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A cross-site analysis of the extent of implementation of the California mathematics and science frameworks.

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A cross-site analysis of the extent of implementation of the California mathematics and science frameworks.

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A CROSS SITE ANALYSIS OF THE EXTENT OF IMPLEMENTATION
OF THE CALIFORNIA MATHEMATICS AND SCIENCE FRAMEWORKS
by
Cynthia Medeiros Belongia
A Dissertation Presented to the
FACULTY OF THE SCHOOL OF EDUCATION
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF EDUCATION
August 1996
Copyright 1996 Cynthia Medeiros Belongia
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UNIVERSITY OF SOUTHERN CALIFORNIA
School of Education
Los Angeles, California 90089-0031
This dissertation, written by
________C y n t-h i* M priai m s B g ln n g ia _______
under the direction o f h ikXLDissertation Committee, and
approved by a ll members o f the Committee, has been
presented to and accepted by the Faculty o f the School
o f Education in partialfulfillm ent o f the requirementsfor
the degree o f
D octor o f E ducatio n
B ate
Dissertation Committee *
DjAMLl
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1
Cynthia Medeiros Belongia Advisor - Dr. David D. Marsh
A CROSS-SITE ANALYSIS OF THE EXTENT OF IMPLEMENTATION
OF THE CALIFORNIA MATHEMATICS AND SCIENCE FRAMEWORKS
School reform in California in the 1980s focused on
changes in content and curriculum. This occurred in
response to a national concern regarding the declining
quality of education experienced by our students. Of
particular interest were the areas of mathematics and
science, due to the fact that, American students were
achieving far below students of other countries.
William Hbnig, past state Superintendent of Education,
has been a leader in guiding and becoming involved in
California's school reform. For the first time in our
state's history, we rejected textbooks from publishers that
did not match with our new model curricula guides and
frameworks.
Inplementing the mathematics and science frameworks
throughout schools in California represented a major
challenge. The purpose of this study was to determine the
extent that districts, schools, and teachers have
implemented the California mathematics and science curricula
and frameworks. This study also sought to examine patters
of implementation, similarities and differences, and to
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compare the extent of implementation of mathematics to
science.
This study was composed of two phases. In phase one,
case studies were developed as part of a major study of
mathematics and science curricula implementation. Phase
two, the focus of this dissertation, involved a cross-site
analysis of the implementation of the mathematics and
science frameworks across 12 districts, schools, and
classrooms in California. They were analyzed in regard to
the extent of implementation of various components in the
model curricula guides and frameworks.
Selected findings include the strongest perceived
implementation was in content at the district level for both
mathematics and science. The strongest correlation, 0.990,
was in science. This correlation was the relationship of
district primary grades with district intermediate grades.
Technology is a component that is perceived as needing
further implementation in both mathematics and science.
The findings and conclusions of this cross-site
analysis have produced some recommendations. School
districts should continue to provide support and inservices
to schools so that implementation may continue and become
stronger. Principals should support teachers in their
efforts to successfully implement the mathematics and
science frameworks. Policies in California should provide
for adequate time to implement frameworks in the future.
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Further study should be done regarding the
implementation process for other frameworks. Further study
should be done regarding the impact of mathematics and
science on student learning. And finally, further study
should be done to investigate which instructional strategies
are more successful and why.
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ACKNOWLEDGEMENTS
This dissertation is a result of the support and
efforts of many people. I am grateful to each and every one
of them.
I would like to acknowledge the members of my
committee, Dr. Picus and Dr. McComas, for their expertise.
I would like to give special thanks to my committee chair,
Dr. Marsh, for his time and patience. His suggestions and
guidance were invaluable throughout the writing of this
dissertation. I am very grateful to him.
Finally, I wish to thank my husband, Don, for always
believing in me.
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iii
TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS................................... ii
TABLES..............................................v
Chapter
I. THE PROBLEM................................. 1
Introduction..............................1
Statement of the Problem...................6
Purpose of the Study.......................7
Importance of the Study....................8
Assumptions...............................9
Delimitations............................ 10
Limitations.......................:......10
Definition of Terms.......................10
Organization of the Study.................12
II. REVIEW OF THE LITERATURE....................13
Introduction.............................13
The Federal Role......................... 13
Standards Development.....................17
The State Role........................... 19
Policy Implementation.....................21
The Extent of Implementation.............. 26
California Mathematics Framework.......... 29
California Science Framework.............. 38
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iv
Conclusion...............................46
III. METHODOLOGY...................................48
Introduction.............................48
Methodology for Phase 1...................49
Methodology for Phase II.................. 63
IV. FINDINGS......................................66
Mathematics..............................66
Science..................................78
Discussion...............................95
V. SUMMARY OF FINDINGS, CONCLUSIONS,
IMPLICATIONS, AND RECOMMENDATIONS............. 102
Introduction........................... 102
Selected findings of mathematics
implementation......................... 105
Selected findings of science
implementation......................... 106
Recommendations........................ 108
VI. REFERENCES...................................Ill
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V
Tables
1. Ratings by the research team regarding the
extent of emphasis given mathematics at
the district level.......................67
2. Ratings by the research team regarding the
extent of emphasis given mathematics at the
school level............................ 70
3. Ratings by the research team regarding the
extent of emphasis given mathematics at the
classroom level......................... 72
4. Ratings by the research team regarding the
extent of emphasis given mathematics
means of all districts................... 74
5. Ratings by the research team regarding the
extent of emphasis given mathematics
means of all schools.....................75
6. Ratings by the research team regarding the
extent of emphasis given mathematics
means of all classrooms.................. 77
7. Ratings by the research team regarding the
extent of emphasis given science
district level..........................79
8. Ratings by the research team regarding the
extent of emphasis given science
school level............................ 81
9. Ratings by the research team regarding the
extent of emphasis given science
classroom level......................... 84
10. Ratings by the research team regarding the
extent of emphasis given science
means of all districts...................86
11. Ratings by the research team regarding the
extent of emphasis given science
means of all schools.....................88
12. Ratings by the research team regarding the
extent of emphasis given science
means of all classrooms..................89
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vi
13. Ratings by the research team regarding the
extent of emphasis for mathematics and
science across all sites and levels.......91
14. Correlations of mathematics and science
emphasis-scores at all levels across
all sites...............................93
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CHAPTER I
THE PROBLEM
Introduction
In retrospect, Sputnik was more than just a primitive
satellite placed in orbit by a nation which Americans
considered inferior. Sputnik served as the triggering
mechanism for educational reform in the United States during
the decades of a crisis in education. Young Americans were
not receiving the quantity, or quality, of instruction in
mathematics and science
necessary to maintain the United States1 position as the
world leader in technology. The seemingly sinister shadow
of Sputnik cast a direct and incisive light on mathematics
and science instruction in the United States. As a result
of this forced self appraisal, a national reform effort was
launched to improve the instruction of science and
mathematics in American public schools.
The National Defense Education Act of 1958 was among
the first attempts to reform science and mathematics
education in elementary and secondary schools. In the
1960s, the National Science Foundation and Office of
Education invested in efforts to change the science and
mathematics curricula on a national level. Congress also
suggested changes in mathematics and science education by
enacting the Elementary and Secondary Education Act of 1965,
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which mandated a series of programs to assist economically
disadvantaged students. The primary focus of this program
was to improve mathematics and science achievement of
students in poverty areas. Two other important efforts to
improve instruction in mathematics and science were the
Biological Sciences Curriculum Study, and Curriculum and
Physical Science Study Committee. These two groups
advocated the inquiry approach to mathematics and science
instruction.
A number of studies were done to investigate the inpact
of inquiry approach programs. Bredderman (1973) reviewed
exemplary science programs in elementary schools. Students
in these programs made better gains than students in
traditional science programs. The students in these studies
were better at: 1) carrying out the process of science; 2)
having more positive attitudes about taking more science;
and 3) retaining more science content. Unfortunately, these
programs had significant implementation problems. More
specifically, Bredderman (1973) synthesized research on the
effectiveness of three major activity-based elementary
science programs used in the 1960s and 1970s: Elementary
Science Study, Science-A-Process Approach, and Science
Curriculum Improvement Study. He found that activity-based
elementary science programs increased achievement in science
processes, intelligence, creative attitude, perceptions,
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language development, science content, and mathematics
areas. In another review, Bredderman (1985) found that
programs that encouraged the use of laboratory science
during the elementary school years resulted in improved
student performance in such areas as mathematics, language
arts, and reading.
This research has established that inquiry-oriented and
activity-based mathematics and science programs have a
number of positive benefits for students. Unfortunately,
they were not widely implemented in the classroom. This
lack of implementation may have occurred because no
consideration was given to the process of change in schools.
As a result, most of the change efforts failed (Atkinson and
House, 1981).
Education has gone through many types of reform and
changes. The country, at the federal, state, and local
levels, has had a long history of interest in the schooling
of children. A Nation at Risk, which was published in 1983,
brought to the forefront many areas of concern about the
quality of education in the United States. It received a
great deal of interest and response from the states and
their departments of education.
During this same year, 1983, the Hughes-Hart Educational
Reform Act, Senate Bill 813, stimulated major reform efforts
in California schools. Odden and Marsh (1988) identify four
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components of this reform act:
1. Higher standards, increased requirements, basic
skills tests, more academic courses, more homework, a return
to traditional high school.
2. Better courses, new curriculum standards, better
texts, curriculum alignment, new teacher roles, quality
indicators, reduction in dropouts.
3. More radical curriculum change, curriculum
integration across content areas, emphasis on writing and
communication, higher order thinking skills, problem
solving, broader use of technology, interpersonal skills.
4. Teacher professionalism, teacher decision making,
national standards board, career ladders, restructured
schools, more parental choice, system incentives, merit
schools.
Curriculum was a major focus of two of the four
components of the Hughes-Hart Educational Reform Act. The
Hughes-Hart Educational Reform Act provided the major
impetus for curriculum reform and implementation. Experts
in the field, as well as teachers in the classroom, united
to write curriculum. These curricula incorporated basic
"core" knowledge, higher order thinking skills, integration
with other subject areas, problemsolving skills, and higher
standards that were attainable for all students. The
California state frameworks in each subject area outline the
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topics, themes, and strategies to be covered for each grade
level. The model curriculum guide follows this outline and
gives specific examples of classroom activities that are
directly related to topics in the framework.
The California mathematics framework includes the seven
strands of number, measurement, geometry, patterns and
functions, statistics and probability, logic, and algebra.
Themes are mental arithmetic, problem solving, concept
understanding, communicating mathematical concepts, and the
use of calculators. Various instructional strategies are
also discussed in the framework. These include the use of
manipulatives, cooperative learning, situational lessons,
concept development, and problem solving. The strands,
themes, and instructional strategies are interwoven and
spiral throughout the mathematics curriculum at each grade
level. There is not a specific scope and sequence for the
seven strands.
Science is divided into three fields of study: life
science, earth science, and physical science. Like
mathematics, students are to be exposed to all fields at
each grade level. Life science includes the topics of
living things, cells, genetics, evolution, and ecosystems.
Earth science discusses astronomy, geology, natural
resources, oceanography, and meteorology. Physical science
includes force, motion, and energy.
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The seven themes in the science framework are
observation, technology, ethical issues, the scientific
process, application, measuring, and describing. The
instructional strategies for science are the same as those
recommended for mathematics. The purpose of manipulatives
is to provide the learner with hands-on experiences.
Cooperative learning benefits students by allowing them to
learn from each other. Both frameworks emphasize spiraling.
This requires review of the information students have
already been exposed to as they move from one grade level to
the next.
Statement of the Problem
Effectively implementing the mathematics and
science frameworks requires major changes in California
public education. Fullan (1982) describes the change
process as three broad phases: initiation, implementation,
and institutionalization. California has completed the
initiation phase and is in the midst of implementation. No
one is sure how successful implementation will be, or how
extensive it will be across the state, at the district
level, or in the classroom. What is needed is a study which
reveals the current extent of implementation at the
district, local, and classroom levels.
The new mathematics and science curricula deviate
greatly from previous reforms and curricula. Current
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emphasis is on concept development, higher-order thinking
skills, cooperative learning, manipulatives, and problem
solving activities that stimulate real-life situations. The
curricula are designed with the idea that all students will
learn and benefit from them. The elite, or top students,
are not the only ones who will be exposed to, or utilize,
higher-order thinking.
The new frameworks set the necessary groundwork for
each discipline. They also give specific examples of
classroom lessons and activities to support topics
discussed. Even so, implementation will require many
changes because of the difference in foci compared to the
previous curricula.
Purpose of the Study
This study undertook to examine the extent to which
districts, schools, and teachers have implemented the new
California mathematics and science curricula frameworks.
The researcher sought to analyze the case studies of 14
elementary schools and districts with regard to the extent
of implementation.
This study sought answers to the following questions:
1. To what extent have elements of the mathematics
framework been implemented in selected schools?
2. To what extent have elements of the science
framework been implemented in selected schools?
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3. What are the similarities and differences of the
implementation of mathematics compared to science?
4. What patterns of implementation exist across
districts, schools, and classrooms in mathematics and
science?
5. How does the extent of implementation at the
district, school, and classroom levels vary by district
size?
Importance of the Study
This study provides information about successful
implementation of the mathematics and science frameworks in
selected elementary schools in the state of California.
Educational leaders and policy makers will gain a clearer
understanding of the current level of implementation of the
California mathematics and science frameworks in the
selected schools. This information will assist leaders and
policy makers in their efforts to enhance the implementation
