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.