GCMP

 

PROJECT TITLE: EDUCATIONAL RESEARCH COUNCIL OF AMERICA MATHEMATICS

                        PROGRAM (ERCMP)

 

 

B. PROJECT DIRECTOR: Mr. John F. Mehegan, Director, Educational

                        Research Council Mathematics Program, 614 West Superior,

                        Cleveland, Ohio 44113, U.S.A.                 (216) 6968222, ext. 241.

 

 

C. PROJECT HEADQUARTERS: 1. Contact: Project director. 2. Special facilities or activities available for visitor viewing: Classes in participating schools and ERC facilities.

 

 

D. PRINCIPAL PROFESSIONAL STAFF: John F. Mehegan, Director; William T. Hale, Assistant Director; S. Edwin Humison, K8 Coordinator; Mrs. Rae Marie Creps, Research Associate; Miss Lucille McCraith, Research Associate; Miss Mary Muesegaes, Research Assistant; Miss Margaret Russell, Research Associate.

 

 

E. PROJECT SUPPORT: 1. Funding agencies: The Cleveland Foundation, The Good Works Foundation, The Grant Foundation, The George Gund Foundation, The Louise H. & David S. Ingalls Foundation, Inc., The Martha Holden Jennings Foundation, The Kettering Foundation, The Laurel Foundation, The Lubrizol Foundation, various industrial firms and individual contributions. 2. Associated agencies: Not answered.

 

 

F. PROJECT HISTORY: 1. Principal originator: Dr. George H. Baird, President, Educational Research Council of America. 2. Date and place of initiation: March, 1959; Cleveland, Ohio. 3. Evolution and development of the project: In 1961 K3 materials were published. In 1965 K6 materials were published. In 1968 junior high materials were published, K6 were revised, and Units for high school students not in academic mathematics. In 1972 individualized K8 materials are being processed.

 

 

G. PROJECT OBJECTIVES: 1. Overall project purpose: To develop, for all children in grades K12, an individualized comprehensive, sequential mathe­matics program that is both mathematically correct and pedagog­ically sound. 2. Specific objectives: To develop skillful computation, measurement skills, and geometric concepts and skills.

 

 

UNIQUE CHARACTERISTICS OF THE PROJECT: A learning continuum with associated behavioral objectives to assist the teacher to individualize the curriculum. Diversified learning materials, i.e., games, investigations, and manipulative materials, are an integral part of the program. The program has a unit format, each unit of work consisting of: 1. A list of entering behaviors.

 

2. A pretest to measure entering behaviors and the behaviors to be induced by study of the unit. 3. Writein pupil pages. 4. Related diversified learning materials. 5. A diagnostic test to be administered before practicing the induced behaviors. 6. A teacher guide with suggestions for prepage activities, use of the pages, and an answer key. 7. A list of terminal objectives. 8. A posttest.

 

 

I. SPECIFIC SUBJECTS, GRADE, AGE AND ABILITY LEVELS: Mathematics for all students in K8, Basic Math for 912 students not in academic mathematics, and use of the computer in mathematics in 712.

 

 

J. MAIN METHODS OF INSTRUCTION USED IN THE PROJECT: Independent study, laboratory investigations, lectures, seminars, discussion sessions, computer assisted instruction, and films and film­strips.

 

 

K. PRESENT COMMERCIAL AFFILIATIONS: Science Research Associates, Inc., 259 East Erie Street, Chicago, Illinois 60611, U.S.A.

 

 

L. DESCRIPTION OF MATERIALS ALREADY PRODUCED: 1. K6 Pupil Texts and Teacher Guides. 2. K6 Tests. 3. Addition, Subtraction, Multiplication, and Division Units (available only to Council Schools). 4. Games, Investigations, and Manipulative Materials. 5. Filmstrips. 6. Junior High Student Texts and Teacher Guides. 7. Informal Geometry Booklets. 8. A BASIC Primer. 9. Elementary Functions with BASIC

10.                  Key Topics for the Primary Teacher.

11.                  Key Topics for the Intermediate Teacher.

12.                  ERC Catalog of Materials and Services.

 

 

M. MATERIALS AVAILABLE FREE: Item 12.

 

 

N. MATERIALS PURCHASABLE: Items 1, 2, 10, 11. Write to Science Research Associates for price list. Items 4, 5, 6, 7, 8, 9. Write to the Educational Research Council for price list.

 

 

0. ADDITIONAL MATERIALS BEING DEVELOPED: Geometry Kits and Measure ment Kits for K8, and units for Fractional Numbers.

 

 

P. LANGUAGE IN WHICH MATERIALS: 1. Were originally written: English. 2. Have been or will be translated: Not answered.


COUNTRIES IN WHICH MATERIALS ARE USED: United States.

 

 

PROJECT IMPLEMENTATION: (In Council Schools) Information on adoption of the entire program is unknown. 1. Total number of teachers using any of the materials: 2,000. 2. Total number of students using any of the materials: 70,000. 3. Total number of schools using any of the materials: 175. 4. The totals stated in 1, 2 and 3 are estimated. 5. Name and location of selected schools where the program is in use: State of Ohio: Aurora, Avon Lake, Bay Village, Berea, Brooklyn, Cleveland Catholic Schools, Chardon, Cuyahoga Heights, Fairview Park, Independence, some Cleveland Lutheran Schools, Hayfield, North Olmsted, Olmsted Falls. Out of State: Bradford, Pennsylvania; Brockton, Massachusetts; Greenville, Michigan; Imlay City, Michigan; Muskegon, Michigan; Niles, Michigan; Owatonna, Minnesota.

 

 

3. TEACHER PREPARATION: 1. Consultant services available for teachers using the materials: The ERCMP staff (all teachers) is available at all times to conduct workshops, teach demonstration lessons, and assist the teacher to implement ERCMP or other programs. 2. Activities conducted for preservice and inservice teacher training: Inservice workshops at Council schools; one, two, or three day workshops in Council schools: $5 per day for Council teachers, $25 per day for NonCouncil teachers. 3. Available preservice and/or inservice teaching materials for science educators to use in preparing teachers: None.

 

 

E. PROJECT EVALUATION: 1. Has the effectiveness of the materials been evaluated: Yes, internally. 2. Published research studies: (a) Comparative Data for the Greater Cleveland Mathematics Tests, Grades 13, Test 1, Form A (A Teacher's Guide to the Interpretation of Scores), 1964. (b) Comparative Data for the Greater Cleveland Mathematics Tests, Grades 13, Tests 24, Form A (A Teacher's Guide to the Interpretation of Scores), 1964. (C) Comparative Data for the Greater Cleveland Mathematics Tests, Grade 4, Tests 12, Form A, Including a Supplement of Data for Tests 34, Form A, 1964. (d) The Performance of GCMP Students on the Stanford Arith­metic Tests, Grades Four through Six, 196465, 1965. (Edward) A Descriptive Analysis of the use of the Greater Cleveland Mathematics Program in Grades One, Two, and Three, 1966. (f) A Technical Report on the Analysis of Test Results from an Investigation of Two Teaching Methods in the Multiplica­tion with Whole Numbers, 1966. 3. Brief abstract of inhouse or unpublished research. (a) Comparative Study of Arithmetic Test Scores Before and

 


After the Introduction of GCMP.

A comparison of the mean grade equivalent scores on the

Arithmetic Reasoning and Computation subtests of the Stan: Achievement Tests indicates that the performance of pupil (Grade 3 and 4) seems to have improved somewhat on both the Arithmetic Reasoning and Computation subtests after intro­duction of GCMP materials.

(b) An Interim Report on the Results of GCMT, Intermediate Series.

A descriptive analysis of the four parts of each of seven tests, corresponding to seven student booklets of the GCMP was made in order to help establish guidelines to evaluate pupils' achievement on the concepts and skills stressed in the program.

(C) Grades 2, 3 and 4 Math Project.

Preparation of the final reports is in process on the com­parative studies of the teaching methods of computational skills to students in grades 24. The programs in the stud­ies include experimental units to be published in 1974, the corresponding materials in the current GCMP and the most

widely used nonGCMP mathematics programs.

The following analyses were made in the studies:

(i) Attainment of each objective by different program groups by various IQ levels.

(in) Comparison of the overall achievement of various program groups after differences in IQ and initial

ability in computation are adjusted (i.e., analysis of covariance using IQ and the initial computational score as the covariates).

(iii) Analysis of errors made by students of varying I levels in the experimental group. Its purpose is to help teachers understand students' misconception and help ERC's Mathematics Department develop remedial

                        materials for these students.

(d) Grade 1 Project.

A comparative study is underway to compare the experiment program to be published in 1974 and the current GCMP.

(Edward) PreAlgebra Projects.

(i) Development of the Diagnostic and Placement Inven tory to be given to students at the end of grade 6 or the beginning of grade 7 to identify students' strength and weaknesses in seven areas: Numeration, whole numbers fractional numbers, decimals, integers, rational numb and geometry.

(in) Evaluation of the prealgebra programs and the accompanying achievement tests.

(f) Basic Mathematics Project.

Report to the Teachers on the Results of the "Circles" Test and the "Boxes and Cylinders" Test.

An investigation of the students' performance on the pretest and posttest on the booklets Circles and

Boxes and Cylinders in the Basic Mathematics Program,

 


After the Introduction of GCMP.

A comparison of the mean grade equivalent scores on the

Arithmetic Reasoning and Computation subtests of the St

Achievement Tests indicates that the performance of pupil

(Grade 3 and 4) seems to have improved somewhat on both

Arithmetic Reasoning and Computation subtests after intro,

duction of GCMP materials.

(b)                   An Interim Report on the Results of GCMT, Intermediate

Series.

A descriptive analysis of the four parts of each of seven

tests, corresponding to seven student booklets of the GCMP

was                 made in order to help establish guidelines to evaluate

pupils' achievement on the concepts and skills stressed b

the                  program.

(C) Grades 2, 3 and 4 Math Project.

Preparation of the final reports is in process on the corni

parative studies of the teaching methods of computational

skills to students in grades 24. The programs in the

ies                   include experimental units to be published in 1974, the

corresponding materials in the current GCMP and the most

widely used nonGCMP mathematics programs.

The                 following analyses were made in the studies:

                        (10) Attainment of each objective by different program

                        groups by various IQ levels.

(in) Comparison of the overall achievement of various program groups after differences in IQ and initial ability in computation are adjusted (i.e., analysis of covariance using IQ and the initial computational score as the covariates).

