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MAE 4310 - Content and Methods of Teaching Elementary Mathematics (1-6)
Florida International University
Fall, 2007
Professor
Bryan Moseley
ZEB 241B University Park
Miami, FL 33199
(305) 348-3213
, websites: http:www.fiu.edu/~moseleyb
Office Hours: Mondays, and Wednesdays 1:30 – 4:00 pm
Required Texts
Van de Walle, John A. (2001). Elementary and Middle School Mathematics: Teaching Developmentally. New York, Longman. (Fifth Edition)
Course package available from http:www.fiu.edu/~moseleyb
Prerequisites
3 mathematics courses intermediate algebra or above; Blocks 1 and 2 completed
I. Purpose of Course
MAE 4310 is designed for the development of knowledge, skills, and dispositions necessary to prepare undergraduate students to become effective teachers of elementary mathematics. This course provides the student with an up-to-date perspective of being a professional within the field of mathematics education. It is designed to involve the learner in an exploratory, hands-on/minds-on problem solving classroom atmosphere that employs manipulative materials regularly. It encourages the prospective teachers to problem solve, communicate with others about mathematics, and make mathematical connections while working individually and within groups to complete activities and assignments. These goals are encompassed and advocated in the documents Principles and Standard of School Mathematics (2000), Teaching Standards (1991), and Assessment Standards (1995) published by the National Council of Teachers of Mathematics (NCTM) and by the Florida Department of Education in the Florida Sunshine State Mathematics Standards (1996). The skills and disposition necessary to deliver instruction to all students, including those with Limited English Proficiency (LEP) and Exceptionalities and Challenges, are developed through a variety of classroom activities and assigned tasks. This course is required in bachelor’s degree program in Elementary Education and Special Education majors and meets the State of Florida requirements for certification in Elementary Education (1-6).
II. Course Objectives
Upon completion of the course students will have the following understandings, skills, and dispositions. These objectives are in line with the specific performance standards for teachers of English for Speakers of Other Languages (ESOL).
Understandings
1. Understand the content, scope and sequence of mathematics curriculum appropriate for elementary children.
2. Understand the developmental and cognitive processes of children’s learning of mathematics including those with Limited English Proficiency (LEP), and exceptional challenges, with special attention to constructivism.
3. Recognize and understand the change process currently underway which model the guidelines set forth in the NCTM Principles and Standard of School Mathematics and Teaching Standards, and the Florida Sunshine State Standards.
4. Understand the relationship between the study of mathematics and other elementary education disciplines; including science, language arts and social science.
Skills
5. Develop an awareness of how to use manipulative devices/mathematical models effectively in the elementary classroom as well with LEP as with non-LEP students.
6. Demonstrate ability to develop effective instructional settings for all students within which to teach mathematics compatible to the NCTM Standards and Florida Sunshine State Standards.
7. Demonstrate ability to use available calculators, computers, internet system and other forms of technology within the elementary mathematics curriculum.
8. Enable all students to become proficient in the use of mathematics as a tool for decision making and as a mode of communication.
Dispositions
9. View learning and teaching of mathematics as processes for constructing mathematical modes of thought.
10. Develop a positive attitude toward the teaching and learning of mathematics.
11. Value the mathematics background and abilities of all children and colleagues.
III Course expectations
This course is designed to involve the students in an activity-oriented setting. Your active participation and attendance in classroom is of crucial importance to accomplish the goals of the course. You are expected to participate in classroom activities, and to complete field experiences satisfactorily.
