I.
COURSE NUMBER/SECTION: MATH 3315/05 and MATH 3315/06
COURSE TITLE: Critical Content of ECE Math I
COLLEGE OR SCHOOL: Science
and Mathematics
SEMESTER / TERM AND YEAR:
Fall 2006
II.
INSTRUCTOR: Dr.
Teresa G. Banker
TELEPHONE: 770
– 499 – 3427 or 770 – 423 – 6327
FAX: 770
– 423 – 6629
E-MAIL: DrBanker@mindspring.com (Subject: Math 3315)
OFFICE: SC
536
OFFICE HOURS: MW 10 - 11:30 am ; Th 1 - 2 pm
Others
by appointment convenient to both
III. CLASS SESSIONS: TR9:30
am – 10:45 am KH1105 (Section 05)
TR
IV. REQUIRED TEXT:
Mathematics For
Elementary School Teachers by O’Daffer,
Charles, Cooney, Dossey, Schielack (3rd Edition)
On-Line Texts:
National
Council of Teachers of Mathematics (1989). Curriculum and Evaluation
Standards for School Mathematics. Reston, VA: NCTM, Available at http://standards.nctm.org.
National
Council of Teachers of Mathematics. (2000).
Principles and Standards for School Mathematics. Reston, VA:
NCTM. Available at
http://standards.nctm.org.
V.
CATALOG DESCRIPTION:
MATH
3315. Critical Content of ECE Math I.
3 credit hours.
Prerequisite: 6 hours of
mathematics.
Designed
for the P-5 teacher. The development of the student’s ability to
understand and communicate fundamental concepts of mathematics through reading,
writing and discussing ideas will be strongly emphasized, along with the
cultural, historical and scientific applications of mathematics. Topics will
include the study of sets; the development of the set of whole numbers and the
set of integers; operations with whole numbers and integers; mathematical
systems and number theory. Emphasis is placed on building concepts through the
use of models, manipulatives, and the appropriate use of technology. Not for
math majors.
VI.
PURPOSE / RATIONALE:
The purpose of this
course is to introduce K–5 preservice teachers to the basic history and
foundations of elementary mathematics through the study of sets, enumeration
systems, properties and algorithms of arithmetic operations, and number
theory. The mathematics faculty at KSU
endorses the purpose as stated by the MAA in A Call for Change
(1991).
Conceptual
Framework Summary:
COLLABORATIVE DEVELOPMENT OF
EXPERTISE IN
TEACHING AND LEARNING
The Professional Teacher
Education Unit (PTEU) at Kennesaw State University is committed to developing
expertise among candidates in initial and advanced programs as teachers and leaders
who possess the capability, intent and expertise to facilitate high levels of
learning in all of their students through effective, research-based practices
in classroom instruction, and who enhance the structures that support all
learning. To that end, the PTEU fosters the development of candidates as they
progress through stages of growth from novice to proficient to expert and
leader. Within the PTEU conceptual framework, expertise is viewed as a process
of continued development, not an end-state. To be effective, teachers and
educational leaders must embrace the notion that teaching and learning are
entwined and that only through the implementation of validated practices can
all students construct meaning and reach high levels of learning. In that way,
candidates are facilitators of the teaching and learning process. Finally, the
PTEU recognizes, values and demonstrates collaborative
practices across the college and university and extends collaboration to the
community-at-large. Through this collaboration with professionals in the
university, the public and private schools, parents and other professional
partners, the PTEU meets the ultimate goal of assisting Georgia schools in
bringing all students to high levels of learning.
Knowledge Base:
Teacher
development is generally recognized as a continuum that includes four phases:
preservice, induction, in-service, renewal (Odell, Huling,
and Sweeny, 2000). Just as Sternberg (1996) believes that the concept of
expertise is central to analyzing the teaching-learning process, the teacher
education faculty at KSU believes that the concept of expertise is central to
preparing effective classroom teachers and teacher leaders. Researchers
describe how during the continuum phases teachers progress from being Novices
learning to survive in classrooms toward becoming Experts who have achieved
elegance in their teaching. We, like Sternberg (1998), believe that expertise
is not an end-state but a process of continued development.
The faculty of Kennesaw State University endorses the
standards for the preparation of teachers of mathematics proposed by the
Mathematical Association of America (MAA) in A Call for Change:
Recommendations for the Mathematical Preparation of Teachers of Mathematics
and by the National Council of Teachers of Mathematics (NCTM) in the Curriculum
and Evaluation Standards for School Mathematics and the Professional
Standards for Teaching Mathematics and subscribed to by the National
Council for Accreditation of Teacher Education.