(iii) Analysis of errors made by students of varying IQ levels in the experimental group. Its purpose is to help teachers understand students' misconception and help ERC's Mathematics Department develop remedial materials for these students. (d) Grade 1 Project. A comparative study is underway to compare the experimental program to be published in 1974 and the current GCMP. (Edward) PreAlgebra Projects. (i) Development of the Diagnostic and Placement Inven­tory to be given to students at the end of grade 6 or the beginning of grade 7 to identify students' strength and weaknesses in seven areas: Numeration, whole numbers fractional numbers, decimals, integers, rational numbers and geometry.

                        (in) Evaluation of the prealgebra programs and the

                                                accompanying achievement tests.

(f) Basic Mathematics Project.

Report to the Teachers on the Results of the "Circles" Tea

and the "Boxes and Cylinders" Test.

                                                An investigation of the students' performance on the

                                                pretest and posttest on the booklets Circles and

                                                Boxes and Cylinders in the Basic Mathematics Program,


After the Introduction of GCMP.

A comparison of the mean grade equivalent scores on the

Arithmetic Reasoning and Computation subtests of the Stan: Achievement Tests indicates that the performance of pupil (Grade 3 and 4) seems to have improved somewhat on both the Arithmetic Reasoning and Computation subtests after intro ¥ duction of GCMP materials.

(b) An Interim Report on the Results of GCMT, Intermediate Series.

A descriptive analysis of the four parts of each of seven tests, corresponding to seven student booklets of the GCNJ was made in order to help establish guidelines to evaluate pupils' achievement on the concepts and skills stressed 11 the program.

(C) Grades 2, 3 and 4 Math Project.

Preparation of the final reports is in process on the com­parative studies of the teaching methods of computational skills to students in grades 24. The programs in the stud­ies include experimental units to be published in 1974, the corresponding materials in the current GCMP and the most

widely used nonGCMP mathematics programs.

The following analyses were made in the studies:

(i) Attainment of each objective by different program groups by various IQ levels.

(in) Comparison of the overall achievement of various program groups after differences in IQ and initial

ability in computation are adjusted (i.e., analysis of covariance using IQ and the initial computational score as the covariates).

(iii) Analysis of errors made by students of varying L levels in the experimental group. Its purpose is to help teachers understand students' misconception and help ERC's Mathematics Department develop remedial

                        materials for these students.

(d) Grade 1 Project.

A comparative study is underway to compare the experiment program to be published in 1974 and the current GCMP.

(Edward) PreAlgebra Projects.

(i) Development of the Diagnostic and Placement Inven­tory to be given to students at the end of grade 6 or the beginning of grade 7 to identify students' strength and weaknesses in seven areas: Numeration, whole numbers fractional numbers, decimals, integers, rational numb and geometry.

(in) Evaluation of the prealgebra programs and the accompanying achievement tests.

(f) Basic Mathematics Project.

Report to the Teachers on the Results of the "Circles" Test and the "Boxes and Cylinders" Test.

An investigation of the students' performance on the pretest and posttest on the booklets Circles and

Boxes and Cylinders in the Basic Mathematics Program,

 

546

 


to determine the gain and attainment of major objectives. The Basic Mathematics Program is intended for noncollege bound students of the tenth or eleventh grade. Pretest and posttest are also available for the tests accom­panying the other books in the Basic Mathematics Program. 4. Evaluative data available to interested individuals: Addi­tional information is available from the Director of the Evalua­tion and Testing Department of the Educational Research Council of America, Rockefeller Building, Cleveland, Ohio 44113.

 

 

J. PROJECT PUBLICITY: The Grade Teacher February, 1971.

 

 

 

 

T¥ SUMMARY OF PROJECT ACTIVITIES SINCE 1970 REPORT: Development of units including pupil pages, behavioral objectives, tests, teacher guide, and diversified materials.

 

 

PLANS FOR THE FUTURE: Publication of a complete K4 program for the school year 197475 and a 58 program for the school year 197576.


---

A. PROJECT TITLE: THE MADISON PROJECT OF SYRACUSE UNIVERSITY AND WEBSTER COLLEGE

 

 

B.                    PROJECT DIRECTOR:      Professor Robert B. Davis, Mathematics Depart

                        ment, Smith Hall, Syracuse University, Syracuse, New York 13210

                        U.S.A.             (315)4763768 or

(315)4765541, ext 23

 

 

C.                    PROJECT HEADQUARTERS:

                        1. Contact:     The Madison Project, 918 Irving Avenue, Syracuse,

                        New York 13210, U.S.A.    (315)4763768.

                        2. Special facilities or activities available for visitor

                        viewing:         By special arrangement it is possible to visit class

                        rooms             in various schools, including culturally deprived situa

                        tions,              nongraded schools using various forms of flexible pro

                        gramming and team teaching, etc.           In addition, it is possible

                        to                     view project films (which also show actual classroom lessons

                        and to talk with project personnel about specific problems of

                        various sorts.                        Some project classrooms center around "mathe

                        matics laboratories."

 

 

D. PRINCIPAL PROFESSIONAL STAFF: Leon Henkin, CoDirector for Berkeley, California Implementation Program; Donald Cohen, Resi dent Coordinator for New York City; Diane Resek, Resident Co­ordinator for Berkeley, California; Beryl S. Cochran and Leah Horwitz, Film Preparation; William McConnell, CoDirector for Implementation Programs; Edith Biggs, Robert Wirtz, Marion Walter, Katherine Vaughn, Katie Reynolds Hannibal, and William Betts, Visiting Specialist Teachers; Herbert Ginsburg, Co­Director for Piagetian Studies; Joyce Statz, CoDirector for LOGO Computer Studies, Lucian Hall, Resident Coordinator for Richmond, Virginia; George Grossman, New York City Bureau of Curriculum.

 

 

E. PROJECT SUPPORT: 1. Funding agencies: National Science Foundation; United States Office of Education; Alfred P. Sloan Foundation; Marcel Hoizer Foundation; and a group of industries and trade unions in the St. Louis area, plus contributions from participating schools and colleges. 2. Associated agencies: Syracuse University; University of California (Berkeley); Webster College; the Public School System of: Berkeley, California; Richmond, Virginia; New York City; Syracuse, New York; and the State Departments of Educa­tion in Delaware and in California.

 

 

F. PROJECT HISTORY: 1. Principal originators: Robert B. Davis, Beryl S. Cochran, Donald E. Kibbey, Sister M. Francetta Barberis, S.L., and Jacqueline Grennan Wexler. 2. Date and place of initiation: 1957; Syracuse, New York and Weston, Connecticut.


3.                     Evolution and development of the project: The Project was

originally started in order to provide University faculty mem

bers who taught teachers with uptodate firsthand experience

in directly teaching children, on the principle that he who

teaches experimental physics should himself be engaged in ex

perimental physics ‑‑ and if the principle holds in physics,

why                 not also in education. The original targetpopulation were

low                  ses children in grade seven who were significantly below

grade level in mathematics. These children were found to po

ssess considerably more mathematical ability than had been sus

pected. (The Project's work in mathematics thus closely

parallels the work of Hughes Mearnes and of Herbert Kohl in the

area of creative writing.) For the next 6 years the Project

sought to explore this unsuspected mathematical ability of

children, working also with high ses children at various grade

levels; in the process of doing this, it became necessary to

develop a new mathematics curriculum, with selection of topics,

sequencing of topics, new notations, new definitions, etc.,

that were more suitable for creative work by young children.

(Thus, in this phase of its activities, the Project generally

resembled Seymour Papert and Wallace Feurzeig's work on LOGO,

and                 William Johntz's work on SEED.) The success of this pro

gram led to the creation of largescale teacher education pro

grams. Joint ventures with the Elementary School Science (ESS)

Project of ES1/EDC, and with the British Nuffield Mathematics

Project (and other British educators) led to a greater use of

manipulatable physical materials, small group work, math labs,

and                 student projects. In its most recent stage, the Project

is focussing on two matters: first, the reorientation of

methods of teaching, of testing, and of curriculum planning

that now seems necessary in the light of the discoveries made

by Jean Piaget and the Geneva group of cognitive psychologists;

and, second, with the new possibilities for school mathematics

that have been created by the PapertFeurzeig development of

the                  LOGO computerprogramming language, and the various LOGO

developments in hardware, in software, in pedagogical techni

ques, and in curriculum design.

 

 

G. PROJECT OBJECTIVES: 1. Overall project purpose: In broad terms, the purpose of the Project can be stated as follows: The Project has seen educational settings where children explore significant aspects of our present culture, and from such exploration learn what this culture is, and how they themselves can function creati­vely within it. (This general theme is well described in Casey and Liza Murrow, Children Come First American Heritage Press, New York: 1971, and in Edith Biggs and James MacLean, Freedom to Learn An Active Learning Approach to Mathematics Addison­Wesley Publishing Company, Inc. Canada: 1969.) The Project is concerned with helping schools and teachers set up such learn­ing environments ‑‑ which implies a need to study them more closely in order to see more clearly what really is involved,


and to prepare appropriate study materials that can be used successfully in such environments. The Project has focussed on mathematics as its main content area partly because Project per­sonnel happen to be mathematicians, and partly because mathe­matics plays a central role in schools and in education. 2. Specific objectives:

(a)                   To study the process of cognitive growth in children.

(b)                   To study effective learning environments.

(C)                  To produce and test learning materials for use by children and by teachers that will reflect what can be found out from activities (a) and (b). The content area is mainly mathematics, plus some science ‑‑ but provision is made for the inclusion of other content areas.

 

 

H. UNIQUE CHARACTERISTICS OF THE PROJECT: The project is different primarily in two ways: first, its concern for the great ability of most children which is untapped by most traditional forms of schooling; and, second, its concern for the laws of human cog­nitive growth.

 

 

I. SPECIFIC SUBJECTS, GRADE, AGE AND ABILITY LEVELS: Subjects: Primarily mathematics, plus some science ‑‑ but opportunities are provided to move into nearly any area of study, by pursuing appropriate themes and appropriate methods. Grade: Project practice is to attempt to avoid gradelevel segregation of children, and consequently Project materials are ungraded. Most materials have been developed for use by children between the ages of 8 years old, up to beginning college work; however, some materials for use by younger children have been developed. Ability levels: Project methods allow for adaptation to any ability level, although the same curriculum is not used for children of widely different abilities or interests.

