician and as a teacher of mathematics. I hope that this course will serve as a platform for further learning, and that you will find yourself intellectually intrigued by the possibilities for mathematics education in our schools.

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Note: The following Schedule provides a preliminary outline of topics and assignments. This schedule may be modified by the instructor as necessary.

PART I: FOUNDATIONS OF MATHEMATICS EDUCATION, ARITHMETIC, AND DIRECT INSTRUCTION

Wednesday, Sept. 8 - Session 1

INTRODUCTION AND REVIEW OF THE COURSE; IMPORTANCE OF PATTERN IN MATH

Class Choice: Quizzes, journal of reflection on readings, or mid-term exam

Group norms, icebreakers

Group Activity: How I use math.

The Dilemma(s) Shaping Mathematics Education: An Historical Perspective

Where are we going this semester?

Types of lessons: direct instruction, investigations/explorations, problem solving

Ways of organizing lessons: whole class, centers, menu activities

Organization of students: individual, heterogeneous, and homogeneous groups

Patterns in math education

Writing instructional objectives

Wednesday, Sept. 15 - Session 2

MATH AS WE KNEW IT: DIRECT INSTRUCTION; THE IMPORTANCE OF PLACE VALUE

Implications for Classroom Teaching

The Missouri Mathematics Project

Modeling: Direct Instruction Lesson

Place value activities

Readings
Good, T. L., Grouws, D.A., & Ebmeier, H. (1983). Active mathematics teaching. New York: Longman Inc. (Chapter 2 Conclusion & Chapter 3, pp. 29-55)
About Teaching Mathematics, Place Value (pp. 173-182)

Begin planning Direct Instruction Lesson

Sign-up for day to teach DI lesson

Due: Contract of which grade you are working for. Write it on a full size sheet of paper and sign it. Be sure to state whether you will take final exam or teach problem solving lesson in a school and whether you will take quizzes or write journal.

Wednesday, Sept. 22 - Session 3

TEACHING ADDITION

Methods and sequence of teaching addition

Activities for addition

Reading

About Teaching Mathematics: Addition and subtraction (pp. 183-193).
California Department of Education (1996). Mathematics Program Advisory. Sacramento: Author

Due: 1) Be prepared to teach your lesson using direct instruction techniques ("A" contracts). Schedule will be as per the sign-up sheet completed in week 2. REFLECTION AND LESSON PLAN DUE ONE WEEK AFTER YOUR PRESENTATION.
2) Turn in journal entry on first two readings (for those who chose journals)

Wednesday, Sept. 29 - Session 4

TEACHING SUBTRACTION

Activities for subtraction

Remedial approaches (Touchmath) - Addition and Subtraction

Discussion: Lessons learned from classroom observations

Reading
About Teaching Mathematics: Part I Raising the Issues (pp. 3-28).

Lotan, R. & Benton, J. (1990). Finding out about complex instruction: Teaching math and science in heterogeneous classrooms. In N. Davidson (Ed.), Cooperative Learning in Mathematics. Addison-Wesley.

Due : Reflection of observation of mathematics lessons (all contracts)

Wednesday, Oct. 6 - Session 5

TEACHING MULTIPLICATION

Activities for multiplication

Reading
About Teaching Mathematics: Multiplication (pp. 194-203).

Johnson, D.W. & Johnson, R.T. (1990). Using cooperative learning in math. In Neil Davidson Cooperative Leaning in Mathematics. Menlo Park, CA: Addison-Wesley Publishing Co.

Wednesday, Oct. 13 - Session 6

TEACHING DIVISION

Activities for division

Reading

About Teaching Mathematics: Division (pgs. 204-211).

Phillips, D. et all. (1994). Beans, Blocks, and Buttons: Developing Thinking. Educational Leadership (Feb. 1994): 50-53.

Wednesday, Oct. 20 - Session 7

TEACHING FRACTIONS AND DECIMALS and PERCENTS

Reading

Fractions and Interactions (This is in your reading packet - has no author)

About Teaching Mathematics, Fractions , Decimals, and Percents (pg. 212-241)

Due: Journals of weekly readings (if this was the class option). They will not be graded at this point - only reviewed for completeness (all contracts).

PART II: EXPLORATION IN THE MATHEMATICAL STRANDS; EXPLORATION AND PROBLEM SOLVING LESSONS

Wednesday, Oct. 27 - Session 8

MEASUREMENT

MIDTERM EXAM -IF THIS WAS THE CLASS OPTION

Reading

About Teaching Mathematics, Measurement (pp. 46-53)

Rowan, T. E. & Robles, J. (1998). Using questions to help children build mathematical power. Teaching Children Mathematics, pg. 504-509.