Thus, this course is designed so that future teachers will:
1. View mathematics as a system of interrelated
principles
2. Communicate mathematics accurately, both
orally and in writing
3. Understand the elements of mathematical
modeling
4. Understand the use of calculators and
computers appropriately in the teaching and learning of mathematics
5. Appreciate the development of mathematics
both historically and culturally (A Call for Change, 1991)
6. Understand the mathematics content that is necessary
to teach grades P-8 in the schools envisioned by the MAA and the NCTM.
In preparing teachers, this course emphasizes not only
the comprehension of the content knowledge, but also the ability to communicate
that content. In addition, the principles
advocated in the NCTM Standards are woven throughout the course, so that
the pre-service teacher will have knowledge of the kind of pedagogy that is
being prescribed and will be able to serve as a change agent. This course will require the students to solve
problems, think critically, and reflect.
Use of Technology:
The Professional Standards Commission requires
technology Standards for Educators.
Telecommunication and information technologies will be integrated
throughout the master teacher preparation program, and all candidates must be
able to use technology to improve student learning and meet Georgia Technology
Standards for Educators. During the
courses, candidates will be provided with opportunities to explore and use
instructional media, especially microcomputers, to assist teaching. They will master use of productivity tools,
such as multimedia facilities, local-net and Internet, and feel confident to
design multimedia instructional materials, create WWW resources, and develop an
electronic learning portfolio.
The use of calculators and computers is an encouraged
and accepted practice to enable students to discover mathematical relationships
and approach real world applications.
"Future teachers will need to be familiar with a variety of
technological tools, including ordinary calculators, graphing calculators, and
computers, as well as appropriate geometric and computational
software." (Thomas W. Hungerford in
"Future Elementary Teachers: The Neglected Constituency," MAA Monthly, January,
1994, pp. 15-21.) Familiarizing the
pre-service teacher with a variety of technological tools is an integral part
of the math sequence for teachers.
Diversity:
A variety of materials and instructional
strategies will be employed to meet the needs of the different learning styles
of diverse learners in class. Candidates will gain knowledge as well as
an understanding of differentiated strategies and curricula for providing
effective instruction and assessment within multicultural classrooms. One
element of course work is raising candidate awareness of critical multicultural
issues. A second element is to cause candidates to explore how multiple
attributes of multicultural populations influence decisions in employing
specific methods and materials for every student. Among these attributes
are age, disability, ethnicity, family
structure, gender, geographic region, giftedness, language, race, religion,
sexual orientation, and socioeconomic status. An emphasis on
cognitive style differences provides a background for the consideration of
cultural context.
Kennesaw State University
provides program accessibility and accommodations for persons defined as
disabled under Section 504 of the Rehabilitation Act of 1973 or the Americans
with Disabilities Act of 1990. A number
of services are available to support students with disabilities within their
academic program. In order to make
arrangements for special services, students must visit the Office of Disabled
Student Support Services (ext. 6443) and develop an individual assistance
plan. In some cases, certification of
disability is required.
Please be aware there are
other support / mentor groups on the campus of Kennesaw State University that address
each of the multicultural variables outlined above.
VII.
GOALS / COURSE OBJECTIVES:
The KSU teacher
preparation faculty is strongly committed to the concept of teacher preparation
as a developmental and collaborative process. Research for the past 25 years
has described this process in increasingly complex terms. Universities and
schools must work together to successfully prepare teachers who are capable of
developing successful learners in today’s schools and who choose to continue
their professional development.
(Conceptual Framework)
MATH 3315, 3316, and 3317 provide a strong mathematical foundation for
prospective ECE teachers.
The
student will be able to:
|
Goals |
Standards These courses address the National Council of Teachers of
Mathematics standards for teacher education listed below. |
Assignments, homework, quizzes, exams, activities, projects |
|
1.
1. Develop
and apply strategies to solve a variety of problems. |
NCTM Standard 1:
Problem Solving NCTM Standard
2: Reasoning/Proof |
|
|
2.
2. Use
the language and symbols of set theory and functions to communicate
mathematically. |
NCTM Standard 3:
Communication, NCTM Standard 5:
Representation |
|
|
3.