of these, and other frameworks and curricula in elementary
schools throughout the state.
District personnel will gain information about
implementation of state frameworks and support for site and
classroom staff. This study provides the results of schools
that had already begun the process of adopting a new
curriculum.
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Principals will benefit from the information provided by
classroom teachers on the extent of implementation at the
school and classroom level. Teachers are the direct contact
with students: the first connection of learning that goes
on in the classroom. Administrators will gain information
on how to be supportive to their staff.
Classroom teachers will continue to be engaged in new
curricula and strategies to implement them. They will
benefit from the information provided by their peers on the
implementation of both the mathematics and science
frameworks. This information is valuable as they continue
to adjust to meet the changing needs of today's students.
Assumptions
The following assumptions can be made regarding the
case studies in this study:
1. The teachers and administrators in this study
responded with honest and authentic information.
2. The school district officials and school site
personnel gave an accurate appraisal and interpretation of
the mathematics and science programs in each school.
3. Valid and adequate data were obtained through the
interview technique used in the study.
4. Classroom observations provided accurate
information regarding the types of instruction and materials
being used in the areas of mathematics and science.
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5. The teachers and administrators were sufficiently
knowledgeable about the students and frameworks to answer
questions concerning the implementation process.
Delimitations
This study was delimited to 14 case studies of
elementary schools located throughout the state of
California. The schools were selected based on their active
engagement in the implementation of the mathematics and
science frameworks. Three methods of data collection used
were: the questionnaire, the interview, and observation.
The data were collected between October 1988 and January
1989. The results of this study represent a secondary
analysis of the 14 case studies.
Limitations
This study included only elementary schools and is
therefore limited in generalizability. The sample was not
random and is also limited in generalizability.
Implementation of only mathematics and science frameworks
were studied.
Definitions Of Terms
Case Study. This is a quantitative and qualitative
method of analysis which seeks to describe a unit in depth,
detail, context, and holistically. For this study, the
elementary school was the unit of data collection and
analysis.
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Cooperative Learning. This includes learning
activities that involve small groups of 4 to 6 students.
Students must work together, interact with materials,
express their thoughts, and discuss alternative approaches
or explanations. It offers students more opportunities to
share ideas than in an entire classroom.
Extent of Implementation. The extent that various
areas of the state frameworks in mathematics and science are
being implemented at the district, school, and classroom
level.
Implementation Plan. This is a plan that outlines key
activities, strategies, roles, and functions. It includes
the roles of all personnel involved.
Manipulatives. These are concrete materials that
provide students a way to connect their understandings about
real objects and their own experiences, to mathematical
concepts.
Model Curriculum Guide. This document is published by
the State of California for each subject area. It sets
forth the essential learnings for the curriculum. It is
intended as evocative models of curriculum content.
Individual schools will probably modify and expand the
content, as appropriate, for their particular student
population.
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Organization Of The Study
Chapter II reviews the literature pertaining to
implementation of educational programs and curricula.
Chapter III discusses the research method procedures
used in the study for data collection.
Chapter IV presents the findings of the study from the
data collected and addresses the specific research
questions.
Chapter V presents a summary of selected findings,
conclusions, and implications related to the extent of
implementation of the mathematics and science frameworks.
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CHAPTER II
REVIEW OF THE LITERATURE
Introduction
The Hughes-Hart Educational Reform Act of 1983 served
as an impetus to California's active role of improving
curricula in the state. New mathematics and science
frameworks have been developed and adopted. What is really
important now is how these frameworks have been implemented,
what affects they have had on curricula, and what changes
have taken place in the classroom. This chapter will
examine the federal governments's role in educational
reform, the state's role, and policy implementation.
Finally, the chapter will outline the mathematics and
science frameworks and the relevance of related, previous
research.
The Federal Role
The federal government entered the field of education
in a new way with the massive 1965 Elementary and Secondary
Education Act (ESEA). This program allocated several
billion dollars a year to special programs, resolved the
historic opposition to federal involvement in education, and
formed the cornerstone of President Lyndon Johnson's Great
Society Initiatives. It also promoted a dual purpose for
the federal government: promotion of equity and support for
excellence in our nation's schools (Elmore, 1983).
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The ESEA was affected by the Improving America's
Schools Act of 1994 (IASA) which provides amendments that
took effect in July of 1995. The Act requires that any
state desiring to receive IASA grants shall submit a plan,
developed in consultation with local educational agencies,
teachers, pupil services personnel, administrators, other
staff, and parents that is coordinated with other programs
under this Act, the Goals 2000; Educate America Act, and
other Acts as appropriate.
Goals 2000: Educate America Act, was signed into law by
President Clinton in 1994. The work, that was begun by
former President Bush, supports certification of voluntary
national education standards and national skill standards,
and encourages the states, through grant aid, to develop
their own standards for education. The eight goals are:
1. School Readiness-All children in America will start
school ready to learn.
2. Improved Student Achievement-All students in America
will be competent in the core academic subjects.
3. Adult Literacy and Lifelong Leaming-Every adult in
America will be literate and possess the skills necessary to
compete in the economy of the 21st century.
4. Teacher Education and Professional Development-All
teachers will have the opportunity to acquire the knowledge
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and skills needed to prepare U.S. students for the next
century.
5. Increased Graduation Rate-The high school graduation
rate will increase to at least 90%.
6. Best in Mathematics and Science-U.S. students will be
first, in the world, in mathematics and science.
7. Safe, Disciplined, and Drug-Free Schools-Every school in
America will be safe, disciplined, and drug-free.
8. Parental Involvement-Every school will promote parental
involvement in their children's education.
Title III of the Act provides funding to states to engage in
comprehensive standards-based school improvement or
"systematic reform." The legislation authorizes five years
of support.
The federal government continues to have policy
objectives that are concerned with education. These laws
have common elements. All address the need to: raise
academic achievement, ensure that all students have equal
opportunity to learn, increase the skills of teachers
through adequate teacher preparation and continuing
professional development, increase parent and community
involvement, support the use of technology, and improve
accountability and assessment.
The vision being developed emphasizes a coherent
system, with high expectations and common standards for all
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students. Such efforts should be seen as an opportunity to
improve the articulation of services to all students. The
government is concerned with equity and excellence, and does
not intend to undermine individual policies and objectives
that have been adopted by the states. The federal
government aims to support states.
It is no longer enough for federal programs to
encourage the delivery of particular services to compel
equitable distribution of resources. Federal resources are
needed to help urban districts. Over the past 20 years,
federal programs have gradually broadened their focus from
the individual student to the school. Today's need is for
the further evolution of the federal strategy, in order to
incorporate an effort to strengthen entire school systems.
The National Science Foundation (NSF) is an agency of
the United States Government that supports science
education. Their mission is to promote the progress of
science; to advance the national health, prosperity, and
welfare; and to secure the national defense. They are
involved in grants and research to strengthen education
programs at all levels. They have funded research in
curriculum since the 1950s. Some of their programs include
Science-A Process Approach, Elementary Science Study, and
Science Curriculum Improvement Study. The impact of these
programs was impressive. Never before had a single
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curriculum initiative had such a wide-spread effect on
science teaching in this country (DeBoer, 1990).
Standards Development
Recently, the National Council for the Teachers of
Mathematics has become a milestone for standard-setting
projects in the United States. They have led the way in
demonstrating the power of national standards, as a tool,
for K-12 mathematics education reform. They were funded by
federal grants and generated a national committee.
Standards were drafted during the summer of 1987 and revised
and printed in 1989. The Standards is a document designed
to establish a broad framework to guide reform, in school
mathematics, during the next decade. In it is a vision of
what the curriculum should include in terms of content
priority and emphasis. The Council is soliciting feedback
from the profession. Its focus on critical thinking and
application of knowledge to real problems have made it
widely accepted by the nation's teachers. Inspired by this
document, there are other efforts to create standards in the
decade of the 90s.
Benchmarks for Science Literacy: Project 2061 was
created by the American Association for the Advancement of
Science (AAAS). Begun in 1985, AAAS has started to develop
the Project 2061, which elaborated a set of tools to help
local, state, and national educators redesign curriculum in
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these areas and ensure its success. Science for All
Americans was published in 1990 and outlines what all
students should know, and be able to do, by the time they
complete high school. In 1993, Benchmarks for Science
Literacy, based on the visions of Project 2061. offered
educators, in every state and school district, a tool to use
in fashioning their own curriculum.
It is a collaborative work by elementary, middle, and
high school teachers, administrators, scientists,
mathematicians, engineers, historians, and learning
specialists. It specifies how students should progress
toward science literacy, recommending how students would be
able to explain ideas in their own words, relate ideas to
other benchmarks, and apply the ideas in novel contexts by
the time they reach certain grade levels.
National Science Education Standards was formally
published by the National Research Council (NRC) in 1996.
NRC organized the National Committee on Science Education
Standards and Assessment in 1992, to develop national
standards for curriculum, teaching, and assessment for K-12
science. They are descriptions of phenomena, concepts,
processes and attitudes that must be experienced and
learned, what all students should understand and be able to
do in science and its application.
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The State Role
The report, A Nation at Risk, stimulated an intense
response in the United States. The Education Commission of
the States reports that there are 120 high-level state
commissions studying education quality. The 1983 meetings
of the National Conference of State Legislatures, Education
Commission of the States, and the National Governors
Association were dominated by state education reform issues.
State capitals are full of six or eight-point plans by state
authorities for educational improvement.
State Superintendents of Education were also reacting
to A Nation at Risk. California's school reform was seen in
Senate Bill 813, the Hughes-Hart Educational Reform Act.
The goals were: (1) to improve the curriculum in schools
by identifying a core academic program, (2) to improve the
performance of students, teachers, and administrators, and
(3) to develop in schools the characteristics associated
with effective schools.
William Honig, in California, has been a leader in
guiding and becoming involved in his state's educational
reform efforts. Under his term, California has produced new
science, mathematics, and social studies frameworks and
curricula for the entire state. California has rejected
texts from publishers that did not match their framework in
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20
mathematics. This rejection was the first for California in
textbook adoption history.
The California Education Round Table issued an action
plan outlining steps to address the state's educational
crisis at a news conference in October 1995. The Round
Table contains members that represent leaders of all
segments of California education-kindergarten through
postdoctoral education. Current State Superintendent of
Public Instruction, Delaine Eastin; University of California
President, Richard Atkinson; California State University
Chancellor and current California Education Round Table
Chair, Barry Munitz; California Community Colleges
Chancellor, David Mertes; California Postsecondary Education
Commission Executive Director, Warren Fox; and a
representative of independent colleges and universities,
Pepperdine President, David Davenport, have come together in
a unique partnership, seeking solutions to the state's
education problems.
These leaders have crafted a document called
Collaborative Initiatives to Improve Student Learning and
Academic Performance, Kindergarten Through College. Working
together, they plan to take the following five steps:
1. Agree on high school graduation standards and clarify
expected competencies for university admission.
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21
2. Strengthen programs and resources for teacher
preparation and professional development.
3. Use technology to improve the quality of education and
streamline access to postsecondary education.
4. Bring additional community and professional resources
into the teaching and learning process.
5. Assess high school student progress more uniformly to
determine if the standards have been met.
State education policy has a new agenda, a new
momentum, and a strong rationale, linking educational
improvement to national economic growth. Education is
currently a crucial state political issue. The role of the
state education leaders is to move quickly, but with a
balanced agenda that does not repeat mistakes that have been
made in the past.
Policy Implementation
According to Odden and Marsh (1989), research on
government program implementation has evolved through
several stages during the past two decades. The first stage
of implementation research concluded that there was a
conflict between local orientations, values and priorities,
and state or federally initiated programs. It appears that
local governments did not have the capacity, nor the will,
to implement innovations that were designed by the federal
government (Murphy, 1971). Implementation problems resulted
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22
from poor program design and the relationship to the local
institutional setting (Odden & Marsh, 1989).
Research in the late 1970s (Kirst & Jung, 1980) showed
that local school districts had learned how to administer
federal education program implementation and had started to
validate the educational priorities of Title I. Following
this, there was a series of research studies which
investigated the state level interaction and local
implementation of several federal and state categorical
programs. According to Odden and Marsh (1989), these
studies found that federal and state programs: (1) were
being implemented in compliance with legislative intent and
accompanying rules and regulations; (2) were providing
extra services to students who needed them; (3) did not
cause curriculum fragmentation in local schools; and (4)
were worthwhile because they provided extra services.
Research during this time tended to study relatively narrow
categorical programs, instead of ones aimed at all students.
Little effort was made to specify in any systematic way the
relationship among the policy problems that were addressed,
the design features of a policy, the implementing
organization, and the political and organizational context
in which the policy must respond (McDonnel & Elmore, 1987).
Implementation of policy, curriculum, etc., requires
change. Change occurs in stages over time and individuals
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23
must be the primary target for change interventions. Hall
and Loucks (1979) have some things to say about change.
First, change is a process. Second, change is highly
personal. Third, change interventions must be tailored to
meet the needs of the user. Finally, change developers need
to continually adjust to the needs of the users and provide
support accordingly. The broad phases of the change process
are initiation, implementation, and institutionalization.
This may take as long as three to five years.
Change is a very personal experience. People are not
always at the same place regarding their concerns and
abilities to make necessary change. Loucks (1982)
determined that it is appropriate to focus on the teacher
throughout the levels of use and stages of concern when
implementing change. In addition, assistance must be
