KENNESAW STATE UNIVERSITY
BAGWELL COLLEGE OF EDUCATION
DEPARTMENT OF ELEMENTARY AND EARLY CHILDHOOD EDUCATION
SPRING 2012
ECE 7740 – The Early Preparation of the Mathematical Mind
I.
COURSE TITLE:
II.
INSTRUCTOR: Feland L. Meadows, Ph.D.
PHONE: 678-797-2161
FAX:
678-797-2199
OFFICE: 3391 Town Pointe Parkway, Suite #4120
fmeadows@kennesaw.edu
III.
IV.
CLASS MEETINGS: January - May, 2012; Mondays and Wednesdays 6:30 – 7:45
TEXTS:
Bransford, J. D., Brown, A. L. and Cocking, R. R. Eds. 2000. How People Learn: Brain, Mind,
Experience, and School. Washington, D.C.: National Academy Press.
Gamow, George, 1988. One, Two, Three…Infinity. New York, N.Y.: Discovery Science Books
Lillard, Angeline Stoll. 2005 Montessori, the Science Behind the Genius. New York, N.Y.: Oxford
University Press.
Montessori, Maria. [1914] 1965. Dr. Montessori’s Own Handbook. New York, N.Y.: Schocken
Books.
Montessori, Maria 1995. The Discovery of the Child. Oxford, England: Clio Press.
Additional readings in selected texts from the bibliography will be assigned.
V.
PURPOSE/RATIONALE:
To present the conceptual framework for the early preparation of the mathematical mind and the
successful teaching of mathematical concepts and operations to young children. To review how
practical life and sensorial presentations and activities prepare children for the introduction of
1
numerical concepts. To demonstrate how young children develop numeration skills when counting
activities and numeral symbols are presented with concrete objects at the developmentally
appropriate times. To model presentations with scientifically designed mathematics materials. To
offer candidates hands-on experience with materials and the opportunity to complete their student
manuals after observing the presentations modeled by the instructor.
VI.
CATALOG COURSE DESCRIPTION:
Students study the conceptual framework for the presentation of numeration and mathematical
activities to young children. The use of Montessori materials that provide children with multiple
opportunities to develop numeration skills, to understand the decimal system, and to practice the four
operations with up to four digits is presented and practiced. In addition, students learn how to present
commutative and squaring operations in ways that allow children to discover their unique
characteristics. Finally, students learn to present numerous math activities and exercises with a wide
variety of different, scientifically designed manipulable materials as well as present special
memorization materials with which children can review and enhance their ability to recall all of the
number facts they have assimilated from the previous activities. This course is aligned with the
standards of the National Council of Teachers of Mathematics (NCTM). This course includes an
extensive field experience. Verification of professional liability insurance is required prior to
placement in the field.
VII.
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.
Philosophy of Montessori Classroom Management
The Montessori classroom is a carefully Prepared Environment in which a rich array of graded,
structured materials that are related to both the curriculum areas and the children’s stages of
development are available for presentation one-on-one to each child by the teacher. Teachers
prepare individualized education plans for every child based upon their observation of the child’s
2
interests and level of development. As a result, children are happy and are much more engaged in
their work than children in classrooms where there is only one lesson plan for the entire class and
some of the children misbehave because they are either bored or do not understand what is going on!
In a Montessori multiage classroom a great deal of positive peer modeling is taking place that
benefits the younger children. The older children, who have been in that class with that teacher for
one or two years, have a very positive influence upon the younger children in the class. Thus, the
younger children quickly learn to emulate the peaceful disposition and the orderly behavior of their
older peers. As a result, Montessori teachers do not have to resort to the “Positive Reinforcement”
and other kinds of teacher imposed “behavior management” strategies that teachers find it necessary
to use in other kinds of classrooms.
VII. 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 candidates with disabilities within their
academic program. In order to make arrangements for special services, candidates 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.
IX.