 

 

J. MAIN METHODS OF INSTRUCTION USED IN THE PROJECT: Independent study, laboratory investigations, seminars, discussion sessions and smallgroup work.

 

 

K. PRESENT COMMERCIAL AFFILIATIONS: Books are presently available from AddisonWesley Publishing Company, Inc., San Hill Road, Menlo Park, California 94025, U.S.A. Twelve films are scheduled for release in the near future by Houghton Mifflin Company, 110 Tremont Street, Boston, Massachusetts 02107. Subtraction and Division Using Beans and Beansticks; Experience with Fractions: Suppose It Comes Out Even; Experience with Fractions: Suppose It Doesn't Come Out Even; Fractions and the Meaning of Division; Fractions on the Number Line, Using String The Number Line, Using the Overhead Projector; Area, Using Geoboards. In addition, some "shoebox" kits for math lab ex­periments are available from Math Media, Inc., P. 0. Box 345, Danbury, Connecticut 06810. These kits are entitled: Discs; Geoboards; Peg Game; Tower Puzzle; Centimeter Blocks, Weights and Springs.

668

 


DESCRIPTION OF MATERIALS ALREADY PRODUCED: 1. Discovery in Mathematics (Publishers, AddisonWesley Pub­lishing Co., Inc.) Student discussion guide, plus text for teachers. This book provides a supplementary program in co­ordinate geometry, axiomatic algebra, and applications to science, suitable especially for grades 48. It is concerned particularly with creative learning experiences of a non­routine nature. 2. Explorations in Mathematics Student discussion guide, plus text for teachers. This book is concerned with intro­ductory ideas in algebra, statistics, mathematical logic, ma­trix algebra, and some applications to physics. Special em­phasis is placed upon historical background, and the study of this book can be closely related to various units in social studies (such as the life and times of Rene Descartes). It is suitable for grades 6 through 9, inclusive. 3. A Modern Mathematics Program as it Pertains to the Inter­relationship of Mathematical Content, Teaching Methods, and Classroom Atmosphere. (The Madison Project). 1963. Report submitted to the Commissioner of Education, U.S. Office of Edu­cation, Fall, 1963. The provides a general view of Madison Project activities. 4. A Modern Mathematics Program as it Pertains to the Inter­relationship of Mathematical Content, Teaching Methods, and Classroom Atmosphere. (The Madison Project). 1965. Report submitted to the Commissioner of Education, U.S. Office of Ed­ucation, Fall, 1965. Note that this is distinguishable from item 3 above only by the date. The 1965 report is the most comprehensive description presently available of Madison Pro­ject materials and activities. 5. The Madison Project A Brief Introduction to Materials and Activities (1965). 6. Notes on the Film: First Lesson. (This pamphlet accom­panies the film of the same name.) 7. Robert B. Davis, Some Remarks on "Learning By Discovery". 8. Robert B. Davis, The Next Few Years. 9. Robert B. Davis, Experimental Course Report/Grade Nine.

10. Doris Machtinger, Experimental Course Report/Kindergarten.

11. Donald Cohen, Inquiry in Mathematics Via the Geoboard.

12. Supplementary Modern Mathematics for Grades 1 through 9. InService Course #1 for Teachers. This is a complete "pack­aged" inservice course, including films, written materials, and laboratory equipment.

13. Supplementary Modern Mathematics for Grades 2 through 9. InService Course #2 for Teachers. This is a sequel to item 12 above.

14. The Journal of Children's Mathematical Behavior, (Vol. 1, No. 1 Winter 197172) presently available. This informal jour­nal discusses the development of mathematical thought in children and how to study it.

15. A Concrete Approach to Introductory Ideas in Mathematics (booklet accompanying film series listed in item 16).

 


16. Film series (16mm, sound, black and white) A Concrete Approach to Introductory Ideas in Mathematics. Individual titles: Readiness for Place Value Numerals; A Sixth Grade Lesson on Place Value Numerals; Subtraction Using Beans; Addi­tion and Multiplication Using Plastic Washers; Addition and

Division Using Beans and Beansticks; Subtraction and Division

Using Beans and Beansticks; Experience with Fractions: Suppose It Comes Out Even; Experience with Fractions: Suppose It Doesn't Come Out Even; Fractions and the Meaning of Division; Fractions on the Number Line, Using String; The Number Line, Using the

Overhead Projector; Area, Using Geoboards.

17. Audio tape recording #D1:                +                      = 2 x               . This is a

                        recording of an actual classroom lesson with fifth grade child

                        ren, proving algebraic theorems from a set of axioms selected

                        by themselves.

18. Film (16mm., sound, black and white) A Lesson with Second Graders. This film shows an actual classroom lesson involving signed numbers, the number line, and Cartesian coordinates.

Viewing this film is one of the best introductions to project activities.

19. Film (16mm., sound, black and white) Complex Numbers via Matrices. This film shows an actual classroom lesson. Seveni grade students use the isomophism between rational numbers an a subset of the set 2by2 matrices to facilitate an extension into complex numbers.

20. Film (16mm., sound, black and white) Matrices. An actual classroom lesson. Fifth and sixth graders explore the algebra of 2by2 matrices.

21.                  Film (16 mm., sound, black and white) Solving Equations

With Matrices. An actual classroom lesson, similar to item 1 above, but less sophisticated. Sixth grade students.

22. Film (16mm., sound, black and white) Average and Variance An actual classroom lesson, with 6th grade children.

23. Film (16mm., sound, black and white) Graphing an Ellipse. An actual classroom lesson, with 7th grade students.

24. Film (16mm., sound, black and white) Circles and Parabola An actual classroom lesson, with 6th grade children.

25. Film (16mm., sound, black and white) First Lesson. An actual classroom lesson, with a mixed class of children from grades 3 to 7.

26. Film (16mm., sound, black and white) Second Lesson. This lesson occurred on the day following that shown in item 25

above, with the same students.

27. Film (16mm., sound, black and white) Weights and Springs. A "laboratory" lesson, with 6th grade children.

28. Film (16mm., sound, black and white) Graphing a Parabola. This is a portion of the film listed in item 20.

29. Film (16mm., sound, black and white) Guessing Functions. A seventh grade class of culturally deprived urban children.

30. "shoebox" packages for physical experiments related to the mathematics program, or for physical and tactile experiences


related to the learning of mathematics. Titles: Discs, Geo­boards, Peg Game, Tower Puzzle, Centimeter Blocks, Weights and Springs.

31. (The Project also makes use of physical materials prepared by Z. P. Dienes, by ESS, by the Nuf field Project, and by others as well as desk calculators of various sorts.)

 

 

M. MATERIALS AVAILABLE FREE: This varies according to the avail­ability of reprints of various articles. Contact the Madison Project, 918 Irving Avenue, Syracuse, New York 13210.

 

 

N. MATERIALS PURCHASABLE: Items 1 and 2 from Section L. Item 1: Student text $3.21; Teacher text $8.40. Item 2: Student text $3.40; Teacher text $9.24. (Order from Regional Office, Addi­sonWesley Publishing Company, Inc.) Item 11 available from Walker Educational Book Corporation, 720 Fifth Avenue, New York, New York 10019. Item 14, The Journal of Children's Mathematical Behavior available from The Madison Project, 918 Irving Avenue, Syracuse, New York 13210. Price (subject to change): $1.00 Items 15 and 16: Available soon from Houghton Mifflin Co., 110 Tremont Street, Boston, Massachusetts 02160. Item 29: "shoebox" kits available from Math Media, Inc., P. 0. Box 345, Danbury, Connecticut 06810. Price for complete set of 6: $19.00. Four or more sets: $17.25 each.

 

 

0. ADDITIONAL MATERIALS BEING DEVELOPED: Please refer to present and future issues of The Journal of Children's Mathematical Behavior.

 

 

P. LANGUAGE OF MATERIALS: 1. As originally written: English. 2. Have been or will be translated: Explorations in Mathe­matics; Parts Two and Five have been translated into Japanese. Japanese translation available from: AddisonWesley Publishing Company, Inc., International Division, Reading Massachusetts.

 

 

Q. COUNTRIES IN WHICH MATERIALS ARE USED: U.S.A., Canada, Great Britain, Japan, Korea, India, Vietnam, Ghana, Nigeria, Uganda, Israel, Australia, New Zealand.

 

 

R. PROJECT IMPLEMENTATION. The project materials are widely used. Exact figures are unknown. Exemplary classrooms may be located by contacting The Madison Project coordinators listed in D. See, especially, classrooms in Berkeley, California and in New York City.

 

 

S. TEACHER PREPARATION: 1. Consultant service available for teachers using the materials: In New York City; in Berkeley, California; in St. Louis, Missouri; in Washington, D. C., and elsewhere. Contact the Project at its Syracuse address for information. Consultants


are prepared to assist teachers, administrators, or interested parents in a variety of ways, including program planning and practical classroom implementation. 2. Activities conducted for preservice and inservice teacher training: Extensive inservice programs are available in New York City, in Delaware, and in California. Details available from the Project. 3. Available preservice and/or inservice teaching materials for science educators to use in preparing teachers: InService Course I (dealing with ways of combining arithmetic, algebra, and analytic geometry to provide a broad elementary school program), consists of printed materials and ten film excerpts available at a cost of $30.00 for rental of the films and $100.00 for 30 copies of the printed materials (or, single copies $3.50). A more diverse inservice or preservice teacher education package which includes consideration of math­ematics in open classrooms is now undergoing trials. Prelim­inary versions are available at a cost of $3.00.

 

 

T. PROJECT EVALUATION: 1. Has the effectiveness of the materials been evaluated: Yes, internally and by the California State Department of Education, Far West Laboratory for Research and Development. 2. Pertinent published research studies: "Research Report of the Specialized Teacher Project 196869." California State Department of Education, Sacramento, California, February 1970; Kathleen Devaney, "An ALERT Report on The Madison Pro­ject," 1972. Available from the Educational Information Pro­ducts Division, Far West Laboratory for Educational Research and Development, 1 Garden Circle, Hotel Claremont, Berkeley, Calif. 94705.; Alan Barson, Beryl Cochran and Robert Davis, "ChildCreated Mathematics," The Arithmetic Teacher, March 1970.; J. Robert Cleary, "A Study of Test Performance in Two Madison Project Schools and One Control School," Webster College, St. Louis, Missouri. 3. Brief abstract of inhouse or unpublished research: By far the best evidence concerning the mathematical behavior of children in Project classes is provided by actual videotape and film records showing what children do: conjecturing theorms proving them, analyzing new problem situations, etc. These films and videotapes show not merely that the children do do all of this ‑‑ they show precisely how the children do it. These films are available for loan or rental. For details write to the Project. 4. Evaluative data available to interested individuals: Please see the preceding remark (question T3).