Due: Be prepared to discuss your lesson using exploration lesson plan ("A" & "B" contracts).

Due: Math web sites ("A" & "B" contracts)

About the Math Web Site Assignment
Find a quality math site related to a K-6 teacher/school. Download and print out the content (if more than 10 pages, print out only the best 10 pages). Write a critique of the web site: What is good about it? What is not so good about it? Who would you recommend it to? What uses would you see for this web site for a classroom teacher? Etc. Etc. Your critique should be 1-2 typed pages.

Wednesday, Nov. 3 - Session 9

PATTERNS & FUNCTIONS

Reading
About Teaching Mathematics: Patterns and functions (pp. 112-124)

California Department of Education (1998). The California Mathematics Academic Content Standards (for grades K-6).

California Department of Education (1999). The California Mathematics Framework for California Public Schools K-12 - Jigsaw: Read the part assigned to you. Assignments will be made in class.
Due: One page summary of your reading assignment from the Math Framework. Students will be assigned parts in class. Be prepared to present your part to the class.

Wednesday, Nov. 10 - Session 10

PROBABILITY & STATISTICS

Playing with Probability: Menu Activities - Rotating Centers

Reading
About Teaching Mathematics: Probability and Statistics (pp. 59-78) and Independent Problem Solving - The Menu (pp. 37-38)

Due: Lesson plan, proof of teaching, and reflection of exploration-type lesson ("B" and "A" contracts)

Due: Revised grade contract for those who wish to revise. Reminder: no one can contract up at this time.

Wednesday, Nov. 17 - Session 11

GEOMETRY

Reading
About Teaching Mathematics: Geometry (pp. 79-99).
Due: Problem solving lesson plan (all contracts) -not reflection, but only the lesson plan.

Wednesday, Nov. 24 - Thanksgiving Holiday

Wednesday, Dec. 1 - Session 12

LOGIC and NUMBER

Reading
About Teaching Mathematics: Logic (pp. 100-111), Number (pp. 125-135)

Due: Journals of weekly readings (for those who chose this option). They will be graded at this point (all contracts)

Wednesday, Dec. 8 - Session 13

TEACHING PROBLEM SOLVING LESSONS TO PEERS

Due: Revised lesson plan on problem solving lesson (all contracts). TEACH PROB. SOLV. LESSON TO PEERS AS PER SIGN UP SHEET.

Wednesday, Dec. 15 - Final

FINISH TEACHING PROBLEM SOLVING LESSONS TO PEERS & FINAL EXAM

- Class will be held at regular time.

- FINISH teaching your problem solving lesson to a group of your peers.

- Final exam (for those who chose this option)

Dr. ELMANO COSTA

EDMC 4120 Math

YOU CAN VISIT AND TEACH YOUR LESSON IN ANY SCHOOL YOU WANT. HOWEVER, IF YOU ARE HAVING A DIFFICULT TIME FINDING ONE, HERE IS A LIST OF PLACES YOU CAN CONTACT.

PRINCIPALS THAT WILL HELP YOU TO FIND CLASSROOMS TO OBSERVE AND DO LESSONS

PRINCIPAL SCHOOL CITY PHONE NUMBER

Al Silveira Yamato Colony Livingston 394-3868

Chris Roe Don Pedro Ceres 538-0161

Gary Jones Crowell Elementary Turlock 634-8198

Nancy Jones Tuolumne Modesto 576-4661

Linda Murphy Wakefield Turlock 667-0895

Isabel Cabral-Johnson Merquin Stevinson 634-4938

Marta Kyte Dennis Earl Turlock 634-1090

Alicia Valenzuela Schendel Delhi 668-6134

Lee Ann Stangler Keyes to Learning Charter School Keyes 634-6467

Paul Kuehn Sipherd Elementary Modesto 524-4844

TEACHERS THAT WILL WELCOME YOU FOR OBSERVATIONS/SAMPLE LESSONS

TEACHER SCHOOL CITY PHONE

Beth Souza Hughson Elementary Hughson 883-4412

Doris Moore Hughson Elementary Hughson 883-4412

Juan Vasquez Livingston Middle Livingston 394-7953

To the teacher:

This letter documents that the following CSUS student taught a lesson employing a problem solving strategy.

