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MACHTINGER, DCEI S D. MADISON PROJECT SUMMATIVE EVALUATION REPORT. ELK GRCVE TRAIN ING AND DEVELOPMENT CENTER, ARLINGTON HEIGHTS, III, OFFICE CI EDOC ATION (DHEW), WASHINGTON, D. C., BUREAU OF ELEMENTARY AND SECONDARY EDUCATION. 69
85P,
EDES PRICE ME$0.50 HC$4.35 *CURRICUIUM DEVELOPMENT, *ELEMENTARY SCHOOL MATHEMATICS, *ELEMENTARY SCHOOL TEACHERS, *INSFRVICE TEACHER EDUCATICN, *INSTRUCTION1L MATERIALS, PROGRAM DESCRIPTIONS, PROGRAM EVALUATION ESEA TITLE III, MADISCt PROJECT MATHEMATICS
ABSTRACT THE PRO JECT HAD TWO ASPECTS: (1) DEMONSTRATION CLASSES WHICH WERE LEST GNED TO INFORM PARTICIPANTS ABOUT MADISON PROJECT MATH, AND (2) I RAINING WCRKSHOPS THAT PROVIDED FOR DIFFUSION OF MATERIALS INTO SCHC CLS. ALTOGETHER 214 LOCAL TEACHERS AND PRINCIPALS TCCK PART IN THE WORKSHOPS RELATED TO MADISON PROJECT MATHEMATICS. EVAIUATI CN CF THE PRCGRAMIS EFFECT ON TEACHERS WAS DONE BY ADMINISTERING A Q ESTIONNAIRE. PARTICIPANTS GAVE A VERY FAVOPLBIE RESPONSE IC THE FROG RAM. NC EVALUATION WAS DONE ON THE EFFECT OF THE FECGRAM CN CHILDREN . THIS WORK WAS PREPARED UNDER AN ESEA TITLE III CONTRACT. (BR)
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SUMMAT I VE
U,S, DEPARTMENT OF HEALTH, EDUCATION & WELFARE OFFICE OF EDUCATION
EVALUATION THIS DOCUMENT HAS BEEN REPRODUCED EXACTLY AS RECEIVED FROM THE
REPORT
PERSON OR ORGANIZATION ORIGINATING IT,
POINTS OF VIEW OR OPINIONS
STATED DO NOT NECESSARILY REPRESENT OFFICIAL OFFICE OF EDUCATION
POSITION OR POLICY,
(It (r)1
41.00 q.,1k Grout Traiiiitiq avid
UtutiopoiaCttifcx. E.S.E.A. TITLE III
17011 West Algomphi
id,, ArIutitin ONighis, II. 40005
Prepared by:
DoTAJL_A.Machtinger, Model Program Coordinator Madison Project Mathematics
Elk Grove Training & Development Center 1706 West Algonquin Road 60005 Arlington Heights, Iii. Gloria Kinney, Director
This report is dedicated to Wes Many, my evaluator. Without his support and help this report probably would not have been written. I would like to acknowledge Mrs. Catherine Ekkebus, my secretary. It was certainly her diligent help in careful planning and meticulous execution of all phases of the program that kept the program viable.
TABLE OF CONTENTS
OVERVIEW OF THE PROGRAM
1
RATIONALE
.,e1
PURPOSE
18
ACTIVITIES
22
EVALUATION
27
REFERENCES
39
ABSTRACT
40
APPENDICES
OVERVIEW OF THE PROGRAM MADISON PROJECT MATH
The Madison Project Math model program offered the following services:
Demonstration, Training, Consulting.
Demonstration During the first spring semester of the T & D's operation, the demonstration was manned by Doris Machtinger and Phyllis Ferrell at Juliette Low School, District #59.
It consisted of a brief orienta
tion progr,am followed by a demonstration of Doris Machtinger working
with Kindergarten and 2nd Grade, then Phyllis Ferrell working with 4th Grade, then either Doris Machtinger or Phyllis Ferrell working with 5th Grade.
This marathon of math classes was followed by a
brief queption and answer period.
Demonstrations were held, by
appointment, Tuesday and Thursday mornings.
During the following school year demonstrations were manned by Doris Machtinger and Judy Lowe at Juliette Low School, District #59. The orientation period was extended to include a description of the program followed by the opportunity to experience the independent exploration materials. Judy Lowe.
The visitors then observed a class taught by
This class lasted 20 to 30 minutes.
by a question and answer period.
This was followed
Demonstrations were held every
Tuesday and Thursday morning by appointment.
During the third operational year demonstrations were held by Mickey Palac at Fairview School, Schaumburg, District #54.
Miss Palac
was provided with a halfday substitute once a week to allow her to be with visitors.
She held an orientation session with the visitors
describing the program and allowed them to experience the independent exploration materials, then demonstrated with her own class fOr 20 to 40 minutes.
This class presentation was followed by a question and
answer period.
Visitors were given a booklet describing the Madison
Project, a list of sources for materials and a sample of one of the more popular pieces of equipment, the geoboard.
Demonstrations were
held every Thursday morning by appointment. Many different variations of workshops were offered.
(Asterisks
indicate that leaders were trained in T & D Madison Project Math Workshops lead by Doris Machtinger.
The Evolution of the Training Program Workshop I
The first Madison Project workshop was held in the spring of 1967.
It was conducted by Doris Machtinger and Phyllis Ferrell. on
10 consecutive Tuesday afternoons. the teachers involved.
Released time was provided for
This first group of teachers were all from
Juliette Low School, District #59, and served as a pilot group.
The workshop leaders presented Madison Project lessons to the teachers.
One teacher out of the group then taught a lesson, not
necessarily a Madison. Project lesson to a small group of students.
Using the Flanders interaction analysis and video tape, the group then attempted to critique, this lesson.
Workshop II
The second Madison Project workshop overlapped the first, but met on Thursday, afternoons.
Most of its participants were from
District #59 and District #25. first in format.
This second workshop followed the
This workshop was also held at Juliette Low School.
*Workshop III
The third workshop was conducted for four weeks during the summer of 1967 at Robert Frost School, District #59.
This workshop was con
ducted mainly by Doris Machtinger and Judy Low with some assistance from Phyllis Ferrell.
This workshop followed a new format.
Project materials were presented to the teachers. 4 groups of 4.
The Madison
They then broke into
One member of each group taught a halfhour lesson to
about 5 to 7 children.
The groups of 4 then combined with another group.
of 4 and the 8 discussed and compared the lessons. Additional information, beyond observation, was provided by the
Flanders interaction analysis and a tool designed by the group to analyze questions.
This workshop served 16 people from Districts #59, #25, and the parochial schools.
The afternoon, sessions of this workshop were divided
between work on a special project and an attempt at some small group interaction conducted by Beecham Robinson.
Workshop IV The fourth workshop was conducted in the fall and winter of 196768 by Doris Machtinger on released time on 10 consecutive Monday mornings at John Jay School, District #59.
In this workshop a similar format to
the above was followed with an exception being that teachers were grouped for teaching sessions with others who taught the same grade level.
The
workshop had 22 participants from Districts #59, #25, #15, DeKaib and Evanston.
Workshop V The fifth Madison Project workshop was conducted during the spring of 1968.
It was held at John Jay School in District #59 by Doris
Machtinger. on released time for 2 weeks (10 full days).
The 16
participants were from Districts #25, #57, #54, and #21. The format was changed.
The materials were presented to the
teachers, who, in groups of 4, as in the summer workshop, presented the materials to small groups of students. its own lesson.
Each group of 4 critiqued
Two teaching sessions were provided so that 2 teachers
in each, group of 4 were able to teach each day.
Openness in these
groups was facilitated by the inclusion of 11/2 hours of group dynamics materials designed to encourage an awareness in each individual of the process in his group and his own unique contribution and pattern of behavior.
These materials included:
1.
Xerox listening course
2.
SRA Teaching Lab
3.
Process observation trio
4.
Morton's article on leveling
5.
NASA Moon game
6.
Tinker toy motivation game
7.
Especially designed tapes illustrative of adult workshop problems
*Workshop VI
This workshop was conducted for 10 halfdays in DeKalb during the spring of 1968.
The leader was Miriam Gulesarian.
Group dynamics and
video taping were included along with the Madison Project Math lessons and practice teaching.
There were 10 participants.
*Workshop VII
This workshop was conducted for 5 full days by Bernice Gliege in District #25'.
There were 8 participants.
This workshop also employed
the format of present,tion of material followed by practice teaching
sessions.
IISTIgh2RKgI The eighth workshop was,conducted during the summer of 1968. This workshop had two phases:
Phase A  Phase A was conducted by Doris Machtinger for 3 weeks at Rupley School, District #59 for 16 people and followed the same format as Workshop V.
*Phase B  Phase B consisted of 3 auxilliary workshops held for 2 weeks each concurrently with Phase A by personnel trained during Workshop V.