 

 

U. PROJECT PUBLICITY: 1. Davis, Robert B. "Report of the Syracuse University­Webster College Madison Project." American Mathematical Monthly Vol. 71, No. 3 (March, 1964) pp. 306308.


2. _. "The Madison Project's Approach to a Theory of Instruction," Journal of Research in Science Teaching Vol. 2 (1964), pp. 146162. 3. , "The Next Few Years," The Arithmetic Teacher Vol. 13, No. 5 (May, 1966), pp. 355362. 4. . The Changing Curriculum: Mathematics. Associa­tion for Supervision and Curriculum Development, NEA, 1967. 5. Yeomans, Edward. Education for Iniative and Responsibility Comments on a visit to the Schools of Leicestershire County. National Association of Independent Schools, Boston, Mass. 2nd edition, February 1968. 6. Pine, Patricia. "New Math Road Show," American Education Vol. 4, No. 7, JulyAugust 1968. 7. M. Vere De Vault and Thomas Kriewall, Perspectives in Ele­mentary School Mathematics, Charles Merrill Company, 1969. 8. "Nuffield Mathematics Project: Teacher's Guides," Mathematics Teaching No. 53, Winter, 1970, pp. 5356. 9. Ginsburg, Herbert, The Myth of the Deprived Child, Prentice­Hall, Inc., Englewood Cliffs, New Jersey, 1972.

10. Davis, Robert B., "Observing Children's Mathematical Be

havior as a Foundation for Curriculum Planning," The Journal of

                        Children's Mathematical Behavior                                                           Vol. 1, No. 1 (Winter197172).

 

 

V. BRIEF SUMMARY OF PROJECT ACTIVITIES SINCE 1970 REPORT: The Project has a new major focus: the careful observation of the mathematical behavior of children. This may provide a sounder foundation for curriculum design, and a more effective point of intervention for changing school mathematics, than any that have been used previously. The "careful observation of child­ren" involves depth studies in the sense of Piaget, and NOT a main focus on superficial verbal behavior.

 

 

W. PLANS FOR THE FUTURE: 1. The process of preparing films and videotapes for release by Houghton Mifflin, or otherwise, will continue with a growing list of films becoming available. 2. The program of observing and describing the mathematical behavior of children will become a main emphasis in Project activity. (Cf., Robert B. Davis, "The Problems of Relating Mathematics to the Possibilities and Needs of Schools and Children," in H. Freudenthal, ed., Educational Studies in Mathematics, D. Reidel Publishing Company (Holland), June 1971. 3. The establishment of consultants and inservice study op­portunities in various geographical areas will be expanded especially in California, New York City, Delaware, Baltimore, and the area around Washington, D.C.). 4. Methodological and even philosophical matters, in specific cases which the Project judges to be of immediate practical relevance, will be pursued. (Cf. Robert B. Davis, Mathematics Teaching ‑‑ With Special Reference to Epistemological Problems. Monograph No. 1 (Fall, 1967), of the Journal of Research and Development in Education, College of Education, University of


Georgia, Athens, Georgia 30601. 5. More attention will be given to mathematics in relation to open education. (Casey and Liza Murrow, Children Come First, American Heritage Press, New York, 1971). 6. An elementary school mathematics program, for presentation to children via the PLATO computer system, will be developed jointly with UICSM. 7. Children will be studied as they learn the BBN/MIT LOGO computer programming language. 8. The Project will participate in an international comparison of how curriculum development and innovation efforts are under­taken in various nations of Europe and Asia.

 

 

 

 


---

A. PROJECT TITLE: MINNESOTA MATHEMATICS AND SCIENCE TEACHING PROJECT (MINNEMAST)

 

 

B. PROJECT DIRECTOR: James H. Werntz, Jr., Professor of Physics, Director, Center for Educational Development, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A.

(612)3734537.

 

 

C. PROJECT HEADQUARTERS: 1. Contact: Minnemath Center, University of Minnesota, 720 Washington Avenue, S.E., Minneapolis, Minnesota 55455, U.S.A. 2. Special facilities or activities available for visitor viewing: None.

 

 

D. PRINCIPAL PROFESSIONAL STAFF: M. R. Boudrye, Research Associate, Administrator.

 

 

E. PROJECT SUPPORT: 1. Funding agencies: University of Minnesota. 2. Associated agencies: Formerly funded by the National Science Foundation.

 

 

F. PROJECT HISTORY: 1. Principal originator: Paul C. Rosenbloom, Professor of Mathematics. 2. Date and place of initiation: 1961; University of Minnesota. 3. Project terminated: September, 1970.

 

 

G. PROJECT OBJECTIVES: 1. Overall project purpose: To produce coordinated mathema­tics and science curriculum for grades K6. 2. Specific objectives: To develop process acquisition, at­titudinal changes and scientific literacy.

 

 

H. UNIQUE CHARACTERISTICS OF THE PROJECT: Broad spectrum of ele­mentary school children of varying capacities and backgrounds.

 

 

I. SPECIFIC SUBJECTS, GRADE, AGE AND ABILITY LEVELS: Coordinated mathematics and science, grades K3; college level, teacher preparatory.

 

 

J. MAIN METHODS OF INSTRUCTION USED IN THE PROJECT: Independent study, laboratory investigations, seminars, and discussion sessions.

K. PRESENT COMMERCIAL AFFILIATIONS: Textbook in mathematics: "Ideas in Mathematics," published by W.B. Saunders Co., Phila­delphia, Pa. 1970.

L. DESCRIPTION OF MATERIALS ALREADY PRODUCED: 1. Minnemath Reports (terminated 1969).


2.                     Coordinated units: 129 for grades K3.

3.                     Overview.

4.                     Living Things in Field and Classroom.

5.                     Extending Man's Senses.

6.                     Ideas in Mathematics.

7.                     Questions and Answers about MINNEMAST.

 

 

M. MATERIALS AVAILABLE FREE: Item 7 only. Please address the pro­ject headquarters.

 

 

N. MATERIALS PURCHASABLE: Item 2 5, information available by writing project headquarters. Item 6 from W. B. Saunders Co., Philadelphia, Pennsylvania, U.S.A.

 

 

0. ADDITIONAL MATERIALS BEING DEVELOPED: Preservice and inservice teacher aids.

 

 

P. LANGUAGE IN WHICH MATERIALS: 1. Were originally written: English. 2. Have been or will be translated: None.

 

 

Q.                    COUNTRIES IN WHICH MATERIALS ARE USED: United States and Canada.

 

 

R. PROJECT IMPLEMENTATION: 1. Total number of teachers using any of the materials: 200. 2. Total number of students using any of the materials: 50,000+. 3. Total number of schools using any of the materials: 125. 4. Number of teachers have adopted the entire program: 20 school systems. 5. Number of students involved: 6,000. 6. Number of schools involved: 125. 7. The totals stated in 1,2,3,5, and 6 are estimated. 8. Name and location of selected schools where this program is in use: St. Paul, Minnesota; West St. Paul, Minnesota; South Hadley, Massachusetts; Pittsfield, Massachusetts; Newton, New Jersey; Quincy, Massachusetts; Redlands, California.

 

 

S. TEACHER PREPARATION: 1. Consultant services available for teachers using the materials: Write to the Center at address in Cl. 2. Activities conducted for preservice and inservice teacher training: Summer workshops, supported by National Science Foundation, in various areas. Information available from NSF, Student and Curriculum Improvement Section, Washing­ton, D. C. 20550. 3. Available preservice and/or inservice teaching materials for science educators to use in preparing teachers: Preservic and inservice materials were planned, and some early develop­ment completed. No funds have been available for completing these materials and early phases are no longer available for distribution.


T. PROJECT EVALUATION:

1.                     Has the effectiveness of the materials been evaluated: Yes,

internally.

2.                     Published research studies:

                        (a) Hively, W., H. Patterson, and Sara H. Page, "A Uni

                        verseDefined System of Arithmetic Achievement Tests",

                        Journal of Educational Measurement Vol. 5, No. 4, Winter

                        1968, p. 275.

                        (b) Johnson, P. E., "On the Communication of Concepts in

                        Science", Journal of Educational Psychology, 1969, Vol. 60,

                        p. 3240.

                        (C) Murray, F., "Reversibility Training in the Acquisition

                        of Length Conservation", Journal of Educational Psychology

                        Vol. 59, No. 2, 1968, p. 8287.

                        (d) Murray, F., "Operational Conservation of Illusion

                        Distorted Length", British Journal of Educational Psych

                        ology Vol. 38, Part 2, June 1968, p. 189193.

3.                     Brief abstract of inhouse or unpublished research:

                        (a) Reports on the direct evaluation of most of the K3

                        units have been completed. These reports contain a detailed

                        description of the test domain for the unit and a summary

                        of the results obtained during the field test of the unit.

                        (b) The MINNEMAST Experiment with Domain Referenced

                        Achievement Testing Systems A detailed description of the

                        evaluation procedures used in the MINNEMAST evaluation

                        project.

                        (C) A Curriculum Evaluation and Revision Based on Domain

                        Referenced Achievement Test System This paper describes

                        how an individual unit (Unit 2) was evaluated and revised

                        based upon the results of that evaluation. It also pre

                        sents the results of a subsequent evaluation.

                        (d) The Use of Sample Test Items As Objectives for

                        Instruction The Effects Upon the Teacher and Upon the

                        Learner. This paper describes a study in which six kinder

                        garten teachers were provided with sample test items for a

                        MINNEMAST unit while a matched sample of six other teachers

                        were provided with the unit only. The study sheds some

                        light on the role of objectives in instruction.

 

 

(Edward)       Future Uses of Domain Referenced Achievement Testing

Systems         This paper outlines some of the potential uses

for Domain Referenced Achievement Testing Systems. It also

points to         some of the pitfalls in those applications.

