MAE 4310 - Content and Methods of Teaching Elementary
Mathematics (1-6)
Fall 2005- Section 02
Professor
Cengiz Alacaci (read: Jayn’kiz
Alajaji)
EB
(305)
348 1067
alacaci@fiu.edu, websites: http://www.fiu.edu/~alacaci,
http://webct.fiu.edu
Office
Hours: Wednesdays 10-12 pm, Thursdays, 2:30-5:30
pm
Required Texts
Van de Walle,
John A. (2001). Elementary and Middle
School Mathematics: Teaching Developmentally.
Course package
available from
Prerequisites
3 mathematics courses intermediate algebra or
above.
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
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
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
Complete a teaching
assignment in the field (FTA),
5
Write an observation
log for each class session in the field,
6
Write a report of
case analysis of teaching (CAT)
7
Take a web-based
tutorials (to be assigned) and write a report on the application part,
8
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. Two 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.
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
Curriculum and Instruction 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. Field
Teaching Assignment (FTA)
You will spend 20 hours at a local
elementary school for field experience.
Please meet with Field Placement Office ASAP (room 230) to make
arrangements for field placement, if you have not done so. You will be provided with a packet to guide
you. You will need to be placed with one
teacher (grades 1-6) for the entire term.
Once you are placed in a school, you
are expected to conduct a teaching assignment (FTA) for this class. You should use the first few hours to become
acquainted with the teacher and the students.
You should conduct the FTA to a whole class of elementary school
children. You may be asked to have a
form filled by your host teacher about your field assignments. Description of the important components of
FTA assignment is below.
Target concept:
You should choose an important and worthwhile mathematical concept or skill to
teach. Your lesson plan should either
teach an important mathematical concept or engage students in problem solving. It is expected that you choose an appropriate
lesson plan format matching the type of lesson objective. Please see Professors’ website for
alternative lesson plan formats. It is
suggested that you consult with the cooperating teacher and the
professor to finalize your choice of topic for the FTA. 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 teach a lesson 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.
Lesson Plan:
Prepare a detailed lesson plan to guide your instruction and prepare also
whatever materials you may need to use for teaching (the teacher could
help). You are encouraged to consult
with your instructor as you plan the lesson.
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.
Teaching and reflection:
After you develop the plan, teach the lesson to a whole class, and write a
reflection (1-2 pages) about your experience of planning and teaching this
lesson. In your reflection, address the
issue of why you choose the topic you decide to teach and what you would do
differently if you had to re-teach this lesson.
You are encouraged to attach copies of student work to your report Your
final report of the FTA should include items:
1
lesson plan,
2
your reflection about
the field teaching experience,
3
copies of any
worksheets or assignments developed/used in the lesson,
4
samples of (e.g.,
copies of selected) student work
5
completed teacher
signature from (this is mandatory.)
Lesson plan: completeness, descriptive
power and internal consistency of the lesson plan (if the lesson plan is not
self-developed, please include the reference information), reference to SSS
benchmarks matching with the lesson objective.
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 two of the following characteristics: effective
communication in the classroom, use of calculators or computers, use of
manipulative materials, cooperative student learning.
Reflection: Your reflection should
address the following issues explicitly: why you choose the concept or topic you teach,
explicit discussion of the contents of the lesson plan in relation to the
corresponding chapter of our textbook, how we know students achieved the objective
of the lesson or not achieved it, what aspects of your lesson seemed to support
or inhibit student learning, how was student communication during lesson, and
how your lesson plan reflects two of the characteristics listed above.
Checklist for FTA Assignment:
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 I used?
4
Did I attach sample
student work?
Reflection
Checklist:
1 Did I write why I picked to teach this
topic?
1.
Did I address how my
reading of the pertinent chapter of the text informed my thinking?
2.
Did I interpret
student work? Did I address how we know whether students achieved or not
achieved the lesson objective?
3.
Did I include a
discussion of the nature of student communication during the lesson?
4.
Did I address how my
lesson plan reflected the two desired characteristics?
5.
Did I attach
completed teacher signature form? (required)
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.