provided in helping teachers implement new practices by
obtaining approvals, resources, and other means of
facilitating them. McLaughlin and Marsh (1978) also found
that a collaborative planning style is necessary to both the
short term and long run success of a planned change effort.
In short, a collaborative planning effort can lead to strong
advocacy and a sense of fit by management.
Jung and Kirst (1986) showed that the expectations and
strict regulations of the federal and state programs were
adapted to programs that could work locally. Local
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24
opposition was transformed into support for new program
initiatives. The programs could be run in compliance with
the rules and regulations, and eligible students obtained
the appropriate services. The stage two implementation
research showed that higher level government programs
eventually get implemented locally, that initial conflicts
get resolved, and that programs are worked out to the
satisfaction of both federal and local parties.
Although stage two implementation research showed that
programs were implemented, they did not always reach their
desired impact. The major characteristic of stage three
implementation was not just to get programs implemented, but
how to make them effective. This research is concerned with
strategies that can be used to make local practitioners
experts in effective practices they need to apply and how
policies at the federal, state, and district levels can be
designed to help local practitioners put these practices
into local use (Odden & Marsh, 1989).
The reforms of the 1980s were different from the
reforms of earlier decades. Previous reforms were concerned
with special programs for specific students while the
reforms of the 1980s were designed to improve the regular
curriculum for all students. These reforms were more
comprehensive than the categorical programs of the 1970s.
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25
One study was the Policy Analysis for California
Education (PACE Study) conducted by Odden and Marsh (1987).
This study was designed to examine the implementation of
both individual provisions of Senate Bill 813 and
implementation of the local district or school vision of
educational quality. This study determined the extent to
which state educational reform programs and policies became
part of the local vision for educational excellence.
The Building Effective Middle Schools study, (Marsh et
al. 1988) was also investigating implementation of the
1980s. The California Superintendent's Middle Grade Task
Force synthesized essential elements of an exemplary middle
school in the report titled, Caught in the Middle. Helping
schools implement these programs provides a challenge. The
study by Marsh et al. was aimed at determining the extent of
the role that the California School Improvement Program
(SIP) can play in the implementation of the vision of a
middle school as presented in Caught in the Middle. The
purpose of this study was to examine schools that had been
especially effective in implementing the middle school
reforms. These sites also had school improvement programs.
The study sought to determine what role school improvement
had played and how the benefits of school improvement
programs at these schools could be extended to other schools
in the planning phase of the school improvement program
cycle.
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26
The Extent of Implementation
The past 15 years of research have clarified factors
having the most influence on implementation. The Rand
Change Agent study (1978) concluded that there were eight
insights about successful implementation. They are: (1)
what the project is matters less than how it is implemented;
(2) more expensive projects are no more likely to be
successful than less expensive projects (3) teachers must
understand the project's goals and presuppositions; (4)
projects aimed at significant educational change cannot be
implemented across an entire school system at once; (5)
decisions concerning the implementation strategies of how to
put the projects into place must be made at the local level
so that the realities of the institutional setting can be
adapted; (6) the school's organizational climate affects
the program's implementation and continuation; (7) the
principal must support the program; and (8) the central
office must constantly help and support the teachers.
Fullan (1982) has identified four major categories that
affect the extent of implementation. First, are the
characteristics of change, including; the need and relevance
of the change, clarity, complexity, quality, and
practicality of the program. Second, are the
characteristics at the school district level including; the
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27
history of innovative attempts, the adoption process,
central administrative support and involvement, staff
development and participation, time line and information
systems, and the school board and community characteristics.
Third, are the characteristics at the school level including
the principal, teacher-teacher relations, and teacher
characteristics and orientations. Fourth, are the
characteristics external to the local system including the
role of government and external assistance.
More recent research has extended and refined the
earlier research. The most comprehensive and extensive
study to date was the Dissemination Efforts Supporting
School Improvement study (DESSI). In this study of schools
across the nation, Huberman and Miles (1984) were able to
determine factors related to successful implementation.
These factors were: (1) high commitment, (2) low latitude,
(3) high levels of stabilization, (4) programs with large
scope and high levels of district support, (5) district
administrators who provided resources, support, and
pressure, and (6) a direct relationship between the size of
the innovation and early attempts at the innovation.
The Concerns Based Adoption Model (CBAM) was to view
the change process in schools (Hall & Hord, 1987). It
looked at the process from the perspectives of probing,
stages of concern, levels of use, innovation configuration,
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28
and feedback from the personnel involved. It is another
method to examine the implementation process.
The study by Marsh and Odden (1990) in California
revealed four lessons about implementation. First, the
antecedent phase was very important for building local
support for the implementation of the new curriculum.
Second, teachers developed expertise about innovation from
other teachers through regional networks. These networks
were a powerful source of assistance. The third lesson
relates to the order of the implementation process. In
California, the "top-down" and "bottom-up" processes became
linked together. The legislation was definitely "top-down."
However, the phases of textbook adoption at the local level
and the writing of curriculum manuals, were done from the
"bottom-up." This linkage made the implementation process
smooth and more acceptable to personnel at the local level.
The final lesson is that policy initiatives were very
important to each phase of reform implementation.
The research community has an inadequate base about tow
state reform can work when it requires such drastic change
in classroom practice, as do California's mathematics and
science curricula. What is needed is an in depth look at
the role that state initiatives can play in mathematics and
science programs. Even though the recent Educational
Commission of the States study suggests that states can be
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29
successful in changing district practice, it does not answer
how to get real changes in classroom practice.
The California study by Marsh and Odden (1990) found
that there was a rapid and strong adoption of the
mathematics and science curricula frameworks. By the end of
the two-year adoption phase, all districts and respective
schools had adopted the state curricula frameworks. The new
frameworks were seen as representing quality programs and
the best of what was known about curricula and instruction
in these areas.
The final lesson is that complete implementation of
these curricula will be complex. They will require major
shifts in the teaching and understanding of mathematics and
science. The good news is that teachers and local educators
have been responsive to these new frameworks and practices.
California Mathematics Framework
The framework compares mathematics to the color
spectrum in a rainbow. The seven strands resemble color
bands; they overlap and blend and there are no definite
boundaries. The seven strands do not represent exclusive
materials that should be presented to students. The
framework does not include a specific scope or sequence for
content. The major topics are ones that fall under the
large mathematics umbrella. The seven strands of number,
measurement, geometry, patterns and functions, statistics
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and probability, logic, and algebra are discussed below.
The first strand, nunber, is used to define quantities.
Students should develop an understanding for the use of
numbers, place value, representation of numbers in other
forms, and absolute values. Students should understand order
of operations, exponents, and number sentences. They should
develop an appreciation of the nature of counting numbers,
characteristics of numbers, and the ability to choose the
most efficient and effective method to solve a problem.
Measurement is the process of assigning numbers to
represent quantitative attributes of an object (California
Mathematics Framework, 1985). Students need to be familiar
with sets, objects to be measured, informal comparisons, and
the best type of measurement to be used in a particular
situation. Students need to develop skills in approximating
measurement, deciding on extent of accuracy, and in
recognizing errors in measurement. Students should use both
United States standard and metric measurements. They must
also be able to convert between, and within, systems of
measurement. At higher levels, students should be able to
use methods of indirect measurement such as the Pythagorean
Theorem, or trigonometric functions to find quantities that
cannot be measured directly. They should be able to use
substitution and formulas as a way to obtain measures such
as area, volume, distance, rate, or time.
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31
Geometry connects students' perceptions of the real
world with the mathematics that is used to solve problems,
and will arise in their lives. In the geometry strand,
students use visual and concrete experiences to understand
mathematical concepts. These should be developed gradually,
starting in kindergarten. Students should be able to
recognize patterns, through observation, and have knowledge
of geometric figures and vocabulary. At higher levels, they
should use transformations in planes, and develop an
understanding of congruence, similarity, parallelism,
symmetry, and perpendicularity.
The study of mathematical patterns and functions
enables students to organize and understand information.
The search for patterns begins at the concrete level and
progresses to inductive reasoning as a method to solve
problems. Experiences with patterns and functions should be
provided by encouraging students' understanding of the
relationship between pairing members of sets, and using
coordinate graphs to represent relationships at different
levels.
Statistics and probability allow students to analyze
and interpret data, and make predictions about future
events. Major themes within this strand include collecting,
organizing, and presenting data. This strand also includes
counting total possible outcomes by using tree diagrams,
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using mean, median, and mode as measures of central
tendency, and understanding concepts of variables and
standard deviation. Higher levels should also add
permutations, combinations, sampling, distributions, and
chance variables.
Logic is the ability to reason. Mathematics offers an
excellent environment to make students aware of the function
of this strand. So much of mathematics follows a routine
and a specific set of rules. Students should develop
logical thinking by participating in activities that require
them to look for patterns, organize their thoughts and
facts, recognize specific applications, and make inferences
from everyday experiences. At higher levels, students
should develop the ability to use the deductive method of
reasoning, judge the validity of reasoning, and apply formal
and informal reasoning processes in mathematics.
Algebra is the strand that links all of the other
strands and is an important step to higher mathematics.
Major themes that should be developed in algebra include
variables, order of operations, equations, and inequalities,
polynomials, the quadratic formula, functions, systems of
equations, vectors, and writing mathematical equations to
represent and solve given problems.
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33
Mathematics Themes
Besides the seven strands that make up the maj ority of
the framework, there are major themes that are discussed.
One of these is estimation and mental arithmetic.
Estimation is the process of judging the reasonableness of
an answer (California Mathematics Framework, 1985) and it is
very important in solving all types of mathematical
problems. Development of this skill requires that it be
incorporated as a beginning step, in solving all mathematics
problems, not just word problems.
Mental arithmetic allows students to explore different
approaches to problems before anything is written on paper.
The distributive and commutative properties are two such
examples. As students gain proficiency in mental
arithmetic, they can become better problem solvers, better
understand concepts, and have a better number sense.
A second theme of the framework is problem solving.
Instruction should be planned to maximize students'
experiences in solving real-life and abstract problems.
Students must take an active role in gaining first-hand
knowledge of the difficulties and tasks involved in problem
solving. The teacher's role is that of facilitator and
counselor; guiding students through different strategies and
alternatives. The teacher should not solve the problem for
them. The framework lists five things teachers should do to
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assist students in becoming better problem solvers.
1. Create a classroom atmosphere where all students
feel comfortable trying new ideas
2. Model problem-solving behavior
3. Invite students to explain their thinking at
all stages of problem solving
4. Allow for the fact that more than one student may
be needed to solve a given problem
5. Present problem situations that represent real-life
so the experience students gain will be
transferable
The teacher should continue to encourage students to
think through the steps and processes involved in problem
solving. Discussions of ideas and approaches guide students
to alternative strategies. Reasonableness and estimation
are also important when examining solutions.
Teaching for concept understanding is another theme.
Many students view mathematics as a set of rules and facts
to be memorized. The importance of mathematics is
relationships and usefulness in the real world. Mathematics
teachers have the important task of helping students
understand the fundamental concepts of mathematics and their
relationships to real-world problems. The framework states
that a major goal is to have students understand the
structure and logic of mathematics, so that they have the
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35
flexibility to recall and adapt the rules to solve problems
because they can see the larger pattern (California
Mathematics Framework, 1985).
Communicating mathematical concepts is the fourth
theme. In order for individuals to communicate, they must
share a common language. Mathematics has its own vocabulary
that is very important if ideas are to be shared and
discussions are to take place in the classroom. Teachers
must define these words in terms that students understand
and also incorporate them into lectures, class activities,
problems, etc. Students may also practice vocabulary by
writing their own problems. This supports problem solving,
as well as, makes the problems real and more relevant to
students.
The last theme is the use of calculators. Because
calculators are efficient and are used in businesses in
different types of tasks, they must be incorporated into the
schools mathematics program. Calculators should be
introduced in the primary grades as well as, used to support
the mathematics program throughout all grade levels. The
framework lists three advantages of calculators.
1. Calculators decrease the time students spend on
computation and increase time they can spend on
important aspects of problem solving
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2. Calculators enable students to deal with large
numbers and allows slower students to complete
assignments with time limits
3. At the secondary level, calculators allow
students to explore solutions to algebraic
equations that are impractical using pencil
and paper computation
Some educators are concerned that the use of
calculators will give students the impression that they will
not have to learn basic number facts. The use of
calculators requires the knowledge of basic facts and tests
students use of estimation, mental arithmetic, and reasoning
in problem solving. It can be used as an essential and
integral part of the mathematics program.
Mathematics Instructional Strategies
Various instructional strategies are discussed in the
state mathematics framework. The use of manipulatives in
the classroom is important in helping students make the
transfer of concepts from the concrete to the abstract.
Students gain direct experience by handling objects related
to a specific problem. Manipulatives may also include
pictures, drawings, diagrams, and other representations of
objects. To be effective, teachers must continue to use
these types of materials, so students develop an
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37
understanding and can refer to the materials as they solve
real problems.
Cooperative learning is an instructional strategy that
benefits all students. To internalize concepts, students
must use them. Activities can be designed for students to
work on in small, heterogeneous groups. Students are more
likely to contribute in small groups, than in whole
classroom discussion, and the attributes of all students