(f) An Introduction to Domain Referenced Achievement

Testing           An overview of the psychological basis for the

evaluation model utilized in the MINNEMAST Project. The

paper also includes a glossary of terms as utilized in the

testing model

(GCMP) The Experimental Analysis of Educational Objectives

Ph.D.Thesis, University of Minnesota, George Rabehl. The

paper represents the philosophical and scientific rationale

for casting the formulation of educational objectives into

an experimental context. It shows that the specification

691

 


of relevant and irrelevant conditions is not a once and for

all activity but requires instead a continuing selfcorrec

tive process involving the steps of hypothesis, application,

analysis, and a reformulation of educational intent. What

is achieved is a framework for analyzing, describing, and

comparing curricular materials; for making inferences from

student performances beyond a finite set of items; and

finally a basis for proposing and interpreting psycholog

ical studies in terms of the actual characteristics of

educational requirements.

(h) A               Comparison of Two Conceptual Frameworks for Teaching

the Basic Concepts of Rational Numbers Ph.D. Thesis, Uni

versity of Minnesota, Donald Sension. This paper compares

the effects of two physical models for teaching fraction

concepts on student performance. It utilizes a Domain

Reference Achievement Testing System.

(i) An Investigation of the Effectiveness of Independent

Study of Novel Mathematics Material in the Elementary

School Ph.D.Thesis, University of Minnesota, Lester

Becklund. The paper presents the results of a study which

examined the role of the teacher in presenting some novel

mathematics. A MINNEMAST game unit on vectors and trans

formations was used.

(j) Arithmetic Achievement Test Performance of MINNEMAST

Mathematics Pupils in the Third and Fourth Grades This

paper presents a summary of the results of a two year

study of the performance of pupils in the MINNEMAST mathe

matics            program on selected arithmetic achievement tests.

(K) The Relationship Between Concepts of Conservation of

                        and Number. The purpose of this study was to

describe the relationship between attainment of concepts

of conservation of length and number. The concepts were

embodied in a compound numberlength task. Two aspects

of performance were investigated: (10) the comparative

performance of solvers and nonsolvers on conservation of

number          and conservation of length, and (2) the stability

of performance characteristics across the age span sampled.

Fiftyfive children, 21 females and 34 males, ages 6

through 9 years, participated in the study.

 

 

U. PROJECT PUBLICITY: 1. Ahrens, R. B., "MINNEMAST ‑‑ The Coordinated Science and Mathematics Program", Science and Children Vol 65, December 1965, p. 811814. 2. Bray, Edmund C., "MINNEMAST, An Elementary MathScience Program", School Science and Mathematics June 1969. 3. Bray, Edmund C., "The MINNEMAST Elementary Mathematics­Science Program", The Physics Teacher May 1968. 4. Maxwell, Graham, "Some Notes and Comments on the Minnesota Mathematics and Science Teaching Project", The Australian Mathematics Teacher March 1969.


5. Rising, Gerald R., "Research and Development in Mathematics and Science Education at the Minnesota School Mathematics and Science Center and the Minnesota National Laboratory", School Science and Mathematics Vol. 65, December 1965, p. 811814. 6. Rosenbloom, P. C., Journal of Research in Science Teaching (1963), p. 276280. 7. Subarsky, Zachariah, "Curriculum Construction for K6 Science and Math ‑‑ a Strategy", Science and Children November 1968. 8. Subarsky, Zachariah, "The Systems Concept in Science", The Instructor January 1968. 9. Victor, Laurence, "Systems: An Organizing Principle for Science Curricula", Science and Children January/February 1968, p. 1720. 10. Werntz, James H., "A Style of Understanding", Nature and Science Vol. 4, No. 12, March 13, 1967.

 

 

V. BRIEF SUMMARY OF PROJECT ACTIVITIES SINCE 1970 REPORT: Prepara­tion for sale of printed materials and laboratory kits.

 

 

W. PLANS FOR THE FUTURE: Continued availability of materials. Write to the Center.

 

693

 


---

A.                    PROJECT TITLE: SCHOOL MATHEMATICS STUDY GROUP (SMSG)

 

 

B. PROJECT DIRECTOR: Dr. E. G. Begle, SMSG School of Education,

                        Stanford University, Stanford, California 94305, U.S.A.

(415)3212300 X2681.

 

 

C. PROJECT HEADQUARTERS: 1. Contact: Project director, SMSG. 2. Special facilities or activities available for visitor viewing: There are no facilities for viewers.

 

 

D.                    PRINCIPAL PROFESSIONAL STAFF: None.

 

 

E. PROJECT SUPPORT: 1. Funding agencies: National Science Foundation. 2. Organizational agencies: Stanford University and the Conference Board of the Mathematical Sciences.

 

 

F. PROJECT HISTORY: 1. Principal originators: Ad hoc Conference of Mathematicians. 2. Date and place of initiation: March 1958; Yale University.

 

 

G. PROJECT OBJECTIVES: 1. Overall project purpose: To bring together classroom teachers and research mathematicians in a joint effort to im­prove the precollege mathematics curriculum. 2. Specific objectives: The primary purpose of the SMSG was to foster research and development in the teaching of school mathematics. The work of SMSG consisted primarily in the development of courses, teaching materials and teaching methods. It was a part of SMSG's task, in cooperation with other mathe­matical organizations, to encourage exploration of the hypotheses underlying mathematics education.

 

 

H.                    UNIQUE CHARACTERISTICS OF THE PROJECT: Not answered.

 

 

I. SPECIFIC SUBJECTS; GRADE; AGE AND ABILITY LEVELS: Mathematics; kindergarten through grade 12; teacher training materials.

 

 

J. METHODS OF INSTRUCTION USED IN THE PROJECT: Normal classroom procedures.

 

 

K.                    PRESENT COMMERCIAL AFFILIATIONS: The monograph series "New

Mathematical Library" is published by Random House, Inc., 457 Madison Avenue, New York, New York 10022, U.S.A. The filmed course for elementary school teachers is distributed by Modern Learning Aids, 1212 Avenue of the Americas, New York, New York, 10036, U.S.A.


L. MATERIALS PRODUCED:

First Course in Algebra:

1.                     Student's Text, Parts I and II.

2.                     Teacher's Commentary, Parts I and II.

 

 

Programed First Course in Algebra (Revised Form h):

3.                     Student's Text, Parts I and II.

4.                     Student's Response Booklet.

5.                     Teacher's Commentary.

 

 

Geometry;

6.                     Student's Text, Parts I and II.

7.                     Teacher's Commentary, Parts I and II.

 

 

Geometry with Coordinates:

8.                     Student's Text, Parts I and II.

9.                     Teacher's Commentary, Parts I and II.

 

 

Intermediate Mathematics:

10.                  Student's Text, Parts I and II.

11.                  Teacher's Commentary, Parts I and II.

 

 

Elementary Functions:

12.                  Student's Text.

13.                  Teacher's Commentary.

 

 

Introduction to Matrix Algebra:

14.                  Student's Text.

15.                  Teacher's Commentary.

 

 

Analytic Geometry:

16.                  Student's Text.

17.                  Teacher's Commentary.

 

 

Algorithms, Computation and Mathematics:

18.                  Student's Text.

19.                  Teacher's Commentary.

20.                  FORTRAN, Student's Text.

21.                  FORTRAN, Teacher's Commentary.

22.                  ALGOL, Student's Text.

23.                  ALGOL, Teacher's Commentary.

 

 

Calculus:

24.                  Student's Text, Parts I and II.

25.                  Teacher's Commentary, Parts I and II.

26.                  Student's Text, Part III.

27.                  Teacher's Commentary, Part III.

 

 

Calculus of Elementary Functions:

28.                  Student's Text (2 parts).

29.                  Teacher's Commentary (2 parts).

777

 


Mathematics for Junior High School:

30.                  Volume 1, Student's Text, Parts I and II.

31.                  Volume 1, Teacher's Commentary, Parts I and II.

32.                  Volume 2, Student's Text, Parts I and II.

33.                  Volume 2, Teacher's Commentary, Parts I and II.

 

 

Introduction to Secondary School Mathematics:

34.                  Volume 1, Student's Text, Parts I and II.

35.                  Volume 1, Teacher's Commentary.

36.                  Volume 2, Student's Text, Parts I and II.

37.                  Volume 2, Teacher's Commentary.

 

 

Introduction to Algebra:

38.                  Student's Text, Parts I and II.

39.                  Teacher's Commentary, Parts I and II.

 

 

Mathematics for the Elementary School:

40.                  Book K, Teacher's Commentary.

41.                  Book 1, Student's Text.

42.                  Book 1, Teacher's Commentary.

43.                  Book 2, Student's Text.

44.                  Book 2, Teacher's Commentary.

45.                  Book 3, Student's Text, Parts I and II.

46.                  Book 3, Teacher's Commentary, Parts I and II.

47.                  Grade 4, Student's Text, Parts I and II.

48.                  Grade 4, Teacher's Commentary, Parts I and II.

49.                  Grade 5, Student's Text, Parts I and II.

50.                  Grade 5, Teacher's Commentary, Parts I and II.

51.                  Grade 6, Student's Text, Parts I and II.

52.                  Grade 6, Teacher's Commentary, Parts I and II.

 

 

Mathematics for the Elementary School ‑ Special Editions:

53.                  Book K, Teacher's Commentary.

54.                  Book 1, Student's Text, Parts I and II.

55.                  Book 1, Teacher's Commentary, Parts I and II.

56.                  Developing Mathematics Readiness in Pre‑School Programs.

 

 

Mathematics Through Science:

59.                  Graphing, Equations and Linear Functions, Students Text,

Part

58.                  Measurement and Graphing, Teacher's Commentary, Part I.

59.                  Graphing, Equations and Linear Functions, Student's Text,

Part                 II.

60.                  Graphing, Equations and Linear Functions, Teacher's

Commentary, Part II.

61.                  An Experimental Approach to Functions, Student's Text,

Part                 III.

62.                  An Experimental Approach to Functions, Teacher's

Commentary, Part III.

Supplementary Units:

65.                  Junior High School, Student's Text.

66.                  Junior High School, Teacher's Commentary.

778

 


67.                  Essays on Number Theory I.

68.                  Essays on Number Theory II.

69.                  Development of the Real Number System.

 

 

Probability:

70.                  Primary Grades, Student's Text.

71.                  Primary Grades, Teacher's Commentary.

72.                  Intermediate Grades, Student's Text.

73.                  Intermediate Grades, Teacher's Commentary.

74.                  Classroom set of Spinners for Primary Grades.

75.                  Classroom set of Spinners for Intermediate Grades.

76.                  Introduction to Probability, Basic Concepts, Student's

Text, Part I.

77.                  Introduction to Probability, Special Topics, Student's

Text, Part II.