Section (a) was held at Keller Jr. High School
in Schaumburg, District #54 by Mickey Palac, John Kropp, Jessie Valerio, and Rosalyn Heftner for 40 people. Section (b) was conducted by Mrs. Jerry Garr at Miner Jr. High School in District #25 for 15 people.
Section (c) was
conducted by Mrs. Arlyle Ferguson and Miss Joy Lutsch at Lions School in District #57 for 16 people.
In all three
sections of Phase B the workshops were held in the afternoons.
Materials were presented to the teachers and the
format of teaching and critiquing was followed.
When time
permitted, a few of the group dynamics games were introduced. Worksh
The ninth Madison Project workshop was held October 2  11 for 16 people at Clearmong School, District #59. Districts #54, #59, #25, #65, and #21. each day on released time. during the summer.
The participants were from
The workshop met from 9 to 4
The format was similar to the one followed
Materials were presented to the teachers.
They
broke into teaching groups of 4 and taught the lessons to a small group of children.
They divided each of 2 halfhour teaching sessions per
day into 15 minute sessions so that one teacher could concentrate on one lesson and so that each teacher taught every day.
Time was allowed
for group dynamics materials and for independent exploration materials. *Workshop X
The tenth Madison Project workshop was held by Mrs. Jerry Garr in District #25 at North School.
The 12 participants in this workshop
came from Districts #25, 115, #65, and #23.
This workshop followed much
the same format as WorksLop IX. *Workshop XI
Workshop eleven was conducted by Mrs. Peg Aiman at Sandburg School in Wheeling for 10 teachers from Wheeling School District #21.
It met
November 18, 19, 20, 25, and 26 for 11/2 hours after school for the teachers involved but during class hours (because of split shifts) at the school housing the workshop. teaching sessions.
Thus children were available for the
The last session of the workshop was conducted for
1/2 day on released time to permit time to consider independent exploration materials and view a film besides the usual agenda.
The workshop
was followed by a visit to each of the teacher's classrooms by Peg Aiman to facilitate implementation of the materials.
Mrs. Aiman was supplied
released time for this.
*Workshop XII
The twelfth workshop was conducted December 2  6 by Carl Seltzer from District #54.
The meetings were held on released time from 9 to 4
each day at Dooley School in Schaumburg School District #54. participants came from Districts #54, #65, #39, and #57.
The 16
The workshop
also followed the format of Workshop IX.
*Workshop XIII
This workshop was conducted on Monday afternoons in the form of
an. inservice course in Mount Prospect.
It lasted 10 weeks, of 1hour
sessions, and was conducted by Arlyle Ferguson and Joy Lutsch for 10 teachers from Mount Prospect.
*Workshop XIV This workshop of 8 sessions was conducted in Evanston, half on released time, half after school, 'by Pat Kean and Sara Weinstein.
The
workshop had 15 participants and consisted of materials presentation, demonstration classes, and discussion.
ConsultingServices The consulting services were customized to the individual needs of the consumer,
They varied from making a presentation at a teachers
meeting to helping a teacher get the materials started in her class, to helping a math consultant set up a workshop.
The Program Coordinator
talked to workshop participants on the phone to try to diagnose problems in the lessons and made "house calls" if a phone diagnosis didn't work. The Coordinator was also available to do oneday workshops. Released Time Released time has been used for 3 purposes: 1.
To release teachers to participate in the workshops.
The
bulk of the released time money was used for this purpose. 2.
To release the demonstration assistant so that she can spend time with visitors.
3.
To release workshop participants who were going to conduct their own workshops, first for nlanning, then to actually conduct the workshop.
Staffing The following people have staffed this program: Model Program Coordinator:
Doris Machtinger
Secretary:
Others:
Catherine Ekkebus
During the first semester of the program Phyllis Ferrell served as cocoordinator.
Demonstration Assistants:
Fall 1967
Spring 1968  Judy Lowe
Fall 1968  Spring 1969  Michaelene Palac Participants
The participants in the workshops were mainly elementary school teachers, but at least 4 districts sent their Math Consultants (Districts #54, #21, #25, and #65).
One principal participated.
the following Districts:
#15, #21, #23, #25, #39, #54, #57, #59, #65,
Teachers came from
#428, Round Lake and both the Lutheran and Catholic Parochial Schools. (List of participants in Appendix) Visitors
Visitors to the program were mainly principals, superintendents and math consultants, though often these were accompanied by a few classroom teachers.
Visitors were mainly from the northern Illinois area, though
some were from as far away as Equador.
Most visitors were from elemen
tary school districts, though a few were from colleges.
The College of
Education from Northern Illinois University sent students to see the demonstration.
A list of visitors is on file.
Demonstration.
The Model Program was demonstrated at Juliette Low School, Elk Grove School District #59 and Fairview School, Schaumburg School Dist.#54. Facilities
The Coordinator and Secretary were housed at the Elk Grove Training and Development Center, 1706 W. Algonquin Road, Arlington Heights, Ill. Workshops were housed in schools in the participating districts.
RATIONALE
Background and History
History of the Modellawas  The Madison Project has been conducting workshops in large cities for about five years. cities include New York, Chicago, Los Angeles and San Diego.
These The
workshops have generally been run during the summer or on Saturdays.
Demonstration classes were conducted by Project staff as examples of how it ought to be done.
Dissemination of the Project's materials was handled mainly through talks by Dr. Davis and films he had made.
Interested people
were welcome to visit Madison Project classes.
The Madison Project was written into the original proposal for the Elk Grove Training and Development Center.
The first year the
model program was coordinated, by Doris Machtinger and Phyllis Ferrell.
During this year, both taught classes at Juliette Low School which were identified as demonstration classes. visitation.
These classes were open to
Together they also taught two workshops on released time
for all the teachers at Juliette Low School and also for interested teachers in districts belonging to the consortium. involved about twentyfive (25) people.
These workshops
During the summer a Madison
Project workshop was set up for sixteen (16) teachers from various districts of the consortium.
Beginning with the Fall of 1967 Doris Machtinger was given full responsibility for coordinating the model program. the demonstration teacher.
Judith Lowe became
The demonstration aspect of the program is
devoted entirely to dissemination of the fact that there is a program called Madison Project Math and that Lhis program is worth adopting.
The training aspect of the model program provides a training program for diffusion of the materials into the schools.
Both the demonstra
tion'and training programs are described above.
There is much written
about the ideal way to teach children and adults including opinions on the interrelationship of needs and climates.
The Madison Project has
taken the position that generally learning of this kind of material takes place best where there is: 1.
general parental and teacher agreement on goals
2.
creative, flexible, welleducated teachers
3.
a very flexible school administration that supports both teacher
it
and student 4.
a nonauthoritarian atmosphere in classroom, school, community and in most of the homes
5.
respect for children as people
6.
general satisfaction of children's needs
7.
mutual respect and affection among all people involved
8.
a general atmosphere of maturity, flexibility, creativity and cooperation in the school and in the community.
Further, the Project has taken the position that learning, i.e., true incorporation, and synthesis of information, is best accomplished
where there is opportunity for discovery.
When this opportunity exists,
there is a chance for the materials themselves to be reinforcing rather than for reinforcement to depend on the pleasing of a teacher.
The Project also has taken the position that the student learns best when he is active rather than passive.
Dr. Davis [1] sums up the
Project's history and impact as follows:
History of the Projct Itself  The Project's earliest exploratory classroom work was done in the academic year 19578 at the Madison School in Syracuse, New York with lowI.Q. culturallydeprived 7th
 10 
graders, under the direction of Professor Robert Davis of Syracuse
University, and Mrs. Jane Downing and Mr. William Bowin of the Syracuse Public Schools.
These children had, in many cases, not
yet learned elementary school arithmetic.
Nontheless,
it seemed
inadvisable for many reasons to teach them remedial arithmetic; for example, they already disliked arithmetic, there was no reason to 1
suppose that repetition of a teaching procedure that had failed in the past would lead to success in the future, these children badly
needed success experiences and a feeling of vitality and challenge in their school work, and arithmetic is, in any case and for any child, a rather isolated small piece of the wide world of mathematics.
Hence, the children were taught portions of algebra and analytic geometry.
Their response was favorable beyond expectation:
they
learned arithmetic (which was, of course, repeatedly required in the alebra and geometry), they learned algebra and geometry, they acquired a new enthusiasm for school (for example, truancy decreased markedly), and they seemed to have modified their personal selfconcepts and aspiration levels.
The instructional procedure was to use "individ
ualized instruction"  students either worked alone, or else in small groups, and the teachers divided their attention among the groups and individual students.
At no time did the teachers attempt to address
the entire class as a total group.
This year might be described as an
attempt by Project personnel to convince themselves that significant improvement in the curriculum was possible. 19589.
Because of the preceding year's success with low1.Q.
culturallydeprived seventhgraders, the Project sought to explore the potential for curriculum improvement with normal seventhgraders, and with normal and bright fourthgraders.
Exploratory teaching during
7
19589 focussed on these groups, in middle class neighborhoods. Unfortunately, at this point the Project's previous use of individualized instruction was lost, and was replaced by teaching via working with the entire class as a total group.