USE OF TECHNOLOGY:
Integrated Use of Technology: The Bagwell College of Education recognizes the importance of
preparing future educators and K-12 students to develop technology skills that enhance learning,
personal productivity, decision making, their daily activities in the 21st century. As a result, the
ISTE NETS*T Technology Standards for Teachers are integrated throughout the teacher preparation
program enabling teacher candidates to explore and apply best practices in technology enhanced
instructional strategies.
Specific technologies used within this course include exploration and use of instructional media,
especially microcomputers, to assist candidates in their acquisition and understanding of the
importance of movement in the education of young children. Candidates will also develop skills in
the use of productivity tools such as multimedia, local-net and Internet, and will feel confident to
design multimedia presentations, use and create www resources, and develop an electronic learning
portfolio.
3
Uses of Technology in the Montessori Teacher Education Program
Students bring their notebook computers to class where they are given documents for 6 Student
Manuals which contain the essential information about every material and presentation that they will
learn to give over the two year period of study. Each of the presentation texts has a section in which
students can key in their description and understanding of each of the more than 1,250 presentations
that the Instructors will model for them in class.
Students are required to search internet sources for information related to certain themes that their
Instructors present in class. They also must search for picture resources with which to illustrate
certain aspects of their teachers’ manuals and to use in the manufacture of Sensorial, Language,
Mathematics and Science teaching/learning materials that they will use with the children.
X.
COURSE GOALS/OBJECTIVES:
Upon completion of this course, candidates will:
1. understand and be able to implement the scientific foundations for the effective teaching of
numerical and computational skills to young children;
2. present mathematical concepts more effectively by using scientifically designed manipulatives
because concrete materials provide a way for children to connect their experiences with real objects
to abstract mathematical concepts;
3. demonstrate the ability to introduce basic mathematical concepts by giving presentations with
scientifically designed mathematics materials.
4. demonstrate the ability to help children acquire the language of mathematics, to assimilate and
recall number facts, to master measurement skills, and to develop computational skills successfully!
Candidates will also:
1. demonstrate their knowledge of how to design the learning environment by ordering and
structuring the mathematics materials correctly on the classroom shelves;
2. demonstrate the ability to diagnose the developmental needs of children they observe;
3. demonstrate the ability to present the developmentally appropriate mathematics materials in the
correct sequence to children based upon their level of development;
MACTE Early Childhood 2.5-6 Competencies to be achieved in this course:
1. a, b;
2. c;
3. a. b. c. d. e.
XI.
ATTENDANCE POLICY:
Classroom attendance and participation is absolutely essential to your success in this course. KSU
policy requires every student to attend all class sessions and related field experiences.
MACTE accreditation requires you to attend a minimum of 90% of the time in order to qualify for
certification. This means that you can only be absent 2 times. The only excused absences are
documented personal illness, bereavement, military duty, or jury duty. Any unexcused absence will
result in the lowering of your grade by 5 points. Anyone who is absent 25% of the time will not pass
this course.
4
Professional conduct requires that you show respect for others. This includes coming to class on
time, staying for the entire class period, paying attention and remaining engaged in the class activities
and cooperating with colleagues in class. In the event of an absence, you are responsible for all
material, assignments, and announcements presented in class.
XII.
REQUIREMENT/ASSIGNMENTS:
1) Class participation and discussion
Paying careful attention to lectures and presentations and participating in discussions in class are
important, because we believe that learning is an interactive endeavor which requires the presence
and participation of all class members to facilitate learning. All candidates are required to read
related chapters of the textbooks and assigned readings before the class meetings. Classroom
discussions will be based upon lectures and presentations of the instructors as well as assigned
research and readings and the questions students bring to the class.
2) Provide evidence of having read and understood assigned texts
Prepare a review of those chapters in the assigned texts which deal with various aspects of the
presentation of mathematical concepts and skills in which you:
a) communicate clearly the premise and purpose of each text,
b) evaluate the influence that the author’s message should have upon education,
c) describe how your work as a teacher can benefit from the author’s ideas.