become visible during various steps of solving a problem.
The focus is on the group solving the problem together,
rather than the individual ability of each member. The
teacher plays an important role in setting the foundation
and modeling appropriate behaviors and strategies for the
process to be a success.
Situational lessons bring mathematics alive for
students. They need to be significant to students and
complex enough that students can derive several different
types of problems from one lesson. These lessons can also
be utilized in illustrating the connection of mathematical
concepts and their application to real-life problems. It
may also serve as a diagnostic tool to the teacher,
identifying the areas of difficulty that will necessitate
future follow up.
Concept development is discussed under teaching for
concept understanding, as a major element of the framework.
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Again, the emphasis is that students visualize the larger
picture of mathematics and how its concepts are
interrelated, not just the use of skills in isolated
practice.
Problem solving is also a major component of the
framework. Its importance as an instructional strategy is
that it allows students to encounter mathematical problems
in real life. Problem solving ties together all the
strands. The emphasis of the framework is to make students
independent learners who have mental strategies that can be
used to attack familiar problems, as well as, apply learned
skills in new situations.
California Science Framework
The California state framework and model curriculum
guide divides science into three fields of study: life
science, earth science, and physical science. Like
mathematics, students are to be exposed to all fields at
every grade level.
In the field of life science, the framework includes
living things, cells, genetics, evolution, and ecosystems.
Students should be able to answer questions such as:
1. What are characteristics of living things?
2. How do structures of living things perform their
functions and interact with each other to
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39
contribute to the maintenance and growth
of the organism?
3. What are the relationships of living organisms
and how are they classified?
4. How do humans interact with other things?
Earth science includes astronomy, geology, natural
resources, oceanography, and meterorology. Astronomy
discusses kinds of objects in the universe, their
relationship to each other, how the universe has evolved,
and how we continue to learn more about the contents and
structure of the universe.
Geology is concerned with rocks, minerals, the history
of the earth, and how plate tectonics has shaped the
evolution of the earth. Study in this area includes
geography, weather, and how the changing earth has affected
plant and animal life on earth. Geology has its own time
continuum that can be seen by examining the earth' s crust
and its contents.
The whole world has become concerned with natural
resources. Students must continue to be made aware and
explore alternatives in conserving the earth's natural
resources.
Oceanography revolves around the water cycle. How does
it affect climate, weather, and life on earth? Oceans are
an important part of the water cycle. How have they changed
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40
over time, and how do they support large amounts of plant
and animal life? A final part of oceanography is the
interaction of humans with the oceans. What may be some
long-term effects on the ocean environment?
Meteorology is the study of the atmosphere and weather.
Students should understand the major phenomena of climate
and weather and how humans are affected by the weather.
Students should understand how we predict weather, and how
we can alter it.
The field of physical science contains matter,
reactions and interactions, force and motion, and energy.
Students need to know what matter is, its properties, where
it comes from, and its chemical structure and physical
properties.
Reactions and interactions may cause change. Students
should study what may happen to the properties of substances
as they interact with other substances. Students should
understand what occurs when a substance changes, and what
controls how it will change.
In the area of force and motion, students should know
what motion is, the kinds of motion, what force is,
characteristics of force, the relation of force to motion,
what machines are, and the principles that govern them.
Under energy, the framework lists the sources of heat,
electricity, light, and sound. Students should understand
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41
what the importance of energy is to humans and how we use
it. Students should understand the basic properties of the
different types of energy, their sources, and how they are
interrelated.
Science Themes
The framework discusses seven themes and their
significance in the science program. The first includes
observing, describing, comparing, and measuring. Students
must be aware of the necessity of the various skills
involved in science. Careful observation means paying close
attention to detail, describing involves verbal and/or
written skills, comparing can be done in many ways, and
measuring will be determined by the items to be measured.
The scientific process is something all students should
be familiar with, and this is best mastered by practice.
Throughout the framework, the emphasis of hands-on and
active student participation is obvious.
How technology and science affect society is a theme of
the science framework. The intention is to help students
understand how science and technology can be useful in daily
living. This is not an isolated unit. This is a topic that
would be discussed throughout the year in many science
lessons.
Ethical issues in science require careful preplanning
by the teacher. The curriculum does not specify that
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students be taught what is right or wrong, but that they are
able to gather information and discuss consequences,
ramifications, etc. Their choices will be based on
knowledge and careful consideration. Group activities
related to a specific topic lend themselves to this theme.
Applying science to everyday life can be incorporated
into almost every science lesson. Again, the emphasis is
that students see the relevance of science and how it
affects them.
Science Instructional Strategies
The instructional strategies for science are the same
as those discussed for mathematics. The use of
manipulatives is to provide the learner with hands-on
experiences with concrete materials that will help them make
the connection to more abstract thinking. Cooperative
learning benefits students by allowing them to learn from
each other, working closely with peers, and being able to
contribute in a positive manner. Problem engagement is
similar to problem solving and situational lessons. The
teacher must set up activities for students to act out and
use their skills in solving real problems. Concept
development, again, goes beyond the knowledge level.
Students should understand the relationships that exist
within the specific areas of science, and their
relationships to other disciplines.
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Both the mathematics and science frameworks emphasize
spiraling throughout the curricula. This requires
continuous review and progression of experiences as students
move from grade level to grade level. The
interrelationships of topics must always be at the forefront
of planning. The use of manipulatives to expose students to
hands-on activities is something that is mentioned in the
curricula. Both the mathematics and science model curricula
standards give specific examples of classroom activities
related to topics in the framework. Research has shown that
students learn best by having these types of experiences.
The last major emphasis is the integration of
knowledge, skills, higher order thinking, etc., across other
disciplines. It is necessary for students to see the
connection that exists between all of the subject areas.
Implementing The New Science And Mathematics Frameworks
National reports and state legislation have initiated
an awareness that something must be done to improve
education. The movement towards science for all students is
an important goal. The depiction of science education in
the past was one of academically oriented instruction
dominated by lectures with some demonstrations. The current
framework for science in California emphasizes hands-on
learning and higher-level thinking skills, as well as
cooperative learning groups.
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At the present time, many groups are rethinking the
goals of science education. Project 2061 is determined to
gain greater specificity concerning concepts that are the
most fundamental to various scientific disciplines. It is
through the union of science, mathematics, and technology
that students can understand the scientific process and how
to use it to solve everyday problems. The trend today is to
implement programs in mathematics and science that use the
inquiry approach. This instructional strategy requires
extensive staff development.
Quality mathematics programs are vital, and teaching
for understanding and estimating skills are two critical
components of the present mathematics program in the
California framework. The research of Charles and Lester
(1984) have concluded that teaching problem solving skills
is also important. This is a major area incorporated into
the framework. The National Assessment of Educational
Progress (1983) revealed that students may have a mastery of
computational skills, but little understanding of
mathematics concepts. Similarly, Good and Grows (1987) have
concluded that mathematics programs have focused too much on
basic skills and not enough on understanding concepts.
The educational reforms of the 1980s were concerned
with improving the regular curriculum for all students, not
just specifically targeted ones. The Hughes-Hart
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45
Educational Reform Act of 1983 reestablished high
expectations for the content taught in California schools;
mathematics and science were no exception. The mathematics
and science frameworks and curricula guides were designed to
assist teachers with implementing quality programs in the
curriculum in an effort to improve student achievement.
During the 1950s and 1960s, curricula in mathematics
and science were developed and introduced in schools and
required students to use an inquiry approach. These
processes came to be called "inquiry oriented." Elaborate
curricula materials were designed to support these inquiry
oriented approaches. Unfortunately, implementation of these
programs was rather limited and only partial implementation
occurred in many settings (Fullan & Pomfret, 1977).
Eventually, some studies were completed in which sites with
high levels of implementation were examined. Bredderman's
analysis in 1983 revealed positive effects for information,
creativity, and the scientific process. From these and
other studies, it was concluded that it is possible to
develop curricula that will achieve model-relevant effects,
as well as, increase learning of information and concepts
(Joyce & Showers, 1988).
During the past few decades, research on training has
progressed enormously. It has been well established that
without strong adequate staff development, a very low extent
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46
of implementation occurs (Fullan, 1982). Teaching through
an inquiry approach requires a high degree of skill, and a
variety of models of teaching are needed, as well as, a
mastery of an academic discipline. Skills for teaching the
inquiry approach require much more than ordinary knowledge
and skills. Teachers need extensive training and practice
(Joyce & Showers, 1988). Unless there is a strong program
in content, materials, and teaching strategies, a low extent
of implementation is likely to result (Hall & Hord, 1987).
Conclusion
Many of the educational reforms of the 1950s and 1960s
failed due to their weak implementation strategies.
Research indicates that the inquiry approach does work in
increasing student achievement. Implementation of the
mathematics and science frameworks requires a high degree of
attention to the accurate duplication of what the state
considers its key components. Fullan (1982) would consider
this a major change because of the uniqueness and
originality of the implementation. McLaughlin and Marsh
(1978) note that a number of studies in education indicate
that the larger the scope of the innovation, the greater the
effort put forth by users and subsequent change of
successful implementation. Furthermore, since implementing
the science and mathematics frameworks in California has
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47
been declared mandatory. Miles (1983) notes that mandatory
policies increase the percentage of use.
The frameworks themselves were a guide in examining the
extent of implementation of mathematics and science. The
research team observed what was going on in classrooms. As
the focus continues on what is happening in classes, it
becomes clearer that the changes envisioned for students,
must be seen and understood throughout the educational
system. This is the linking of the "top-down" and "bottom-
up" processes that were found by Marsh and Odden (1990).
Schools must receive support, staff development, training,
etc., from side administrators, central office personnel,
and state officials. If students are to become more
involved in learning, so then must the people that influence
their education. All people involved in education must be
encouraged to use an even greater degree of creativity in
their work. Teachers need to be supported more than ever
before. Teachers, through their administrators, need the
building blocks to affect the learning of the diverse
students that come into their classrooms every day. The
literature supports the direction California is taking in
reforming its curricula and the impact it will have on
students. The foundation for change, and buy in from the
participants, have been laid.
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I
48
CHAPTER III
METHODOLOGY
Introduction
There were two phases to the study. The first phase was
a comparative case study of factors related to successful
implementaion of the new mathematics and science curricula
frameworks in California using qualitative methods. It
involved two faculty members and doctoral students in the
collection and refinement of case studies of elementary
schools and districts regarding the implementation of the
California mathematics and science frameworks. The second
phase was to conduct a cross-site analysis of the extent of
implementation of the key components in the frameworks.
Phase II is the focus of this dissertation.
The first phase of the study was designed to identify
the factors involved with successful district, school, and
classroom implementation of the California state mathematics
and science frameworks. The study sought to identify the
following:
* the impact of state policy levers on implementation
* the strategies used by schools and districts in
implementing the program
* the teaching strategies and materials that were
being used in the classroom
* the key impacts on teacher and student achievement
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49
Phase I of the study concluded with an analysis of the
individual sites.
Phase II of the study is the focus of this dissertation
which was to conduct a cross-site analysis of the extent of
implementation of the California mathematics and science
curricula frameworks across all sites in order to answer
five more specific research questions:
1. To what extent have components of the mathematics
framework been implemented in selected schools?
2. To what extent have components of the science
framework been implmented in selected schools?
3. What are the similarities and differences of the
implementation of mathematics compared to science?
4. What patterns of implementation exist across
districts, schools, and classrooms in mathematics and
science?
5. How does the extent of implementation at the
district, school, and classroom levels vary by district
size?
Methodology for Phase I
In Phase I, each case study was of a school site that
was advanced in implementation of the new mathematics and
science frameworks. Each case study provided an in-depth
examination of a district and school site, so that the
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50
relationship of adoption and implementation practice of
curriculum could be studied.
Sample Selection
Each of the sites involved in this study was selected
based on criteria established by Drs. Alan Odden and David
Marsh of the School of Education at the University of
Southern California. The criteria for site selection were:
1. An elementary school having grades kindergarten
through fifth or above, but not higher than eighth
2. A student population with low or average socio
economic status
3. A school site engaged in the second or third year
of implementation of the mathematics and science
frameworks and in particular schools which were
actively involved in new science activities or
manipulatives concept approach to mathematics
4. A school actively involved in improving the
pedagogical skills of teachers and/or
instructional supervision skills of
administrators in implementing new curricula
The sites reflected the diversity of students found in
the state of California and included small to large suburban
size school districts. These schools were selected from all
of the geographic regions of the state. The largest and
smallest districts in the state were not included because of
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51
the need to identify patterns of implementation that could
be useful to other districts in the state. Moreover,
schools that already had excellent programs were excluded
because of the need to study the improvement process.
Instrumentation
This was a qualitative study of districts and schools
throughout the state of California. Qualitative studies
allow data collectors to study selected issues in greater
depth and detail. The data collection is not limited by
predetermined categories of analysis and therefore
contributes to the depth and detail of the qualitative data
(Patton, 1987). Qualitative data are also able to explain
the processes that are occurring and can preserve a
chronological flow.
The case study format was chosen as the qualitative
method to be used. Case studies are useful when it is
necessary to understand a particular problem in great depth,
