A. PROJECT
TITLE: UNIVERSITY OF ILLINOIS ARITHMETIC PROJECT AT
EDUCATION
DEVELOPMENT CENTER THE ARITHMETIC PROJECT
B. PROJECT
DIRECTORS: Prof. David A. Page, Department of Mathematics, University of
Illinois at Chicago Circle, Box 4348, Chicago, Illinois 60680, U.S.A. Mr. Jack
Churchill, Education Development Center, 55 Chapel Street, Newton,
Massachusetts 02160, U.S.A.
C. PROJECT
HEADQUARTERS:
1.
Contact: Mr. Jack Churchill (617)969-7100.
2.
Special facilities or activities available for visitor
viewing:
Visitors are welcome to inspect written materials of
the
course and to view one or more of the course films by
appointment.
D.
PRINCIPAL PROFESSIONAL STAFF: Jack Churchill, Associate Director and Editor.
E. PROJECT
SUPPORT: 1. Funding agencies: National Science Foundation; Education
Development Center; Ford Foundation; Carnegie Corporation. 2. Associated
agencies: University of Illinois; Education Development Center.
F. PROJECT
HISTORY: 1. Principal originators: David A. Page and Jack Churchill. 2. Date
and place of initiation: 1958; University of Illinois, Urbana, Illinois. 3.
Evolution and development of the project: The Project was formed with a grant
from the Carnegie Corporation of New York. David Page had previously worked
with the late Max Beberman at the University of Illinois Committee on School
Mathematics from its early years, and had worked with the Physical Science
Study Committee. After five years of developing topics and testing them in
elementary classrooms, the Project moved to Education Development Center (then
Educational Services Inc.) in Massachusetts, to prepare materials which would
help teachers learn how to introduce the ideas in their classrooms. Some five
years of further development and refining went into these materials, including
use in 17 institutes for teachers in schools in the Boston area and Illinois.
The result was a 19-week packaged, self-contained course which was released in 1969 for both
in-service and pre-service use. The completed course has been used with
over 2500 teachers in approximately 75 school systems and colleges, and was
revised in 1972 on the basis of this experience. The program is now available
in two parts, each containing ten sessions, which may be used separately.
G. PROJECT
OBJECTIVES: The central theme of the project is that the study of mathematics
should be an adventure, requiring and deserving hard work. Children who grasp
some of the inherent fascination of real mathematics while they are in
elementary school are well on the way to success in further study of
mathematics and science. Students who are not to continue a formal study of
mathematics deserve a taste of the subject that is at least as appealing. The
project is not attempting to develop a systematic curriculum for any grade level,
in the view that determining an adequate curriculum is not possible until more
alternatives exist to choose among. What is needed are frameworks that provide
day-to-day, "here-is-something-to-try" ideas for the classroom. The emphasis is on things that the
teacher can begin working with soon. The term "new mathematics" is
avoided by the project. More properly, the project seeks novel ways of doing
old mathematics new structure or schemes within
which can be found large numbers of interrelated problems revealing significant
mathematical ideas. Teachers participating in an institute work a number of sequences of such problems each week
to become acquainted with the mathematics, and then begin to make up and try
out their own sequences. Throughout its work, the project has found that
improved computational skills usually follow work with its materials. Children
will do impressive amounts of computation in order to solve problems that
interest them.
UNIQUE
CHARACTERISTICS OF THE PROJECT: The Project is designed to convey both
mathematics and pedagogy in an indirect way; to free teachers from the
limitations inherent in any particular text or program; to enable teachers to
capitalize on interesting ideas wherever and whenever they appear (as often
from students as from texts); to encourage teachers to uncover and follow their
own best instincts about what is interesting in mathematics; in short, to teach
the creative teaching of mathematics.
No specific teaching style is prescribed; the emphasis on the creativity of the teacher is in the spirit of
open education, although open classroom styles are not shown in the films. The
Project's target population is all teachers of young children. Course materials
are more valuable in grades 2 through 6 than in K-l. Within this range, however, the Project's topics can be adapted and applied extensively either
in themselves or in connection with other programs.
SPECIFIC
SUBJECTS, GRADE, AGE AND ABILITY LEVELS: Mathematics, grades kindergarten
through six; in-service and pre-service elementary teachers.
MAIN
METHODS OF INSTRUCTION USED IN THE PROJECT: Independent study, seminars,
discussion sessions and classroom teaching with children. The course for
teachers is based on written lessons, films of classes, discussions, careful
correcting of written work with attention to sources of errors, and the
inventing and adapting by participating teachers of new materials for classes.
K. PRESENT
COMMERCIAL AFFILIATIONS: None.
L. DESCRIPTION
OF MATERIALS ALREADY PRODUCED:
1. General
Information.