The reason for this was
primarily the involvement of new teachers, not accustomed to individualized or smallgroup instructiou.
The procedure of working with
the total class as a single group remained normal Project practice
until 1963, when various Project advisors (especially Leonard Sealey of Leicestershire, England) reopened this issue.
The year 19589
began the Project's concern for elementary school children, and for normal (or even bright) children. 195962.
In 1959 the geographical focus of Project work shifted
from upstate New York to Connecticut, and Mrs. Beryl S. Cochran of the Weston, Connecticut Public Schools became the dominant Influence on the Project's exploratory teaching.
The Project's efforts acquired,
thereby, some new emphases, which characterized most Project work for the next few years: i)
ii)
iii) iv)
Teaching to the entire class as a single group Preferences for homogeneous grouping within a school Emphasis on working with top groups, in grades 2 through 6 Following the same children for as many years as possible (usually about 5 years)
v)
Use of visiting specialist teacher for mathematics, to work with the regular classroom teacher
vi)
Emphasis on demonstrating that bright children in grades 2 through 6 could learn a very large amount of sophisticated
mathematics (even completing large sections of high school
and collegelevel mathematics)
12
vii)
Extensive study of how these children learned so much, with particular emphasis on creativity and sdiscovery.
The Project's exploratory teaching of this period involved the most sophisticated mathematical content, and the greatest emphasis on creativity, that the Project had ever experienced, and  for grades 3 through 7  these lessons are probably still the most "advanced"
(in these senses) that have been taught by any project thus far.
The
lesson learned here  and recorded on film, audio tape, and in other
ways  that bright children in grades 2 through 7 can learn a very large amount of mathematics in a creative way, and enjoy doing it (in fact, enjoy it immensely), ought not to be forgotten.
The Madison
Project has subsequently deemphasized this aspect, because of the very great difficulty of locating teachers who can teach such classes, but the fact remains:
Much of the mathematics nowadays learned in
high school and in college can be learned easily by bright elementary school children in grades 2 through 6, and the children can enjoy it very much.
At some time our society must pay heed to this unused
potential  particularly in, view of the fact that such matheLatical
experiences are viewed by the children as exciting and pleasurable, not as unpleasant.
These "advanced" classes (especially at Weston, Connecticut) have been studied 1,y Psychoanalyticallytrained psychiatrists (C. Brooks
Fry, M.D., and Carol Fry, M.C.), who have emphasized the children's great eagerness and their unusual absence of anxiety; they have been studied from the point of view of the children's own perceptions and
preferences by the clinical psychologist Herbert Barrett; and they have been studied from the point of view of objective measures of mathematical achievement by J. Robert Cleary, of Educational Testing Service.
 13 
But perhaps most of all the growth of these children over a period of 5 years has been recorded in detail on film, video tape, and audio tape.
One can observe how these children approach problems in math
ematics and mathematical physics.
Their power and their enthusiasm
are impressive.
For these "advanced" classes, it is worth adding that "bright" children means approximately the top third of the entire student population in, suburban communities such as Weston, Connecticut; the overall average. I.Q. for these "advanced" classes is about 120, but this
point should not be pursued in, detail since I.Q. does not seem to
play an especailly decisive role in the achievement of these students. It should not be overemphasized.
It is worth emphasizing, however, that attempts to replicate these results in other schools have not always succeeded.
There is
apparently some combination of attributes in certain schools that makes it possible to succeed in these schools in a way that is not possible in general.
The Madison Project has not succeeded in identi
bying the attributes of a school that make such "advanced" classes possible, and this is probably one of the Project's most regrettable failures.
Project personnel and consultants believe that the attributes necessary for success probably include: General Parental and teacher agreement on the desirability of these goals, and on over all educational goals in general ii)
iii)
Creative, flexible, welleducated teachers
A very flexible school administration and school organization, that supports both teacher and student in every possible way
 14 
A nonauthoritarian atmosphere, in the class, in the
iv)
school, in the community, and in most of the homes
Respect for children as people
v)
General satisfaction of children's needs, including needs
vi)
for physical activity, affection, attention, autonomy, etc.
Mutual respect, and even affection, among all the people
vii)
involved:
parents, teachers, children, and ad"inistrators
A general atmosphere of maturity, flexibility, creativity,
viii)
and cooperation in the school and in the community The identification of necessary attributes is elusive.
None
theless, the fact remains, in some schools, but not in others, it is
possible for "bright" elementary school children to learn a large amount of high school and college mathematics, in a creative way, and enjoy doing it.
No one who witnessed the Weston classes can escape from the feeling that this fact must be important. 1961present.
In 1961 the Project opened a third office, at
Webster College, In Webster Groves, Missouri. At the present time the Project has three offices:
at Syracuse
University, Syracuse, New York; at Weston, Connecticut; and at Webster College.
Since 1961 the Project has cooperated in a variety of teacher
training programs at Webster College, to the extent that new emphases have appeared in Project work:
The major emphasis has been on teacher education, both preservice (college undergraduate) and inservice ii)
In ter s of student selection, the Project began in 1961
working primarily with "ordinary" collegebound students, in "ordinary" school situations, but still with considerable
 15
emphasis (wherever possible) on the use of specialist
mathematics teachers for the intermediate grades. The Project began to be concerned with larger numbers of
iii).
teachers and larger numbers of students, spread geographically over much of the United States (and even in Canada, Australia, England, and Africa).
As a result of the preceding amphases, the Project began to
iv)
distinguish more sharply between tentative, exploratory lesson sequences, and reliablytested stable lesson sequences.
Only the latter were used in largescale teacher education work.
The Project had a number of unsatisfactory experiences in
v)
attempting to work with junior high school students (grades 7 and 8).
Students at this grade level pose especially difficult
problems for curriculum planning; this has been, in general, the experience of a large number of curriculum projects.
Probably much more study of children of this age is needed, together with a far greater effort to use the results of such studies in designing school programs, and in allocating grades among the various buildings (e.g., 84, or 66, or 444, or 633, etc.). 1963present. i)
Beginning in 1963, several new emphases appeared:
The students whom the Project follows for 3, 4, or 5 consecutive years were, of course, getting older and moving into later grades.
Largely as a result of this, together with
unresolved doubts about the program for grades 7 and 8, the Project began to focus considerable effort on grade 9.
scale, the Project reviewed its At the other end of the age
ii)
and exploratory teaching in nursery school, kindergarten, desultory and grades 1 and 2  which had until then been
systematic attack on disorganized  and began a concerted this grade level. exploratory teaching of mathematics at following returns to earlier Perhaps most important are the directions:
work with culturallydeprived The Project began largescale
iii)
and in Chicago, with unexpectedly urban children, in St. Louis gratifying results.
by Leonard Sealey of LeicesterThe Project, stimulated in part
iv)
original interest in individshire, England, has renewed its procedure of dividing a class ualized instruction and in the "committees" or "small groups" of of (say) 30 students up into about 3 or 4 each.
seldom if ever In either case, the teacher
the entire class. stands at the front of the room and addresses for a while, then Instead, the teacher sits' with one group
moves on to another, etc. let students work alone or Finally, as a result of the desire to
combine some mathematics with some in small groups, of the desire to to reach "non  verbal" children whose and of the desire physical science, function naturally in a world of ability may be great but who do not the 'Project has acquired another and abstractions, verbal behavior
emphasis: v)
to its effort to produce The Project has given new impetus
form of a library of "individualized study materials," in the experiments, mathemat"shoebox" kits for various scientific
ical puzzles, etc.
 17 
PURPOSE
Basic beliefs underlying the philosophy of the Madison Project are the following: 1.
There is a need to broaden and expand the scope of the existing math programs to incorporate more areas of math than usually found in the arithmetic programs.
The Madison Project materials
will broaden that base. 2.
The traditional teaching of math has tended to focus more on students' failures and weaknesses than their successes. children lack all important success experience.
Thus
The Madison
Project materials will provide the success experiences necessary for learning and a general good attitude toward math. Axe
The Madison Project model program provided the following promises. for educational change: 1.
By providing teachers a chance to be exposed to this material and helping them use it in their classroom, we are beginning to induce a change on the curriculum in mathematics.
2.
By providing training for teachers on a released time basis
we are asserting that continued education is an essential part of today's teaching and should be included in, not added to the existing work Riad. 3.
By emphasizing the assisting role 'for the teacher in place of
the directive instructing role, we are making a subtle change in the whole social climate of the classroom directed at
making school a more human place and pleasure rather than a chore.
This change will be essential considering the trend for
students to spend more and more of their life in school.
 18 
The objectives of the model program, as originally formulated,
were divided into two categories, demonstration and training.
The
behavioral objectives of the demonstration were: 1.
Visitors to the program would talk to collegues about their experience.
2.
Visitors would order the Madison Project materials.
3.
Visitors would provide a source of people for workshops
The behavioral objectives of the training program were: 1.
Teachers Would be able to perform specific Madison Project skills.
2.
Teachers would be able to teach the Madison Project materials.
3.