 

 

Supplementary and Enrichment Series:

78.                  SP‑16 Algebraic Structures.

79.                  SP‑23 Radioactive Decay.

80.                  SP‑26 Mathematical Theory of the Struggle for Life.

81.                  SP‑27 1 + 1 = ?.

82.                  SP‑28 Order and the Real Numbers: A Guided Tour.

83.                  SP‑29 The Mathematics of Trees and Other Graphics.

 

 

Reprint Series:

84.                  RS‑1 The Structure of Algebra.

85.                  RS‑2 Prime Numbers and Perfect Numbers.

86.                  RS‑3 What is Contemporary Mathematics?.

87.                  RS‑4 Mascheroni Constructions.

88.                  RS‑5 Space, Intuition and Geometry.

89.                  RS‑6 Nature and History of

90.                  RS‑7 Computation of ir

91.                  RS‑8 Mathematics and Music.

92.                  RS‑9 The Golden Measure.

93.                  RS‑10 Geometric Constructions.

94.                  RS‑11 Memorable Personalities in Mathematics: Nineteenth

Century.

95.                  RS‑l2 Memorable Personalities in Mathematics: Twentieth

Century.

96.                  RS‑l3 Finite Geometry.

97.                  RS‑l4 Infinity.

98.                  RS‑15 Geometry, Measurement and Experience.

 

 

Spanish Translations:

99. Matematicas Para El Primer Ciclo, Secundario, 2 parts (JI‑RS) 100. Matematicas Para El Primer Ciclo Secundario, 2 parts, Comentario (CJI‑RS). 101. Matematicas Para El Primer Ciclo Secundario, 2 parts (JII‑RS) 102. Matematicas Para El Primer Ciclo Secundario 2 parts, Comentario (CJII‑RS). 103. Matematicas Para La Escuela Secundaria, Primer Curso de Algebra, 2 parts (F‑RS), set.

 

104.                Matematicas Para La Escuela Secundaria, Primer Curso de

Algebra, 2 parts, Comentario (CF‑RS).

105.                Matematicas Para La Escuela Secundaria, Geometria, 2 parts

(G‑RS), set. $3.00.

106.                Matematicas Para La Escuela Secundaria, Geometria, 2 parts

Comentario (CG‑RS). $3.00.

107.                Matematicas Para La Escuela Secundaria, Matematica

Intermediate, 2 parts (I‑RS). $3.00.

108.                Matematicas Para La Escuela Secundaria, Funciones

Elementales (E‑RS). $2.00.

109.                Matematicas Para La Escuela Secundaria, Introduccion Al

Algebra De Las Matrices (A‑RS). $2.00.

110.                Geometria Analitica (GA). $2.00.

111.                Matematicas Para La Escuela Primaria, Grado 4, 2 parts,

Comentario (SE‑4). $4.00.

112.                Matematicas Para La Escuela Primaria, Grado 5, 2 parts,

Comentario (SE‑5). $4.00.

113.                Matematicas Para La Escuela Primaria, Grado 6, 2 parts,

Comentario (SE‑6). $4.00.

114.                Estudios De Matematicas, Conceptos de Geometria

Intuitiva (SM‑5). $2.00.

115.                El Curso Conciso En Matematicas Para Los Profesores De

Escuela Primaria (SM‑9). $2.50.

116.                Introduccion A Sistemas Numericos (SM‑14). $2.50.

 

 

Soviet Studies in the Psychology of Learning and Teaching

Mathematics:

117.                Volume 1 ‑ The Learning of Mathematical Concepts.

118.                Volume II ‑ The Structure of Mathematical Abilities.

119.                Volume III ‑ Problem Solving in Arithmetic and Algebra.

120.                Volume IV ‑ Problem Solving in Geometry.

121.                Volume V ‑ The Development of Spatial Abilities.

122.                Volume VI ‑ Instruction in Problem Solving.

 

 

Investigations in Mathematics Education:

123.                A Journal of Abstracts and Annotations, Volume 1.

124.                A Journal of Abstracts and Annotations, Volume 2.

125.                A Journal of Abstracts and Annotations, Volume 3.

126.                A Journal of Abstracts and Annotations, Volume 4.

Studies in Mathematics:

127.                Euclidean Geometry Based on Ruler and Progractor

Axioms (SM‑2).

128.                Structure of Elementary Algebra (SM‑3).

129.                Geometry (SM‑4).

130.                Concepts of Informal Geometry (SM‑5).

131.                Number Systems (SM‑6).

132.                Intuitive Geometry (SM‑7).

133.                Concepts of Algebra (SM‑8).

134.                Brief Course in Mathematics for Elementary School Teachers

(SM‑9).

135.                Applied Mathematics in the High School (SM‑b).

 

780

 


104.                Matematicas Para La Escuela Secundaria, Primer Curso de

Algebra, 2 parts, Comentario (CF‑RS).

105.                Matematicas Para La Escuela Secundaria, Geometria, 2 parts

(G‑RS), set. $3.00.

106.                Matematicas Para La Escuela Secundaria, Geometria, 2 parts

Comentarlo (CG‑RS). $3.00.

107.                Matematicas Para La Escuela Secundaria, Matematica

Intermediate, 2 parts (I‑RS). $3.00.

108.                Matematicas Para La Escuela Secundaria, Funciones Elementales (E‑RS).

$2.00.

109.                Matematicas Para La Escuela Secundaria, Introduccion Al

Algebra De Las Matrices (A‑RS). $2.00.

110.                Geometria Analitica (GA). $2.00.

111.                Matematicas Para La Escuela Primaria, Grado 4, 2 parts,

Comentario (SE‑4). $4.00.

112.                Matematicas Para La Escuela Primaria, Grado 5, 2 parts,

Comentario (SE‑5). $4.00.

113.                Matematicas Para La Escuela Primaria, Grado 6, 2 parts,

Comentario (SE‑6). $4.00.

114.                Estudios De Matematicas, Conceptos de Geometria

Intuitiva (SM‑5). $2.00.

115.                El Curso Conciso En Matematicas Para Los Profesores De

Escuela Primaria (SM‑.9). $2.50.

116.                Introduccion A Sistemas Numericos (SM‑l4). $2.50.

 

 

Soviet Studies in the Psychology of Learning and Teaching

Mathematics:

117.                Volume 1 ‑ The Learning of Mathematical Concepts.

118.                Volume II ‑ The Structure of Mathematical Abilities.

119.                Volume III ‑ Problem Solving in Arithmetic and Algebra.

120.                Volume IV ‑ Problem Solving in Geometry.

121.                Volume V ‑ The Development of Spatial Abilities.

122.                Volume VI ‑ Instruction in Problem Solving.

 

 

Investigations in Mathematics Education:

123.                A Journal of Abstracts and Annotations, Volume 1.

124.                A Journal of Abstracts and Annotations, Volume 2.

125.                A Journal of Abstracts and Annotations, Volume 3.

126.                A Journal of Abstracts and Annotations, Volume 4.

 

 

Studies in Mathematics:

127.                Euclidean Geometry Based on Ruler and Progractor

Axioms (SM‑2).

128.                Structure of Elementary Algebra (SM‑3).

129.                Geometry (SM‑4).

130.                Concepts of Informal Geometry (SM‑5).

131.                Number Systems (SM‑6).

132.                Intuitive Geometry (SM‑7).

133.                Concepts of Algebra (SM‑8).

134.                Brief Course in Mathematics for Elementary School Teachers

(SM‑9).

135.                Applied Mathematics in the High School (SM‑10).

136.                Mathematical Methods in Science (SM‑11).

137.                A Brief Course in Mathematics for Junior High School

Teachers (SM‑12).

138.                Inservice Course for Primary School Teachers (SM‑13).

139.                Introduction to Number Systems (SM‑14).

140.                Calculus and Science (SM‑l5).

141.                Some Uses of Mathematics (SM‑16).

142.                Mathematical Concepts of Elementary Measurement (SM‑17).

143.                Puzzle Problems and Games Project (SM‑18).

144.                Reviews of Recent Research in Mathematics Education (SM‑l9).

 

 

Conference Reports:

145.                Conference on Elementary School Mathematics (CR‑1).

146.                Orientation Conference for SMSG Experimental Centers (CR‑2).

147.                Orientation Conference for SMSG Elementary School Experi‑

mental Centers (CR‑3).

148.                Orientation Conference for Geometry with Coordinates (CR‑4).

149.                Conference on Future Responsibilities for School Mathe‑

matics (CR‑5).

150.                Mathematics Education for Below Average Achievers (CR‑6).

151.                A Conference on Mathematics for Gifted Students (CR‑7).

152.                A Conference on Mathematics Education in the Inner City

Schools (CR‑8).

153.                A Conference on Responsibilities for School Mathematics in

the 70's (CR‑9).

 

 

NLSMA          Reports:

154.                No. 1 X‑Population Test Batteries.

155.                No. 2 Y‑Population Test Batteries.

156.                No. 3 Z‑Population Test Batteries

157.                No. 4 Description and Statistical Properties of

X‑Population Scales.

158.                No. 5 Description and Statistical Properties of

Y‑Population Scales.

159.                No. 6 Description and Statistical Properties of

Z‑Population Scales.

160.                No. 7 The Development of Tests.

161.                No. 9 Non‑Test Data.

162.                No. 10 Patterns of Mathematics Achievement in Grades 4,5,

and 6: X‑Population.

163.                No. 11 Patterns of Mathematics Achievement in Grades 7 and 8

X‑Population.

164.                No. 12 Patterns of Mathematics Achievement in Grades 7 and 8

Y‑Population.

165.                No. 13 Patterns of Mathematics Achievement in Grade 9:

Y‑Population.

166.                No. 14 Patterns of Mathematics Achievement in Grade 10:

Y‑Population.

167.                No. 15 Patterns of Mathematics Achievement in Grade 11:

Y‑Population.

168.                No. 16 Patterns of Mathematics Achievement in Grade 10:

Z‑Population.


169.                No. 19 The Non‑Intellective Correlates of Over‑and

Under‑

achievement in Grades 4 and 6.

170.                No. 21 Correlates of Mathematics Achievement: Attitude and

Role Variables.

171.                No. 22 Correlates of Mathematics Achievement: Cognitive

Variables.

172.                No. 23 Correlates of Mathematics Achievement: Teacher Back‑

ground and Opinion Variables.

173.                No. 24 Correlates of Mathematics Achievement: School‑

Community and Demographic Variables.

174.                No. 25 Correlates of Mathematics Achievement: Teacher

Assigned Grades.