Rubric for Evaluation of Case Analysis
Assignment
|
Category |
Score |
Description |
|
Inadequate |
0- 2 |
Student does not turn in the
assignment. The student’s writing does not give evidence of reading and
understanding the assigned case. |
|
Minimal |
3-6 |
Student’s responses to the questions
are incomplete. Responses to the questions do not reflect understanding the
mathematical task of the case.
Responses to most questions include opinions that are not supported by
evidence from the case |
|
Satisfactory |
7-8 |
Responses reflect understanding of
the mathematical task of the case. There is evidence of understanding and
active reflection on the content of the case. Answers to most of the
questions are complete, although there are missing elements for one or two
questions, or evidence supporting opinions are missing for some
questions. |
|
|
9-10 |
Responses reflect a thorough understanding
of the mathematical task, teacher’s statements about her goals, task
selection, classroom dynamics and after-class reflections. Answers to questions are complete.
Responses reflect informed opinions about the case content, are supported by
evidence, and connected to issues discussed in class earlier. |
This assignment is chosen for the efolio system for this course. Efolio
system is
f. Report of field observations
You are expected to keep an observation
log for your field observations. You
should make an entry for each class session you observe. Your report should
have the name of school and the teacher on the cover page. Each entry should be
approximately one page in length. Your entries should start with the following
information:
- date and time of the class,
- number of students present that day,
- mathematics content (topic) covered,
-
instructional methods used by teacher such as lecturing, cooperative group
work, use of manipulative materials,
calculators, etc.,.
- chronological description of the
lesson
In your descriptions, try to avoid
using evaluative statements, and focus on the facts. At the beginning of your observation report,
include information about name of school, name of teacher, grade level of students
that you are observing, and any special characteristics of students (such as
varying levels of English proficiency and exceptionalities).
After the last entry, please write and
include a 2-3 pages summary of your observation logs. In this summary, you should tell about the
range and nature of mathematical topics, concepts and skills covered, dominant
forms of instruction, dominant forms of student behavior and interaction during
lessons, any significant issues that seemed to support or hinder student
learning, and -in your opinion- what can be done to help all students
learn better. Try to connect with issues
we discuss in class in the summary.
Your final field observation log report
should include a copy of the yellow form that you will submit to Karyl
Boynton’s office.
f.
Self-paced
tutorial on graphing
For
this assignment, you will need an internet capable computer with Excel
software. Plan to spend about an hour to
visit a website. You are going to take a
self-paced tutorial on graphing by visiting http://www.fiu.edu/~graphing. Read the contents of the website carefully
and complete all the sections and make sure you understand the contents. After completing the tutorial, print all the
scenarios in the “Apply Your Knowledge”
section. Create graphs of the data
contained in the scenarios using Microsoft Excel with appropriate titles,
legends, and make sure the axes are named, units are specified, and appropriate
range is used for the numerical axes.
Use your common sense and mathematical knowledge to create graphs that
best help answer the questions in the scenarios. After completing the graphs, write a 1 page
reflection about what you learned in this tutorial, and what you liked or did
not like about it and how the website can be improved. Attach this reflection
to the printouts of the graphs and submit on the due date.
h. Portfolio
For this assignment, you are asked to
organize major components of class work in a 3-hole punch binder. For example, you should create section
dividers for each type of assignments such as mathematical investigations,
field observation logs, field teaching, graphing assignment and critical
analysis of teaching report, and place your graded work in the corresponding
section of the binder. Please make sure
also that you place the video reflections in a separate section of your
portfolio.
SCHEDULE OF CLASS
ACTIVITIES – Fall 2005 / MAE 4310
|
Class
|
Date |
Topic,
Focus issues, Exams |
Readings/Assignments |
|
1 |
Aug 30 |
Course Overview – Understanding In
Mathematics - I |
-- |
|
2 |
Sept 6 |
Developing
understanding in mathematics – II, and
teaching through problem solving Focus
issue: Structure of elementary math curriculum |
Ch.s 3 and 4 |
|
3 |
Sept 13 |
Developing early number concepts |
Due: Initial report of field observations |
|
4 |
Sept 20 |
Developing meanings of operations |
|