Teachers would teach Madison Project materials in their classroom.
4.
Teachers would transfer the relaxed, discovery type low pressure technique inherent in the Madison Project lessons to other subjects.
5.
Teachers would open their classes to their collegues.
6.
Teachers would merge Madison Project lessons with regular work.
The objectives of the training program stayed the same throughout the three years, bolt the objectives of the demonstration program shifted.
The demonstration program served as a service to the Northern Illinois area to provide an opportunity for the community to see an operating model of a Madison Project program.
It's objectives were to publicize
the existance of the program and deploy its materials, not to get participants in the workshops.
Relation'of the Model Prsoram to the Basic Questions of T 6 D A major portion of the training program was devoted to encouraging participants to expose and study, openly and objectively, their own behavior.
Ass Madison Project lessons were "practiced" by each teacher
with the aid and support of three other teachers.
These "practice"
lessons were critiqued, often with the aid of the s'lander's Interaction
 19
Analysis Scale and audio and video tape.
Further, teachers in the
program were encouraged to demonstrate the new materials with their collegues and discuss with them their new techniques. The whole format of the Madison Project materials is such as to imply.a change in teacher role.
These materials are discovery materials
and not 'conducive to the traditional paradign of: teacher
to student ,i0back to teacher.
Information 0 to
The materials are informa
tion laden, the teacher serving only as a catalyst for studentmaterial interaction.
The specific skills teachers learned in the Madison Project program are:
Pebbles in the bag Postman stories
Tictactoe
Graphing lesson: Et +A= 12 Graphing lesson:
3 x
+ 1 =ia
Guess the function Quadratic equation lesson Area with geoboards
Area equation on graph Tin Foil geometry The effects of the program on students is both obvious and subtle.
Obviously the students will have mastered those skills which their teachers present to them, hopefully the same ones mentioned above.
More subtle is the question of attitude and transfer of learning. It is hoped that their attitude toward math will become more optimistic,
that when they are faced with a mathematical problem, they will assume
they can solve it rather than that they will fail.
It is also hoped
that they will begin seeing math as a tool to help shine light upon other disciplines.
Lastly, it is hoped that they will love math for
its own intrinsically captivating self  derive pleasure from the
discipline in the abstract without additional rewards.
ACTIVITIES
Demonstration
During the three years of demonstrating the Madison Project Math materials for the Elk Grove Training and Development Center the following activities were used: 1.
Orientation
2.
Observation
3.
Participation
4.
Discussion
The initial orientation was a very brief, sketchy description of 'the Madison Project Math materials.
The interest of the participants
encouraged us to extend this to a very detailed description of the history of the program and its materials.
The initial demonstrations
had a long observation period in which the visitors watched as many as five halfhour classes.
Their apparent boredomindicated
by glassy
eyes and frequent yawning, encouraged us to shorten this observation period to one twentyminute session.
This proved to be long enough to
give credibility to the claims made about the materials during the orientation.
Initially there was no opportunity for participation since most of the time was being spent on observation of demonstration classes.
We noticed during the brief orientation period that our visitors were hesitant to put down the manipulative material and often made us late to the demonstration classes.
When we changed format we made this
experience with the manipulatives an integral part of the demonstration program.
 22
Under the original format our visitors were so tuckered out after hours of observation that they had very little to say.
Under the latter
format, after hearing about the Madison Project Math, seeing it demonstrated and experiencing the materials, the visitors were eager to react to what they had seen and experienced.
They were encouraged to consider
the implications of the material in their home setting as well as its implications generally.
IERiakIK The following activities were used in the training programs of Madison Project Math:
Presentation Independent manipulation of materials Independent study
Microteaching Critiquing Group dynamics games Xerox listening course Simulation materials (SRA)
The Madison Project Math materials were presented to the teachers in the same way as they would be presented to the students.
The teachers
then practicetaught these materials before a group of their peers using a small group of students. teachers.
These lessons were then critiqued by the
Each teacher had the chance to teach four or five times during
each workshop.
This gave the workshop leader a chance to help the teachers
clear up areas in the presentation that may have been hazy and gave the teachers a chance to try out the new materials with help and guidance before they went back to their own classrooms.
23
During all the workshops
teachers had the chance to manipulate the independent exploration material for themselves, following the included instructions so that they would know what the students were going to experience.
In two
of the workshops time was provided for the teachers to pursue interesting projects in depth themselves with the workshop leader serving as a resource person.
In some of the workshops group dynamic games, such as the NASA
game, tinker toys motivation game, and the trio process observation were used.
These were used mainly to expose participants to situations
in which they were forced to notice their own behavior patterns.
It
was hoped that they could perhaps relate their behavior in those groups to their effect on children.
It was also hoped that they would develop
a deeper, more trusting relationship with the teachers in their critique groups, thus making the critique experience more real and more in depth. In two workshops the Xerox listening materials were presented.
The pre and post tests included with this showed a 100% improvement for everyone but we questioned its transfer value when not listening to Xerox listening tapes.
The SRA simulation materials were used in most of the workshops. These were used mainly to get teachers to start talking to one another on how they handle problems in their own classrooms.
This opened up
discussion on goals, appropriateness of gcals and in general provided teachers with a chance to reevaluate their own basic values and beliefs in education.
Dissemination
The activity most often used to disseminate Madison Project Math program was a personal visit to the superintendent to describe'the materials.4
24
and see if the district would be interested.
Occasionally a presenta
tion was made to an administrators' meeting, or a group of teachers on Institute Day.
Other Activities
During the three years of the program three large group meetings were held.
These were held to provide teachers the apportunity to hear
"great" men and their. ideas.
The first of these meetings featured
author John Holt, the second, the Director of the Madison Project, Dr. Robert B. Davis and the last, author Niel Postman. T_
echniques
It is difficult to separate activities from techniques.
I have
designated the things the participants did as activities; the things the Model Program, Coordinator did were techniques.
used in demonstration were quite elementary.
The techniques
The demonstrator listened
and tried to ascertain the visitors objectives in being there, then responded accordingly.
During the training sessions the techniques used included various degrees of lecture, personal experience and confrontation. interesting technique developed WAS the microteaching.
The most
For this
technique, modified from its form as conceived by Dwight Allen at Stanford University, teachers were divided into groups of four.
One
member of the group presented a concept to four or five students while the others watched.
If the teacher doing the presenting got into trouble
the other teachers helped out. (The mood was kept very informal.)
The
other three teachers in the group watched the presentation, often did a Flander's interaction analysis on the lesson, an analysis of questions asked and kept record of anything else the group felt was of interest.
25

After the lesson the group critiqued the lesson, concentrating on the method of presenting the new materials and the interaction with the children.
A suggested list of questions for discussion is included
in Appendix B.
EVALUATION
Formative Evaluatioll
The formative evaluation process of the Madison Project Math was basically twofold.
First, data was gathered from each workshop partici
pant and second, visitors to the demonstration school were asked to complete an evaluative form.
The evaluation procedure for the workshops initially consisted of a content and process test and subjective comments pertaining tO''specific asked items.
This data, particularly the mathematics skills test for the
participants, was deemed of little value for it failed to provide pertinent information to the stated objectives. were changed.
Accordingly, the procedures
Throughout the program different techniques were tried.
The last of the formative evaluation consisted of pre and post measures of participant competencies for each of the Madison Project Math lessons, a "This I Believe" measure affording each participant an opportunity to
express philosophical beliefs concerning the teaching of mathematics and a general comments statement from which reaction to each workshop was determined (See Appendix C for forms).
Other evaluative techniques were employed during certain of the
workshops in an effort to gain different formative data.
These techniques
included a pre and post measure of a derivation of the "DrawAMan" test
and pre and post workshop audio tape analysis.
The modified "DrawAMan"
was used in an effort to determine any modification of the teacher's perception of his relationship with students as a result of the workshop. This technique was perhaps the most meaningful of all techniques tried,
but was discontinued because it was too expensive.
The audio tape analysis
was employed to ascerta3n any major changes in teacher classroom verbal behavior after completioa of the Madison Project Math Workshop.
27
The feedback from the formative data was analyzed for each workshop.
One of the major changes introduced early in the program as a
result of this data was,
the inclusion of children as an integral part
of the learning experience of workshop participants.
After presenting
the teacher partidipants with specific lessons, the teachers had an
opportunity to immediately try them with childen.
This practice enabled
them to ascertain the specific aspects of the lesson that needed strengthening or to clarify any questions that arose as a result of actually teaching the lesson to a group of students.
Early results indicated that the optimal group size was 16, so an attempt was made to keep workshop enrollment around this number. There was no question but that the most productive use of time
resulted in the workshop that met everyday as opposed to once a week. After Fall, 1967, therefore all workshops were conducted on this basis. Indications from the formative data were that a catalyst was necessary to promote "groupness" and group dynamics games were incorporated into the workshops after Fall, 1967. Requests for Madison Project Math workshops were so numr'rous that the Model Program Coordinator could not fill the demand.
Beginning in
Spring, 1968 an effort was made to train some people to be able to conduct their own workshops.