175.                No. 26 Correlates of Mathematics Achievement: Summary.

176.                No. 28 Teacher Effectiveness in Mathematics Instruction.

 

 

ELMA Technical Reports:

177.                No. 1 Kindergarten Test Batteries, Description and

Statistical Properties of Scales.

178.                No. 2 Grade 1 Test Batteries, Description and

Statistical Properties of Scales.

179.                No. 3 Grade 2 Test Batteries, Description and Statistical

Properties of Scales.

180.                No. 4 Grade 3 Test Batteries, Description and Statistical

Properties of Scales.

 

 

Geometry Units for Elementary School:

181.                Sets of Points, Student's Text.

182.                Unit I ‑ Teacher's Commentary.

183.                Congruence, Student's Text.

184.                Unit II ‑ Teacher's Commentary.

185.                Congruence and Familiar Geometric Figures, Student's Text.

186.                Unit III ‑ Teacher's Commentary.

187.                Measurement of Curves (length), Students Text.

188.                Unit IV ‑ Teacher's Commentary.

189.                Measurement of Plane Regions (Area), Student's Text.

190.                Unit V ‑ Teacher's Commentary.

191.                Measurement of Space Regions, (Volume), Student's Text.

192.                Unit VI ‑ Teacher's Commentary.

193.                Measurement of Angles, Student's Text.

194.                Unit VII ‑ Teacher's Commentary.

195.                Side and Angle Relationships for Triangles, Student's Text.

196.                Unit VIII ‑ Teacher's Commentary.

197.                Circles and Constructions, Student's Text.

198.                Unit IX ‑ Teacher's Commentary.

199.                Whole Numbers as Coordinates of Points, Student's Text.

200.                Unit x ‑ Teacher's Commentary.

201.                Integers as Coordinates of Points, Student's Text.

202.                Unit XI ‑ Teacher's Commentary.

 

 

Secondary School Mathematics:

203.                Chapters 1 and 2, Student's Text.

204.                Teacher's Commentary.


205.                Chapters 3 and 4, Student's Text.

206.                Teacher's Commentary.

207.                Chapters 5 and 6, Student's Text.

208.                Teacher's Commentary.

209.                Chapters 7 and 8, Student's Text.

210.                Teacher's Commentary.

                        211.                Chapters 9 and 10, Student's Text.

                        212.                Teacher's Commentary.

                        213.                Chapters 11 and 12, Student's Text.

                        214.                Teacher's Commentary.

                        215.                Chapters 13 and 14, Student's Text.

                        216.                Teacher's Commentary.

                        217.                Chapters 15 and 16, Student's Text.

                        218.                Teacher's Commentary.

                        219.                Chapters 17 and 18, Student's Text.

                        220.                Teacher's Commentary.

                        221.                Chapters 19 and 20, Student's Text.

                        222.                Teacher's Commentary.

                        223.                Chapters 21 and 22, Student's Text.

                        224.                Thacher's Commentary.

                        225.                Chapters 23 and 24, Student's Text.

                        226.                Teacher's Commentary.

                        227.                Chapters 25 and 26, Student's Text.

                        228.                Teacher's Commentary.

                        229.                Chapters 27 and 28, Student's Text.

                        230.                Teacher's Commentary.

 

 

Secondary School Advanced Mathematics:

231.                Chapters 1 and 2, Student's Text.

232.                Teacher's Commentary.

233.                Chapter 3, Student's Text.

234.                Teacher's Commentary.

235.                Chapters 4 and 5, Student's Text.

236.                Teacher's Commentary.

237.                Chapters 6 and 7, Student's Text.

238.                Teacher's Commentary.

239.                Chapter 8, Student's Text.

240.                Teacher's Commentary.

 

 

Secondary School Mathematics ‑ Special Editions:

                        241.                Chapters 1, 2, and 3, Student's Text.

                        242.                Chapters 4 and 5, Student's Text.

                        243.                Chapters 6 and 7, Student's Text.

                        244.                Chapters 8 and 9, Student's Text.

                        245.                Teacher's Commentary for Chapters 1‑9.

                        246.                Chapters 10 and 11, Student's Text.

                        247.                Chapters 12, 13, and 14, Student's Text.

                        248.                Chapters 15 and 16, Student's Text.

                        249.                Chapters 17 and 18, Student's Text.

                        250.                Teacher's Commentary for Chapters 10‑18.


Miscellaneous Publications:

251.                Very Short Course in Mathematics for Parents.

252.                Philosophies and Procedures of SMSG Writing Teams.

253.                SMSG: The Making of a Curriculum.

 

 

New Mathematical Library:

254.                Niven ‑ Numbers: Rational and Irrational (NML‑l).

255.                Sawyer ‑ What is Calculus About? (NML‑2).

256.                Beckenback and Bellman ‑ An Introduction to Inequalities

(NHL‑3).

257.                Kazarinoff ‑ Geometric Inequalities (NNL‑4).

258.                Davis ‑ The Lore of Large Numbers (NML‑6).

259.                Zippin ‑ Uses of Infinity (NML‑7).

260.                Yaglom ‑ Geometric Transformations I (NHL‑8).

261.                Olds ‑ Continued Fractions (NML‑9).

262.                Ore ‑ Graphs and Their Uses (NML‑10).

263.                Hungarian Problem Book I (NNL‑11).

264.                Hungarian Problem Book II (NML‑12).

265.                Aaboe ‑ Episodes from the Early History of Mathematics

(NML‑l3).

266.                Grossman and Magnus ‑ Groups and their Graphs (NML‑14).

267.                Niven ‑ Mathematics of Choice (NML‑15).

268.                Friedrichs ‑ From Pythagoras to Einstein (NML‑l6).

269.                The Contest Problem Book II (NML‑l7).

270.                Chinn and Steenrod ‑ First Concepts of Topology (NML‑l6).

271.                Coxeter and Greitzer ‑ Geometry Revisited (NNL‑19).

272.                Ore ‑ Invitation to Number Theory (NML‑20).

273.                Yaglom ‑ Geometric Transformations II (N}IL‑21).

274.                Sinkov ‑ Elementary Cryptanalysis (NML‑22).

275. Honsberger ‑ Ingenuity in Mathematics (NML‑23). NEWSLETTERS Information concerning SMSG was disseminated through its Newsletters which appear at irregular intervals. The following Newsletters are still available until the supply is exhausted: 276. No. 15. Reports on various SMSG Projects. 277. No. 17. Lists Supplementary Publications and selected list of inexpensive books for supplementary use. 278. No. 19. Report of a survey of in‑service programs for mathematics teachers. 279. No. 21. Reference guide to the New Mathematical Library Description, topical classification and index with suggested grade levels. 280. No. 23. Panel on Supplementary Publications. 281. No. 24. Reports on various SMSG projects. 282. No. 25. Articulation of Content of SMSG Texts, grades 7-10. 283. No. 28. Articulation of Content of SMSG Texts, grades 1‑3 and 4. 284. No. 30. Status Reports, Recent Publications. 285. No. 33. Mathematics for Disadvantaged and Low Achieving Students. 286. No. 35. Status Reports ‑ Recent Publications.


 

287. No. 36. Final Report on a New Curriculum Project. 288. No. 37. SMSG Publications.

 

 

MATERIALS AVAILABLE FREE: Newsletters Nos. 15, 17, 19, 21, 23, 24, 25, 28, 30, 33, 35, 36 and 37; Report No. 1 ‑ The Pro­grammed Learning Project; Report No. 2 ‑ The Special Curriculum Project; Pilot Program on Mathematics learning of Culturally Disadvantaged Primary School Children; Report No. 3 ‑ A Film­Film Text Study; Report No. 4 ‑ The Special Curriculum Project: 1965‑66; Report No. 5 ‑ The Slow Learner Project: The Second­ary School "Slow‑Learner" in Mathematics; Report No. 7 ‑ Pre­liminary Report on an Experiment with Junior High School Very Low Achievers in Mathematics: Report No. 7 ‑ Final Report on an Experiment with Junior High School Very Low Achievers in Mathematics; Report No. 8 ‑ The Mathematics Through Science Study: Attitude Changes in a Mathematics Laboratory; Report No. 9 ‑ Teacher Knowledge and Student Achievement in Algebra. ELMA Reports No. 1 ‑ A Longitudinal Study of Mathematical Achievement in the Primary School Years: Description of De­sign, Sample, and Factor Analyses of Tests; No. 2 ‑ A Longi­tudinal Study of Mathematical Achievement in the Primary School Years: Curriculum and Socio‑Economic Comparisons and Predictions from Previous Achievement. Available on request from SMSG Headquarters.

 

 

MATERIALS PURCHASABLE: Prices subject to change: See Newsletter No. 37, March 1972. For New Mathematical Library series, a special school edition is available to students and teachers from Random House, Inc./School Division, P. 0. Box 457, Westminster, Maryland 21157, U.S.A. Attn: Order Department for $1.95 per copy. A hard‑bound library edition priced at $2.95 is available from the same address.

 

 

ADDITIONAL MATERIALS BEING DEVELOPED: Other NLSMA reports in preparation.

 

 

LANGUAGE IN WHICH MATERIALS: 1. Were originally written: English. 2. Have been or will be translated; Arabic, Bengali, Chinese, Cypriot, Dutch, French, Greek, Indonesian, Italian, Japanese, Korean, Portugese, Swedish, Turkish, Vietnamese.

 

 

COUNTRIES IN WHICH MATERIALS ARE USED: Not answered.

 

 

PROJECT IMPLEMENTATION: Not answered.

 

 

CHER PREPARATION:

¥                       Consultant services available for teachers using the

materials: None.

Activities conducted for pre‑service and in‑service teacher training: None.


3.                     Available pre‑service and/or in‑service teaching materials

for                   science educators to use in preparing teachers: Studies

in Mathematics, Volumes 1‑19.

 

 

T. PROJECT EVALUATION: 1. Has the effectiveness of the materials been evaluated: Yes, by project staff. 2. Pertinent published research studies: NLSMA Reports. 3. Brief abstract of in‑house or unpublished research: Other NLSMA Reports in preparation. 4. Additional evaluative data available to interested in­dividuals: Arrangements for this are being planned.

 

 

U. PROJECT PUBLICITY: Begle, E.G. "SMSG: The First Decade" The Mathematics Teacher Volume LXI, No. 3, March 1968, p.239‑245.