Thank you for giving a student in EDMC 4120, Curriculum and Instruction: Mathematics an opportunity to teach in your class.

Sincerely,

Elmano Costa

Assistant Professor

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PROBLEM SOLVING LESSON

Name of CSUS student: ________________________________________________________

Lesson title: __________________________________________________________________

Name of book in which lesson was found ___________________________________________

Page of book _____________________ Date Published _____________

School: ______________________________________________________ Grade: _________

Date in which lesson was taught: ___________________ Time lesson was taught: __________

Print name of teacher _____________________________ Teacher phone number __________

Signature of teacher __________________________________________ Date _____________

Student's signature ___________________________________________ Date _____________

YOUR ASSIGNMENT IS COMPLETED IF IT INCLUDES THE FOLLOWING:

1) Type and attach your reflection of about 2 pages.
a. Describe what you and the students did (1 points) - about half a page

b. What did you learn about teaching math from this experience? (3 points) - about 1 and 1/2 pages

2) Attach the original lesson plan and the revised lesson plan (attach the revised plan only if changes were made). 3) ATTACH STUDENT WORK AS PROOF THAT YOU TAUGHT THIS LESSON. If there was no student paperwork which can be attached, submit a video tape of the lesson. If no student work is included, there will be no credit for the assignment.

PROBLEM SOLVING LESSON PLAN

CONSIDERATIONS / DIRECTIONS

A problem solving lesson is not a skill lesson with direct instruction, nor an exploration/investigation where the procedures are straightforward. Problem solving lessons have these three characteristics: a) There is no obvious answer b) There is no obvious way of going about finding the answer c) They require lots of thinking, usually in a "many heads together (group work)" format Remember that the age of the children is an important consideration on what makes a good problem solving lesson. Generally, what may be problem solving for younger children is not a problem for older children.
Two people may work together on a plan but each must teach it individually. WRITING THE LESSON PLAN
Your lesson plan should be typed and one to two pages (but no longer than three pages). It will be graded on appropriate choice of problem solving lesson, quality of writing, thoroughness and attention to both management and instructional detail. When reading your lesson plan I should have a clear sense of exactly what you and the children will be doing. It should be clear that you have thought of the management issues such as materials, grouping, time allocation, etc.

PLEASE WRITE YOU LESSON PLAN USING THE FOLLOWING FORMAT

I. CLASS CONTEXT

Grade level

Small group or whole class

Any other pertinent information

II. OBJECTIVE(S) Specifically state what you want the students to learn from this lesson. (Begin thinking of how will you assess whether they learned the objective?) Good lessons have few objectives (1-2 objectives). III. THE LESSON PLAN TO BE TAUGHT IN THE CLASSROOM - THREE STEP LESSON PLAN 1. INTRODUCTION/ANTICIPATORY SET How will you introduce the lesson, capture the students interest, focus them on the problem to be solved? Do you need to do a review to connect this lesson to the students previous learning? Will you demonstrate the activity, give directions, etc.??
2. PROCEDURE / DEVELOPMENT (THE ACTIVITY) Describe the problem solving activity in detail.

How do you plan to manage it?

What questions will you ask during the lesson to further student's thinking.

3. WRAP-UP/DEBRIEFING How will you close the lesson and have students "pull together" what they have learned?

List two to five key questions you will ask the students.

IV. ASSESSMENT How will you assess student learning? (How will you find out if they met the objective?) V. FOLLOW-UP PRACTICE (OR INDEPENDENT PRACTICE) Will the students have any homework based on this lesson? (if yes, what?)

Will any pertinent activity follow this lesson? (if yes, what?)

CALIFORNIA STATE UNIVERSITY, STANISLAUS

Department of Teacher Education

One University Circle • Turlock, CA 95382

Sec. (209) 667-3357 Fax (209) 667-3358

Elmano M. Costa, Ed. D.

Coordinator of Multiple Subject Credential Programs

Coordinator of Internship Programs

Co-Director, California Reading and Literature Project, CSU Stanislaus

Voice Mail (209) 667-3638 E-mail ecosta@toto.csustan.edu

To the teacher:

This letter documents that the following CSUS student taught a lesson in which the students explored/investigated a math concept.

Thank you for giving a student in EDMC 4120, Curriculum and Instruction: Mathematics an opportunity to teach in your class.

Sincerely,

Elmano Costa

Assistant Professor

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EXPLORATION/INVESTIGATION LESSON