and when much information can be gained from observations
and interviews. This format was also chosen because it
allowed data collectors to capture individual differences
and unique variations involving the extent of implementation
of the frameworks throughout the state of California. The
case study sought to describe each district and school in
depth, detail, and context for purposes of giving an
overview.
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52
In order that the data collected would be of comparable
quality to allow comparison and analysis across 17 sites,
several strategies were built into the study design. First,
a common conceptual framework in the adoption and
implementation process was developed by reviewing background
information on mathematics and science, curriculum
implementation, general implementation, local
implementation, educational change, and curriculum
innovations.
The conceptual framework for this study was developed
by Dr s. Alan Odden and David Marsh and was based on six
features of policy implementation literature. These
principles are the following:
* Educational reform implementation research should
integrate analysis of the content of the reform,
the process of its implementation of the local
setting and its effects
* Educational reform implementation research should
focus on the influence of the reform on the overall
local educational system as well as on the content,
implementation process, and more specific impacts
* Educational reform implementation research should
integrate a macro (state level) with micro
(district/school level) focus for analyzing
the above issues
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* Educational reform implementation research should
draw on the distinction between developmental and
redistributing types of governmental programs
* Educational reform implementation research should
use recent research on the local change process
and relate the results to the macro context,
to the content of the reform, and to the
outcomes at the local level
* Educational reform implementation research should
identify several types of outcomes, including
impacts on the individuals within the local
educational systems and impacts on the systems
themselves (Odden & Marsh, 1989).
The application of the above design principles by Odden
and Marsh constituted a conceptual framework for studying
the implementation of the mathematics and science
frameworks.
Inplementation and context factors were derived from
several sources. The Dissemination Efforts Supporting
School Improvement Study of Successful Curriculum Reform
(Crondall et al., 1983) examined innovations several years
after implementation in order to determine if any had become
institutionalized. This study found that innovations lost
their effectiveness when they were not adopted faithfully.
This study also revealed the importance of choosing a proved
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54
innovation and stressing fidelity in its implementation.
Ten factors, depending on their presence or absence,
influence decisions regarding adoption or rejection of
specific change programs, policies, or directions (Fullan,
1982). Educational innovations are not introduced into a
vacuum but into a complex set of relationships and factors
that can be intensified or shifted when an innovation is
introduced (Huberman & Miles, 1984).
To more fully understand the conceptual framework, the
doctoral students in this study completed a literature
review that was read and summarized by all the participants.
These areas included: good mathematics, good science,
higher-order thinking skills, special needs students, staff
development, implementation process, and state policies and
programs. The data collectors had also received courses on
implementation and change theories and qualitative research
methods.
The Phase I study was designed to gather specific data
through interviews, questionnaires, and direct observations.
Open-ended questions were also asked to obtain a broader
understanding of the interrelationships of the key elements
of the study. The research team reviewed the literature
needed for this study before they developed the
questionnaires. The questionnaires were pilot tested with
four teachers and were then reviewed for this study.
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55
The doctoral students spent time interviewing district,
school, and classroom personnel. This allowed them to
become familiar with the individuals, sites, and procedures.
This process helped in facilitation of data gathering that
involved a number of people over a period of several days.
Strategies were used to ensure that the data analyzed
was of sufficient quality and was comparable across sites.
These strategies included the following:
1. Use of a conceptual framework for studying
mathematics and science implementation
in order to focus the data collection and
the write-ups and analyses.
2. Use of data from a site both in terms of
specific, high-directive questions and topics
and in terms of more global, less directive
questions that allowed the unique relationships
within a site to be reported. The write-up of
this information, at both the specific topic
and global level, helped communicate individual
site information more effectively to the cross
site analysis team.
3. Use of multiple rounds of data collection so that
the researchers had time to analyze the data
between rounds and discover any missing
information.
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4. Use of extensive data collector training that
included data collection procedures and case
study write up formats.
Data Collection
In Phase I, a common training was provided for the
doctoral students. Before the case studies, the doctoral
students met with Drs. Odden and Marsh to discuss the study.
The meeting included an overview of the research problem,
training in the use of data collection, case study
methodology, site selection, and discussion of final issues
and problem solving. The University of Southern California
Study of Mathematics and Science Curricula Implementation
(Marsh and Odden 1988), a research document, included
relevant literature, background materials, and a detailed
outline of the study and data collection instruments.
The study team conducted research at the district,
school and classroom levels. Most of the data collection
took place at the school sites and in classrooms.
Two rounds of data collection were completed in order
to provide the researchers time to analyze additional
information. The following indicates the focus and average
number of days of fieldwork for each school:
Round I
District Fieldwork
* Interview key district administrators-2 days
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* Review district curriculum
Site Fieldwork
* Interview principal-2 days
* Collect outcome data
* Interview mentors, teacher leaders
Round II
District Fieldwork
* Reinterview key district administrators-1 day
Site Fieldwork
* Reinterview principal-3 days
* Observe mathematics and science instruction
in eight classrooms
* Interview the same eight classroom teachers
regarding classroom practice
* Interview teachers of special programs
Total fieldwork days 8 days
Data were collected in October, November, and December
of the 1988-89 school year. The doctoral students completed
a case write- up and met in January 1989. A common time
frame was necessary so that the researcher could reconstruct
the implementation process that had developed in the
preceding years. Round I of the data collection focused on
understanding the nature of the mathematics and science
programs being implemented, as well, as the initiation,
adoption, and implementation processes and strategies.
Round II focused on impacts and outcomes and confirming
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understandings from Round I. Each round of data collection
produced vast amounts of qualitative and quantitative
information.
To gather related data, all teachers at the school
sites were asked to complete a questionnaire related to the
mathematics and science programs. Half the teachers
completed the mathematics questionnaires, and the other half
of the teachers completed the science questionnaires.
Questionnaires were distributed equally among the grades and
were given randomly to grade level teachers. The principal
completed similar questionnaires.
Data were collected in these major areas: initiation
and adoption, key components of the curriculum,
implementation, outcomes for teacher practice, test data,
school wide programs, and integration of mathematics and
science.
Initiation and Adoption
During the first round of data collection, researchers
collected qualitative data that described district and
school site initiation and adoption processes for the
mathematics and science programs. Through interviews,
researchers identified the roles of the superintendent,
assistant superintendent, school board, principal, mentors,
curriculum personnel, teachers, and other personnel involved
in the initiation and adoption process. The interview
questions were structured to provide common data across all
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59
sites. District and school site documents were collected
and analyzed to supplement the interview data and give a
more comprehensive understanding of the initiation and
adoption area.
Key Components of the Curriculum
A second part of Round I focused on the linkages
between the state, district, and school site formal
curriculum. These linkages were identified through
interviews, direct observations, and comparisons of school
site and district curriculum to the state frameworks. Key
elements of the program and materials used at the school
site were identified. School site and district documents
were analyzed. The content of these materials were compared
to the concepts, strategies, and key elements in the state
mathematics and science frameworks. By examining these
district documents and data, the researchers were able to
determine the extent to which the curriculum was expressed
at the district and school site levels, the extent to which
the state frameworks affected the district and school site
formal curriculum, and how the curriculum addressed the
needs of students with different abilities.
After reviewing the formal curriculum documents, the
researchers completed a checklist that rated the emphases
and content of the formal mathematics and science curricula.
They also completed a checklist that rated the emphases and
content of the formal mathematics and science curricula and
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summarized the key elements present in the documents. The
key elements of the curricula in mathematics and science
included goals and objectives, content, instructional
strategies, materials used, grouping of students,
instructional time, and evaluation. The key components
checklists used the following rating scale:
3 = Extensive emphasis in curriculum guide
2 = Moderate emphasis in curriculum guide
1 = Limited emphasis in curriculum guide
0 = No emphasis or BC - being considered
NI = No information available
The formal mathematics curriculum was analyzed for
content in the areas of numbers, measurement, geometry,
patterns and functions, statistics and probability, logic,
and algebra. The thematic emphases included: estimation and
mental arithmetic, problem solving, teaching for concept
understanding, communicating mathematics concepts, and the
use of calculators. Instructional strategies included the
use of manipulatives, cooperative learning, situational
lessons, concept development, and problem solving. In
science, the researchers focused on evidence of a balance
between life, earth, and physical science content and
thematic emphases in the scientific process and hands-on
laboratory activities, ethical issues related to society,
and the application of science to everyday life.
Instructional strategies included the use of manipulatives,
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61
laboratory experiences, and cooperative learning.
The Implementation Phase
Data were also collected during Round I through
completion of questionnaires by the principal and teachers
regarding time allocated by content area, class size,
facilities, instructional materials, teacher course
preparation, selection of teachers, and teacher evaluation
systems.
Interviews were used to gather information regarding
local implementation factors. These factors included the
role of cross-role teams, description of the implementation
plan, initial content, skills and awareness training,
curriculum development, change, alignment, administrative
commitment, pressure, monitoring, latitude and fidelity,
ongoing assistance, teacher effort, and the influence of the
state policy levers.
Additional data were also sought to identify and
explain the impact of state policies and programs on the
implementation process in the district, at the school site,
and in the classroom. Staff members were asked to comment
on the effect of the following state policy levers:
* Curriculum frameworks
* Textbook adoption process
* California Assessment Program (CAP)
* School Improvement Program/Quality Review
* State assistance efforts
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* Mentor teacher program
* District/school quality indicators
* Administrator training centers
Researchers completed a low-inference chart to rate the
impact of these state policy levers on implementation at the
site.
Outcomes: Teacher Classroom Practice
To determine the degree of impact of the new
mathematics and science curricula on classroom practice,
teachers were chosen at random, four each for mathematics
and science (2 at the primary level and 2 from intermediate
grades) to be observed and interviewed. Teachers were
observed for approximately thirty minutes to an hour, and
data was recorded regarding a lesson summary, text and
materials used, lesson variation by type of student, and the
teacher's plans for the following semester. The researchers
rated the degree of use of framework content, emphases, and
strategies as well as approaches used in the lessons.
Interviews were also completed to focus on teacher
descriptions of the curriculum for the month of November and
their plans for the next semester. These results were
recorded on a rating sheet using the same scale and key
elements as data collected for the district and school site
levels.
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63
Data Analysis
After collection of the data was aonpleted by the
researchers, another meeting was held in January 1989. At
that time, the data collectors pooled data verbally and
reported findings to the group. They identified tentative
themes and offered high-inference interpretations regarding
their findings. The individual case study write-ups led to
the writing of dissertations.
Methodology for Phase II
The purpose of this dissertation was to conduct a
cross-site analysis of the extent of implementation of the
key elements in the mathematics and science frameworks
across all the districts and school sites (Phase II of the
Study). The case studies that were eventually used in the
cross-site analysis were selected using two criteria.
First, only those case studies written up and made available
to the research team within six months of data collection
were used. Second, available case studies were reviewed for
sufficiency of information. This screening yielded a total
of 14 case studies for the cross-site analysis. The
analysis at the classroom level produced 12 cases for cross
site analysis.
Stage One: Data Organization
Information about coiqponents of the mathematics and
science frameworks were recorded by the doctoral students on
several charts. Information was gathered in both subj ect
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64
areas at the district, school, and classroom levels. All of
these charts were pulled from the case studies and
segregated by subject area and level of information
gathering. The charts were also sorted to separate primary
from intermediate grades. The districts were arranged by
size from largest to smallest by total student population.
Each district was identified by a letter of the alphabet
from A to N.
Stage Two: Data Recording
Data from the charts was imputed into a computer
program. The data was identified by a letter (A-N), subject
area, grade level, district, school or classroom, and
specific component of the framework that was addressed.
From this, the information was manipulated in different ways
to view various comparisons of the information. The
computer print out showed raw scores, percentages, and total
district counts of rating scores. Correlations were
calculated for each component of the frameworks compared to
each of the other components at the district, school and
classroom levels. It was also calculated by primary and
intermediate levels. The subject areas of mathematics and
science are displayed separately.
Stage Three: Development of Tables
During this stage, information produced by the computer
was examined and presented in a manner that was visually
easier to understand. In order to do this several types of
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65
tables were designed. For mathematics and science, tables
were constructed at the district, school, and classroom
levels, that show the percentage of responses to each of the
zero to three ratings, in each component of the state
framework. These tables also show primary, intermediate,
and overall means for each component across all sites.
For mathematics and science, tables were constructed at
the district, school, and classroom level to show the means
of primary and intermediate components for all sites. This
table also shows a total primary mean, a total intermediate
mean, and a district mean in both mathematics and science.
One table was constructed to show overall means in
mathematics and science at the primary and intermediate
levels in the areas of content, themes, and instructional
strategies. This table also displays means for total
primary and total intermediate, in both mathematics and
science.
A final table shows the correlations between the
different components in mathematics and science with
different levels of the system; district, school, and
classroom. These correlations were computed using Pearson's
R.
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66
CHAPTER IV
FINDINGS
The purpose of this study was to examine the extent to
which districts, schools, and classroom teachers have
implemented components of the California mathematics and
science frameworks. The study also sought patterns of
implementation, similarities and differences in
implementation, and comparisons of districts by size. The