At least 7 Madison Project Math workshops have been
conducted by those trainees.
The major summative evaluation focus has been upor the training of workshop participants. ipants.
A followup questionnaire was mailed to 154 partic
Responses were received from 120 or 78%.
The information gathered pertained to the following basic questions related to the attainment of the basic program objectives: 1)
the extent to which participants actually have or have not employed
 28 
the Madison Project Mathematics activities in their classrooms. 2)
possible reasons for not using the activities
3)
the extent of student understanding of each activity
4)
degree of confidence expressed by each participant toward his ability to teach the Madison Project Math activities
5)
the extent to which teachers who have not attended a workshop have evidenced an interest in attending such a program
6)
the extent to which workshop participants have discussed Madison Project Mathematics with other jeachers about the program
7)
the extent to which Madison Project Mathematics materials have either been purchased or constructed by schools
8)
the attitude of workshop participants toward the adequacy of their personal mathematics preparation for the program
9)
a general rating of the value of the workshops of the participants
()Iterations
A total of 21/i teachers and administrators participated in the
Madison Project Math workshops.
Complete list is on file.
A total of 264 educators visited the demonstration sessions.
list is also on fil, Various means were used to collect data.
They included:
1)
Summative questionnaire (Nov.., 1968)
2)
Formative Questionnaire (post test, all workshops)
3)
Content & Pedagogy Test (post test  1 workshop)
4)
DrawAMan test (pre & post test  2 workshops)
5)
This I Believe test ( pre & post test  2 workshops)
6)
Audio tapes (pre. & post  1 workshop)
7)
Brickbats & bouquets (every second day  all workshops)
The forms are compiled in Appendix
29 
This
Treatment of Data 1)
Content analysis was applied to the "This I Believe" data in an effort to ascertain changes of beliefs toward the teaching of mathematics
2)
Chisquare analysis was applied to the formative questionnaire to determine changes in competencies to use the Madison Project Mathematics activities
3)
The summative questionnaire, being descriptive in natures was
tabulated and cumulative results reported. 4)
Content analysis was applied to the audio tapes in an effort to determine changes in the verbal behavior of the workshop participants
5)
the pre and post measures of the modification of "DrawAMan" test were analyzed by a trained psychologist for observable alterations of behavior
Sumary of Findings The extent to which workshop participants have used the Madison Project Mathematics activities is reported in. Table 1.
The activity
used most frequently was Tictactoe (101) while the area equation on graph was'used least (18).
Table 2 presents the opinion of the teacher participants regarding the understanding by their students of the various Madison Project Mathematics activities.
As can readily be determined, the teachers were of
the opinion that the activities were, by and large, very well or well understood.
Few teachers indicated a poor understanding on the part of
students while no teachers reported very poor understanding on the part of the students.
30
Tictactoe
Postman stories
Pebbles in the bag
=4X
geometry
Tin Foil
.
Area equation on graph
geoboa rds
Area with
lesson
Quadratic equation
Guess the function
3x 0+ 1
lesson
Graphing
1axe 12
lesson
Graphing
"..=MO!........e.11.1011.11.0...111.1.111....+,1pro
I
I
ft
22
58
WI
80
have used I have not used but intend to do so
..59
I
16
22
the grade is inaeprosiriate
15
like the lesson '
cont
the materials are unavai;able
I have not used and do not intend to do so because:
CHECK THE APPROPRIATE SPACES
TABLE
6
5
2
4
7
..,..1.1111111MOT,
e..Fc....
2
4.
other
iver oorly # 1
24
57
42
8
did not use this
75
79
Tin foil geometry
equation
on graph
Area
38
19
poorly
Area with geoboards
31
83
49
well
69
I
I
well
lesson
Quadratic equation
Guess the function
3x0+ 1 *LN,
lesson
Graphing
Graphing lessor +,64 = 12
Tictactoe
Postman stories
Pebbles in the bag
ver
n my opinion most of the students understood these activities:
CHECK THE APPROPRIATE SPACES
TABLE 2
Table 3 presents the responses of the teachers when asked about their ability to use the Madison Project Mathematics activities with the children.
For no lesson do the insecure, very insecure responses
outnumber the very confident, confident indications.
There is, however,
considerable variance with regard to confidence in the ten different activities.
It can be noted that the two activities which the teachers
indicate to be the ones with which they are insecure are those which were listed as being used least frequently (quadratic equation lesson and area equation on graph).
The workshop participants were next asked whether or not they were
aware of other teachers in their building who had not attended a Madison Project Mathematics workshop that wanted to use Madison Project Math. Of the 120 who responded to this question, 72 or 60% said "yes" and 44 or 36.6% replied "no".
Four or 3% offered replies but did not respond
either "yes" or "no" to the question.
The Mason Project workshop participants were next asked whether they had talked to teachers responsible for teaching mathematics in schools other than their own about Madison Project Mathematics.
Eighty
two (68.3%) replied "yes" to the question while 38 (31.7%) responded "no"
Actual materials purchase or construction by the workshop participants was deemed to be rather good evidence of the degree of commitment to Madison Project Math,
Table 4 displays this data.
The participants next were asked whether or not their math background was sufficient to enable them to participate effectively in the workshop.
One hundred fifteen (95.8%) indicated that their mathematics
background was sufficient whereas five (4.2%) replied that it was not. In conclusion, the teachers were querried as to the overall value of the workshops to them.
Sixtyone (53%) replied that the Madison
Project Math workshops had been highly beneficial; fiftythree (46%)
33
54
25
35
Area equation on graph
Tin foil geometry
=A
81
84
confident
Area with geoboards
lesson
Quadratic equation
Guess the function
3x0+ 1
Graphing lesson
lesson
Graphing
Tictactoe
Postman stories
Pebbles in the bag
ver
1
t
46
16
33
27
confident I
f insecure I I
12
9
1
1
very insecure
How do you fee 1 about your ability to use these activities with children?
voacmcLV401.11.1010..r.mill.",...c
CHECK THE APPROPRIATE SPACES
TABLE 3
..,
TINIIIIL
......,.
..........................mmree...;*
TABLE
4
Number of Schools Making Some
Number of Schools
Workshop Date
Purc192LETILpment
Pan.1114.4.41.....1.*.I.N.,
6/21  7/21/67
11
13 4.1,14., g4001.0...1.1,1
Nate .14,1001. MI/MX .1.1.0.00...41 0.0401.
10/67  1/68
ono ono
do
V4WINII
4
3/5  15/68 r
it
4/15  23/68 ./.004,40094V,041grni. 441011,1001.A0 WAISF
0/ II,Lon V eV
iernayfp
4110.40r 4004i*
on4111.,440
I 0.,01 0M1 WInborMWIA.041614.4.0.10..101il
010.04~40.0./.40.004.......10.004bigifiihMOMNIO 0/04..hilliileiMainEddinii0
/0040 MY/404
6
6 06/".04
00.0.0.104..4I1614104Ma4;01.
10
13
7/12/68
1110AVOMMIN.V.oulaV444444.4140v0.44.4.,4044****.
6/24  7/9/68 0,1,4(.04,41.44144.4.1.11
0,
44
14
5/3/68
41111060,*111..0014.1M,01V.0101/
11
11
mu, Y rwl,V4v,,
6/24
',too..., a. r
9
12
.11Movio4p,oalovs,..
4/22
0.
e
o,
.0, rm..... 0,,
...........WfmoOM....0440..or{.
VII
30
39 "44IFIN
10/7  11/68 4444.4III40.44.444144.4101.1oVarvION4(4....4.4.,.V.444
o, lv....+0,,,, row*
V
10
10
l 44,444.A.ov*.,*
35
vo,20.104
*v.
4...IWON01000.11011710.10010.10100
noted that it had been beneficial and one (1%) replied the workshop had been of little value to him.
In summary of the 154 workshop participants 120 responded to a questionnaire.
The data appears to indicate favorable responses
to the Madison Project Mathematics workshops.
More specifically, the
data suggests that Madison Project Mathematics has transferred from the workshops to the classroom where, it is being used by the teachers:
that children appear to understand the activities; that teachers are generally confident in their ability to teach the activities; that the participants have discussed Madison Project Mathematics with their colleagues; and that other teachers are desirous of training in Madison Project Math; that commitment to Madison Project Math is evidenced by the acquisition of necessary materials for teaching and finally that those who participated in the workshops were of the opinion that the program was beneficial to them.
The basic questions of the Elk Grove Training and Development Center are related, to two basic concepts  changing role perceptions
and teacher behavior and the acquisition of specific skills by the participating professionals.
While Madison Project Mathematics was concerned with both of these facets, the one most readily measured was that dealing with skills acquisition.
The gaining of additional requisite skills and techniques
for the teaching of mathematics was a prime concern of the Madison Project Math workshops.
The summative data suggests that these tech
niques and skills are being employed in the classrooms.
Ultimately the
impact of this instruction will be evidenced from the large numbers of children to be exposed to Madison Project Mathematics.