In addition to attending class, the student is expected to complete the following activities and assignments:
1. Read chapters of the text and other assigned materials on a timely manner,
2 Take quizzes and scheduled exams,
3 Participate in assigned mathematical investigations,
4 Develop and submit a problem solving lesson plan in elementary mathematics,
5 Write a report of an analysis of case of teaching (ACT)
6 Take a web-based tutorial and write a report on the application section,
7 Prepare a portfolio of the major course assignments in the course
Final course evaluation will be based on your performance on the above activities and assignments. The following schedule of grades will be used for this course:
B+ / 87 % / C+ / 77 %A / 93 % / B / 84 % / C / 74 % / D / 65 %
A- / 90 % / B- / 80 % / C- / 70 % / F / Below 65 %
IV. Student Responsibilities
A. Attendance
Students are expected to attend all class sessions unless they have a documented evidence of medical excuse or civic duty (e.g., jury) preventing their attendance. Students are also expected to arrive on time, and stay the entire class session. If the student misses three (or more) class sessions without documented excuse, and/or if he/she establishes a pattern of tardiness in class, the highest final grade that can be earned in the class will be C. Three instances of tardiness will be considered equivalent to one absence. If the student has to miss a class because of an excused reason, it is his/her responsibility to provide instructor with evidence of doctor’s visit no later than the next class session. After an absence, the student should obtain class notes, hand-outs, other information from classmates. Students are also requested to meet their needs outside during the class break time (e.g., visiting vending machines) to minimize interruptions.
B. Assignments
All class assignments are to be completed and turned in to the instructor in a timely manner for one to earn a satisfactory grade of B or better for this course.
Assignments must reflect students’ own thought and effort. You will be notified which assignments should be done as group work, otherwise students turn in all assignments that reflects his/her individual work. Plagiarism will result in an F grade for the assignment (this includes exams) and, possibly the class.
If a student has a legitimate excuse, (s)he may turn in assignments at a later date with the condition that the student makes arrangements with the instructor prior to due date. Assignments turned in late without a legitimate excuse lose 5 % of its full points for each day it is late except weekend days. All assignments should be turned in the class session of the due date. If the student turns in an assignment late, he/she should have it stamped to show the date and time of the submission by secretaries in the Educational and Psychological Studies area. The student may drop assignments under instructor’s door after it is stamped. Late or on time, turning in assignments in instructor’s mail box is not accepted. Non-stamped and late assignments placed in instructor’s mail box will not be accepted. Unless otherwise specified, all assignments must be;
- typed, spell checked, not less than 10 pt size font, and more than 14.
- professional (ideas expressed clearly, correct grammar, neat in appearance,
- stapled in upper left corner,
- presented with a cover sheet with the following information: i. assignment name e.g., field observation log, ii. your name, iii. course name, and number, section and iv. date.
Instructor reserves the right to question students orally about their own papers for clarification and to see if they fully understand what they have written.
The instructor reserves the right to keep all student papers on file indefinitely. You should keep a copy of your work before you submit.
In the following, you will find the descriptions of specific assignments. The instructor may make modifications in these assignments to better achieve course objectives.
V. Description of course assignments
a. Mathematical investigations
You will be given mathematical tasks for this assignment. The problems will be carefully selected from among those that have more than one correct answer or they can be solved in more than one way. The problems will provide instances of the potential connections between mathematics and other disciplines and with real life.
There are three purposes of these mathematical investigations:
a. to give students a chance to experience first-hand what is meant by mathematical problem solving, mathematical reasoning, mathematical communication, and making mathematical connections with real world and representing mathematical ideas in multiple ways.
b. to model, demonstrate and experience teaching mathematics via problem solving,
c. to polish students’ mathematical knowledge and skills (which is needed to build knowledge of mathematical pedagogy - This is the least important purpose among the three.)
You are expected to work on these tasks before the class and produce written record of your work. In the next class session, you will be given time to continue working on the task and share your solution with a small group of classmates. Then you may be asked to share the result of your work on the task with the whole class. You will be asked to hand in your individual work for assessment.
Evidence of your genuine effort to solve the problem, and clarity and completeness of your written communication of the solution will be more important than the correctness for evaluation of your work. Your written work is assessed based on a 4-point rubric. Categories of the rubric are described below.
Symbol / score / explanation of score( - ) / blank / Student does not submit any work.