 

 

V. BRIEF SUMMARY OF PROJECT ACTIVITIES SINCE 1968 REPORT: Contin­uation of new junior high school curriculum project. Addi­tional analyses of NLSMA data.

 

 

W. PLANS FOR THE FUTURE: Phase out of all current activities, except publication program for existing materials and main­tainance of NLSMA data bank, on August 31, 1972.

 

786

 


---

A. PROJECT TITLE: SECONDARY SCHOOL MATHEMATICS CURRICULUM IMPROVEment STUDY

 

 

B. PROJECT DIRECTOR: Howard F. Fehr, Teachers College, Box 120, Columbia University, New York, New York 10027, U.S.A.

 

 

C. PROJECT HEADQUARTERS: 1. Contact: Project director. 2. Special facilities or activities available for visitor viewing: Experimental classes ‑ Courses I‑VI ‑ around metropolitan New York; or reference to some persons in charge of SSMCIS programs in schools in other parts of the country.

 

 

D. PRINCIPAL PROFESSIONAL STAFF: Director: Howard F. Fehr; Research Associates: Jeremy Kilpatrick, James Lovett; Research Assis­tants: John Camp, David Fuys, Howard Kellogg.

 

 

E. PROJECT SUPPORT: 1. Funding agencies: U.S. Office of Education and National Science Foundation. 2. Associated agencies: Teachers College, Columbia University.

 

 

F. PROJECT HISTORY: 1. Principal originator: Howard F. Fehr. 2. Date and place of initiation: November, 1965; Teachers College, Columbia University. 3. Evolution and development of the project: Based on OECD seminars in Paris (1959), Dubrovnik (1960), Athens (1965), and the Cambridge Report (1963), a group of twenty mathematicians and educators met in June 1966 to formulate a position paper stating the aims and procedures of the study, to construct a blueprint for the proposed 7‑12 mathematics courses, and to make detailed recommendations for the mathematical content of Course I. Using these recommendations as a guide, a team of eight mathematics educators wrote a textbook for Course I. In each subsequent year (1967‑72) a pre‑planning conference of SSMCIS staff and advisors and a June working conference in­cluding writers met to review and revise previous texts and to make specific recommendations for the next text to be written.

 

 

G. PROJECT OBJECTIVES: 1. Overall project purpose: To formulate, construct, and test a unified secondary school mathematics program (7‑12) for Uni­versity‑bound students. 2. Specific objectives: To write, evaluate, and revise text materials and teachers commentaries for Courses 1‑VI; to assist experimental schools in the implementation of the SSMCIS pro­gram.

H. UNIQUE CHARACTERISTICS OF THE PROJECT: 1. SSMCIS materials are geared to the college‑bound student in the upper 20% of academic ability.

818

 


2. Traditional division of school mathematics into arithmetic, algebra, geometry, advanced algebra, calculus is replaced by a unified study of mathematics in which all branches of math­ematics are unified through fundamental concepts (set, relation, mapping, and operation) and structures (group, ring, field, and vector space). 3. Probability, statistics, computer programming, and linear algebra are integrated into the program. 4. Course VI materials are composed of a text suitable for a half year of study and five booklets (Algebra and Morphisms; Applications of Probability; Statistics; Matrices, Determinants, and Eigen Values; Differential Equations) which provide the teacher and students with options in choosing topics of study.

 

 

SPECIFIC SUBJECTS, GRADE, AGE AND ABILITY LEVELS: Mathematics: Grades 7‑12; ages 11‑18; upper 20% of academic ability.

 

 

MAIN METHODS OF INSTRUCTION USED IN THE PROJECT: Independent study, lectures, discussion sessions, and the computer, used as a tool in problem solving.

 

 

PRESENT COMMERCIAL AFFILIATIONS: None.

 

 

DESCRIPTION OF MATERIALS ALREADY PRODUCED: 1. Text and Teachers Commentary. 2. Course I, Book 1, 2 Final Version. 3. Course II, Book 1, 2 Final Version. 4. Course III, Book 1, 2 Final Version. 5. Course IV, Book 1, 2 Final Version. 6. Course V, Book 10, 2 Revised. 7. Course VI, Book 1 Experimental, not available to public. 8. Booklets Algebra and Morphisms; Matrices, Determinants, and Eigen Values; Statistics. 9. Bulletins.

 

 

MATERIALS AVAILABLE FREE: Bulletin 7 (Spring 1972). Send name and address to be included on our bulletin mailing list.

 

 

MATERIALS                         PURCHASABLE: Teachers College Press, 1234 Amsterdam

                        Avenue,         New York, New York 10027, U.S.A.

                        Textbooks: Courses I‑IV Part I and Part II $3.25 each part;

                        Courses         I‑IV Teachers Commentary $5.25.

 

 

ADDITIONAL MATERIALS BEING DEVELOPED: Course V (grade 11) text; Course VI (grade 12) text; and additional booklets.

 

 

LANGUAGE IN WHICH MATERIALS: 1. Were originally written: English. 2. Have been or will be translated: Hebrew, French, and per­haps Spanish.

COUNTRIES IN WHICH MATERIALS ARE USED: United States of America;Israel; Quebec, Canada; Belgium; Brazil.

 

 

R. PROJECT IMPLEMENTATION: 1. Total number of teachers using any of the materials: 300. 2. Total number of students using any of the materials: 12,000. 3. Total number of schools using any of the materials: 200. 4. The totals stated in 10, 2 and 3 are estimated. 5. Name and location of selected schools where the program is in use: The materials are used in various cities and districts throughout the U.S.A. (In particular: California, Connecticut, Maryland, Michigan, Missouri, New Jersey, New York).

 

 

S. TEACHER PREPARATION: 1. Consultant services available for teachers using the mater­ials: SSMCIS director and staff research assistants can be contacted by telephone or by mail for assistance regarding program implementation. 2. Activities conducted for pre‑service and in‑service teacher training: Summer institutes aimed at preparing teachers to teach the SSMCIS materials are sponsored by N.S.F. ‑‑ See N.S.F. announcement. 3. Available pre‑service and/or in‑service teaching materials for science educators to use in preparing teachers: None.

 

 

T. PROJECT EVALUATION: 1. Has the effectiveness of your materials been evaluated: Yes, internally. 2. Published research studies: Fey, James T.,PATTERNS OF VER­BAL COMMUNICATION IN MATHEMATICS CLASSES, Unpublished Ph.D. dissertation, Teachers College, Columbia University, 1968. Hoban, Brother Michael, C.S.C., TRANSFORMATION GEOMETRY IN THE JUNIOR HIGH SCHOOL, Unpublished Ph.D. dissertation, Teach­ers College, Columbia University. 3. Brief abstract of in‑house or unpublished research: SSMCIS evaluation efforts have been primarily formative in nature and include: Staff visits to experimental classes, written teach­ers' comments about text materials, bi‑yearly staff‑teachers meetings, and end‑of‑course exams. Other evaluation being conducted at the present time includes: Student Attitudes Survey and Comprehensive Course III Exam­ination. Reports concerning them are available as of May, 1972. 4. Evaluative data available to interested individuals: Tech­nical Reports regarding Attitude Survey and Course III Evalu­ation are available as of May, 1972.

 

 

U.                    PROJECT PUBLICITY: Not answered.

 

 

V. BRIEF SUMMARY OF PROJECT ACTIVITIES SINCE 1970 REPORT: Producing, experimenting and writing Courses IV, V, VI for grades 10, 11, 12. Training teachers in N.S.F. institutes.

W. PLANS FOR THE FUTURE: Completion of the total program by June 30, 1973.

---

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

846

 


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‑to­try" 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).

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(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.

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P. LANGUAGE IN WHICH MATERIALS: 1. Were originally written: English. 2. Have been or will be translated: Undetermined.

 

 

Q.                    COUNTRIES IN WHICH MATERIALS ARE USED: United States.

 

 

R. PROJECT IMPLEMENTATION: 1. Total number of teachers using any of the materials: Over Over 2500 teachers. 2. Total number of students using any of the materials: Not known. 3. Total number of schools using any of the materials: Ap­proximately 75. 4. Number of teachers who have adopted the entire program: Not known. 5. Number of students involved: Not known. 6. Number of schools involved: Not known. 7. The totals stated in 1 and 3 are estimated. 8. Name and location of selected schools where the program is in use: Seameo Regional Centre for Education in Science and Mathematics, Penang, Malaysia; Perkins School for the Blind, Watertown, Massachusetts; City College New York, New York; Fairfax County Public Schools, Bailey's Crossroads, Virginia; Model Cities In‑Service, New Bedford, Massachusetts; Shrewsbury Public Schools, Shrewsbury, Massachusetts; Principia College, Elsah, Illinois; Watertown Public Schools, Watertown, Massachu­setts; University of North Carolina, Chapel Hill, North Carolina; University of Virginia, Falls Church, Virginia; Burlington Pub­lic Schools, Burlington, Massachusetts; Marywood College, Scranton, Pennsylvania; Lesley College, Cambridge, Massachusetts.

 

 

S. TEACHER PREPARATION: 1. Consultant services available for teachers using the materials: Upon request the project can arrange for former pro­ject staff members and others familiar with the course to serve as consultants. 2. Activities conducted for pre‑service and in‑service teacher training: The project no longer conducts institutes; the course materials are designed to be fully effective without specially trained instructors. (See No. 3 below.) 3. Available pre‑service and/or in‑service teaching materials for science educators to use in preparing teachers: The pro­ject's principal activity has been to produce pre‑service and in‑service materials which are contained in the course described here. Costs will be determined by the publisher of the materials when one is selected. For costs during the in­terim distribution period write to: University of Illinois Arithmetic Project, Education Development Center, 55 Chapel Street, Newton, Massachusetts 02160.

T. PROJECT EVALUATION: Effectiveness of the materials has been evaluated by the project staff.

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U. PROJECT PUBLICITY:

1.                     Science editorial, 18 May 1962.

2.                     NCTM Bulletin for Leaders, September, 1968.

3.                     Arithmetic Teacher December, 1967.

4.                     Arithmetic Teacher November, 1968.

5.                     American Mathematical Monthly March, 1970.

6.                     Grade Teacher February, 1971.

7.                     Local newspaper items.

 

 

V. BRIEF SUMMARY OF PROJECT ACTIVITIES SINCE 1970 REPORT: Some

                        editing of the course and simplification of format have been

carried out in response to experiences in ongoing institutes.

 

 

W. PLANS FOR THE FUTURE: The project has concluded its major

course‑production activity at EDC.