If one multiplies
the number of workshop participants by an average classroom size (30
 36 
pupils), some 6000 children will be effected by Madison Project Math per year
When this, in turn, is multiplied by the number of years
teachers will be involved in the teaching of mathematics, the number of students that may be effected by the Madison Project Mathematics program becomes significantly large.
describIn writing recommendations, one is always torn between ing the unattainable ideal situation or the practical alternative that 'accomplishes the goals. fine.
On a practical. level, the program ran
The demand for workshops was more than the budget allowed.
Since I fully endorse the released time format, one recommendation
would be either more money for released time or more matched funds from the districts for the same purpose.
The area of evaluation is one area that presents sticky problems. There is a need for more illuminating techniques In three areas. main evaluation done has been called, formative.
The
However, in fact,
each this formative evaluation, was really summative with respect to workshop.
There is a need to develop unobtrusive techniques to help
well as make plans for a workshop leader make daytoday decidions as the next workshop.
The technique used for the summative data relied entirely on answers to questionivaires.
There is no data about "how well" a teacher
teaches the lesson she reports she is teaching.
Techniques need to be
developed for this purpose.
Lastly, this program did not evaluate the effect of the program on the children.
Minimally, attempts should have been made to demon
hindered by exposure to strate that the children's performance was not these materials.
Once this pessimistic outlook was dispensed with, an
attempt should have been made to show that childrents performances were enhanced and their attitudes toward math improved.
Tools to do these
jobs also need to be developed. I must point out that the Elk Grove Training and Development Center provided an excellent staff of supportive, compassionate coworkers.
Admin
istrators were always to be counted on for support if a problem came up. 38
REFERENCES
1.
Davis, Robert B., A Modern Mathematics Program as it
Pertains to the Interrelationship of Mathematical Content ing Methods and Classroom Atmosphere.
Teach
(The Madison Project)
Cooperative Research Project No. D093, of the Office of Education, U.S. Department of Health, Education and Welfare. sity  Webster College.
1965.
39
Syracuse Univer
ABSTRACT
The Madison Project Mathematics is a program that was imported from outside the local area by the Elk Grove Training and Development Center.
This math program is best described as supportive and supple
mentary.
It assumes the content of the basic programs and takes this
content one step further.
The Elk Grove Training and Development Center offered workshops and a demonstration program in the math project from January, 1967 through June, 1969.
The Model Program Coordinator was Mrs. Doris
Machtinger; Demonstration Assistants were Mrs. Judy Lowe and Miss Michaelene Palac; 264 educators visited the program; 214 teachers and principals took part in the workshops.
The visitors came from all
over the United States, Puerto Rico, Equador and other countries. Workshop participants were mainly from the local area.
However,
Madison Project Math has been incorporated in the curriculum as a result of this program in such distant places as Charleston, Ill., Evanston, Ill., Wilmette, Ill., Fish Creek, Wis., Columbia, Neb., Corpus Christi, Texas, and Grand Forks, N.D.
It is estimated that
at least 6000 children a year will be exposed to Madison Project Math lessons as a result of this progra
.
All the school districts cooper
ating made the minimal commitment of ordering the materials besides sending teachers to the workshops.
The demand for Madison Project
Mathematics is still high in this area.
It is only regretful that
funds are not available to continue this program.
APPENDIX A
Chronological Overview
WORKSHOP PARTICIPANTS
DATE
LEADER
6/21  7/21/6
Doris Machtinger
NO. OF PARTICIPANTS 16
NO. OF SCHOOLS IN DIST. #25 #59 Par. #15 #25 #59 #65
7
5 2
10/671/68
3/415/68
Doris Machtinger
Doris MachtInger
21
16
4 6 4 1 4 3 2
4 6
4/1518,23/68 4/225/3/68 6/247/12/68 (Leadership)
Bernice Gliege Miriam Gulesarian Doris Machtinger
8 10
7
'16
2 1 1 2 2 1
8
7
6/247/9/68
Michalene Palac Rosalyn Hefner John Kropp Jessie Valerio Joy Lutsch Arlyle Ferguson Jerry,Garr
71
6 3 1
6 12 4 5 2 7
2
10/7/11/68
Doris Machtinger
16
1 4
4
11/1822/68
Jerry Garr
12
11/1826/68 12/26/68
Peg Aiman Carl Seltzer
10 15
1 2 1 1 8 1 7
2 7
1 3
#428 #21 #25 #54 #57 #25 #428 #15 '#25
#54 #59 #65 #116 Par. #15 #21 #23 #25 054 #57 #59 #65 Par. Wis. #21 #25 #54 #59 #65 #15 #23 #25 #65 #21 #39
#54 #57 #65
APPENDIX
B
Syllabi Followed in the Workshop
ELK GROVE TRAINING
&
DEVELOPMENT CENTER
DISCUSSION GUIDE
Questions to be answered in group discussion by people observing the lesson.
1.
What content was covered:
2.
What techniques were used?
3.
Which kids responded to which parts of the lesson?
4.
Describe the behavior of each childA
5.
Speculate on how much each child got out of the lesson.
6.
Who enjoyed the lesson the most?
7.
Who seemed to enjoy the work the least?
What problems arose?
9.
How were they handled?
Why?
Why?
Discussion Guide Page 2
10. How else could they have been handled?
11. Will the problem be a problem for tomorrow's teacher?
12. How will it be handled then?
13.
(For this lesson's teacher to answer) again, what would you do differently?
If you could do this lesson over
14. What was the best part of this lesson that you will repeat if you can?
15. What is the lesson going to be tomorrow?
DM/ce
a.
Content
b.
Special action with respect to special problems.
6/12/68
11
JUNE
#54  S.P.A.
MONDAY, 1ST
MONDAY, 24TH
,
#54  Davis Film
MONDAY, 8TH #25  S.R.A.
WEDNESDAY, 3RD
#54  Cuisennaire Rod Film
#54  Video Tape
TUESDAY 2ND
#57  Video Tape
#25  Davis Film
#57  Cuisennaire Rod Film
#25  Cuisennaire Rod Film
TUESDAY, 9TH
FRIDAY, 28T1f
TUESDAY, 25TH
THURSDAY, 27TH
WEDNESDAY, 26TH
CALENDAR
I
I
#57
Graphing Introduction to Geoboards
+3 4
Graphing
#54
3 xri
More graphing
#25
Dist.
Postman stories Addition
TicTacToe Number line Pebbles in the bag
#57
DAY 6
Postman stories Addition, Subtraction & Multiplication
TicTacToe Number line Pebbles in the bag
#54
Graphing Geoboard area
Geoboards
Geoboards & Graphing
DAY 7
Guess the function
Postman stories Addition & Subtraction
Number line TicTacToe Pebbles in the bag Pet Shop
DAY 2
#25
Dist.
DAY 1
Tinfoil geometry 5 sq. geometry Paper folding
Graphing Geoboard area
Shoeboxes & Paper folding
DAY 8
Postman stories Multiplication Quadratic equations
Quadratic equations
Postman stories Multiplication Open sentences
DAY 3
Shoeboxes Pattern game
Tinfoil 5 sq. geometry
Tinfoil 5 sq. geometry
DAY 9
Film and rods
Guess the function Pattern game
Guess the function Quadratic equation
DAY 4
I
T
,6
Mop up
Paper folding Shoeboxes
Mop up
DAY 10
Graphing and variations of TicTacToe
Graph a +6=
3 x 0 + 4
0+6= 9
Graph Introduce
*DAY 5
2:30
2:00.
1:00
12:00
11:30
11:00
10:00
9:00
x
Critique
Microteach
Break
+
Postman
Lunch
Critique
Microteach
_
Coffee Break
Trio, leveling, trio
#
P.I.B.
MONDAY
Finite differences
NASA Moon Game
Guess the function Open sentences Quadratic equations
TUESDAY
.

Harder graphing
.
Men Haar Hoolim
Easy graphing
WEDNESDAY
.
_
.._
i'
ESS & L.c. kids
Graphing
&
Tin foil geometry
IIIIIIIIIIIIIIIIIIIIIIIII
1
.
11
Geoboards
T
Bring in other games
..,.....
Gattegno Film
Shoe boxes
a;V
Real math
Kids & Critique
Kids & Critique
Use of Inservice package
1.003:00
3:004:00
_
Adult Simulation
Graphing & Geoboards
_
_
Trio, leveling, trio
P.I.B. #
10:20
9:00
3:004:00
1:003:00
10:15
9:00
MONDAY
1
1
I
t
!
..,..
package
Use of In service
Kids & Critique
Tinker toys for motivation
Graphing & Geoboards
Math
1
WEDNESDAY
,lt*,,...,NLY.,',..11....71...a
Use of Inservice package 
Kids & Critique
Xerox listening material
Xerox listening material
2:45
Baughman
Kids & Critique
NASA
Guess the function Even and odds
,ele.r.1.............a.......... t
Kids & Critique
SRA
Postman Even and odds
TUESDAY
it
Kids & Critique
Plans for own worksho
5 square geometry
.