3. Understand
and appreciate our numeration system by relating counting, grouping, and
place value concepts and to further develop number sense. |
NCTM Standard:
Number & Operation, NCTM Standard 4:
Connections |
|
|
4.
4. Identify
properties and characteristics of mathematical systems beginning with the
natural numbers and building to the integers to use a mathematical idea to
further his/her understanding of other mathematical ideas. |
NCTM Standard:
Number & Operation |
|
|
5.
5. Use
the concepts and principles of number theory to look at an area of
mathematics that is as alive today as it was in early Greece and to build a
foundation for the future study of the rational numbers. |
NCTM Standard 2:
Reasoning and Proof |
|
|
6.
6. Use
a variety of estimation techniques to predict, conjecture, and determine
reasonableness of results, especially when using technology. |
NCTM Standard:
Number & Operation, NCTM Standard 6:
Technology |
|
|
7.
7. Express
rational numbers in equivalent forms such as fractions, decimal, percents,
exponential and scientific notation. |
NCTM Standard:
Number & Operation |
|
|
8.
8. Use
ratio and proportion to build mathematical models in order to solve
real-world problems. |
NCTM Standard:
Number & Operation |
|
|
9.
9. Explore
the operations, properties, and uses of real numbers. |
NCTM Standard:
Number & Operation |
|
|
10.
10. Use
a variety of tools, physical models, and appropriate technology to develop an
understanding of geometric concepts and relationships and their use in
describing the world in which we live. |
NCTM Standard 6:
Technology |
|
|
11.
11. Interpret
measurements of many kinds of two- and three-dimensional objects. |
NCTM Standard:
Measurement |
|
|
12.
12. Identify
properties, patterns, and families of geometric figures. |
NCTM Standard:
Geometry |
|
|
13.
13. Communicate
comprehension of the National Council of Teachers of Mathematics Principles and Standards for School
Mathematics. |
NCTM Standards |
|
MATH 3315 Outline:
A.
Problem Solving
B.
Understanding Whole Number Operations and
Properties
C.
Using Estimation and Computation
D.
Exploring Number Theory
E.
Understanding
Integer Operations and Properties
VIII.
COURSE REQUIREMENTS / ASSIGNMENTS:
1. Students
are expected to be prepared for each class.
Class presentations will focus on clarifying overall concepts. Homework will be assigned after topics are
discussed. Students are expected to work
on class related preparation and homework approximately two hours outside of
class for each hour in class.
2. There
will be two tests during the semester and a comprehensive final exam. The final exam will be in two parts: a
take-home part and an in-class part. There will be no make-up tests. (see grading)
3.
Group / Class Work: There will be opportunities for students to work in
cooperative learning groups to solve problems.
There will be periodic daily quizzes and assignments. Sample work will be evaluated either
individually or as group assignments, where each member of the group receives
the same score.
4. Reflections:
Research shows that reflective teachers are better teachers. My personal
research shows that reflective mathematics students are better mathematics
students. A reflection is due on six Thursdays of your choice, but the first
and last weeks are not eligible. The deadline for receiving the reflection is
Saturday at midnight. You may submit reflections from the specific website at www.resbuy.com/math . If this website
does not work for some reason, you may do direct email to DrBanker@mindspring.com, addressing
the three questions for this purpose. Reflections submitted before Thursday
will receive no credit (a possible 5 points each).
5.
NCTM
Standards and GPS document: Students
will read assigned sections of the Georgia Performance Standards and one
assigned article from Teaching Children Mathematics. Student will respond to questions on the
article and other readings. Students will write a paper analyzing the GPS
document given particular guidelines.
IX.
EVALUATION AND GRADING:
There will be: Possible Points
2
tests 200
Comprehensive Final 200
Reflections 30
NCTM
& GPS Papers (40 each) 80
Attendance 30
Group/Class
Work/Quizzes 100+
Total Possible
Points 640+
Grades
will be assigned as follows (based on percent of points earned and points
available):
Grading scale: A
(90-100%) B (80-89%) C (70-79%)
D (60-69%) F(below
60%)
At semester’s end if the final exam is a higher score than the lowest test
score, I will add 80% of the difference (after scaling the final exam to 100
points) to the lowest test score, including scores for missed tests. This
policy, in general, can raise the course average as much as a letter grade.
X.
ACADEMIC
INTEGRITY:
Every KSU student is
responsible for upholding the provisions of the Student Code of Conduct, as
published in the Undergraduate and Graduate Catalogs. Section II of the Student Code of Conduct
addresses the University’s policy on academic honesty, including provisions
regarding plagiarism and cheating, unauthorized access to University materials,
misrepresentation/falsification of University records or academic work,
malicious removal, retention, or destruction of library materials,
malicious/intentional misuse of computer facilities and/or services, and misuse
of student identification cards.
Incidents of alleged academic misconduct will be handled through the
established procedures of the University Judiciary Program, which includes
either an “informal” resolution by a faculty member, resulting in a grade
adjustment, or a formal hearing procedure, which may subject a student to the
Code of Conduct’s minimum one semester suspension requirement.
XI.
ATTENDANCE
POLICY
Class attendance is
assumed and will be monitored. In the
event of an absence, the student is responsible for all material, assignments,
and announcements presented in class. Assignments will NOT
be accepted late.
There are no make-ups for missed tests and quizzes. Students are expected to attend every class.
Each absence will cost 2 points, and each tardy of 5 to 15 minutes will cost 1
point. Tardies of more than 15 minutes may result in an absence.
XII.
COURSE TIMELINE: IMPORTANT DATES (T E
N T A T I V E)
January 5– 11 Late
registration & Drop/Add
January 5 First day of classes
January 15
Holiday--no
class
February15 Test 1
February 22 NCTM article paper
March 2 Last day
to withdraw without academic penalty
March 3 -
9 Spring
Break
March
22
No class
April 5 GPS
lesson plan
April 17 Test
2
April 29 Last
day of classes
May 1 Final Exam (
May 3 Final Exam (
XIII.
REFERENCES AND BIBLIOGRAPHY
National
Council of Teachers of Mathematics, Teaching Children Mathematics
(formerly Arithmetic Teacher),
National
Council of Teachers of Mathematics, Journal for Research in Mathematics Education,
National Council of
Teachers of Mathematics, Addenda Series, Reston, VA,
Patterns
(Grades K-6)
Number
Sense and Operations (Grades K-6)
Developing
Number Sense in the Middle Grades (Grades 5-8)
Patterns
and Functions (Grades 5-8)
National
Research Council (2001) Adding it up:
Helping children learn mathematics. J. Kilpatrick, J. Swafford,
and
B. Findell (Eds.). Mathematics Learning Study Committee,
Center for Education, Division of Behavioral and Social Sciences and Education.
Washington, DC: National Academy Press.
TRAC Center, Kennesaw State University, has many
materials appropriate to primary and middle school mathematics
Note:
The information contained in the course policies and the course outline
is subject to change with notice.
WITHDRAWAL FROM THE UNIVERSITY OR FROM INDIVIDUAL
COURSES AND ACADEMIC INTEGRITY
Fall Term, 2006
Withdrawal
Students who find that they cannot continue in college for the entire semester after being enrolled, because of illness or any other reason, need to complete an online form. To completely or partially withdraw from classes at KSU, a student must withdraw online at www.kennesaw.edu, under Owl Express, Student Services.
The date the withdrawal
is submitted online will be considered the official KSU withdrawal date which
will be used in the calculation of any tuition refund or refund to Federal
student aid and/or HOPE scholarship programs. It is advisable to print the
final page of the withdrawal for your records. Withdrawals
submitted online prior to
Students may, by means of the same online withdrawal and with the approval of the university Dean, withdraw from individual courses while retaining other courses on their schedules. This option may be exercised up until March 2, 2007.
This is the date to withdraw without academic penalty for Fall Term, 2006 classes. Failure to withdraw by the date above will mean that the student has elected to receive the final grade(s) earned in the course(s). The only exception to those withdrawal regulations will be for those instances that involve unusual and fully documented circumstances.
Academic Integrity
Every KSU student is responsible for upholding the provisions of the Student Code of Conduct, as published in the Undergraduate and Graduate Catalogs. Section II of the Student Code of Conduct addresses the University’s policy on academic honesty, including provisions regarding plagiarism and cheating, unauthorized access to University materials, misrepresentation/falsification of University records or academic work, malicious removal, retention, or destruction of library materials, malicious/intentional misuse of computer facilities and/or services, and misuse of student identification cards. Incidents of alleged academic misconduct will be handled through the established procedures of the University Judiciary Program, which includes either an “informal” resolution by a faculty member, resulting in a grade adjustment, or a formal hearing procedure, which may subject a student to the Code of Conduct’s minimal one semester suspension requirement.