( √ -) / marginal / Student submits her/his work, but does not produce a complete and understandable solution. For example, solution does not reflect understanding the task, there are serious contradictions within the solution, solution is not explained thoroughly, student states how the problem can be solved, but does not carry out the solution
( √ ) / satisfactory / Solution reflects understanding the problem, solution involves a reasonable method (which may or may not yield a “correct” answer), solution includes a complete and clear explanation of what is done.
(√+ ) / superior / Solution reflects understanding the problem, using a reasonable method, successful carrying out of the method, and interpretation of findings.
b. Write A Problem-Solving Lesson Plan In Elementary Mathematics
Target concept: You should choose an important and worthwhile mathematical concept or skill to teach. Your lesson plan should engage students in problem solving. It is expected that you choose an appropriate lesson plan format matching the type of lesson objective. Please see course package for alternative lesson plan formats. Please identify clearly the benchmark statement of the Sunshine State Standards (SSS) for mathematics that matches the lesson objective or target concept you choose. Plan to write a lesson plan on a topic other than the following: 1. value of coins (e.g. teaching shopping situations), 2. basic facts (drilling for number facts) 3. telling time.
Prepare and write an original lesson plan. You are also required to read and relate with the corresponding section or chapter of the textbook (Elementary and Middle School Mathematics: Teaching Developmentally) with your lesson as you plan it. Lesson plan should include the following information; objective, grade level, materials needed, class organization, introduction, development of the lesson, summing up, and assessment of student learning.
Completeness, descriptive power and internal consistency of the lesson plan, reference to the appropriate SSS benchmarks are necessary qualities of the lesson plan. Please be very specific about the mathematical content of the lesson. In this respect, the lesson plan required of this course is different than a lesson plan you would do for other courses. Just listing the topics you cover will not be sufficient, you should be as specific as possible about the concepts you teach, and explanations you make and examples you give. Your teaching should reflect at least one of the following characteristics: use of calculators or computers, use of manipulative materials, cooperative student learning.
Lesson Plan Checklist:
1 Does my lesson plan include objective, pertinent SSS benchmark in words, grade level, materials, class organization, important questions to ask, examples given, how to introduce, how to explain, how to sum up the lesson, and how student learning was assessed?
2 Is my lesson plan explicit about the target mathematical content (specific examples given, concepts taught, activities performed, key vocabulary used, important explanations made)
3 Did I attach sample blank forms, or worksheets to be used?
c. Classroom participation
Discussion and instructional simulations are important components of this class. You are expected to come each class session having read the assigned materials and actively participate in all class sessions and activities.
Students should give their attention to whoever has the speaking floor, professor or fellow student. It is important that you respect the speaker and class discussion by giving it your attention.
Cellular phones and pagers should be turned off during class sessions.
d. Quizzes and midterm
You may be given quizzes based on assigned readings to assess your understanding of the issues covered. You will also take a midterm at an announced date. Missed quizzes and midterm due to unexcused absences can not be made up.
e. Analysis of a case of teaching (ACT)
There is little doubt that much of teacher’s professional development occurs when he/she is in the field by practicing teaching, by planning, teaching, making adjustments, and making decisions on foot during instruction. Other than one’s own practice, a channel of professional development based on experience is to reflect on others’ teaching. The purpose of this assignment is to let you carefully examine cases of teaching mathematics and have a chance to reflect on them. It is hoped that these analyses will help better understand issues we discuss in class.
You will be asked to read and analyze a case of teaching given by the professor. You should come to class having written your answers to the discussion questions placed at the end of the case. This will be the case analysis assignment that you will turn in. We will discuss the case and your responses in class. Before you read the case, you should understand and work on the mathematical task given at the beginning. You will find the set of discussion questions at the end of cases. Write answers to these questions and submit on the due date. While preparing the written responses for the questions, make sure that you support your opinions by giving examples from the text. Unsubstantiated opinions in the report will not receive full credit.