Content Rules for "Guess the Function"
....T.C",".
1
1
1
Microteaching 3
Graphing
FRIDAY
Kids & Critique
Luncheon
Puzzling Gattegno film Evaluation
Lab  shoeboxes
joo...mr.ssm...wk,
4
rt
1
.".'""...4"'"''"F......""'.."""'."4.'''''"""e"P"'' 1
Kids & Critique
It
Ideal School Conference
THURSDAY
APPENDIX
C
Evaluation Instruments
DATE
NAME
POSITION
Please indicate how you feel about the effectiveness of the following parts of your visit to the Madison Project Math Program:
1.
Orientation
2.
Envolvement (opportunity to work with the shoe boxes)
3.
Classroom visitation
4.
Debriefing session
In order to get soma Seelingforvhatarethemostvaluabletype of Madison Project experiences for teachers, we need some data on the use of these mateials in classes. Would you please fill out the following questionnaire and return it to me? Thank you. W ta
0 td
I
0 11
04 Please check the appropriate columns. You may want to put in more than one
v
o rd
44
.2 g
4 I> :',
A 4)
a)
§1
r044 1.4
check.
0 13 V
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,..r...........
Tictactoe .............,.
Pebbles in the Bag .......
Postman Stories
Guess the Function
_____ ..............,
G:mphing
i +,f
I
\
No. ,
1
..._.
Graphing
'
1+ M /
Geoboards
Shoeboxes
Any anecdotes or comments you think may be useful
.....
(312) 259.8050
Recently we had the pleasure of meeting you and demonstrating for you the Madison Project Mathematics materials. As we discussed during your visit, the coordinator of the Madison Project model program is available to offer consultant services for this program. We are interested to know if we can be of any further help to you. In order to ascertain our effectiveness as a demonstration program, we need to have some information from you. Would you be kind enough to fill out this information sheet and return it to us. Thank you.
Sincerely yours,
Doris Machtinger, Madison Math Coordinator DM/ce Encl.
LEADERSHIP IN NEW EDUCATIONAL DIRECTIONS, A TITLE III PROGRAM OF E.S,E.A.
ELK GROVE TRAINING
&
DEVELOPMENT CE"NTE"R
Madison Project
1.
Did you use any of the methods and/or materials presented in the Madison Project demonstration before you saw the demonstration? Methods:
Yes
No
Materials:
Yes
No
Not sure e.semommoINNalao
Not sure
If yes, which ones?
2.
Have you talked to any of the following persons about your visit to the Madison Project demonstration and the things (methods, materials, ideas) you saw and heard? '(Check those persons you talked with) principal
superintendent
teacher 0111011101011111111111110
other
school board member
curriculum coordinator (Please specify)
have not talked to anyone 3.
Have you started to use (are you using) any of the ideas and/or materials presented by the Madison Project demonstration? Ideas:
Yes
No
Materials:
Yes
No
If yes, which ones?
4.
Do you plan to use any of the ideas and/or materials presented by the Madison Project demonstration? Ideas:
Yes
No
Not sure
Materials:
Yes
No
Not sure
If yes, which ones?
Madison Project
Page 2 5.
6.
7.
Would you like to consult with the Coordinator to help you implement and/or discuss the program? Discussion:
Yes
No
Will let you know
Implementation:
Yes
No
Will let you know
Do you feel your ideas about teaching and methods of teaching have been changed as a result of visiting the Madison Project demonstration? Ideas:
Definitely changed
1
2
3
4
Definitely NOT changed
Methods:
Definitely changed
1
2
3
4
Definitely NOT changed
Materials: Definitely changed
1
2
3
4
Definitely NOT changed
Comfients (suggestions, criticism, etc.) and/or questions you have concerning the Madison Project program?
DM/ce 11/28/67
Grade
like 3 x1:1+4 =4
Graph equations
like CI 441 pg 7
Graph of equations
Quadratic Equations
from given data (What's my rule?)
Wite an equation
Multiplication of signed numbers
Addition & subtraction of signed numbers
......___

I can do this myself
appropriate columns.
Please 'check the
Plotting points on a graph
DIRECTIONS:
'Leader' s Name
Workshop
Wstrict
School
Name
.
I know about it but I can't do it myself
....
.
I don't know what you mean by this
.
I know it well enough to teach
MADISON PROJECT MATH CONTENT QUESTIONNAIRE
it.
ELK GROVE TRAINING
&
DEVELOPMENT CENTER
MADISON PROJECT EVALUATION SHEETS
Name
Grade you teach
School
Workshop leader
Length of workshop
Dates of workshop_
DM/ce  9/30/68
34:1 +
Graphing lesson
Tin foil geometry
geometry
5 square
Area equation on graph
Area with geoboards
Quadratic equation lesson
ve.OV,.
411100400
e, .0YMb
do
0.111111
I cannot
i will do I will no; do
like
I do not
CHECK THE APPROPRIATE COLUMNS FOR THE FOLLOWING MADISON PROJECT LESSONS
If kids were available for testing the new materials, please comment on how you felt initially and how you feel now about this experience:
General comments about this workshop:
ELK GROVE TRAINING
&
DEVELOPMENT CENTER
Madison Project Math
BOUQ
ETS
BRICKBATS
MADISON PROJECT MATH WORKSHOP
1.
I
believe this about students' ability to perform in math:
2.
I
believe this about students' attitudes toward math:
3.
I
believe this about the best classroom climate for teaching math:
4.
I
believe this about the best kind of grouping for teaching math:
5.
I
believe parents feel like this about modern math:
6.
I
feel like this about modern math:
DM/ce  10/1/68
1 L,;;Tokii, Trm
mod
ioq
Po4,10(2m4,46/i/olr
1706 West Algonquin Rd., Arlington Heights, III. 60005
(312) 2598050
December 18, 1968
Dear Madison Project Workshop Participant;
The Elk Grove Training and Development Center is trying to put together a comprehensive evaluation report of the effectiveness of its programs. We very badly need your cooperation in our effort to help supply what data we can. Please help us by filling out the enclosed questionnaire and returning it immediately. Thank you.
Sincerely yours,
h
nger, Coordinator Doris Mac Madison Project Math DM/ce Encl.
LEADERSHIP IN NEW EDUCATIONAL DIRECTIONS, A TITLE III PROGRAM OF E.S.E.A.
I.
Tin Foil geometry
Area equation on graph
Area with geoboards
lesson
Quadratic equation
Guess the function
3x 1:3+ 1 =2N
lesson
Graphing
0+,41= 12
Graphing lesson
Tictactoe
Postman stories
Pebbles in the bag
.
_...
TI have used
I have not used but intend to do so the grade level is inappropriate I
don't like the lesson
the materials are unavailable
I have not used and do not intend to do so because:
CHECK THE APPROPRIATE SPACES
other
.
....
Tin foil geometry
Area equation on graph
geoboa rds
Area with
lesson
Quadratic equation
Guess the function
3)cl:1+1=A
lesson
Graph in
0+4 = 12
Graphing lesson
Tictactoe
Postman stories
Pebbles in the bag
ver
well
,
well I
Poorly
..
very poorly I
did not use this
In my opinion most of the students understood these activities:
CHECK THE APPROPRIATE SPACES

......._.
=1.1
Tin foil geometry
Area equation on graph
geoboa rds
Area with
Quadratic equation lesson
Guess the function
3x0+ I
Graphing lesson
lesson
Graphing
Tictactoe
Postman stories
Pebbles in the bag
very confident confident insecure
very insecure
How do you feel about your ability to use these activities with children?
CHECK THE APPROPRIATE SPACES
IV.
am aware of other teachers in my building who have not attended a Madison Project Math workshop who want to use Madison Project Math. I
Yes
V.
have talked to teachers responsible for teaching mathematics in schools other than my own about Madison Project Math. I
Yes
VI.
No
No
Please check those materials your school has purchased specifically for Madison Project Math activities: Geoboards Peg games Shoe boxes
Teacher's edition of Discovery Test Teacher's edition of Exploration Test Student's edition of Discovery Test Student's edition of Exploration Test Other games commercially available seen at Madison Project workshop.
VII.
.V111.
Briefly comment on the reaction of the children to the Madison Project Math
Was your math backgrounu sufficient to enable you to participateteffectively in the workshop? Comment:
Yes
No
X.
I
feel the Madison Project Math workshop was: Highly beneficial
Of little value
Beneficial
Of no value
School Level
Name
I
teach or
Date of workshop attended
.11.1111Pt7IM,L,,T,
MADISON PROJECT MATH
Fol low Up Questionnaire
In an effort to continually examine our Madison Project Math program we are asking those teachers who have participated in the workshops to provide us with current information. It is our belief that such information obtained after you have had an opportunity to return to your classroom and try some of the activities will be most helpful to our ongoing evaluation.
Please provide the information requested and return the questionnaire in the selfaddressed envelope by
Many thanks for your help in this matter!
Sincerely,
Doris Machtinger, Coordinator Madison Project Math DM/ce Encl.
APPENDIX
D
Consultants to the Program
DIRECTORY OF CONSULTANTS
John Holt
Neil Postman Judith Lowe
Gerald Baughman Robert B. Davis
0
APPENDIX
E
Relevant Materials
NONPROFIT ORG.
qAk 6rovsTrahiii(46) mod
U. S. Postage
PAID
Mt. Prospect, III. Permit No. 33
lscusloputivAf6orfsr
1706 West Algonquin Rd., Arlington Heights, III. 60005
The Elk Grove Training and Developri at Center has been organized to help meet the demand that Education keep pace with mushrooming mass of new information, scientific discovery, and innovation in methods and techniques. Members of the Center consotorium include public, private, and parochial schools, colleges and universities, and the cooperative Educational Research Laboratory, Inc.
Funded under Title III of the
Elementary and Secondary Education Act.
Afgre
AREA CODE 312/2598050
FOR INFORMATION OR AN APPOINTMENT
WE DON'T '6";14S1 4TLi Ael.21q1 6WILDREN
47TRUCiOtE TO 5E606/15 Tic touch, to manipulate materials in a laboratory at This is the heart of Madison Project Mathematics that introduces children to the wide spectrum of sop concepts. Directed by Dr. Robert B. Davis of Syracuse
College, the Madison Project is an exciting supple velopment project outstanding in its approach to and to the discovery method of learning.
The materials used by the Madison Project are de range of the daily mathematics curriculum. By car and by increasing the vitality and relevance of th with mathematics, Madison Project stimulates stu mathematical environment.
Self exploration materials, and classroom discus
MAL I atIA
.STUMNT6) NOR °61.4Apsi
TM;
INITiATSD 5E60105 MATURE ADULT. Pt: R'.13.1DavO
141i,02EN fN TI161R
als in a laboratory atmosphere, to discover) a unique approach roject Mathematics ide spectrum of sophisticated mathematical B. Davis of Syracuse University and Webster
an exciting supplementary curriculum dein its approach to independent exploration
(
I
Qj"
staples of the Madison Project. Simple, but clever in concept, the selfexploration materials are housed in an attractively decorated shoe box a delight to both students and teacher, yet complete in their mathematical accuracy. Alone, or in small groups, students enjoy playing with the mathematics rviterials, following direction cards or inventing and carrying out their own mathematics projects.
arning.
Bison Project are designed to broaden the curriculum. By careful readiness building, and relevance of the students' experience
oject stimulates students to explore their
d classroom discussion materials are two
Classroom discussions build on actual experiences. It is impossible to suppress young minds as they seek to test and compare newly discovered mathematical vistas.
In the world of mathematics, the big idea for little people is the Madison Project. You're invited to contact the program's coordinator, Doris Machtinger, at the Elk Grove Training and Development Center. Phone (area code 312) 2598050 for information or an appointment concerning demonstrations.
L"
evvi
annp
ELK GROVE TRAINING
&
DEVELOPMENT CENTER
MADISON PROJECT
The Madison Project is a supplementary mathematics program. It has been directed by Dr. Robert B. Davis of Syracuse University and Webster College and has been funded mainly by the U.S. Office of Education, with additional funds from a long list of subscribers.
The project started in the Madison Junior High School in Syracuse, New York as an attempt to solve the problem of weak skills and lack of sympathy for a "mathematical" approach in college freshmen:, Soon after it began, the program moved down into the elementary school, since, after all, tit IS where the work really begins, The Madison Project tries to keep the materials of a nature that is refreshing to both teacher and student, while maintaining mathematical accuracy. The teaching approach nurtured in the very form of the materials is one of respect for the student as a person with ideas worth cultivating. The materials fall, basically, into two categories, selfexploratory materials and classroom discussion materials.
The selfexploration materials corrist of a set of apparatus and some direction cards, housed in a shoe box, attractively colored blue. Students enjoy playing with the materials, alone or in small groups, following the direction cards or inventing their own tasks. The materials are ideal for learning center materials, mathlab materials and, of course, material for the activity shelf in a selfcontained classroom. The classroom materials again can be roughly broken into two categories. While Madison Project materials do not teach children their basic skills, they do provide the children with some tools that they generally do not have at their disposal, e.g., working with negative numbers. Some of the Madison Project lessons are designed to teach children these tools. These tools are usually taught through the use of games, games a7 common as tictactoe. Once the tools are mastered, the really exciting lessons can follow. These lessons are concerned with allowing the children to use their new tools, to explore their power, to test out their mathematical environment. These lessons are especially conducive to discovery teaching. The Elk Grove Training & Development Center is sponsoring a model program of the Madison Project materials for the third year. The materials are being demonstrated by Miss Micky Pelee at Fairview School in Schaumburg School District #54, Mr. Wayne E. Schaible, Superintendent; Mr. Marvin Johnson, Principal. The program is coordinated by Mrs. Doris Machtinger. The I C, D Center is interested in helping interested schools adopt any part of this progra to fit their needs. if you are interested, contact Mrs. Doris Machtinger at the I & D Center, phone 2598050
DM/ce 9/11/68
y, 0449\4.
*
f
<
$16.25 15.00 ea.




$6.00 2.50
Order from:
$6.00 2.50
AddisonWesley Pub. Co., Inc. 106 W. Station Barrington, 60010 or South*St. Reading, Mass. 0186
Teacher's Edition    Student's Edition    
Exploration in Mathematics   by Dr. R.B. Davis
Teacher's Edition Student's Edition
 by Dr. R.B. Davis
Math Media Division N & M Associates P.O. Box 1107 Danbury, Conn. 06810
Discovery in Mathematics
Omer from:
1 set of 6 4 sets of 6 ea.   
Geoboard & Workcards Tower Puzzle & Workcards Centimeter Blocks & Workcards Discs & Workcards Weights, Springs & Workcards Peg Game & Workcards
Shoe boxes with instruction cards and materials.. Set of 6 includes:
inLaanla2IExpioration Material 
Order from:
InService
Madison Project c/o Webster College Webster Groves, Mo.
Package
63119
$3.00 ea.
Houghton Mifflin Company 1900 S. Batavia Ave. Geneva, Iii. 60134
Service Package  
Order from:
Add 8% for handling charges Add State and Local taxes where they apply
$1.20 ea.
Colored Centimeter Rods (Kit of 19 rods)
Centimeter Rods  
MATERIALS USED IN THE TRAINING PROGRAM
Xerox Effective Listening Kit
Xerox Corporation 600 Madison Ave. New York, N.Y. 10022
S.R.A. Teaching Problems Lab
Science Research Assoc., Inc. 259 E. Erie St. Chicago, Iii. 60611
Leveling: A Method For Communicating Significant Personal Information
R.B. Morton
NASA Moon Game Tinker Toy Motivation Game Process Observation Trio Especially designed tapes illustrative of adult workshop problems
DECISION MAKING EXERCISE INSTRUCTIONS: You are a member of a space crew originally scheduled to rendezvous with a mother ship on the lighted surface of the moon. Due to mechanical difficulties, however, your ship was forced to land at a spot some 200 miles from the rendezvous point. During reentry and landing much of the equipment aboard was damaged and, since survival depends on reaching the mother ship, the most critical items available must be chosen for the 200 mile trip. Below are listed the 15 items left intact and undamaged after landing. Your task is to rank order them in terms of their importance for your crew in allowing them to reach the rendezvous point. Place number 1 by the most important item, the number 2 by the second most important, and so on through number 15, the least important.
Box of matches
Food concentrate 50 feet of nylon rope
Parachute silk Portable heating unit
Two .45 calibre pistols 11.111111Mkaa
One case dehydrated Pet milk Two 100 lb. tanks of oxygen
.1ma....Maggleam
Steller map (of the moon's constellation) Life raft
Magnetic compass 5 gallons of water Signal flares First aid kit containing injection needles
Solarpowered FM receivertransmitter
SUPERINTENDENT'S
coma lAwrence 9.180647.09
eonnnuraiy &aloft:had Ss Aoot Zisitgai 54
SCHAUMBURG TOWNSHIP, CO OK COUNTY P.O. ROSELLE, ILLI NOIS NLACKHAWK SCHOOL II lino4 Blvd. & Schaumb erg Read Hoffman Estates, Min ois 60172
April 1, 1968
Mrs. Dory Machtinger Elk Grove Training & Developmental Center 1706 W. Algonquin Rolling Meadows, Illinois Dear Dory: I would like to share with you toy observations of the'four people that we sent to your Madison Math Workshop in March. I had a meeting with than last week to discuss ideas that they might have concerning the summer workshop. I was impressed not only with their opinion of the Madison materials but also with their attitudes. You could sense that these people had worked constructively together and were also able to critise and discuss each others suggestions without any offense being taken. Whatever there exposure in your workshop was, you certainly conveyed to these people a sense of unity and purpose. These traits will :sake them better pereAke, as well as better teachers. Thank you for your efforts and help.
Sincerely, JJ
R. J. Cisek, Principal Blackhawk & Twinbrook Schools
RJC:dn