researcher analyzed case studies of 14 elementary schools
and districts.
This chapter reports the findings of the cross-site
analysis of the 14 districts and elementary schools. First,
is a description on the extent of implementation of
components of the mathematics framework and the extent of
implementation of components of the science framework. In
the tables that present districts with the letters "A"
through "N", the districts are in descending order by size
of the pupil population.
Mathematics
Table 1 displays the ratings by the research team of
the extent of implementation of the mathematics framework at
the district level. It also shows the means for primary
grades, kindergarten through third, intermediate grades,
fourth through sixth, and the overall mean for all grades.
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TABLE 1
RATINGS BY THE RESEARCH TEAM REGARDING THE EXTENT OF EMPHASIS GIVEN MATHEMATICS AT THE DISTRICT LEVEL
A SUMMARY OF PERCENTAGES AND MEANS ACROSS DISTRICTS
PRIMARY LEVEL INTERMEDIATE LEVEL
NONE LIMITED MODER. EXTENS.
EXTENT OF EMPHASIS 0 1 2 3
COMPONENTS OF MATH FRAMEWORK
CONTENT
NUMBER 7.1% 0% 7.1% 85.7%
PLACE VALUE 14.3% 71% 28.6% 50%
MEASUREMENT 7.1% 0% 71% 85.7%
GEOMETRY 7.1% 71% 14.3% 71.4%
PATTERNS & FUCTIONS 7.1% 14.3% 7.1% 71.4%
STATISTICS & PROBABILITY 14.3% 14.3% 14.3% 57.1%
LOGIC 21.4% 7.1% 28.6% 42.9%
ALGEBRA 35.7% 7.1% 21.4% 35.7%
THEMES
ESTIMATION 14.3% 14.3% 14,3% 57.1%
PROBLEM SOLVING 14.3% 0% 0% 85.7%
TEACHING FOR CONCEPTS 21.4% 0% 21.4% 57.1%
COMMUNICATING CONCEPTS 23.1% 7.7% 46.2% 23.1%
USE OF CALCULATORS 46.2% 0% 38.5% 15.4%
INSTRUCTIONAL STRATEGIES
USE OF MANIPULATES 15.4% 7.7% 0% 76.9%
COOPERATIVE LEARNING 30.8% 0% 46.2% 23.1%
SITUATIONAL LESSONS 30.8% 7.7% 38.5% 23.1%
CONCEPT DEVELOPMENT 23.1% 0% 38.5% 38.5%
PROBLEM SOLVING/ INQUIRY 15.4% 0% 15.4% 69.2%
NONE LIMITED MODER. EXTENS. PRIMARY INTER. OVERALL
0 1 2 3 X X X
7.1% 0% 7.1% 85.7% 2.7 2.7 2.7
7.1% 7.1% 21.4% 64.3% 2.1 2.4 2.25
7.1% 0% 28.6% 64.3% 2.7 2.5 2,6
7.1% 0% 14.3% 78.6% 2.5 2.6 2.55
14.3% 21.4% 7.1% 57.1% 2.4 2 2,2
14.3% 7.1% 28.6% 50% 2.1 2.1 2.1
21.4% 14.3% 28.6% 35.7% 1.9 1.8 1.85
28.6% 14.3% 21.4% 35.7% 1.3 2.8 2.05
14.3% 14.3% 21.4% 50% 2.1 2 2.05
15.4% 0% 0% 84.6% 2.6 2.5 2.55
14.3% 7.1% 28.6% 50% 2.1 2.1 2.1
54% 23.1% 28.5% 23.1% 1.7 1.7 1.7
30,8% 15.4% 30.8% 23.1% 1.2 1.5 1.35
23.1% 7.7% 15.4% 53.8% 2.4 2 2.2
23.1% 7.7% 38.5% 23.1% 1.6 1.5 1.55
30.8% 7.7% 30.8% 30.8% 1.5 1.6 1.55
23.1% 0% 38.5% 35.5% 1.9 1.9 1.9
15.4% 7.7% 15.4% 61.5% 2.4 2.2 2.3
N=14
o \
- j
68
The ratings were:
3 = extensive emphasis
2 = moderate emphasis
1 = limited emphasis
0 = no emphasis
In content, the eight strands of the framework are listed.
Number, place value, measurement, geometry, patterns and
functions, and statistics and probably received an extensive
rating by over 50 percent of the researchers at both the
primary and intermediate levels. Logic and algebra received
extensive ratings by 42.98 percent and 35.7 percent at the
primary level, and 35.7 percent for both at the intermediate
level. All of these strands, except logic, had overall
means at the moderate level of 2.0 or above.
Themes contains five components. Estimation, problem
solving, and teaching for concepts received extensive
ratings by at least 50 percent of the researchers at the
primary and intermediate levels. Communicating concepts
received an extensive rating by 23.1 percent at both levels.
Use of calculators received no emphasis by 46.2 percent at
the primary level and 30.8 percent at the intermediate
level. The same three of the five that received the
extensive ratings also had overall means of at least 2.0.
Communicating concepts and use of calculators had overall
means of 1.7 and 1.35 respectively.
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69
In. the area of instructional strategies, only two of
the five components received extensive ratings of over 50
percent; use of manipulatives and problem solving/inquiry.
Coooperative learning, situational lessons, and concept
development received ratings of extensive by 23 to 35
percent of the researchers at both the primary and
intermediate levels. Overall means illustrate this same
emphasis in two out of the five components.
Table 2 displays this same information at the school
site level. In content, the pattern varies somewhat. The
same six out of eight strands tend to receive the extensive
rating by most of the researchers. Geometry was given this
rating by 35.7 percent of the researchers at the primary
level and by 50 percent at the intermediate level.
Statistics and probability received an extensive rating by
35.7 percent of the researchers. Again, logic and algebra
received an extensive rating by less than 50 percent of the
researchers at both the primary and intermediate levels.
These same two strands received the lowest overall mean of
1.75 and 1.43 respectively.
The pattern for the five components under themes was
the same as at the district level. The first three received
an extensive rating by at least 50 percent of the
researchers. Communicating concepts and use of calculators
received extensive ratings by less than 50 percent at both
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TABLE 2
RATINGS BY THE RESEARCH TEAM REGARDING THE EXTENT OF EMPHASIS GIVEN MATHEMATICS AT THE SCHOOL LEVEL
A SUMMARY OF PERCENTAGES AND MEANS ACROSS SCHOOLS
PRIMARY LEVEL INTERMEDIATE LEVEL
NONE LIMITED MODER. EXTENS. NONE LIMITED MODER. EXTENS. PRIMARY INTER. OVERAl
EXTENT OF EMPHASIS 0 1 2 3 0 1 2 3 X X X
COMPONENTS OF THE MATH FRAMEWORK
CONTENT
NUMBER 7.1% 7.1% 14.3% 71.4% 7.1% 7.1% 7.1% 78.6% 2.50 2.60 2,50
PLACE VALUE 21.4% 0% 28.6% 50% 14.3% 7.1% 21.4% 57.1% 2.10 2.20 2.10
MEASUREMENT 7.1% 7.1% 28.6% 57.1% 7.1% 7.1% 42.9% 42.9% 2.40 2.20 2.30
GEOMETRY 14.3% 14.3% 35.7% 35.7% 14.3% 14.3% 21.4% 50% 1.90 2.10 2,30
PATTERNS & FUCTIONS 14.3% 14.3% 7.1% 64.3% 14.3% 21.4% 21.4% 42.9% 2.20 1.90 2.10
STATISTICS & PROBABILITY 14.3% 21.4% 21.4% 42.9% 14.3% 14.3% 35.7% 35.7% 1.90 1.90 1.90
LOGIC 21.4% 14.3% 35.7% 28.6% 21.4% 21.4% 14.3% 42.9% 1.70 1,80 1.70
ALGEBRA 42.9% 7.1% 21.4% 28.6% 35.7% 14.3% 14.3% 35.7% 1.40 1.50 1.40
THEMES
ESTIMATION 21.4% 14.3% 14.3% 50% 21.4% 14.3% 14.3% 50% 1.90 1.90 1.90
PROBLEM SOLVING 15.4% 7.7% 15.4% 61.5% 15.4% 7.7% 15.4% 61.5% 2.20 2.20 2.20
TEACHING FOR CONCEPTS 15.4% 7.7% 15.4% 61.5% 14.3% 21% 28.6% 50% 2.20 2.10 2.20
COMMUNICATING CONCEPTS 16.7% 16.7% 25% 41.7% 15.4% 15.4% 38.5% 30.8% 1.90 1.80 1.90
USE OF CALCULATORS 30.8% 38.5% 15.4% 15.4% 23.1% 15.4% 38.5% 23.1% 1.20 1.60 1.40
INSTRUCTIONAL STRATEGIES
USE OF MANIPULATES 15.4% 7.7% 14.4% 61.5% 15.4% 15.4% 23.1% 46.2% 2.30 2.00 2.10
COOPERATIVE LEARNING 38.5% 7.7% 30.8% 23.1% 38.5% 0% 46.2% 15.4% 1.40 1.40 1.40
SITUATIONAL LESSONS 23.1% 15.4% 38.5% 23.1% 30.8% 23.1% 15.4% 30.8% 1.60 1.50 1.50
CONCEPT DEVELOPMENT 15.4% 15.4% 30.8% 38.5% 23.1% 7.7% 23.1% 46.2% 1.90 1.90 1.90
PROBLEM SOLVING/ INQUIRY 15.4% 15.4% 30.8% 38.5% 15.4% 15.4% 30.8% 38.5% 1,90 1.90 1.90
N=14 o
71
the primary and intermediate grade levels. These same two
components have the lower overall means of 1.89 and 1.39.
The other three had overall means of above 2.0.
Table 3 shows the information at the classroom level.
The first six of the eight strands still have most of the
extensive ratings, however the pattern seems to change at
this level. Number and place value have the highest
percentage at the extensive rating. Next are measurement,
and patterns and functions at the primary and intermediate
levels. Geometry drops off with extensive ratings of 20.8
percent at the primary level and 27.3 percent at the
intermediate level. The three that received the lowest
percentages at the extensive rating are statistics and
probability, logic, and algebra. These same patterns are
illustrated in the overall means. These three components
have the lowest means.
The pattern for themes is similar to the district and
school level in that estimation, problem solving, and
teaching for concepts received the highest percentages at
the extensive rating. There is a change. Communicating
concepts and use of calculators have a higher percentage
rating of extensive, compared to schools and district level.
This change in pattern is also reflected in the overall
means. The first three components have overall means of at
least 2.22, the last two, on communicating concepts and use
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TABLE 3
RATINGS BY THE RESEARCH TEAM REGARDING THE EXTENT OF EMPHASIS GIVEN MATHEMATICS AT CLASSROOM LEVEL
A SUMMARY OF PERCENTAGES AND MEANS ACROSS CLASSROOMS
PRIMARY LEVEL INTERMEDIATE LEVEL
NONE LIMITED MODER. EXTENS. NONE LIMITED MODER. EXTENS. PRIMARY INTER. OVERAL
EXTENT OF EMPHASIS 0 1
COMPONENTS OF THE MATH FRAMEWORK
CONTENT
2 3 0 1 2 3 X X X
NUMBER 0% 0% 20.8% 79.2% 0% 4.5% 31.9% 63.6% 2.58 2.60 2.59
PLACE VALUE 0% 4.2% 46.2% 54.2% 4.5% 0% 50% 45.5% 2.50 2.36 2.43
MEASUREMENT 8.3% 8.3% 41.7% 41.7% 9.1% 9.1% 45.5% 36.3% 2.12 2.09 2,11
GEOMETRY 5.3% 16.7% 54.2% 20.8% 9.1% 27.3% 36.3% 27.3% 1.88 1.82 1.85
PATTERNS & FUCTIONS 8.3% 8.3% 37.5% 45.9% 9.1% 18.2% 40.9% 31.8% 2.21 1.95 2.08
STATISTICS & PROBABILITY 20.8% 25% 75% 16.7% 27.3% 18.2% 36.3% 18.2% 1.50 1.45 1.48
LOGIC 16.7% 33.3% 37.5% 12.5% 18.2% 18.2% 36.3% 27.3% 1.08 1.72 1.49
ALGEBRA
THEMES
37.5% 25% 25% 12.5% 27.3% 27.3% 22.7% 22.7% 1.13 1.41 1.27
ESTIMATION 4.2% 8.3% 20.8% 66.7% 0% 9.1% 40.9% 50% 2.50 2.14 2.46
PROBLEM SOLVING 8.3% 8.3% 33.3% 50.1% 9.1% 9.1% 36.3% 45.5% 2.25 2.18 2.22
TEACHING FOR CONCEPTS 0% 0% 33.3% 66.7% 4.5% 4.5% 40.9% 50.1% 2.75 2.36 2.56
COMMUNICATING CONCEPTS 4.2% 8.3% 41.7% 45.8% 4.5% 13.6% 45.5% 36.4% 2.29 1.86 1.99
USE OF CALCULATORS
INSTRUCTIONAL STRATEGIES
37.5% 12.5% 20.8% 29.2% 22.7% 4.5% 36.4% 36.4% 1.42 1.86 1.64
USE OF MANIPULATES 4.2% 4.2% 12.5% 79.1% 9.1% 22.7% 36.4% 31.8% 2.67 1.91 2.29
COOPERATIVE LEARNING 4.2% 12.5% 33.3% 50% 18.2% 13.6% 27.3% 40.9% 2.29 1.91 2.10
SITUATIONAL LESSONS 12.5% 20.8% 25% 41.7% 18.2% 9.1% 31.8% 40.9% 1.96 1.96 1.96
CONCEPT DEVELOPMENT 0% 16.7% 20.8% 62.5% 1.5% 9.1% 10.9% 45.5% 2.46 2.27 2.37
PROBLEM SOLVING/ INQUIRY 4.2% 25% 25% 45.8% 9.1% 13.6% 31.8% 45.5% 2.13 2.15 2.14
N=14 w
73
of calculators, is below 2.0.
The comparison of means across district in mathematics
is displayed in Table 4. The same ratings were used to
calculate the means for extent of emphasis in content,
themes, and instructional strategies at the primary and
intermediate levels. The ratings were:
3 = extensive emphasis
2 = moderate emphasis
1 = limited emphasis
0 = no emphasis
Twelve of the fourteen districts have means at the moderate
level, 2.0, in most of the areas under primary. Districts
”F" and "L" have means of less than 2.0. These two
districts are not the smallest or largest districts. This
same pattern exists for intermediate content, themes, and
instructional strategies.
When comparing primary means to intermediate means,
four of the fourteen districts had higher primary means.
Seven districts had higher means in intermediate compared to
primary. Three of the districts have the same means for
primary and intermediate. Twelve of the fourteen districts
had total district means of at least 2.0. The same two
districts, "F" and "L" had means below the moderate level.
Table 5 displays the same information at the school
site level. The same rating system was used. The patterns
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TABLE 4
RATINGS BY THE RESEARCH TEAM REGARDING EXTENT OF EMPHASIS GIVEN MATHEMATICS
MEANS OF ALL DISTRICTS
DISTRICT A B C D E F G H I J K L M N
Primary Content 2.50 2.80 3.00 2.50 2.60 1.40 1.90 1.90 3.00 2.60 2.00 1.60 3.00 3.00
Primary Themes 2.60 2.40 2.80 2.00 2.20 Nl 2.80 2.20 1.40 2.80 2.00 0.80 2.40 2.40
Primary Strategies 2.60 3.00 2.80 2.80 2.60 Nl 2.40 2.40 Nl 2,00 2.80 0.80 2.00 2.80
Inter. Content 2.60 2.60 2.10 2.80 2.30 1.60 2.60 1.90 3.00 2.90 2.00 1.90 3.00 3.00
Inter. Themes 2.60 3.00 1.40 2.00 2.20 Nl 2.80 2.20 1.40 2.80 2.00 1.20 1.40 2.40
Inter. Strategies 2.40 3.00 1.40 2.80 2.80 Nl 2.40 2.40 Nl 2.00 3.00 0.60 2.00 2.20
Total Primary 2.57 2.73 2.87 2.43 2.47 1.40 2.37 2.13 2.20 2.47 2.27 1.07 2.47 2.73
Total Intermediate 2.53 2.87 1.63 2.53 2.43 1.60 2.60 2.13 2.20 2.57 2.33 1.23 2.47 2.53
Total District 2.55 2.80 2.25 2.48
* DISTRICTS A THROUGH N ARE IN ORDER FROM
2.45 1.50 2.48 2.13
LARGEST TO SMALLEST
2.20 2.52 2.30 1.15 2.47 2.63
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TABLE 5
RATINGS BY THE RESEARCH TEAM REGARDING EXTENT OF EMPHASIS GIVEN MATHEMATICS
MEANS OF ALL SCHOOLS
DISTRICT A B C D E F G H I J K L M N
Primary Content 2.3 2.8 2.4 2.1 2 1.4 2.1 1.9 3 2.6 2 0.3 3 3
Primary Themes 2.4 2.8 2 2.2 2.2 Nl 2.8 2.2 3 2.8 2 0.8 2.4 3
Primary Strategies 2.8 3 1.4 2 2.2 Nl 2.4 2.4 Nl 2 2.8 0.6 2 2.4
Inter. Content 2.5 2.9 1.6 2.3 2.4 1.6 1.9 1.9 3 2.9 2 0.3 3 3
Inter. Themes 2.4 3 1.8 2.3 2.4 Nl 2.8 2.2 2.3 2.8 2 0.8 2.4 2.8
Inter. Strategies 2 3 1.6 1.4 2.8 Nl 2.4 2.4 Nl 2 3 0.6 2 2.8
Total Primary 2.5 2.87 1.93 2.1 2.13 1.4 2.43 2.13 3 2.47 2.27 0.57 2.47 2.8
Total Intermediate 2.3 2.97 1.67 2 2.53 1.6 2.37 2.13 2.7 2.57 2.33 0.57 2.47 2.87
Total School 2.4 2.92 1.8 2.05 2.33 1.5 2.4 2.13 2.85 2.52 2.3 0.57 2.47 2.84
* DISTRICTS A THROUGH N ARE IN ORDER FROM LARGEST TO SMALLEST
76
here are similar to the district patterns. Most of the
schools have means at the moderate level in primary content,
themes, and instructional strategies. School "F" and "L"
again fall below 2.0. School "L" even falls below the 1.0
rating of limited emphasis. No information was available
for school "F" in themes and instructional strategies.
At the intermediate level this pattern also adds school
"C". It has a mean of less than 2.0 in content, themes, and
instructional strategies. Also, no information is listed
for schools "F" and district "I". Schools "F" and "L" also
have means of less than 2.0. School "L" again has the
lowest means in the components of 0.3, 0.8, and 0.6 in
content, themes, and instructional strategies.
When comparing primary means to intermediate means,
five of the fourteen schools had higher means at the primary
level. Six of the schools had intermediate grades rated
higher. The remaining three schools have the same mean at
the primary and intermediate levels. The overall means
across all the schools do not seem to follow a pattern when
comparing larger districts to smaller districts by the size
of pupil population.
The pattern changes more drastically at the classroom
level. This is shown in Table 6. No information was
available at the classroom for schools "E" and "N". Of the
twelve remaining classes, four had means below the moderate
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TABLE 6
RATINGS BY THE RESEARCH TEAM REGARDING EXTENT OF EMPHASIS GIVEN MATHEMATICS
MEANS OF ALL CLASSROOMS
DISTRICT A B C D E F G H I J K L M N
Primary Content 1.94 2.94 1.06 1.63 Nl 1.44 2.75 1.75 1.44 1.75 2.13 1.63 2.13 Nl
Primary Themes 2.2 3 1.5 1.8 Nl 1.7 2.7 2.6 2 1.9 2.5 1.9 2.3 Nl
Primary Strategies 2.7 3 1.8 1.6 Nl 2.2 3 3 2.1 2.4 2.8 1.9 1.7 Nl
Inter. Content 2.13 2.13 1 1.56 Nl 1.31 2.94 1.75 2.13 2.25 2.38 1.13 2.5 Nl
Inter. Themes 2.9 1.7 1.4 1.6 Nl 1.9 2.7 2.6 2.8 2.3 3 1.7 1.9 Nl
Inter. Strategies 2.5 1.6 1.4 1.8 Nl 1.7 2.5 3 2.7 2.6 2.8 0.7 1.7 Nl
Total Primary 2.28 2.98 1.45 1.68 Nl 1.78 2.82 2.45 1.85 2.02 2.48 1.81 2.04 Nl
Total Intermediate 2.51 1.81 1.27 1.65 Nl 1.64 2.71 2.45 2.54 2.38 2.73 1.18 2.03 Nl
Total Classroom 2.4 2.4 1.36 1.67 Nl 1.71 2.77 2.45 2.2 2.2 2.61 1.5 2.04 Nl
* DISTRICTS A THROUGH N ARE IN ORDER FROM LARGEST TO SMALLEST
78
level. These were "C", "D", "F", and "L". This drop is
consistent in content, themes, and instructional strategies
at both the primary and intermediate levels.
At the classroom level, seven of the 12 have a primary
mean that is higher than the intermediate mean. One set of
classes has the same mean for primary as for intermediate.
Primary appears to have a greater extent of emphasis when
compared to intermediate.
Science
Science data is displayed in Tables 7-12. Table 7
shows the percentages and means for all of the science
components at the district level. In content there are
three: life, earth, and physical science. All of these
components received an extensive rating by at least 69
percent of the researchers. The overall means were 2.6,
2.65, and 2.6. These are above the moderate rating of 2.0.
In themes there are seven components. Observing and
hands on activities received extensive ratings by 69.2
percent of the researchers at the primary level. This is
followed by scientific process, inferring, ethical issues,
and apply to everyday life. These components received
extensive ratings by 25 to 30 percent of the researchers.
There is a drop in extensive rating by the researchers in
science technology with only 7.1 percent. This pattern
continues at the intermediate level. The overall means are
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TABLE 7
RATINGS BY THE RESEARCH TEAM REGARDING THE EXTENT OF EMPHASIS GIVEN SCIENCE AT THE DISTRICT LEVEL
A SUMMARY OF PERCENTAGES AND MEANS ACROSS DISTRICTS
PRIMARY LEVEL INTERMEDIATE LEVEL
NONE LIMITED MODER. EXTENS. NONE LIMITED MODER. EXTENS. PRIMARY INTER. OVERAL
EXTENT OF EMPHASIS 0 1 2 3 0 1 2 3 X X X
COMPONENTS OF THE SCIENCE FRAMEWORK
CONTENT
LIFE SCIENCE 7.1% 0% 14.3% 78.6% 7.1% 0% 14.3% 78.6% 2.6 2.6 2.6
EARTH SCIENCE 7.1% 0% 15.4% 76.9% 7.1% 0% 0% 85.7% 2.6 2.7 2.65
PHYSICAL SCIENCE 7.1% 0% 23.1% 69.2% 7.1% 0% 7.1% 85.7% 2.5 2.7 2.6
THEMES
OBSERVING 15.4% 7.7% 7.7% 69.2% 15.4% 0% 23.1% 61.5% 2.3 2.3 2.3
SCIENTIFIC PROCESS 15.4% 7.7% 30.8% 46.2% 14.3% 7.1% 14.3% 64.3% 2.1 2.3 2.2
INFERRING 15.4% 7.7% 46.2% 3.8% 15.4% 7.1% 23.1% 53.8% 1.9 2.2 2.05
HANDS ON ACTIVITIES 15.4% 0% 14.5% 69.2% 15.4% 0% 23.1% 61.5% 2.4 2.3 2.35
SCIENCE TECHNOLOGY 21.4% 37.5% 35.7% 7.1% 21.4% 21.4% 50% 7.1% 1.3 1.4 1.35
ETHICAL ISSUES 25% 25% 25% 25% 25% 25% 25% 25% 1.5 1.5 1.5
APPLY TO EVERYDAY LIFE 14.3% 21.4% 35.7% 28.6% 15.4% 15.4% 30.8% 38.5% 1.8 1.9 1.85
INSTRUCTIONAL STRATEGIES
USE OF MANIPULATIVES 15.4% 7.7% 15.4% 61.5% 15.4% 7.7% 15.4% 61.5% 2.2 2.2 2.2
COOPERATIVE LEARNING 33.3% 0% 33.3% 33.3% 33.3% 0% 33.3% 33.3% 1.7 1.7 1.7
PROBLEM ENGAGEMENT 23.1% 15.4% 30.8% 30.8% 23.1% 7.7% 30.8% 38.5% 1.7 1.7 1.75
CONCEPT DEVELOPMENT 15.4% 7.7% 0% 76.9% 15.4% 0% 7.7% 76.9% 2.4 2.4 2.45
N=14
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80
above 2.0 in four of the seven themes. Observing,
scientific process, inferring, and hands on activities are
above technology, ethical issues, and apply to everyday
life. These three all had overall means of below 2.0; the
other four have overall means above 2.0.
Instructional strategies includes use of manipulatives,
cooperative learning, problem engagement, and concept
development. Use of manipulatives received an extensive
rating by 61.5 percent of the researchers and concept
development received it from 76.9 percent at the primary