2. Ways
to Find How Many.
3. Maneuvers
on Lattices.
4. Well-Adjusted Trapezoids.
5. Number
Lines for the Orbiting Atomic Teacher.
6. Do
Something About Estimation.
7. Teaching
Creativity in Mathematics.
8. Arithmetic
With Frames.
9. Functions.
10. A Sample and
Description of Course I.
11. Book: Number
Lines Functions and Fundamental Topics
12. Written Lessons:
(a)
Introduction to Frames and Number Line Jumping Rules.
(b)
Consecutive Jumps. Distances Jumped. Competing
Number
Line Jumping Rules.
(c)
Parentheses and "Multiplying Before You Add". Stand-
still
Points.
(d)
Effects of Using Rules in Different Orders.
(Edward)
Introduction to Maneuvers on Lattices.
(f)
Frame Equations. Midpoints. Rules Moving Two Points.
(GCMP)
Rules Moving Two Points, Continued. Composition of
Number
Line Rules.
(h)
Composition, Continued.
(i)
Some Wrong Answers. Composing Number Line Rules to
Move
Two Points to Two Points.
(j)
Artificial Operations.
(k)
More Work With Artificial Operations.
(1)
Maneuvers on Lattices, Continued.
(m)
More Work With Competing Rules. Lower Brackets.
(n)
Lower Brackets and Upper Brackets.
(0)
Graphing Equations With Lower and Upper Brackets.
(p)
Simultaneous Equations. Points and Lines in a Plane.
(q)
Number Plane Jumping Rules.
(r)
Number Plane Rules, Continued.
13. Films:
(a) A First
Class With Number Line Rules and Lower
Brackets
(Lee Osburn, Grade 5).
(b) Which Rule
Wins (Phyllis R.
Klein, Grade 3).
Cc) Standstill Points
(David A. Page, Grade 5).
(d) Three A's
Three B's and One C (David A. Page, Grade 5).
(Edward) A Seven-Fold Lattice (Francis X. Corcoran, Grade 5).
(f) Frames
and Number Line Jumping Rules (Lee Osburn,
Grade 5).
(GCMP) Rules
Moving Two Points (David A. Page, Grade 5).
(h) Introduction
to Composition (Marie L. Hermann, GCMP
Grade 5).
(i) Surface
Area With Blocks CPhyllis R. Klein, Grade 1).
(i) Some
Artificial Operations (Phyllis R. Klein, Grade 4).
(K) Counting
With Dots (David A. Page, Grade 2).
(1) A
Periodic Lattice (Phyllis R. Klein, Grade 5). (m) Lower and Upper Brackets
(Carol Daniel, Grade 4). (n) Inequalities With Lower Brackets (Francis X.
Corcoran, Grade 5). (of) Graphing With Square Brackets (David A. Page, Grade
5). (p) Graphing Absolute Value Equations (Marie L. Hermann, Grade 2). (q)
Jumping Rules in the Plane Part I (Lee Osburn, Grade 6). (r) Jumping Rules in
the Plane Part II (Lee Osburn, Grade 6). (s) Rotations in the Plane (David A.
Page, Grade 5). 14. Supplements: (a) Answers to Common Questions About the
Institute. (b) Computing With Positive and Negative Numbers. (C) Answers to
Questions About the Film "Standstill Points" (d) Dividing By Zero.
(e) Maneuvers on Lattices. (f) Arithmetic With Frames. (GCMP) Functions. (h)
Using Blocks to Introduce Other Bases of Numeration to a Fourth Grade. (i)
"Surrounding" With Centimeter Blocks. (j) Well-Adjusted Trapezoids. (K) Ways to Find How Many. (1)
More Suggestions for Lattices. (K) Using Centimeter Blocks to Introduce Prime
Numbers to a Third Grade. (1) Graphing Number Line Jumping Rules. (m) More
Problems With Composition of Number Line Rules. (n) Graphing Simultaneous
Equations. (of) Examples of Questions Dealing With DDxD. (p) More Work With
Number Plane Rules. (q) Hybrid Rules: Jumping Rules From the Line to the Plane
and From the Plane to the Line. (r) Bibliography. 15. Discussion Notes (for
each written lesson and film). 16. Corrector's Guides (for each written
lesson).
M.
MATERIALS AVAILABLE FREE: Items 1-10
are free in small quantities
from Education
Development Center.
N.
MATERIALS PURCHASABLE: Items 2 and 3, $0.20 each in quantities larger than 2,
available from Education Development Center. Item 11, $3.80 (deduct 25%
discount on orders from schools), available from the Macmillan Company, 866
Third Avenue, New York, New York 10022. Information on the cost of course materials is available from EDC.
0.
ADDITIONAL MATERIALS BEING DEVELOPED: None.