3) Survey the literature, conduct research and submit a report
a) Survey the literature related to the early preparation of the mathematical mind;
b) Conduct research in the literature to identify studies that support and/or inform the researchbased conceptual framework of this course;
c) submit a double spaced, 10 page report of your findings.
4) Practice all of the materials presentations
a) Conduct an analysis of movement related to each presentation.
b) Practice, practice, practice with the materials daily.
c) Attend the three hour supervised practice session every week.
d) Present materials and teaching strategies to classmates.
e) Have your classmates serve as your control of error.
f) Be prepared to demonstrate your acquired skills in presenting materials with children.
5) Be prepared to demonstrate a sequence of 3 to 5 Montessori materials presentations you
have mastered in this course to students in the Traditional M.Ed. Program.
6) Participate in all required fieldwork experiences
a) Develop your ability to observe child behavior with understanding in the light of the knowledge
and insights you have gained in this course.
b) Observe one child in a math activity and prepare an observation which includes his/her attitude
in the class, the selection of activities, work or failure to work, competence in the work selected, and
demeanor after completing the work.
5
7) Prepare effectively for tests and examinations.
Assignments: All assignments must be typed and should represent your best efforts to produce high
quality, graduate level work.
1. All assignments must be typed double spaced in 12 pt. Times New Roman font.
2. Place your name, the course number and title and the date at the top RIGHT of the first page.
3. Staple the pages of each work together. DO NOT place them in a plastic folder.
4. Be sure to keep a hard copy of each paper you turn in.
5. Each paper should represent your best efforts to produce the highest possible quality of work.
6. Late Work: Assignments are considered late if not turned in during class on the due date.
There will be a 10% deduction of total possible points for each day that work is late.
Assignments are always accepted early.
Tests: All tests must be taken on the day and time they are scheduled. No rescheduling of
tests/quizzes will occur.
XIII.
EVALUATION AND GRADING:
1) Class participation and discussion
2) Book Reviews
3) Research and Report
4) Field Work Observation Report
5) Completion of Teacher’s Manual
6) Presentation to Traditional M.Ed. Class
7) Tests and Final Examination
10
20
20
10
10
10
20
Total 100
Grades will be assigned as follows:
91-100
81-90
71-80
61- 70
0 - 60
A
B
C
D
F
XIV. 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.
XV. DISRUPTIVE BEHAVIOR:
The University has a stringent policy and procedure for dealing with behavior that disrupts the
learning environment. Consistent with the belief that your behavior can interrupt the learning of
6
others, behavior fitting the University’s definition of disruptive behavior will not be tolerated. Refer
to the Kennesaw State University Undergraduate Catalog, 2003-2004, pages 314-315 for further
details.
Other General Policies and Regulations of Student Life have been developed by Kennesaw State
University. These policies (Handling Student Code of Conduct Violations at KSU) include:
1Academic Misconduct, 2) Disruptive Behavior, 3) Sexual Assault, are found on pages 240-244 of
the 2003-2004 Kennesaw State University Undergraduate Catalog.
It is expected, in this class, that no professional should need reminding of any of these policies but
the policies are there for your consideration. The activities of this class will be conducted in both the
spirit and the letter of these policies.
XVI. COURSE OUTLINE:
1. The First Psycho-Arithmetic Level:
Weeks 1 & 2
The introduction of quantities
The sequence of natural numbers
The introduction of number symbols
The introduction of zero
The introduction of the four operations
2. The Second Psycho-Arithmetic Level:
Week 3
Introduction to the decimal system: The Royalty of Number.
Formation of quantities with the decimal system
The Grand Display of the decimal system
3. The Third Psycho-Arithmetic Level:
The First Stage – The Four Operations
Weeks 4 & 5
Static exercises in the four operations with the decimal system material
The Regrouping Exercise
Dynamic exercises in the four operations with the decimal system material
The Second Stage - Introduction of the Sequence of Numbers between Tens
Teens with beads and boards
Tens with beads and boards
The passage of the tens
Fraction Skittles
The Clock
Third Stage - Linear Counting
Week 7
100 Bead Chain and 100 board
Skip counting with the power of two chains
1,000 bead chain
Formation of numbers with beads
Combinations of ten
The Snake Game
Fourth Stage - The 4 Operations with the Colored Bead Stair
Addition: Vertical and horizontal facts
Addition: Commutative operations
Addition: Combinations of Ten
7
Weeks 8 & 9
Week 6
Addition: Tables
Addition: Binomials
Multiplication: Vertical and horizontal facts
Multiplication: Commutative operations
Multiplication: Taking a number 10 times
Multiplication: Many different ways of making a number
Multiplication: Tables
Multiplication: Squaring a Number
Multiplication: Tables up to the Square
Multiplication: Polynomials
Subtraction: Vertical and Horizontal Facts
Subtraction: Tables
Table Rods: The four operations
4. The Fourth Psycho-Arithmetic Level: The Memorization Materials
First Stage – Addition
Week 10
Addition Strip Board: Facts
Addition Strip Board: Formation of Sets of Ten
Addition Strip Board: Addition of the Double Strips
Addition Strip Board: Tables
Addition Charts
Second Stage – Multiplication
Multiplication Board: Facts
Multiplication Board: Tables
Multiplication Charts
Week 11
Third Stage – Subtraction
Week 12
Subtraction Strip Board: Facts
Subtraction Strip Board: Take Away from Sets of Ten
Subtraction Strip Board: Tables
Subtraction Charts
Fourth Stage – Division
Week 13
Division Board: Facts Without Remainders
Division Board: Facts With Remainders
Division Board: Tables
Division Charts
Review of All Stages
Week 14
XVII. REQUIRED READINGS:
Required readings are the ones identified above.
8
XVIII. ADDITIONAL RESEARCH REFERENCES:
Mathematics References
Aczel, Amir D. 1996. Fermat’s Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem.
New York, NY: Four Walls Eight Windows
Julius, Edward H. 1992. Rapid Math: Tricks & Tips, 30 Days to Number Power. NY: John Wiley & Sons, Inc.
Sardar, Ziauddin; Ravetz, Jerry & Van Loon, Borin. 1999. Introducing Mathematics. New York, NY: Totem
Books
Seife, Charles. 2000. ZERO – The Biography of a Dangerous Idea. New York, NY: Viking/Penguin Group.
Stenmark, Jean Kerr; Thompson, Virginia & Colley, Ruth. 1986. Family Math. Berkeley, CA: Laurence Hall
of Science, University of California, Berkeley.
Vancleave, Janice. 1991. Math for Every Kid. New York, NY: John Wiley & Sons, Inc.
Vorderman, Carol. 1996. How Math Works – 100 Ways Parents and Kids can Share the Wonders of
Mathematics. London, England: Dorling Kindersley Limited
Theoretical Framework of Early Childhood Education References
Berk, L. E. & A. Winsler. 1995. Scaffolding Children’s Learning: Vygotsky and Early Childhood Education.
Washington, D.C., NAEYC
Brainerd, C. J. 1978. Piaget's Theory of Intelligence. New Jersey: Prentice Hall, Inc.
Bruner, J. 1960. The Process of Education. Cambridge, MA: Harvard University Press.
Bruner, J. 1966. Toward a Theory of Instruction. Cambridge, MA: Harvard University Press.
Bruner, J. & Maya Pines. 1971. The Development of Intelligence in Babies, in Segal, J. (Ed.)
Mental Health Program Reports, Washington, D.C.: U.S.D.H.E.W.
Bruner, J., K. Kaye, & K. Lyons. 1971. The Growth of Human Manual Intelligence in Maya Pines, Bruner, J.
1973. Going Beyond the Information Given. New York: Norton.
Bruner, J. 1983. Child's Talk: Learning to Use Language. New York: Norton.
Bruner, J. 1986. Actual Minds, Possible Worlds. Cambridge, MA: Harvard University Press.
Bruner, J. 1990. Acts of Meaning. Cambridge, MA: Harvard University Press.
Bruner, J. 1997. Celebrating divergence: Piaget and Vygotsky in Human Development,
Vol. 40, No.2, pp 63-73.
Bruner, J., J. Goodnow, & A. Austin 1951. A Study of Thinking. New York Wiley.
Evans, R. 1973. Jean Piaget: The Man and His Ideas. New York: E. P. Dutton & Co., Inc.
Fowler, William, 1962. Cognitive Leaning in Infancy and Childhood in Psychological Bulletin
Vol. 59, No.2, pp. 116-152. American Psychological Association.
Gardner, H. 1983. Frames of mind: The theory of multiple intelligence. N.Y.: Basic Books
Gindis, B. 1999 Vygotsky’s Vision: Reshaping the Practice of Special Education for the 21st Century; in
Remedial and Special Education, Vol.20, No. 6.
Kramer, R. 1988. Maria Montessori, A Biography. N.Y.: Addison-Wesley.
Lillard, Paula Polk 1973 Montessori, a Modern Approach. N.Y.: Schocken Books
Meadows, F. 1993 Evaluation of a Model Early Childhood Education Program for At-Risk Children in California,
IUSD Monograph.
Moll, L. (Ed.) 1990. Vygotsky and education: Instructional implications and applications of
sociohistorical psychology. Cambridge, MA: Cambridge University Press.
Montessori, Maria 1994 The Absorbent Mind. Oxford, England: Clio Press
Montessori, Maria 1995 The Discovery Of The Child. Oxford, England: Clio Press
Montessori, M. [1914] 1965. Dr. Montessori’s Own Handbook. N.Y.: Schocken Books.
Montessori, M. 1915. The California Lectures of Maria Montessori, 1915. Oxford: Clio Press
9
Montessori, Mario M., Jr. 1976. Education for Human Development. N.Y.: Schocken Books
Montessori, M. [1936] 1988. The Secret of Childhood. N.Y.: Ballantine Books
Piaget, J. 1972. To Understand Is To Invent. New York: The Viking Press, Inc.
Rogoff, B. 1990. Apprenticeship in thinking: Cognitive development in social context.
N.Y.: Oxford University Press.
Sigel, I. and R. Cocking. 1977. Cognitive Development from Childhood to Adolescence:
A Constructivist Perspective. New York: Holt, Rinehart and Winston.
Singer, D. & Revenson, T. 1978. A Piaget Primer: How a Child Thinks. New York: International Universities
Press, Inc.
Standing, E.M. 1984. Maria Montessori: Her Life and Work. New York: New American Library-Plume Books
Vygotsky, L. S. l997. The Collected Works, Volumes 3 and 4. M. Hall, trans., R.W. Rieber, Ed.
Vygotsky, L. S. [1930-1935] 1978. Mind in society: The development of higher mental processes.
Eds. & trans. M. Cole, V. John-Steiner, S. Scribner, & E. Souberman. Cambridge, MA: Harvard
University Press.
Vygotsky, L. S. 1956. Selected Psychological Investigations. Moscow: Izdstel’sto Akademii
Pedagogicheskikh Nauk SSSR.
Vygotsky, L. S. 1962. Thought and Language. Cambridge, MA. MIT Press.
Wertsch, J. V., ed. 1985 Culture, Communication and Cognition: Vygotskyan Perspectives. N.Y.: Cambridge
University Press.
Wertsch, J. V., & B. Rogoff. 1984. Eds. in Children’s learning in the “zone of proximal development” 1-6.
San Francisco: Jossey-Bass.
Wittmer, D.S., & Honig, A.S. 1994. Encouraging positive social development in young children. in
Young Children 49 (5): 4-12.
Wolery, M., & Wilbers, J. S. eds. 1994. Including children with special needs in early childhood programs.
Washington, D.C. : NAEYC.
10