level. The intermediate levels were also high at the
extensive rating. Cooperative learning and problem
engagement received an extensive rating from at least 30
percent of the researchers at both the primary and
intermediate levels. This same pattern is reflected in the
overall means.
Table 8 illustrates this same information at the school
site level and calculates the information across all 14
schools. The pattern changes for content. All three
components receive an extensive rating by at least 53
percent of the research team at the primary level. It drops
off for physical science at the primary level to 35.7
percent giving an extensive rating. This continues in the
overall means. Life and earth science are above 2.0 and
physical is below 2.0.
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TABLE 8
RATINGS BY THE RESEARCH TEAM REGARDING THE EXTENT OF EMPHASIS GIVEN SCIENCE AT THE SCHOOL LEVEL
A SUMMARY OF PERCENTAGES AND MEANS ACROSS SCHOOLS
PRIMARY LEVEL INTERMEDIATE LEVEL
NONE LIMITED MODER. EXTENS. NONE LIMITED MODER. EXTENS. PRIMARY INTER. OVERALL
EXTENT OF EMPHASIS 0 1 2 3 0 1 2 3 X X X
COMPONENTS OF THE SCIENCE FRAMEWORK
CONTENT
LIFE SCIENCE 21.4% 0% 14.3% 64.3% 23.1% 0% 15.4% 61.5% 2.21 2.15 2.81
EARTH SCIENCE 21.4% 0% 28.6% 50% 21.4% 0% 21.4% 57.1% 2.07 2.14 2.11
PHYSICAL SCIENCE 21.4% 14.3% 28.6% 35.7% 23.1% 7.7% 15,4% 53.8% 1.79 2 1.9
THEMES
OBSERVING 21.4% 0% 14.3% 64.3% 21.4% 0% 21.4% 57.1% 2.21 2.14 2 18
SCIENTIFIC PROCESS 23.1% 7.7% 30.8% 38,5% 23.1% 15.4% 15.4% 46.2% 1.85 0.185 1.85
INFERRING 23.1% 7.7% 30.8% 38.5% 23.1% 15.4% 23.1% 38.5% 1.85 1.77 1.81
HANDS ON ACTIVITIES 23.1% 0% 15.4% 61.5% 23.1% 7.7% 30.8% 3.85% 2.15 1.85 2
SCIENCE TECHNOLOGY 21.4% 42.9% 28.6% 7.1% 21.4% 35.7% 35.7% 7.1% 1.21 1.29 1.25
ETHICAL ISSUES 23.1% 30.8% 23.1% 23.1% 23.1% 30.8% 23.1% 23.1% 1.46 1.46 1.465
APPLY TO EVERYDAY LIFE 21.4% 21.4% 21.4% 35.7% 23.1% 23.1% 30.8% 23.1% 1.71 1.54 1.63
INSTRUCTIONAL STRATEGIES
USE OF MANIPULATIVES 23.1% 7.7% 23,1% 46.2% 23.1% 154% 23.1% 38.5% 1.92 1.77 1.85
COOPERATIVE LEARNING 33.3% 0% 33.3% 33.3% 33.3% 8.3% 33.3% 25% 1.67 1.5 1.59
PROBLEM ENGAGEMENT 21.4% 14.3% 28.6% 35.7% 23.1% 7.7% 38.5% 30.8% 1.79 1.77 1.78
CONCEPT DEVELOPMENT 21.4% 0% 21.4% 57.1% 21.4% 0% 35.7% 42.9% 2.14 2 2.07
N=14
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82
The pattern for the seven components in themes changes
slightly when compared to the district pattern. Observing
and hands on activities received an extensive rating by over
61 percent of the research team. Four, of the other five
components, and extensive ratings by 23 to 38 percent.
Again, science technology dropped off with only 7.1 percent
giving it an extensive rating. This pattern is the same for
both primary and intermediate themes. An exception is that
hands on activities is given an extensive rating by only
38.5 percent of the team at the intermediate level compared
to 61.5 percent at the primary level. Overall means in
themes is also the lowest in science technology and the
highest in observing. This pattern is different than at the
district level because the means fall below 2.0 in five of
the seven components.
Instructional strategies has four components in
science. Mathematics had five. The four in science are use
of manipulatives, cooperative learning, problem engagement,
and concept development. Concept development received the
highest percentages at the extensive rating at both the
primary and intermediate levels of 57.1 percent and 42.9
percent respectively. The other three components received
from 25 to 46 percent of the extensive rating at the primary
and intermediate levels. This same pattern is reflected in
the overall means. Concept development is above 2.0 and the
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83
other three are slightly below 2.0.
The percentages and means for the classrooms are shown
in Table 9. Here the pattern for content changes again.
The intermediate level shows the extensive ratings are
similar for all three components ranging from 58.3 percent
for earth and physical science and 66.7 percent for life
science. The primary grades show 70.9 percent giving life
science an extensive rating. Much larger than the 45.9
percent of extensive given to earth and physical science.
The primary grades appear to have implemented life science
to a greater extent. This is also consistent with the
overall means. Life science has the highest overall mean of
2.54.
Themes at the classroom level do not follow the same
pattern as the district and school levels. The percentages
of primary classes receiving an extensive rating only vary
from 29.2 to 62.5 percent. The primary ratings are again
the highest in observing and hands on activities. Ethical
issues is also again low with only 20.8 percent of the
researchers giving it an extensive rating. The other four
components of themes range from 50 to 54.2 percent that
received an extensive rating. This pattern is also
illustrated in the overall means. Here the highest overall
mean is again in observing and the lowest means, below 2.0,
are in ethical issues and science technology.
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TABLE 9
RATINGS BY THE RESEARCH TEAM REGARDING THE EXTENT OF EMPHASIS GIVEN SCIENCE AT THE CLASSROOM LEVEL
A SUMMARY OF PERCENTAGES AND MEANS ACROSS CLASSROOMS
PRIMARY LEVEL INTERMEDIATE LEVEL
NONE LIMITED MODER. EXTENS. NONE LIMITED MODER. EXTENS. PRIMARY INTER. OVERALL
EXTENT OF EMPHASIS 0 1 2 3 0 1 2 3 X X X
COMPONENTS OF THE SCIENCE FRAMEWORK
CONTENT
LIFE SCIENCE 0% 12.5% 16.6% 70.9% 8.3% 0% 25% 66.7% 2.58 2.5 2.54
EARTH SCIENCE 8.3% 16.6% 29.2% 15.9% 8.3% 4.2% 29.2% 58.3% 2.13 2.38 2.26
PHYSICAL SCIENCE 4.2% 16.6% 33.3% 45.9% 12.5% 4.2% 25% 58.3% 2.01 2.29 2.15
THEMES
OBSERVING 0% 8.3% 12.5% 79.2%
SCIENTIFIC PROCESS 1.25% 20.9% 16.6% 50%
INFERRING 8.3% 8.3% 33.4% 50%
HANDS ON ACTIVITIES 0% 8.3% 33.4% 58.3%
SCIENCE TECHNOLOGY 16.6% 41.8% 25% 16.6%
ETHICAL ISSUES 29.2% 35.7% 12.5% 20.8%
APPLY TO EVERYDAY LIF 0% 16.6% 29.2% 54.2%
INSTRUCTIONAL STRATEGIES
USE OF MANIPULATIVES 0% 8.3% 12.5% 79.2%
COOPERATIVE LEARNINC 4.2% 16.6% 29.2% 50%
PROBLEM ENGAGEMENT 4.2% 8.3% 33.3% 54.2%
CONCEPT DEVELOPMEN 0% 8.3% 20.9% 70.8%
4.2% 4.2% 29.2% 62.5% 2.71 2.5 2.61
0% 25% 29.2% 45.8% 2.04 2.21 2.13
0% 8.3% 37.5% 54.2% 2.13 2.46 2.3
0% 8.3% 29.2% 54.2% 2.5 2.38 2.44
8.3% 25% 37.5% 29.2% 1.52 1.88 1.65
16.6% 29.2% 20.9% 33.3% 1.25 1.71 1.48
4.2% 16.7% 33.3% 45.8% 2.38 2.21 2.3
0% 12.5% 29.2% 58.3% 2.7 2.46 2.58
8.3% 8.3% 25.1% 58.3% 2.25 2.33 2.29
4.2% 20.8% 25% 50% 2.38 2.21 2.3
0% 4.2% 33.3% 62.5% 2.63 2,58 2.61
N=14
oo
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In instructional strategies the extensive rating
dropped off at the school level when compared to the
district level. At the classroom level it again jumps up
for use of manipulatives and concept development. They
received an extensive rating from 58.3 to 79.2 percent of
the team. Cooperative learning only received an extensive
rating from 5 percent of the researchers at the primary
level compared to intermediate. Problem engagement received
and extensive rating by at least 50 percent of the team at
the primary and intermediate levels. The overall means in
instructional strategies for classrooms are all above 2.0.
They range from 2.29 for cooperative learning to 2.61 for
concept development.
Table 10 shows the means for science across all
districts in content, themes, and instructional strategies
for the primary and intermediate grade levels. Content, at
the primary and intermediate levels consistently has a
higher mean when compared to themes and instructional
strategies across all districts. No information is noted in
several components in three districts.
When looking at primary and intermediate means for
science, eight out of the fourteen district have the exact
same mean for primary and intermediate. Two of the
districts have a higher mean for the primary grades and four
of the districts have a higher mean for intermediate grades.
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TABLE 10
RATINGS BY THE RESEARCH TEAM REGARDING EXTENT OF EMPHASIS GIVEN SCIENCE
MEANS OF ALL DISTRICTS
DISTRICT A B C D E F G H I J K L M N
Primary Content 3 2 3 3 2 3 2.7 3 3 3 Nl 3 3 3
Primary Themes 2.7 2.4 1.4 2 1.9 Nl 1.9 1.7 2.1 2.6 2.4 2 2 2.6
Primary Strategies 2.5 2.8 Nl 3 1.5 Nl 2.5 2.5 2 2.3 2.3 1.5 2 3
Inter. Content 2 2 3 3 3 3 2.7 3 3 3 Nl 3 3 3
Inter. Themes 2 2.4 1.4 2 1.3 Nl 1.9 2 2.1 2.9 2.4 2.7 2 2.7
Inter. Strategies 2 2.8 Nl 3 1.5 Nl 2.5 3 2 2.3 2.3 1.5 2 3
Total Primary 2.73 2.4 2.2 2.67 1.8 3 2.37 2.4 2.37 2.63 2.35 2.17 2.33 2.87
Total Intermediate 2 2.4 2.2 2.67 1.93 3 2.37 2.67 2.37 2.73 2.35 2.4 2.33 2,67
Total District 2.3 2.4 2.2 2.67 1.87 3 2.37 2.53 2.37 2.68 2.35 2.28 2,33 2.77
* DISTRICTS A THROUGH N ARE IN ORDER FROM LARGEST TO SMALLEST
00
a\
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The means across the district totals are at, or above 2.2,
in thirteen of the fourteen districts. Only district "D"
has a mean of below 2.0, with 1.87.
School means across all the sites are displayed in
Table 11. The pattern continues here that content
consistently receives a higher mean when compared to themes
and instructional strategies. There is no information
available in some components for districts "F" and "K". In
primary content, eight of the districts had a mean of 3,
extensive emphasis. In intermediate content, nine of the
districts had means of 3.
Six of the districts have means that are the same for
their primary and intermediate grades. Three of the
districts have a higher mean for primary compared to the
five that have intermediate grades with higher means.
Across the totals, like the district level, thirteen of the
districts have means of over 2.0. Only District "D" has a
mean that is below 2.0
Table 12 shows the means across all classrooms for
science. The pattern that was seen at the district and
school level is not seen here at the classroom level.
Content does receive high moderate to high means by over
half of the classes. Here instructional strategies also
receives moderate to high means by over half the classes at
the primary and intermediate levels. No information was
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TABLE 11
RATINGS BY THE RESEARCH TEAM REGARDING EXTENT OF EMPHASIS GIVEN SCIENCE
MEANS OF ALL SCHOOLS
DISTRICT A B C D E F G H I J K L M N
Primary Content 2 3 3 2 2 2 2.7 3 3 3 Nl 3 3 3
Primary Themes 2.4 3 1.8 1.7 2.1 Nl 2.2 1.7 2.1 2.6 2.4 2 2 2.6
Primary Strategies 2.5 3 1.5 2 2.8 Nl 2 2.5 2.7 2.3 2.3 1.5 2 3
Inter. Content 2 3 3 2 3 2.3 2.7 3 3 3 Nl . 3 3 3
Inter. Themes 2 3 1.8 1.3 1.3 Nl 2.2 2 2.1 2.9 2.4 2 2 2.7
Inter. Strategies 2 3 2 2 1.5 Nl 2 3 2.7 2.3 2.3 1.5 2 3
Total Primary 2.3 3 2.1 1.9 2.3 2 2.3 2.4 2.6 2.63 2.35 2.17 2.33 2.87
Total Intermediate 2 3 2.27 1.77 1.93 2.3 2.3 2.67 2.6 2.73 2.35 2.17 2.33 2.9
Total District 2.15 3 2.19 1.84 2.12 2.15 2.3 2.53 2.6 2.68 2.35 2.17 2.33 2.89
* DISTRICTS A THROUGH N ARE IN ORDER FROM LARGEST TO SMALLEST
o o
00
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TABLE 12
RATINGS BY THE RESEARCH TEAM REGARDING EXTENT OF EMPHASIS GIVEN SCIENCE
MEANS OF ALL CLASSROOMS
DISTRICT A B C D E F G H I J K L M N
Primary Content 1.83 3 1.33 2 Nl 2.17 3 3 2 2.17 3 2.17 3 Nl
Primary Themes 2.21 2.93 1.5 1.93 Nl 2.21 2.21 2.86 1.86 1.5 3 1.36 1.29 Nl
Primary Strategies 2.5 3 2.38 2.63 Nl 2.25 3 3 2 1.5 2.88 1.75 3 Nl
Inter. Content 2 3 1 2.5 Nl 1.5 2.67 3 2.5 2.5 2.67 3 2.5 Nl
Inter. Themes 1.79 2.64 1.5 2.36 Nl 1.71 2.86 2.86 2.14 2.64 2.36 2.14 1.23 Nl
Inter. Strategies 1.89 2.5 2 2.88 Nl 1.88 3 3 2.5 3 2,63 2.63 1.13 Nl
Total Primary 2.18 2.98 1.74 2.19 Nl 2.21 2.74 2.95 1.95 1.72 2.96 1.76 2.43 Nl
Total Intermediate 1.89 2.71 1.5 2.58 Nl 1.7 2.84 2.95 2.38 2.71 2.55 2.59 1.62 Nl
Total District 2.04 2.85 1.62 2.39 Nl 1.96 2.79 2.95 2.17 2.22 2.76 2.18 2.03 Nl
* DISTRICTS A THROUGH N ARE IN ORDER FROM LARGEST TO SMALLEST
o o
v £ >
90
available for classes "E", and "N".
Six of the class means were higher for the primary
grades compared to five at the intermediate grade levels.
Again, no information was available for "E" and "N". The
means for all classes are 2.03 to 2.95. Only "C" and "F"
are below 2.0 The classes are consistently given ratings at
the moderate and extensive levels.
Mathematics Compared to Science
A comparison of means is displayed in Table 13 for
mathematics and science for content, themes, and
instructional strategies for primary and intermediate
grades. It also shows the total primary means and the total
intermediate means.
At the primary level, science has a higher means at the
district, school, and classroom levels. The range of themes
across all levels is closer. Mathematics is slightly higher
at the district, school, and classroom levels.
Instructional strategies does not follow a pattern in the
primary grades. It is higher for mathematics at the
district level, higher in science at the school level, and
higher in science at the classroom level.
In the intermediate grades, science ranks above
mathematics again in content at the district, school, and
classroom levels. Science is slightly higher at the
district level in themes. Mathematics is higher in themes,
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PRIMARY CONTENT
PRIMARY THEMES
PRIMARY STRATEGIES
INTERMEDIATE CONTENT
INTERMEDIATE THEMES
INTERMEDIATE STRATEGIES
TOTAL PRIMARY
TOTAL INTERMEDIATE
GRAND TOTAL
EXTENT OF EMPHASIS
TABLE 13
RATINGS BY THE RESEARCH TEAM REGARDING EXTENT OF EMPHASIS
FOR MATHEMATICS AND SCIENCE ACROSS ALL SITES AT ALL LEVELS
DISTRICT SCHOOL CLASSROOM
MATH SCIENCE MATH
2.41 2.82 2.06
2.22 1.99 2.35
2.42 2.33 2.17
2.45 2.82 2.24
2.11 2.14 2.31
2.25 2.33 2.17
2.35 2.38 2.19
2.27 2.43 2.24
2.31 2.41 2.22
SCIENCE MATH SCIENCE
2.67 1.88 2.39
2.2 2.18 2.07
2.32 2.35 2.49
2.78 1.93 2.4
2.13 2.21 2.19
2.25 2.08 2.42
2.4 2.14 2.32
2.39 2.07 2.34
2.39 2.11 2.33
i=NONE 1=LIMITED 2=MODERATE 3=EXTENSIVE
VO
92
at the school and classroom levels. All of the means in
Table 13 are above 2.0, the moderate rating. Intermediate
instructional strategies is higher in science at the
district, school, and classroom levels.
Across the grand totals at the bottom of the table,
science has a higher mean for all levels. The spread of
means is the largest at the classroom level with science
given 2.33 and mathematics given 2.11. The smallest
difference in means is at the district level, with 2.31 for
mathematics and 2.41 for science. Science appears to have
a slightly higher extent of implementation across all levels
at both the primary and intermediate grade levels.
Correlations
Table 14 displays the correlations calculated with
Pearson's R at the .05 level. A +1 signifies a perfect
positive correlation. The closer the correlations are to
this figure, the stronger the relationship between the two
items. The Table shows mathematics and science across the
top and the components of content, themes and instructional
strategies for both. Across the left hand side of the table
are the items (variables) that are being compared and the
correlation being computed. Correlations are considered
moderate at the .60 level and significant at the .75 level
(Horowitz, 1979).
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TABLE 14
CORRELATIONS OF MATHEMATICS AND SCIENCE EMPHASIS - SCORES AT ALL LEVELS ACROSS ALL SITES
MATHEMATICS SCIENCE
CONTENT THEMES INST. STRA CONTENT THEMES INST. STRA.
DISTRICT PRIMARY WITH SCHOOL PRIMARY 0.640 0.610 0.510 0.370 0.410 0.400
DISTRICT INTERMEDIATE WITH SCHOOL INTERMEDIATE 0.620 0.640 0.460 0.400 0.260 0.370
DISTRICT PRIMARY WITH DISTRICT INTERMEDIATE 0.930 0.980 0.920 0.950 0.980 0.990
SCHOOL PRIMARY WITH SCHOOL INTERMEDIATE 0.960 0.990 0.930 0.970 0.980 0.950
SCHOOL PRIMARY WITH CLASS PRIMARY 0.280 0.340 0.160 0.150 0.190 0.290
SCHOOL INTERMEDIATE WITH CLASS INTERMEDIATE 0.550 0.050 0.090 0.410 0.100 0.001
CLASS PRIMARY WITH CLASS INTERMEDIATE 0.520 0.100 0.510 0.580 0.380 0.200
DISTRICT PRIMARY WITH CLASS PRIMARY 0.020 0.310 0.110 0.520 0.380 0.160
DISTRICT INTERMEDIATE WITH CLASS INTERMEDIATE 0.070 0.210 0.130 0.250 0.200 0.280
CALCULATED WITH PEARSON’S R AT THE .05 LEVEL
U3
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In mathematics, the correlations are moderate in
content when comparing district primary with school primary
and district intermediate with school intermediate. In
themes, these same two correlations are also moderate. This
is not true of instructional strategies. The strongest
correlation exists in district primary with district
intermediate in content, themes, and instructional
strategies. These are all at the .92 level and above. This
is a very significant correlation.
The next three correlations in mathematics show a
significant correlation in school primary with school
intermediate in content, themes, and instructional
strategies. No other correlations in mathematics are
moderate or significant.
Science correlations are also significant in district
primary with district intermediate. These, like
mathematics, are very significant. They range from .95 to
.99. A moderate correlations does not exist for district
intermediate with school intermediate or district primary
with school primary as was in mathematics.
The second set of correlations for science display the
same pattern as mathematics. School primary with school
intermediate shows a very significant correlation in
content, themes, and instructional strategies. These range
from .95 to .98. There are no other significant
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95
correlations for science.
The following correlations did not qualify as moderate
or significant for mathematics and science:
SCHOOL PRIMARY WITH CLASS PRIMARY
SCHOOL INTERMEDIATE WITH CLASS INTERMEDIATE
CLASS PRIMARY WITH CLASS INTERMEDIATE
DISTRICT PRIMARY WITH CLASS PRIMARY
DISTRICT INTERMEDIATE WITH CLASS INTERMEDIATE
Discussion
This study examined the extent districts, schools, and
classrooms have implemented the California mathematics and
science frameworks. Previous research focused on how to get
policies implemented, not on the strategies utilized to make
the implementation successful. Reforms of the 1980s were
concerned with improving education for all students, not
just the high achievers.
The ratings used by the researchers on the extent of
implementation were:
3 = extensive emphasis
2 = moderate emphasis
1 = limited emphasis
0 = no emphasis
Mathematics strands were perceived by the researchers
as being extensively implemented. The two strands that
received lower overall means at the district, school, and
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96
classroom levels, were logic and algebra. These were not
previously emphasized in the framework or textbooks. Algegra
and logic are now intertwined into mathematics textbooks for
teachers to incorporate in their lessons.
In themes, the use of calculators received a low rating
by the researchers. Perhaps this is because it was new to
the mathematics framework and new to teachers in the
classroom. This had not been a focus of mathematics
previously in public schools. Problem solving tended to
receive a moderate mean of at least 2.2 and above at the
district, school, and classroom levels. This had been a
component that was in the previous framework and was also
common in mathematics textbooks. Teachers recognize the
importance of students being able to solve word problems
that would be similar to the types of problems they will
encounter in the real world.
The use of manipulatives, as an instructional strategy,
was consistently given a rating of extensive by over 50
percent of the researchers at the primary grade level. This
was also a focus of the framework. Districts, schools, and
classrooms were perceived by the researchers as extensively
implementing this component of the framework. Textbook
publishers offered them as part of the "sales package" when
school districts purchased from them.
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97
This extent of implemention was supported by Senate
Bill 813. One of its goals was to improve curriculum in
core academics. This adoption was the first time California
had rejected textbooks from publishers because they did not
meet the needs of our students. Huberman and Miles (1984)
determined that high commitment and district support are key
factors related to successful implementation. The science
and mathematics frameworks were seen as quality curriculum
(Odden, 1991). To strengthen the implementation, the study
by Odden and Marsh (1990) in California revealed that the
"top-down" and "bottom-up" process became linked together.
This linkage made the implementation process more smooth.
By the end of the two-year adoption phase, all districts and
respective schools had adopted the state curricula
frameworks.
Science content means were above 2.5 at the district
level and above 2.0 at the school and classroom levels. The
overall mean in physical science at the school level was
1.9. These moderate levels support implementation of the
science framework. Primary and intermediate grades received
an extensive rating by over 50 percent of the researchers at
the district level in life, earth, and physical science.
Classroom ratings were slightly higher for the intermediate
grades. Classroom means were all above the moderate rating
of 2.0.
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98
Themes received means of over 2.0 in four of the seven
components at the district level. This drops off for the
school level and rises again at the classroom level. The
component that consistently received the lowest mean is
science technology. This is true at the district, school,
and classroom levels. Since this was a new focus of the
framework, perhaps teachers did not have the expertise or
materials to fully implement it.
Cooperative learning was the component under
instructional strategies that received the lowest mean at
all three levels. This strategy had not been one that was
listed in the previous framework. It is a strategy that is
currently seen, and is being used by teachers, in many
subject areas. By being a part of the framework, it seems
to have become a part of many classroom teachers1 techniques
and instructional strategies.
Problem engagement is an instructional strategy that
also received means at the moderate and limited levels. The
National Council of the Teachers of Mathematics' standards
focus on critical thinking and the application of knowledge
to real life problems. The framework, again, supports
changes that are a focus at the national level. It is
important for students to have skills that will benefit them
in life and the workplace.
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99
In comparing the extent of mathematics and science
implementation illustrated on Table 13, science consistently
has higher means in all components at all three levels. The
mathematics framework came out before the science framework.
It was seen as a quality framework that was supported by the
state. Perhaps this momentum continued as the science
framework followed. Educators across the boards in, the
central offices, schools, and classrooms, were implementing
these curricula at a moderate to extensive level. Grand
totals show science rated higher at the district, school,
and classroom levels.
The correlations that are significant in Table 14 can
tell us just as much about the extent of implementation, as
do the numbers that are significant. District with district
and school with school correlations are the strongest. This
illustrates that the linkage was strong in these places.
The lowest figures are in district primary with class
primary and district intermediate with class intermediate.
This may show that the linkage and articulation between
these levels is weak. The implementation of curricula from
the district, through the school, to the classroom level
could be strengthened.
The fact that the correlations were significant between
the primary and intermediate grades at the school level,
supports the idea that the curriculua at this level was
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1 0 0
being implemented to a great extent. Teachers at all grade
levels were consistently implementing the mathematics and
science frameworks. This was the perception of the
researchers as they observed lessons on mathematics and
science in the classrooms. They were seeing the components
of the frameworks in action. Teachers had begun to
demonstrate their ability to incorporate many parts of the
frameworks in their daily lessons.
Science means that are displayed in Table 13 are
consistently higher than the mathematics means at the
district, school, and classroom levels. Many elementary
teachers teach mathematics every day. This is not always
true of science. Perhaps teachers spend more time on
planning and preparing a science lesson because it is not
part of their daily routine. It is a lesson they may only
present once a week. More research could be directed toward
how teachers feel about their professional preparation for
teaching mathematics compared to science.
The State continues to support mathematics and science
in Goals 2000, through the California Education Roundtable,
and by the State Superintendent of Education, Delaine
Easton. The Roundtable wants to assess students more
uniformly to see if they have met certain standards. This
will come in the future as California continues to examine
and revise its statewide testing system. Collaborative
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Initiatives to Improve Student Learning wants to provide
programs and resources for teacher professional development,
use of technology to improve education, and test students
more consistently. These steps will continue to support the
successful implementation of the mathematics and science
frameworks in California. Educators and state officials must
communicate and keep abreast of how curricula is operating
in the classroom and how it is affecting children.
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1 0 2
CHAPTER V
SUMMARY OF FINDINGS, CONCLUSIONS,
IMPLICATIONS, AND RECOMMENDATIONS
Introduction
School reform in California in the 1980s focused on
changes in content and curriculum. This occurred, in
response to, a national concern regarding the declining
quality of education experienced by our students. Of
particular interest were the areas of mathematics and
science, due to the fact that, American students were
achieving far below students of other countries.
Attempts at curriculum reform were nothing new;
programs designed a few decades ago, were supposed to
improve the quality of education. These efforts failed
because of poor implementation strategies. In recent years,
we have increased our knowledge and expertise regarding the
change process and how innovations become implemented.
A Nation at Risk began the impetus for educational
reform in the 1980s. States responded in mass to create
plans to improve the schooling of children. The Federal
government has become involved in education with Goals 2000.
This plan specifically lists as number 6 of its 8 goals:
United States students will be first, in the world, in
mathematics and science. President Clinton signed the
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103
Educate America Act, Goals 2000 in 1994. This vision has
high expectations for students and common standards. The
government is concerned with equity and excellence and aims
to support states and their policies.
In California, mathematics and science frameworks were
designed with the idea that these major subject areas were
for all students, not just the elite. How to implement
these new programs in the classroom became a major concern
of policy makers and administrators. The frameworks called
for varied teaching strategies to be used with hands-on
experiences and the inquiry-approach. The frameworks also
required revisions of the curricula to include higher-order
thinking skills and problem-solving activities related to
the real world.
William Honig, past state Superintendent of Education
in California, has been a leader in guiding and becoming
involved in California's school reform that is seen in
Senate Bill 813. One of its three major points is to
improve the curricula in schools by identifying a core
academic program. For the first time in this State's
history, textbooks from publishers were rejected that did
not match with our frameworks.
The California Education Round Table, along with
Delaine Easton, State Superintendent of Education, outlined
steps to address the state's educational crisis in 1995.
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104
One of these is high school standards and expected
competencies for university admission. The state has a new
agenda and momentum for education. It remains a critical
political issue as state leaders try to move quickly, yet
carefully. They do not want to repeat mistakes that have
been made in the past.
Purpose of the Study
Inplementing the mathematics and science frameworks
throughout schools in California represented a major
challenge. The purpose of this study was to determine the
extent that districts, schools, and teachers have
implemented the California mathematics and science curricula
and frameworks. This study also sought to examine patterns
of implementation, and similarities and differences across
districts, schools, and classrooms. The study also looked
at the comparison of the extent of implementation of
mathematics to science.
Methodology
This study was composed of two phases. In phase I,
case studies were developed as part of a major study of
mathematics and science curricula implementation. Each case
study provided an in-depth examination of the school site
and district so that the relationships of adoption and
implementation procedures and varied outcomes, including
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105
classroom practices and curriculum content, could be
examined.
Phase II, the focus of this dissertation, involved a
cross-site analysis of the implementation of the mathematics
and science frameworks across 12 districts, schools, and
classrooms case studies. They were analyzed, in regard to,
the extent of implementation of various elements in the
model curricula guides and frameworks.
Selected Findings of Mathematics Implementation
At the district level, the strands of number,
measurement, and geometry all had means above the moderate
level of 2.0. The highest rating of extensive, was 3.0.
These strands of the mathematics framework, were perceived
as having the most extensive level of implementation.
Problem solving, under themes, had a mean of 2.55 out
of 3.0 at the district level. The district curriculum
guides are illustrating that problem solving is a high
priority. Students need to feel comfortable solving
mathematical problems in real-life situations and
applications. Problem solving/inquiry also received the
highest mean of 2.3 in instructional strategies.
The same pattern of number, measurement, and geometry
having the highest mean also exists at the school level.
Problem solving ranked highest under themes. There is a
change under instructional strategies at the school level.
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106
The highest mean, 2.10, slightly above moderate, was for
manipulatives.
Selected Findings of Science Implementation
Science in content with earth, life, and physical
science, all received a mean of at least 2.6 out of a
possible 3.0 at the district level. Observing and hands on
activities were the components that were perceived as
moderately implemented under themes. Concept development
ranked highest of the instructional strategies with a mean
of 2.45.
At the school level, physical science drops off and
does not rate at the moderate level like earth and life
science. Observing and hands on activities are the leaders
under themes and concept development is now the highest
rated in instructional strategies.
The classrooms jump up again with a moderate rating
of over 2.0 in life, earth, and physical science. Life
science rates a 2.54 out of a possible 3.0. Observing and
hands on activities are again the highest ranked for
themes. Concept development and the use of manipulatives
get rated over 2.5 under instructional strategies.
Mathematics Compared to Science
Science received higher marks than mathematics in most
of the means that are illustrated in Table 13. The
mathematics framework was developed, written, and published
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107
before the science framework. Both subjects received
moderate means of 2.0 or above in the extent of
implementation at the district, school, and classroom
levels. The researchers felt the frameworks were being
implement across the board in content, themes, and
instructional strategies. Mathematics had laid the
groundwork for science to be successful. The federal and
state trends and begun. The science framework continued in
this vein to reach all students, get them engaged in their
learning, and have them participate in real life and hands
on activities.
Conclusions and Implications
This study was a cross-site analysis of 14 districts
regarding the extent of implementation of the mathematics
and science frameworks in California. Several conclusions
can be made:
1. The strongest perceived implementation was in
content at the district level, for both science
and mathematics.
2. District, school, and classroom means, in
mathematics and science, we all above 2.11.
3. The strongest correlation, .990, was in science.
This correlation was the relationship of district
primary grades with district intermediate grades.
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108
4. The researchers perceived the extent of
implementation for mathematics and science to be
from the moderate to extensive level.
5. Technology is a component that is perceived as
needing further implementation.
From this study, it can be concluded that the
mathematics and science frameworks have been implemented to
a great extent at the district, school, and classroom
levels. The highest extent has been at the district level.
Recommendations
The findings and conclusions of this cross-site
analysis have produced the following recommendations.
1. Districts should continue to provide support to
schools so that implementation of the frameworks
may continue and become stronger.
2. Districts should provide inservices in appropriate
lessons in logic and the use of calculators for
their teachers.
3. Districts should continue to support, through
funding and inservices, the use of technology in
the classroom.
4. Principals should continue to support teachers in
their efforts to successfully implement the
mathematics and science frameworks.
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109
5. Policies in California should provide for adequate
time to implement frameworks in the future.
Teachers receive new frameworks in some subject
each year.
Recommendations for Further Study
Further study should be done regarding the
implementation process of other frameworks. Mathematics and
science are only two of the subject areas that are taught in
schools. It would be valuable to investigate the
similarities and differences that are seen in implementation
and components of other frameworks. This comparison could
include looking closely at the process and steps that are
taken as a framework is new and how this may change as the
adoption and implementation of the framework progress.
It will be important to study the impact these
frameworks have on student learning. California does not
currently have a state wide testing system or assessment
tool. How are we to know how successful teachers are at
implementing the frameworks if we can not measure the
knowledge students have gained from one year to the next?
The state needs to move forward in developing a state
assessment program to measure student progress and student
learning.
Further study should be done to investigate which of
the instructional strategies are more successful in
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1 1 0
mathematics and science. Are there similarities and
differences? Why are certain instructional strategies more
successful? Does it have anything to do with the subject
matter, age of the student, etc.? Answers to these
questions will help guide educators and administrators
toward more successful teaching and learning at their
schools. We are in the business of delivering a type of
service. We should be aware of the how we can do a better
job and what key aspects of teaching and learning have the
greatest impact on children. We have the important and
critical task of preparing young people for the 21st
century.
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I l l
REFERENCES
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Asset Metadata

Creator Belongia, Cynthia Medeiros (author)

Core Title A cross-site analysis of the extent of implementation of the California mathematics and science frameworks.

Contributor Digitized by ProQuest (provenance)

Degree Doctor of Education

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag Education, administration,education, curriculum and instruction,Education, Mathematics,education, sciences,OAI-PMH Harvest

Language English

Advisor Marsh, David D. (committee chair), McComas, W. (committee member), Picus, O. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c17-510327

Unique identifier UC11350194

Identifier 9705072.pdf (filename),usctheses-c17-510327 (legacy record id)

Legacy Identifier 9705072.pdf

Dmrecord 510327

Document Type Dissertation

Rights Belongia, Cynthia Medeiros

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA