September, 1997
Judy Curran Buck, Director
Plymouth State College
Rod Mansfield, Principal Investigator
Executive Director, NH-MaST Coalition
Karen J. Graham, Principal Investigator
University of New Hampshire
The Advisory Council
Eleanor Abrams
University of New Hampshire
Chris Bauer
University of New Hampshire
Tom Bassarear
Keene State College
Richard Evans
Plymouth State College
Janice Ewing
Colby-Sawyer College
Keith Ferland
Plymouth State College
Beverly J. Ferrucci
Keene State College
Katy Fralick
Plymouth State College
Christy Hammer
State Department of Education
Jerry Jasinski
Keene State College
Karen Laba
Notre Dame College
Martha Miller
South School, Londonderry
Paul Reinbold
Alvirne High School/Rivier College
Matt Treamer
Lancaster School, Lancaster
Mark Turski
Plymouth State College
TABLE OF CONTENTS
Acknowledgments
The project staff of the Preservice Education Review Project acknowledges and thanks those individuals who reviewed drafts of this document.
Michele Bartlett
Rundlett Junior High School
David Burgess
Rivier College
Enid Burrows
Plymouth State College
Robert Devantery
Winnacunnet High School
Betty Erickson
Kearsarge Regional Elementary School
Joan Ferrini-Mundy
University of New Hampshire, Mathematical Sciences Education Board
Susan Janosz
Manchester West High School
Douglas Kaufman
University of New Hampshire
James Leitzel
University of New Hampshire
Diane Lonergan
Bedford Elementary School
Michael Morgan
Lin-Wood Middle School
Grace Nelson
Bradford Elementary School
Fernand Prevost
University of New Hampshire
Jeffery Pribyl
Mankato State University
Arthur Proulx
Newmarket High School
Doug Reynolds
New York State Supervisor (Retired)
Althea Sheaff
Barrington Elementary School
Mary C. Vahey
Excellence in our schools presupposes a large corps of well-trained teachers. Educational reform has touched every district in the state with the publication of statewide curriculum frameworks that identify what students should know and be able to do in mathematics and in science. With an aging teacher population, it is time to seriously look at pre-service teacher education...
Funded under the provisions of Title II, Dwight D. Eisenhower Professional Development Program and the Division of Educational Improvement of the New Hampshire State Department of Education, the Preservice Education Review Project (PERP) was developed in answer to the above call to write a Consensus Model for Preservice Teacher Education in Mathematics and Science. The vision is based upon a two-year extensive review of state and national documents, research, other preservice teacher education efforts nationally, and the advice of stakeholders within the State of New Hampshire. (See Appendix for the names of stakeholders who attended four regional conferences designed to review initial drafts of this document). This document is the consensus of the project staff on what preservice teacher preparation in mathematics and science should be. It is the result of the efforts described above and intense discussion among several constituencies.
The proficiency standards presented in this document represent what prospective teachers in New Hampshire should know and be able to do: the knowledge they need about the way students think, learn, and behave; the knowledge they need relative to instruction and technology; and the knowledge they need in the content areas of mathematics and science. The grade level breakdowns of elementary (K-4), middle school (5-8), and secondary (9-12) are consistent with national documents. Individual institutions may need to make adjustments for other certification areas, e.g., PreK-3, when developing individual programs.
The recommendations contained in this document are intended for all stakeholders of mathematics and science teacher education so that mathematics and science teachers in New Hampshire will be prepared to meet the challenges of the 21st century. We emphasize that "stakeholders" includes all faculty in the mathematics, science, and education departments at institutions involved in teacher preparation. We strongly recommend that the proficiency standards within this model be adopted by:
the State Professional Standards Board as standards for certification
and accreditation;
all teacher preparation programs within the state;
all school personnel at the K-12 level to ensure that candidates
for positions in mathematics and science possess these qualifications;
and
superintendents as qualifications for the hiring of teachers.
Teacher Development
Preservice teacher candidates should be viewed as novices at the beginning of a lifelong learning continuum of personal and professional growth. Through reflection and assessment, they begin their professional development by synthesizing their understanding of the content they will teach, the methods of pedagogy, and the characteristics of learners into a philosophy of teaching. The diagram on the next page dynamically illustrates the growth of knowledge in the three key areas of content, pedagogy, and knowledge of the learner, as well as the developing teacher's growing integration of that knowledge. The reader should note the gradual emergence of the "master teacher" (T in diagram).
As the diagram indicates, as preservice candidates participate in activities
that model exemplary teaching, their knowledge, skill, and experience broaden.
The preservice teacher's fundamental understanding of content, pedagogy,
and the learner uniquely develops and matures.
We believe that there are five factors essential for this continuous
development:
rich content experiences with instructors that model informed teaching
practices;
early and continual field experiences;
valuable mentoring by colleagues;
a passion for the subject and the profession; and
a desire and commitment to stay current with the subject, technology,
and educational practices.
Weakness in any of these factors makes a practitioner less effective.
Any preservice program must address these components in an integrated manner.
The lifelong learning continuum in the development of a master teacher
Assumptions Underlying the Development of the Consensus Model
The model contained in this document is based on a set of assumptions derived from our synthesis of current research, national recommendations, state documents, and professional discussions.
1. Prospective teachers enter preservice preparation programs with diverse academic, cultural, and socioeconomic backgrounds, beliefs, and experiences, and will teach in school communities just as diverse.
2. Effective teacher preparation programs require close cooperation, coordination, and commitment among all stakeholders. This requires the sustained effort of policy makers, all faculty, prospective and inservice K-12 teachers, administrators, parents, and the general public.
3. The knowledge, beliefs, and practices of teachers determine what happens in their classrooms. Teacher candidates must be empowered and supported as they increase their knowledge, challenge their beliefs, and expand their practice.
4. Individuals learn as they construct meaning from tasks in which they are actively involved. Physically and intellectually active learning environments which integrate subject matter, instructional theory and practice, and challenging field experiences need to be provided for prospective teachers.
5. Recurring opportunities for prospective teachers to reflect upon, practice, and refine the teaching/learning process are critical components of a teacher preparation program.
6. Content knowledge must be strong and incorporate the ideas in recent national reform documents, but content knowledge alone is not sufficient. It is essential to connect content knowledge to an understanding of current instructional theory and practice, both general and specific to the content area.
7. The mathematics/science and pedagogical knowledge that elementary, middle school, and secondary teachers experience in their preparation program must reflect the educational goals for, and the developmental needs of, the respective student populations.
8. The classroom teacher is a key to the development of mathematical and/or scientific literacy by all students, and provides for differences in gender, socioeconomic background, culture, ethnicity, and ability.
9. Extensive instruction and practice in the use of current and emerging technologies is essential if prospective teachers are to be effective in the technology-rich classrooms and schools of the 21st century.
10. Prospective teachers must experience and practice systematic and purposeful use of various methods of assessment.
11. Prospective teachers need to see themselves as life-long learners.
They must be committed to a career-long process of professional growth,
which is essential for continued effectiveness in a rapidly changing profession.
General Recommendations for Teacher Preparation Programs
There is no single utopian program that will provide prospective teachers with the proficiencies presented in this document. Each institution engaged in teacher preparation must struggle with how to assist prospective teachers in attaining these competencies. To do this requires infusing all courses and activities within the teacher preparation program with the substance, techniques, and opportunities that promote effective teaching.
In all cases, faculty must maintain familiarity with evolving standards in content and pedagogy in order to help prospective teachers acquire the knowledge and skills necessary to implement those standards in their classrooms. Any program developed in response to the evolving changes in mathematics and science education must continually be evaluated and revised to maintain its effectiveness and relevance in a rapidly changing profession. Further, the institution must provide the faculty with the necessary resources to implement new courses and strategies that prepare teachers for the demands of the 21st century.
Any effective teacher education program must be as concerned with how prospective teachers will teach as with what they will teach. This requires active communication and collaboration among all the stakeholders, particularly between the faculty within the mathematics and science departments and the faculty within the education department, so that the courses and activities of each department complement and reinforce each other in line with the program's vision. The acquisition of the hierarchy of skills and competencies necessary for effective teaching is complex and progressive in nature. All stakeholders are responsible for instituting a program that allows prospective teachers to move forward along the continuum of skills and competencies in an integrated and coordinated manner. Because teachers generally teach in the way they were taught, faculty in all departments must model effective instructional practice.
A blend of theory with practice is particularly important in the relationships between the faculty of the teacher preparation institution and the schools in which its prospective teachers will be placed. In all field experiences, the program must ensure that prospective teachers are placed with teachers who are models of effective instructional practice and willing partners in the development of new teachers. Effective avenues of communication must be established between college faculty and teachers and administrators in school districts so that prospective teachers receive a coherent message about what constitutes effective teaching and learning.
Various studies have been critical of existing teacher preparation programs suggesting that, all too frequently, programs consist of nothing more than a collection of courses, field experiences, and student teaching. The faculty designated to supervise the various aspects of the teacher preparation process are often separated by departments and/or colleges. In an attempt to make teacher preparation a connected process, performance-based approaches are gaining acceptance across the country. A number of states and institutions have now developed programs that include performance standards and alternative forms of assessment for teacher preparation (Diez, 1990). These initiatives are giving the prospective teacher more of the responsibility for learning to teach by engendering their active participation in the process of performance assessment (Lyons, 1996). Prospective teachers gather evidence to demonstrate learning (portfolios), use videos in self-assessment, collaborate with other interns as well as supervisors, and continue work in these areas after obtaining a teaching position. Another technique being used has been called "authoring" - interns must defend their own readiness to teach. By using this and other self-assessment techniques, prospective teachers become more actively involved and challenged in their preservice experience.
In surveying the current literature on teacher preparation, the following
are advocated characteristics of teacher preparation programs. This list
is not meant to be all inclusive, but rather to serve as a focus for discussion
in the restructuring or revision of current teacher preparation programs.
The teacher preparation program must:
1. Maintain a Vision
The program is more than a listing of the courses required by prospective
teachers to be certified; it also includes statements justifying those
requirements. A vision statement articulates the rationale supporting the
design and structure of the program to ensure the integration of different
components.
2. Monitor Growth
The program establishes a process for monitoring the professional growth
of the prospective teachers through effective counseling, the establishment
of proficiency standards, and the assessment of the prospective teachers'
attainment of those standards.
The program establishes performance-based methods of assessment, e.g.,
prospective teachers gather a body of evidence to demonstrate growth and
learning (portfolios), use videos in self-assessment, react to case studies
of mathematical issues arising in the context of classroom discourse.
3. Encourage Reflection
All faculty model reflective practices and expect the same of prospective
teachers throughout the program.
Any program that develops as a response to the evolving changes in
education must continually be examined and revised to maintain its effectiveness
and relevance in a rapidly changing profession.
4. Utilize Resources
The faculty evaluates and makes use of appropriate instructional resources
throughout the program (e.g., technological resources, media, curriculum
materials, trade books).
The program provides prospective teacher candidates with the opportunities
to evaluate and utilize instructional resources.
5. Identify and Address Ethical Issues
The program engages prospective teachers in identifying, discussing,
and confronting ethical issues (e.g., gender bias, discriminatory practices,
release of information).
6. Embed Social and Cultural Context into Experiences
The program provides opportunities for prospective teachers to work
with diverse students in various settings.
The program establishes the means by which prospective teachers interact
not only with students and mentor teachers, but with support staff, administrators,
parents, and the community.
7. Develop Social Skills
The program helps prospective teachers to develop the social skills
necessary to interact effectively with people of various backgrounds and
beliefs.
8. Model Effective Practice
The courses in the mathematics/science and education departments model
effective instructional practices.
Faculty employ a variety of assessment tools to monitor student progress.
9. Meld Theory and Practice
The program integrates theoretical and practical understanding of the
developmental and learning needs of students.
The program provides opportunities for prospective teachers to observe
and explore effective teaching practices at the intended teaching level.
The program provides opportunities for prospective teachers to reflect
on observed practices.
Case studies are used in the program to explore issues about teaching
and learning.
Field experiences begin early in the program and become progressively
more challenging.
Students mature physically, socially, and intellectually as they advance through the school system. Classroom teachers must be aware of these developmental and cognitive changes and be prepared to deal with them professionally. Major progress in understanding teaching and learning in science and mathematics has been achieved through the development of a leading theory of knowledge and research that examines this position.
Constructivism has emerged as a theory of knowledge that puts the learner at the center of the learning process. According to this theory, mathematical and scientific ideas are constructed within the mind of each learner by means of invention, elaboration, re-organization, abstraction, and generalization (Fosnot, 1996). Ideas are constructed when children assimilate new experiences into preexisting structures of knowledge. The theory resonates with the long-standing intuitive belief of many science and mathematics educators that the route to understanding requires students to participate in inquiry (Piaget, Vygotsky).
Constructivism holds implications for practice from early elementary through college level settings (Kamii, 1994). Just as children from birth begin to grow physically and socially, they also actively begin to gather and construct knowledge through their interactions with objects and people in their environment. While there are many paradigms about how children develop intellectually, there is general consensus that children pass through several stages of cognitive development.
Teachers can facilitate the construction of knowledge by creating situations
that allow the learner to generate and test his or her own questions, to
explore contradictions, and to promote reflection and dialogue. Students
of all ages need concrete and sensory-rich experiences as the basis for
the development of logical thinking and abstract thought. Mathematical
and scientific knowledge is actively constructed by reflecting on the physical
and mental actions that take place during experiential learning experiences.
Students in today's schools possess a rich diversity of cultures, experiences, and needs. It is this diversity that creates new classroom environments and challenges mathematics and science educators to present clearly defined goals, develop and utilize effective instructional strategies, and design lessons that focus on appropriate contexts. Prospective teachers need to be made aware of different learner perspectives in order to better develop a culturally responsive pedagogy. They need to develop a new paradigm for teaching within a multicultural setting that does not emphasize culture, but rather embraces cultural differences and enhances the student's potential for learning in a new arena.
In New Hampshire in 1997, there are about 1300 students who speak a primary language other than English at home, and who are receiving English as a Second Language (ESL) services in schools. Civil Rights laws mandate that schools provide adequate services for these students and that no school program or event discriminates against students because of their linguistic minority status. (The same Civil Rights laws protect students of color and all females from discrimination.) An unfortunate occurrence (which has been documented across the nation, including New Hampshire) is the inappropriate placement of Limited English Proficiency (LEP) students into special education classes. Immigrant students, perhaps with exemplary mathematics and science backgrounds and abilities, might lose out on the appropriate courses if educators do not understand the process of learning a second language.
National reform movements in mathematics and science have identified the need for citizens who are mathematically and scientifically literate. Both the National Council of Teachers of Mathematics (NCTM) and the National Science Teachers Association (NSTA) have declared that all students should become mathematics and science literate. Therefore, it is imperative that prospective teachers learn to create classroom environments that accommodate individual needs and differences.
Mathematics and science educators must actively address the needs of
these diverse populations in order to improve curricular and instructional
teaching strategies and to provide a supportive environment for change
in the teaching and learning of mathematics and science. They must find
instructional methods that will prepare an increasingly diverse group of
students with a wide variety of educational goals and personal aspirations.
The challenge to teachers, administrators, parents, policy makers, and
educational researchers is to continue to find effective ways to link curriculum,
pedagogy, and assessment, which will enable all students to recognize and
capitalize upon their mathematical and scientific potential.
Recent research has documented the underachievement in mathematics and science of certain racial, gender, and socioeconomic groups (National Center for Educational Statistics, 1993; National Research Council, 1991). Mathematics and science educators need to develop new policies and strategies that not only take into account students' differing racial, gender, and social backgrounds, but also accommodate differences in learning styles, intellectual capacities, and dispositions toward mathematics and science.
Prospective teachers need practice in creating a range of learning opportunities to allow all students to meet all levels of expectations. Effective learning cannot take place in an environment where the learner does not feel safe and valued. Prospective teachers should be aware of the methods and available resources to improve school culture and climate. Many methods and models address teachers' disparate interaction style with students, which arise, usually unconsciously, from different expectations for females, race/ethnic and linguistic minorities, the physically and mentally challenged, and other groups historically under-represented in the fields of mathematics, science, and technology. Many methods and models that in previous decades promoted equity in teaching and learning for specific groups of students are now understood to increase the success of all students. (Clewell et al, 1992)
A curriculum that does not resonate with the life experiences of a student
will have limited impact. Effective prospective teachers must have training
in gender-fair and multicultural curricula. They must possess a working
knowledge of interventions that increase the participation of historically
under-represented groups in mathematics-, science-, and technology-related
courses and careers. The prospective teacher needs to be aware of differences
in students' abilities, especially in the case of special education students
with physical, mental, and/or learning disabilities. They must shift focus
away from any exceptionality and toward a view of the special education
student as a whole person possessing strengths in many intelligence areas.
Prospective teachers must have the necessary resources and knowledge to
allow students to engage in meaningful mathematics and science activities,
regardless of their race, gender, social class, and physical or intellectual
capacities.
Proficiency Standards in Knowledge of the Learner for All Teachers
of Mathematics or Science
Prospective teachers of mathematics or science will:
Articulate a framework for understanding children. This includes knowing
that children mature mentally, physically, and socially at different rates
and that this influences their judgment, actions, and academic progress.
Demonstrate knowledge of the physical, cognitive, social, and emotional
development issues at the age level they are teaching.
Identify and implement a curriculum that provides for important differences
in gender, socio-economic status, culture, and ethnicity.
Identify and implement a curriculum that provides for important differences
in learning styles; concrete and abstract thought processes; deductive
and inductive reasoning; and auditory, visual, and tactile modalities.
Identify and implement a curriculum that takes into account the varied
prior experiences and knowledge all students bring to the classroom.
Provide all students with opportunities to gather and process
information through a variety of learning activities and teaching methods.
Provide all students with opportunities for active involvement
in the teaching and learning process through interaction with teachers
and peers.
Instructional Theory and Practice
To develop the connections between instructional theory and practice (pedagogy) and content knowledge, teachers must have the opportunity to develop an integrated view of teaching and learning in their discipline. Teachers develop their knowledge in the same way that students learn: through continuous experience. Experience, however, is not sufficient. Teachers must also have opportunities to engage in analysis of the individual components of teaching - content, learning, and instructional theory and practice--and make connections among them. Prospective teachers need the time and opportunity to describe their own views about learning and teaching, to conduct research on teaching, and to compare, contrast, and revise their views as they observe the various instructional models used by their peers and mentors. Through these processes and a variety of field experiences they come to understand the nature of exemplary teaching.
Field experiences for prospective teachers need to begin early in preservice
teacher programs and continue throughout the program to allow them adequate
opportunities to practice and reflect on their teaching. Whenever possible,
the contexts for learning to teach mathematics and science should involve
students with varying needs, real student work, and cutting-edge curriculum
materials. Trial and error in teaching situations, continual thoughtful
reflection, insightful interaction with peers and mentors, and use of appropriate
teaching tools such as technology and journals are critical components
of all field experiences. Numerous and varied experiences in teaching content,
coupled with the components just listed, combine to develop
the kind of integrated understanding characteristic of exemplary teachers.
Teacher preparation institutions, therefore, must ensure that all prospective teachers of mathematics or science:
Have regular, ongoing opportunities to participate in both informal
and formal learning situations.
Reflect on classroom and institutional practices using various techniques
for self and collegial reflection such as peer coaching, portfolios, and
journals.
Understand, analyze, and apply feedback about their teaching to improve
their practice.
Share teaching experiences with mentors, teacher advisers, lead teachers,
and resource teachers to support their professional development.
Seek and value contemporary research about teaching and learning.
Participate in doing mathematics and science in coursework and field
settings.
Integrate and coordinate content with appropriate instructional theory
and practice to meet the needs of a diverse student population.
Observe and implement exemplary models of technology use to enhance
teaching and learning.
Interact and network with the people involved in education programs
and schools, including teachers, teacher educators, policy makers, members
of professional and scientific organizations, parents, and business representatives
to enhance the learning and teaching of science and mathematics.
Proficiency Standards in Instructional Theory and Practice For All
Teachers of Mathematics or Science
All prospective teachers of mathematics or science will:
Proficiency Standard 1: Understand the Development and Needs of Children
Exhibit and utilize a knowledge of how the physical, cognitive, social,
and emotional development of students influences learning.
Articulate how various factors affect learning, including: age, exceptionalities,
interests, experiences, learning styles, ethnicity, gender, and socio-economics
factors. Apply that understanding to meet the learning needs of all students.
Proficiency Standard 2: Apply Knowledge of How Children Learn Mathematics and Science
Plan units and lessons that enable children to construct new concepts
actively and connect these concepts to those they already know.
Plan units and lessons that proceed from concrete representations to
symbolic representations in ways that make sense for each learner.
Provide the learner with clear examples and non-examples of the concepts
being learned.
Provide multiple representations of concepts being learned.
Provide opportunities for students to exhibit their understanding of
important ideas -- with other learners, with the teacher, in writing, and
orally.
Proficiency Standard 3: Use Appropriate Instructional Practices
Teach in an integrated manner so that their students develop strong
conceptual understanding of content.
Model and nurture important habits of mind including problem solving,
communication, and reasoning.
Design instruction that finds what is meaningful about mathematics
and science within the world of understandings, interests, and experiences
of the student.
Develop daily, unit, and yearly plans that emphasize connections among
mathematics, science, and other disciplines.
Use basic instructional practices appropriately, e.g., cooperative
learning, long-term projects, lecture/discussion, demonstration, small
group investigations.
Organize and manage classrooms that provide active engagement in learning
by all students.
Support students in being inquisitive and making conjectures.
Proficiency Standard 4: Create an Environment Which Promotes Learning
Apply an understanding of the relationships of motivation, time, and
space in the development of learning activities.
Create an environment that is physically and emotionally safe.
Support students in constructive risk-taking and in building self-confidence.
Model fairness by providing each student opportunities to succeed.
Proficiency Standard 5: Use Appropriate Assessment Techniques
Effectively monitor the level of student understanding and use that
knowledge in planning instruction.
Assess student achievement and readiness using a variety of methods,
including appropriate use of technology.
Align assessment with the curriculum and modes of instruction.
Assess one's own teaching through reflection, student feedback, and
collegial discussion.
Proficiency Standard 6: Utilize Appropriate Resources
Use available resources to enhance the learning and teaching of science
and mathematics.
Construct, use, and adapt curricular materials, manipulatives, and
resources to meet the needs of all students.
Display a working knowledge of important national and state documents.
Describe exemplary models of utilizing technology to enhance teaching
and learning.
Review district curricula to determine whether practice is in concert
with the curricula.
Teaching in a Technological World
Technology offers new ways to learn, teach, and manage schools. Teachers are using computers and telecommunication to form networks to compare experiences and exchange ideas. They are acquiring curricula and other instructional information over educational networks. They are using computers to track and guide student development. Through these processes, teachers are using technology not only to reinvent schools, but to reinvent their roles as teachers and learners.
Teacher preparation programs should demonstrate how technology can be
used to reduce the time and effort committed to classroom management duties,
thus freeing time and energy for the more exciting and creative components
of the teaching/learning process.
Prospective teachers must observe the classrooms of master teachers
in which technologies are used in appropriate ways, and discuss with them
what impact the technology has had on their classroom.
Teachers and educational researchers are beginning to explore how various new technologies can help deepen the conceptual understanding of students by facilitating a broader and richer array of explorations. The question of "What if" can be readily addressed by altering the conditions of an experiment or simulation using a few mouse clicks. Meaningful relationships embodied in a set of data can be displayed numerically and graphically within seconds of asking a question. Multimedia resources provide stimulating multisensory experiences. Given the public pressure to infuse schools with technology, prospective teachers need to determine whether various uses of these tools represent marginal or substantial advantages for learning.
Preservice programs must provide coursework in information technology, and opportunities for prospective teachers to engage actively in building links to their communities and the wider world using the best technology available. With access to the internet, teacher preparation candidates can use available technologies to continue their professional development as teachers, e.g., by subscribing to listservs and accessing bulletin boards or websites of colleges and universities, government departments, and libraries. Teacher preparation institutions must provide access to these resources as part of their programs and require prospective teachers to use them for assignments within courses and as part of their field experiences.
In summary, technology must be integral to the development and growth
of the prospective teacher both in extending his/her knowledge of science
and mathematics and in learning the theories, skills, and practices of
science and mathematics teaching.
Proficiency Standards in Technology for All Teachers of Mathematics
or Science
All prospective teachers of mathematics or science will:
Apply basic statistical and computer skills during the study of mathematical
and scientific phenomena by gathering data, analyzing information, and
communicating ideas (including data display and graphing).
Use technology and other tools appropriately and effectively in the
learning and teaching of science and mathematics, e.g., computers, graphing
calculators, computer-based laboratory (CBL) units, interactive video,
and telecommunications technology.
Use networking and information technologies to solve problems and broaden
their scope of inquiry, e.g., explore library data bases, take virtual
tours of museums, and access community resources from the world wide web.
Locate, use, and evaluate primary sources of data (e.g., government
documents, experts, databases) to support inquiry.
Investigate the interrelationships among science, mathematics, technology,
and society to enhance integration of knowledge in both their learning
and teaching.
Seek models of how technologies can be used to enhance instruction,
to gather and analyze data, and to communicate more effectively.
Define and seek to establish laboratory settings that provide all students
with appropriate access to the tools and materials required for science
and mathematical explorations, e.g., computer-based labs and simulations.
Investigate and evaluate the strengths and limitations of exemplary
educational software, instructional kits, and other media resources.
Be an advocate for physical learning environments, such as adaptive
technologies, that provide for differences in gender, socio-economic background,
culture, ethnicity, and physical and academic abilities.
Proficiency Standards in Mathematics
The 21st Century will demand a more highly skilled and technology literate workforce. It will demand a view of mathematics as a connected discipline rather than a series of isolated subdisciplines such as algebra, geometry, and calculus. Available technology will allow students who have been excluded in the past to participate more fully in the exploration of mathematical concepts and problems. The new century will demand teachers who are prepared to meet its challenges and prepare all students as mathematically literate citizens.
The Curriculum and Evaluation Standards for School Mathematics published in 1989 by NCTM suggests a vision for the teaching and learning of mathematics which has, as its primary goal, the development of mathematical power for all students. The Curriculum and Evaluation Standards together with the companion documents, Professional Standards for Teaching Mathematics (NCTM, 1991) and Assessment Standards for School Mathematics (NCTM, 1995) call for substantial changes in not only what mathematics is taught but how it is taught. All three documents as well as other national reports such as the MAA's A Call for Change (1991) have significant implications for the preparation of mathematics teachers. The vision is nicely summarized in the Professional Standards for Teaching Mathematics :
To reach the goal of developing mathematical power for all students
requires the creation of a curriculum and an environment, in which teaching
and learning are to occur, that are very different from much of current
practice. The image of mathematics teaching needed includes elementary
and secondary teachers who are more proficient in:
selecting mathematical tasks to engage students' interests and intellect;
providing opportunities to deepen their understanding of the mathematics
being studied and its applications;
orchestrating classroom discourse in ways that promote the investigation
and growth of mathematical ideas;
using, and helping students use, technology and other tools to pursue
mathematical investigations;
seeking and helping students seek, connections to previous and developing
knowledge;
guiding individual, small-group, and whole-class work (p.1).
As is the case nationally (MAA,1991), the mathematics teacher preparation programs currently in place in many of New Hampshire's institutions of higher education fall short in preparing teachers to implement the NCTM standards in their classrooms. The Mathematical Association of America in its document A Call for Change (1991) suggests that:
In order for teachers to implement the curriculum envisioned by the NCTM Standards , they must have opportunities in their collegiate courses to do mathematics: explore, analyze, construct models, collect and represent data, present arguments, and solve problems. The content of collegiate level courses must reflect the changes in emphases and content of emerging school curriculum and the rapidly broadening scope of mathematics itself. (p. xi)
The following sections outline the proficiency standards in mathematics
content and the mathematical habits of mind that all prospective teachers
should possess to be effective mathematics teachers in the next century.
Significant weight was placed on the national recommendations contained
in A Call for Change in writing the proficiency standards. Although
many of the desired content proficiencies are the same for teachers of
all levels, there are some differences among the three levels, particularly
regarding the depth of content knowledge expected. In addition, it is unreasonable
to think that the desired level of competency can be acquired through a
single mathematics survey course or through the mathematics methods course.
Innovative thinking about the structure of the whole curriculum is required.
Proficiency Standards for Mathematical Habits of
Mind
To many people, mathematics is seen primarily as a set of concepts and procedures to be learned and applied, e.g., arithmetic, probability, statistics, algebra, geometry, calculus, etc. To most mathematicians, however mathematics is far more than this--it represents a way of making sense of the world. As the chapters of On the Shoulders of Giants: New Approaches to Numeracy ( ) emphasize, we encounter pattern, dimension, quantity, uncertainty, shape, and change in both our everyday and work lives. Scientists have developed structures to explain and predict scientific phenomena and historians have developed structures to enable us to better interpret historical events. Likewise, mathematicians have developed structures that help us to understand our world. For example, these structures help us to accurately describe and predict change, create buildings that are both aesthetically pleasing and structurally sound, and understand the connection between symmetries at the molecular level and properties of compounds.
We agree with the growing body of knowledge (citation) that asserts
that one cannot learn the important ideas of a discipline without simultaneously
developing important habits of mind. These habits of mind have been articulated
in many ways by various authors. They include character attributes such
as persistence, openness to new ideas, creativity, and self-confidence.
They also include ways of thinking about doing mathematics such as monitoring
progress when solving problems, looking for connections, or believing that
mistakes are a natural part of the learning process. Mathematical habits
of mind are exhibited in many ways, such as:
Not only knowing how to interpret graphs but also being skeptical--asking
where the data came from and looking to see if the graph presents a fair
representation of the data;
Understanding that logical deductive reasoning is necessary in analyzing
and understanding statements in both legal and business meetings;
Realizing that the ability to determine rough estimates is still important
in spite of the enormous capabilities of technology;
Seeing symmetry in nature, in a dance performance, in a painting, in
architecture--everywhere.
Fundamental to this constellation of attributes and behaviors is a driving desire to ask "Why? ". The questions "Why?" and "How do we know?" should permeate the mathematical classroom. Such curiosity manifests itself when the learner is not completely satisfied when s/he arrives at an answer. More than simply understanding and being able to explain how s/he got the answer, the learner pushes the limits of his/her knowledge and abilities by extending or generalizing the problem. This posture has been the driving force behind the development of knowledge.
When the learner has developed mathematical habits of mind, he or she more fully appreciates the usefulness of mathematics in everyday life, in work settings, and in other disciplines. The development of these habits of mind together with a mastery of mathematical concepts and procedures produces mathematical power within the learner. A learner who has mathematical power can explain concepts and execute procedures; apply this knowledge to solve problems within mathematics and in other disciplines; use mathematical language to communicate ideas; reason and analyze; and see and articulate the many connections within mathematics and between mathematics and other disciplines. (see NCTM, 1989, p. 205)
By the end of their program, all prospective teachers of mathematics will be able to:
Exhibit a curiosity about mathematics, indicating a desire to understand
the "why's?" behind the "whats?".
Recognize and stress the importance of hard work, persistence, and
risk-taking in learning mathematics.
Demonstrate self-confidence while solving various types of mathematical
problems.
Value the process of exploration and investigation of mathematical
concepts in making and testing conjectures and in verifying or contradicting
those conjectures.
Recognize the need for and rely on proofs and logical arguments using
an axiomatic approach to verify hypotheses. Although experiments are useful
in developing conjectures, deductive reasoning is needed to validate these
conjectures.
Realize the need to explain mathematics in different ways to people
with different backgrounds or levels of understanding and recognize that
an intuitive explanation is an important complement to a detailed argument.
Recognize the role of estimation and the need to always examine the
reasonableness of solutions.
Recognize the need for using heuristics in solving problems and analyzing
the appropriateness of different heuristics based on any assumptions and
limitations.
Demonstrate that solving problems in mathematics involves analyzing
examples and appreciating the subtleties of any assumptions or limitations.
Value the use of technology to explore and investigate mathematical
concepts, to enhance students' understanding of concepts, to open doors
to students with disabilities, and to save time, though it does not replace
the need to learn basic skills or concepts.
Articulate the power of mathematics as an academic discipline that
acts as the language of nature and as a tool for quantitative reasoning.
Proficiency Standards in Mathematics Content
ALL prospective teachers of mathematics will:
Proficiency Standard 1: Mathematical Ideas
Learn mathematics on their own and in conjunction with others.
Develop general and personal strategies for solving problems.
Use mathematical reasoning to understand concepts, solve problems,
and test conjectures.
Proficiency Standard 2: Connections
Justify the mathematical concepts underlying the procedures (i.e. can
explain the why behind the how).
Articulate connections among different representations of mathematical
concepts (e.g. models of fractions, representations of functions).
Describe connectedness among seemingly different fields or topics of
mathematics.
Articulate connections among mathematics and other disciplines.
Transfer mathematical knowledge from one context to another.
Proficiency Standard 3: Communication
Communicate mathematical concepts and solutions both in written and
oral ways using varying levels of formality to students of varying levels
of insight.
Articulate the role of language, notation, and graphical representation,
in the development of mathematical concepts.
Proficiency Standard 4: Mathematical Models
Know what mathematical models are and how they are used.
Use and construct appropriate models, when relevant, to help students
understand abstract mathematical concepts.
Recognize strengths and constraints of a given model.
Proficiency Standard 5: Technologies
Use various technologies to explore mathematical ideas, solve problems,
and help all students participate fully in studying significant mathematics.
Articulate the role of technology in mathematics education.
Proficiency Standard 6: Perspectives
Articulate the increasingly important role of mathematics in society.
Appreciate the contribution to mathematics of various cultures and
individuals.
Articulate the historical development of major school mathematics concepts.
Provide examples of how mathematics is practiced by mathematicians
and professionals in various fields, such as insurance, engineering, and
business.
Prospective ELEMENTARY SCHOOL TEACHERS of mathematics will:
Proficiency Standard 1: The Nature and Use of Number
Use numbers as a logical, predictable system for expressing and relating
quantities.
Analyze and compare features and basic computation techniques in selected
ancient and modern numeration systems.
Operate with, and use properties of, integers, whole numbers, fractions,
and decimals in problem solving.
Solve a wide variety of problems using estimation and mental arithmetic,
calculators, computers, paper and pencil algorithms, and manipulative materials.
Proficiency Standard 2: Measurement and Geometry
Determine what needs to be measured, select an appropriate unit of measurement,
and then select an appropriate tool with which to measure.
Solve problems involving linear, area, volume, mass, and temperature
measures by using both the English system of measurement and the metric
system.
Use a variety of tools (e.g., ruler, graduated cylinder, protractor,
compass), physical models (e.g., tangrams, Pattern Blocks), and technology
(e.g., LOGO , Tesselmania (MECC)) to demonstrate an understanding
of geometric concepts and relationships, and their use in describing the
world.
Demonstrate an understanding of motion geometry (slides, flips, turns,
and glide reflections) by using the concepts of motion geometry to solve
simple problems and relate them to other ideas such as tessellations.
Solve simple problems of two- and three-dimensional geometry that involve
parallelism, perpendicularity, congruence, similarity, and symmetry.
Demonstrate relational understanding of important geometric concepts
associated with visualization, description, and classification of geometric
figures.
Construct simple proofs and write logical arguments.
Proficiency Standard 3: Patterns and Functions
Demonstrate the role of patterns as an underlying, fundamental theme
in mathematics.
Recognize, describe, analyze, and compare mathematical relationships
by creating pictures, charts, and graphs.
Analyze a variety of functional relationships using concrete materials
(e.g., Pattern Blocks, Color Tiles, cubes ) and represent those functions
using graphs, tables, and formulas.
Demonstrate an understanding of common algorithms and algebraic notation
by using them in solving simple problems and by communicating the solution
using appropriate terminology.
Demonstrate a basic understanding of classes of functions and their
properties; e.g., linear, exponential, polynomial, and periodic.
Proficiency Standard 4: Collect, Represent, and Interpret Data
Analyze and display data by using various charts/graphs (e.g., bar graphs,
pie charts, line graphs, stem and leaf plots, box and whisker plots, scatter
plots) manually and by using appropriate technology.
Collect data from real world experiences, experiments, or surveys;
organize and display the data using various methods (e.g., charts, graphs,
tables, Venn diagrams); and analyze and interpret that data.
Determine which measure of central tendency is best for a given set
of data, recognize outliers, and analyze the distribution of the given
set of data.
Critically examine and analyze data for reliability and validity.
Demonstrate an understanding of randomness by conducting sampling experiments.
Demonstrate an understanding of experimental and theoretical discrete
probabilities using tree diagrams and sample spaces.
Formulate and solve problems that involve collecting and analyzing
data.
Prospective MIDDLE SCHOOL TEACHERS of mathematics will possess the mathematical knowledge of prospective elementary school teachers but the depth of study will increase.
In addition, prospective middle school teachers will:
Proficiency Standard 1: Number Concepts and Relationships
Demonstrate an ability to use models to explore and explain relationships
among fractions, decimals, percents, ratios, and proportions.
Model operations on the various subsets of the real numbers using concrete
materials and connect the models across those systems (e.g., the area model
for multiplication).
Explain real number concepts and the relationships among the decimal
representations for repeating decimals, terminating decimals, and irrational
numbers.
Effectively use estimation strategies and techniques to judge the reasonableness
of answers, to approximate solutions, and to perform mental calculations
for all four basic operations.
Use physical materials and models to explore and explain properties
of number systems.
Demonstrate knowledge of the concepts of limits and infinity and their
role in the historical development of topics relating to real numbers,
geometry, and calculus.
Articulate the properties of the complex number system, including the
field properties order, density, and completeness.
Proficiency Standard 2: Geometric Ideas
Employ common geometric ideas such as the Pythagorean theorem, similar
triangles, and trigonometry to solve problems involving direct and indirect
measurement.
Connect the ideas of algebra and geometry through coordinate geometry,
graphing, vectors, and motion geometry.
Demonstrate an ability to encounter new geometry content and connect
it to other mathematical topics when appropriate.
Use dynamic geometric software such as Cabri Geometry , The
Geometers Sketchpad , and LOGO to explore geometric relationships.
Apply topological ideas such as paths, vertices, and traversable networks.
Demonstrate knowledge of non-Euclidean geometries and the historical
development of Euclidean and non-Euclidean geometries.
Proficiency Standard 3 : Algebraic Ideas
Use algebraic notation and common algorithms in solving simple problems
and communicate those ideas using proper terminology.
Demonstrate an understanding of common sequences (e.g., arithmetic,
geometric, Fibonacci) and explore patterns and functional relationships.
Represent those relationships using variables, when appropriate to solve
problems.
Demonstrate a variety of functional relationships using concrete materials
(e.g., Pattern Blocks, Algeblocks, Algebra Tiles) and graphing utilities.
Represent those functions using graphs, tables, and formulas.
Describe what a function means both intuitively and using formal mathematical
language.
Represent functions using symbols, tables, graphs, and verbally, and
be able to move from one representation to another.
Solve real-world problems involving linear and quadratic equations
and inequalities by using traditional techniques and graphing methods that
use technology.
Use concrete examples to explore selected algebraic structures, such
as groups, rings, fields, and vector spaces. Apply them, where appropriate,
to real-life situations.
Solve problems using matrices.
Demonstrate algebraic reasoning and communication skills while solving
algebraic problems.
Proficiency Standard 4: Probability and Statistics
Collect data from real world experiences or surveys, organize and display
the data using various methods (e.g., charts, graphs, tables, Venn diagrams),
analyze and interpret the data, and write convincing arguments based on
the data.
Solve elementary statistical problems relating to measures of central
tendency (mean, median, and mode), measures of dispersion (standard deviation,
range, and interquartile range), regression equations (lines of best fit,
median-median line), and non-linear regression.
Display data using a variety of methods, including box-and-whisker
plots, stem-and-leaf plots, and scatter plots.
Find experimental and theoretical discrete probabilities using sample
spaces, tree diagrams, and other representations.
Plan and conduct simulations to determine experimental probabilities.
Compute the mathematical expectation of simple games and lotteries.
Solve simple problems using probability, inference, and the testing
of hypotheses.
Use combinations and permutations to solve counting problems.
Analyze and critique arguments based on a statistical analysis.
Proficiency Standard 5: Calculus Concepts
Recognize particular types of change such as linear, quadratic, and
exponential.
Use graphs, diagrams, charts, physical models, and graphing technology
to explore the notions of limit, differentiation, and integration, and
to interpret the relationships among them.
Construct infinite sequences and series, relating them to non-terminating
decimals and the approximation of functions.
Solve real-world problems involving average and instantaneous rates
of change, area, volume, and curve lengths, and relate those to differentiation
and integration.
Prospective SECONDARY SCHOOL TEACHERS of mathematics will possess the mathematical knowledge of prospective elementary and middle school teachers but the depth of study will increase.
In addition, prospective secondary school teachers of mathematics will:
Proficiency Standard 1: Number Systems and Algebraic Ideas
Demonstrate an understanding of the axiomatic development of the Real
and Complex Number Systems.
Demonstrate an understanding of general algebraic systems (groups,
rings, vector spaces, integral domains, fields) and their properties.
Proficiency Standard 2: Geometry
Demonstrate an understanding of geometric reasoning including Euclidean
and non-Euclidean geometries, models, proofs, constructions, transformational
geometry, analytic geometry, vector geometry, and trigonometry.
Use geometry to build mathematical models for a variety of applications.
Proficiency Standard 3: Probability and Statistics
Demonstrate an understanding of basic concepts of probability and statistics,
including discrete and continuous probability, descriptive and inferential
statistics, correlation analysis, binomial distributions, and expected
value.
Explore the relationship between statistics and probability using various
methods such as hypothesis testing, correlation, analysis of variance,
and estimating parameters and error.
Proficiency Standard 4: Functions, Calculus, and Topology
Demonstrate an understanding of both single and multi-variable calculus
relating to limits, differentiation, integration, and infinites series.
Demonstrate an understanding of continuous functions between general
topological spaces.
Demonstrate and understanding of connectedness and compactness as they
relate to geometry and analysis.
Discuss the uses of functions, calculus, and topology in mathematics,
business, physical science, behavioral science, and social science.
Proficiency Standard 5 : Discrete Processes
Exhibit a familiarity with discrete processes that include mathematical
logic, mathematical induction, recursion, algorithms, equivalence relations,
and matrices.
Apply elementary logic to solve problems involving set theoretic concepts,
(e.g., DeMorgan's laws for union and intersection, Venn diagrams).
Use a variety of counting techniques and appropriate technology to
solve complex computational problems.
Proficiency Standards In Science
"According to Science for All Americans (National Center for Research in Teaching and Learning, 1994), the scientifically literate person is someone who:
(1) has integrated knowledge of the different disciplines of science,
mathematics, and technology,
(2) has a deep conceptual understanding of scientific concepts and
ideas, and
(3) appreciates that both the knowledge and the practice of science
are dynamic and constructed." (p. 3)
If this is the requisite competence for a scientifically literate person, then one expects that all teachers of science will have at least this level of understanding of science and scientific enterprise. In the proficiency standards for K-12 science teachers stated below, these general requirements are defined in greater detail. The knowledge and experience of science teachers is the key element in achieving the goals of scientific literacy for all students in our schools. Therefore, institutions preparing teachers of science must ensure that graduates of their programs develop the content knowledge, skills, and habits of mind needed to teach effectively in the schools of the 21st century.
Although many of the proficiencies are the same for teachers at all levels, there are differences among the three levels, particularly regarding the depth of science knowledge required. Preparation programs that allow prospective teachers to experience science as scientists do, while also making extensive connections within the discipline, across disciplines, and to the world at large provide rich opportunities for prospective teachers to achieve these standards of proficiency.
There are many approaches that institutions can take to ensure that prospective teachers have the essential science skills and knowledge. Scientists and educators at each institution must review the proficiencies and decide how, and in what contexts, preservice teachers can best achieve the level of competency described. Scientific knowledge is expanding at an exponential rate. Teachers at all levels must prudently select and teach those concepts and principles that will allow students to increase effectively both the breadth and depth of their science knowledge. It is unreasonable to think that the appropriate level of competency can be acquired through a single non-laboratory science survey course or a science methods course. Nor will increasing the number of science credits required necessarily lead to the desired outcome. Rather, innovative thinking regarding the structure of the total curriculum is required.
It is essential to integrate knowledge from the various fields of science
as well as relate science to the other major disciplines. Mathematical,
technical, and communication skills become extremely important for science
teachers if we are to achieve the goal of scientific literacy for all Americans.
As educators, we must constantly delineate for prospective teachers the
important interface of scientific knowledge with societal values and thought
to ensure that they are prepared for classrooms of the 21st century.
Proficiency Standards in Science Content
ALL prospective teachers of science will:
Proficiency Standard 1: The Nature of Science
Exhibit a growing understanding of science as a process by which knowledge
evolves.
Employ the appropriate tools of science, including technology.
Represent science as public knowledge.
Incorporate scientific habits of mind into instruction. (see following
section entitled Scientific Habits of Mind ).
Express how scientific arguments must be evaluated by gathering and
weighing experimental evidence in a systematic manner, and demonstrate
the ability to carry out this type of evaluation.
Proficiency Standard 2: Life Sciences
Demonstrate an understanding of the basic concepts and principles of the life sciences, including but not limited to the following:
Cellular Nature of Organisms
Characteristics and Life Cycles of Organisms
Interelationships of Organisms, Populations, and the Environment
Structure and Function in Living Systems
Reproduction and Heredity
Evolution and Natural Selection
Regulation and Behavior
Diversity and Adaptation
Matter, Energy, and Organization in Living Things
(Adapted from Table 6.3, National Science Education Standards, p.106)
Proficiency Standard 3: Physical Sciences
Demonstrate an understanding of the basic principles and concepts of the physical sciences, including but not limited to the following:
Properties of Objects and Materials
Position and Motion of Objects
Relationships between Forces and Motion
Properties of Heat, Light, Electricity, and Magnetism
Mechanisms of Energy Transfer
Structure of Atoms and Molecules
Interactions of Matter and Energy
Entropy and the Conservation of Energy
Interactions of Matter and Energy
(Adapted from Table 6.2, National Science Education Standards, p.106)
Proficiency Standard 4: Earth/Space Sciences
Demonstrate an understanding of the basic principles and concepts of the earth and space sciences, including, but not limited to the following:
Properties of Earth Materials
Objects in the Sky
Changes in Earth and Sky
The Universe, including its Origin and Evolution
Solar System
Earth History, including its Origin and Evolution
Structure of the Earth System
Forms of Energy in the Earth System
Geochemical Cycles
(Adapted from Table 6.4, National Science Education Standards, p. 107)
Proficiency Standard 5: Common Themes
Know and give examples which illustrate the common themes found in all of the sciences, including but not limited to:
Systems
Models
Constancy or Stability
Change
Evolution
Scale
Proficiency Standard 6: Effectiveness in "Doing" Science
Be able to address the question, "How do I know?" in respect to their
own knowledge of science.
Design, conduct, and evaluate scientific investigations that integrate
knowledge of content, skills, and habits of mind.
Communicate the results of their own investigations clearly, logically,
and persuasively.
Proficiency Standard 7: Scientific Tools and Instruments
Employ appropriate tools to observe, measure, record, and analyze the
natural world.
Demonstrate effective skills in the use of tools and instruments in
laboratory and field work.
Describe how scientific tools have extended the ability of humans to
understand the natural world.
Engage in recognized safe practices in the use of laboratory and field
materials.
Proficiency Standard 8: Local, State, and National Studies and Documents.
Review and critically evaluate local curricula and compare them to state
and national standards documents.
Display a working knowledge of the NH State Science Framework
and the separately published Addenda to the Framework.
Possess a working knowledge of Benchmarks for Scientific Literacy
(American Association for the Advancement of Science), the National
Science Education Standards (National Research Council), and the Scope,Sequence,
and Coordination of Science Education (NSTA).
Be cognizant of, and adopt when appropriate, the current recommendations
of professional organizations for improving science instruction.
Proficiency Standard 9: Mathematics
(See previous section on Proficiency Standards in Mathematics )
Demonstrate competency in mathematics which is at least sufficient to
support science instruction at their level of teaching.
Gather data effectively during explorations of natural phenomena and
display and summarize the data in various forms.
Analyze data using various forms of representation, e.g., graphing,
ratio and proportion, and equations.
Make reasoned judgments using estimation and statistics.
Proficiency Standard 10: Communication
Articulate their personal philosophies of science education.
Engage in reflective thinking about their own instructional ideas and
strategies.
Discuss with peers contemporary issues in science education.
Communicate the results of science investigations in a meaningful manner.
Articulate and give examples of the interrelationships among science,
mathematics, and technology as well as the interplay between science and
society.
Articulate and communicate the relationship between science and society
during different historical periods.
Use a variety of means to communicate scientific ideas, e.g., presentation
software, data base and spread sheet analyses, case studies and similar
qualitative research products, and quantitative findings.
Proficiency Standard 11: Professional Development
Become involved in professional organizations appropriate to their teaching
fields.
Participate in inservice activities offered during their field experiences.
Identify personal strengths and weaknesses and develop plans for life-long
learning and improvement.
Design plans for rigorous professional development throughout their
teaching careers, which will enhance both their scientific and pedagogical
knowledge and their understanding of the learner.
Prospective ELEMENTARY SCHOOL TEACHERS of science will:
Achieve content competency listed under all teachers of science through
a series of laboratory/field based courses in the life, physical, and earth/space
sciences.
Enhance their understanding of scientific concepts and techniques in
the life, physical, and earth/space sciences through application to real
world phenomena.
Employ computers and other technologies to communicate, gather data,
and analyze information.
Develop scientific literacy sufficient to confidently use information
found in such journals as Science and Children , Discover Magazine
, and Science News .
Prospective MIDDLE SCHOOL TEACHERS of science should possess all of the scientific knowledge of prospective elementary school teachers.
In addition, all prospective middle school teachers will:
Increase their understanding of the concepts and processes of the life,
physical, and earth/space sciences through an undergraduate degree in one
of the sciences or equivalent coursework in the three major sciences. A
degree in one of the sciences should be complemented with courses in the
other major sciences.
Enhance their understanding of concepts and techniques in the life,
physical, and earth/space sciences through application to real world phenomena.
Design, conduct, and evaluate research investigations that promote
a deeper understanding of scientific inquiry and the relationship of science
to the real world.
Develop scientific literacy sufficient to confidently use information
found in such journals as Science Scope, Scientific American, Discover,
and
Science News .
Prospective SECONDARY SCHOOL TEACHERS of science should possess all the scientific knowledge of prospective elementary and middle school teachers.
In addition, all prospective secondary school teachers will:
Build on their understanding of the concepts and processes of the life
sciences, physics, chemistry, or earth/space science by acquiring a baccalaureate
degree with a major in their field(s) of certification.
Broaden their understanding of concepts and techniques in science disciplines
beyond their field(s) of certification in order to support interdisciplinary
learning and authentic science research in their classrooms.
Enhance their understanding of concepts and techniques in the life,
physical and earth/space sciences through application to real world phenomena.
Design, conduct, and evaluate research investigations that promote
a deeper understanding of scientific inquiry and the relationship of science
to the real world.
Develop scientific literacy sufficient to confidently use information
found in such journals as The Science Teacher, American Biology Teacher,
Journal of Chemical Education, The Physics Teacher, Science , and
Science News .
Proficiency Standards In Scientific Habits Of Mind
Science is a way of knowing that provides justifiable explanations about, or models of, the natural world. These models establish a structure for organizing observations and experimental data. The value of a particular model depends on how consistent it is with known empirical evidence and how reliable it is in predicting behavior in other related systems. For example, atomic theory is a model that explains chemical behavior and Newtonian mechanics is a model for explaining physical motion. Each is organized from an accumulation of empirical data into a generalized set of relationships and is reinforced by reliable predictive ability.
Not all claims to knowledge are equal in scientific study. Criteria for evaluating theories and explanations exist and should be part of the science education of teachers and students. These criteria provide a rationale for comparing the merits of conflicting theoretical positions. They offer a way to frame discussion of past scientific controversies, such as whether continents drift, as well as everyday matters, such as evaluating nutrition fads or alleged paranormal phenomena. The issue of what is, and what is not, science continues to evolve because there is an ongoing discussion among scientists, sociologists, science historians, and philosophers of science regarding the nature of scientific knowledge.
The processes by which scientific models change may involve quiet evolution or noisy revolution. They are fueled by all of the motivations, both noble and selfish, that are features of any human enterprise. Nevertheless, science as a cultural tradition is characterized by a set of shared values, attitudes, and skills -- "scientific habits of mind" -- that distinguish it from other modes of thought. More than anything else, science is guided by the question "How do we know?". This question embodies the idea of skepticism, holding claims to knowledge as tentative pending investigation of the validity of assumptions, representativeness of the data base, the logical structure of arguments, and the existence of alternative explanations.
This question "How do we know?" should permeate science instruction as well and should be a central pillar in the preparation of those who intend to teach science. This attitude contrasts with a frequent emphasis in courses at all levels on the "What" of science rather than on the "How". Although descriptions of scientific phenomena, theories, and applications can be fascinating, a survey of this knowledge alone does not promote a personal understanding of the processes and nature of science. Consequently, to "learn science" means that one must "do science" in order to become scientifically literate.
The traditional picture of learning how to "do science" in schools, however, is often interpreted as teaching "the scientific method". It is described in most science texts as a linear five-step process of hypothesis generation, experiment design, data collection, data interpretation, and conclusions. A student's knowledge of science is evaluated according to whether they know these steps and are able to use them, e.g., in a science project. This approach falls far short of the vision of science as a way of knowing, and is a misrepresentation of what scientists do and how scientists think. The goal of instruction in science is not to teach an explicit approach to science, but to inculcate a way of thinking and an ability to justify that thinking about the natural world.
Another interpretation of "doing science" is the development of process
skills, such as observing, classifying, comparing, measuring, organizing
data, communicating, inferring, and predicting. Certainly, scientists do
these things and teaching science should include giving students opportunities
to learn these skills. However, there is a danger that instruction may
encourage these behaviors without encouraging the thought processes and
value system that support them.
All prospective teachers of science will:
Design and carry out a scientific investigation, including formulation
of research questions, collection of data, interpretation of data, and
public reporting and presentation of results.
Demonstrate curiosity, honesty, openness, and skepticism; use logical
argument and empirical standards in their own scientific investigations;
and actively promote these characteristics in their science instruction.
Articulate how the growth of scientific understanding is sustained
by collaboration, accurate and truthful reporting, and public review of
results.
Understand that science can only address questions that are empirically
testable and understand that models that are incapable of being tested
(in particular, of being proven incorrect) are not scientific models.
Utilize scientific habits of mind in making decisions about issues
such as personal and community health, global resource management, population
dynamics, and risk management.
Communicate effectively why science can inform, but not determine,
public policy decisions regarding societal issues, which inherently involve
value judgments.
Utilize well-considered examples from the history of science in designing
instruction
Give examples that illustrate that science is a part of society; that
scientists are influenced by societal, cultural, and personal beliefs;
and that, in turn, scientific knowledge influences society, culture, and
personal beliefs.
Distinguish between science, which concerns questions about the natural
world, and technology, which concerns human adaptation to the natural world.
Understand and encourage development of the notion that scientific
understanding at any point in time is uncertain; scientists continue to
sharpen and extend models that more fully explain events in the natural
world.
The improvement of instruction for all students at the elementary and
middle school levels requires strong leadership at individual schools.
This leadership has been recognized by the PERP Advisory Council, working
K-8 teachers, and conference participants as an important means for making
real and sustained progress toward improving elementary mathematics and
science instruction. Currently there is no elementary mathematics or science
specialist certification in the State of New Hampshire. The Advisory Council
recommends that a certification or an endorsement for elementary specialists
be introduced.
An elementary school mathematics or science specialist serves the school
by 1) raising the level of content knowledge and pedagogical competence
of the staff, 2) coordinating instructional efforts within and between
buildings, and 3) aiding in the implementation of a high quality program.
This person may be a regular classroom teacher who assumes responsibility
for programs beyond her/his own classroom, may be a classroom teacher with
a content specialty on an interdisciplinary team of teachers, or may have
an independent position specifically defined for the development and implementation
of curriculum and instructional activities within one or more schools.
Professional Characteristics of the Mathematics or Science Specialist
at the Elementary School Level
Content specialists at the K - 8 level should possess the knowledge
of content, pedagogy, and the learner as outlined in this document for
a middle grades teacher
Increase their understanding of mathematics or science concepts through
an undergraduate degree or equivalent coursework for middle school subject
matter certification. In science, a degree in one field should be complemented
with courses in the other major sciences.
Apply the results of research in education to their own teaching and
assist their colleagues in using these results.
Utilize an awareness and understanding of national reform efforts and
curriculum innovations to develop and maintain relevant and dynamic programs.
Apply knowledge of curriculum development, implementation, and evaluation
in monitoring and improving programs.
Be active in professional organizations (e.g., NCTM, NSTA, The New
Hampshire Affiliate of the Association of Teachers of Mathematics in New
England [NH-ATMNE], and the New Hampshire Science Teachers Association
[NHSTA]).
Demonstrate an ability to design and conduct professional development
activities regarding content and pedagogy.
Assist staff in designing and implementing alternative assessment strategies.
Demonstrate an ability to work effectively with fellow teachers as
a colleague and as a leader.
Review and recommend teaching materials, such as student manipulatives,
calculators, and software, and assist teachers in integrating these into
instruction.
Novice Teacher Induction Programs
Unfortunately, Joyce's first moments of her teaching career (see margin) are not unusual. Beginning teachers in the United States often are given the most difficult classes and assigned the most tiresome duties. When space is at a premium, new teachers are often the ones who "float" between classrooms, a task that places severe demands on the organizational and planning skills of even a veteran teacher. Without a structured program offering advice and assistance to the beginner, the new teacher is left to sink or swim: to rely on untested skills, to deal with unimagined situations, to solve intractable problems.
Teacher educators see a serious need to become involved in the induction of new teachers into the profession. Records indicate that as many as 30% of teachers leave the profession in their early years (National Commission on Teaching and America's Future, 1997). Like Joyce, the 'unsuccessful' teacher is discouraged and often feels deceived by a preservice program that affirmed her qualifications but left her unprepared for her first challenges. Supporting the development of new teachers as they begin their careers involves the commitment of the preparing institution as well as the school community.
Recognition of the difficulties faced by beginning teachers has inspired numerous worthwhile programs to support and encourage their success. A recent report included case studies of induction programs in several Pacific Rim countries (http://www.ed.gov/pubs/APEC). The key characteristics of these programs can be summarized as follows:
New teachers are viewed as professionals along a continuum.
New teachers are not expected to do the same job as experienced teachers without significant support.
New teachers are nurtured. Interaction with other teachers is maximized.
Teacher induction is a purposeful and valued activity for the mentoring colleagues, for the supportive administrators, and for the preservice institution.
The culture of shared responsibility and support encourages all the school's staff to contribute to the development of the new teacher.
In all the sites studied, the emphasis in new teacher assessment is on constructive advice rather than critical evaluation.
Most encouraging about reports of effective induction programs is that the strategies that promote these principles do not require unreasonable investment of resources. Assigning new teachers to less difficult classes, and offering periodic release from duties so that beginners can observe in veteran teachers' classrooms can alleviate the isolation new teachers feel. Placing new teachers in classrooms adjoining supportive 'buddy' teachers allows for frequent interaction between veterans and novices. Encouraging 'team' planning or teaching provides the novice with expert models, and opens the door to conversations about a wide range of issues the newcomer may find difficult to discuss.
The development of exemplary teachers begins with a quality preservice
education program and continues with successful experiences during the
early years of service. The Advisory Council recommends that teacher educators
and practicing teachers collaborate to support the induction of new members
in order to enhance the quality of the teaching profession.
Building Bridges Between K-12 and 13-16
Collaboration Among Mathematics, Science, and Education Departments
in Teacher Preparation Institutions
Collaboration among mathematics, science, and education departments is essential for the development of competent first year teachers. For the prospective teacher learning to teach mathematics and/or science occurs through a variety of experiences: study of content, pedagogical preparation, field experiences; and with a variety of college/university faculty: content faculty, teacher educators, and supervising teachers. At institutions of higher education, it is not uncommon to find a diverse group of faculty, often housed in separate departments, involved in teacher preparation. It is also not unusual for these faculty to have differing expectations, values, and assumptions regarding what is important in teacher preparation. The lack of cohesiveness, which may result from these factors, often leads preservice teachers to experience contradictions and inconsistencies among the many components of their programs (MSEB, 1996) or to fail to grasp the applicability of knowledge from one discipline to another. In addition, preservice teachers may cognitively separate methods from content when these courses are offered in different departments. If the primary goal of a teacher preparation program is to "produce" quality first year teachers, then it is imperative that all faculty communicate and collaborate effectively across departments as well as across institutions.
To establish greater coherence in teacher preparation programs, cross-department communication and teamwork needs to be encouraged and supported among those involved in the teacher preparation process. Institutions of higher education need to break down the walls that separate departments by fostering substantive, professional discussions between discipline-based and education faculty. Goodlad has said "...The dispersion of the teacher preparation effort has resulted in teacher education being nobody's clearly defined responsibility" (1991, p.6). Content faculty, education faculty, and supervisors each need to recognize their critical responsibility in the training of the prospective teacher. Working together, they can assure that the teacher preparation program follows a logical sequence and that all proficiency standards have been covered.
The National Research Council (1996) has recommended that content should
not be separated from methods in preparing future teachers; the two should
be embodied in the same course or have parallel, desirable outcomes that
require interdepartmental interaction.
Faculty should seek ways to reinforce and integrate learning, rather
than maintaining artificial barriers among disciplines. Continuous collaboration
between content and education departments would foster interdisciplinary
education and allow preservice teachers to see the relationship betweeen
content and methods.
There is value in partnerships among colleges and universities, as well
as among faculty within institutions. Cross-college arrangements allow
for an interchange of ideas and information aimed at the improvement of
teacher preparation programs. Rather than teacher preparation institutions
competing with one another, teacher educators can support and encourage
each other, building collegiality between institutions and promoting excellence
in teacher education across the state. The NSF has encouraged and supported
collaboratives across institutional boundaries. Though there is still a
long way to go, the level of conversation about pedagogy among faculty
is increasing (NSF, 1996).
Collaboration between K-12 Schools and Teacher Preparation Institutions
To achieve the vision for the preparation of mathematics and science teachers put forth in this document, there must be a strengthening of the communication and collaboration between the administration and staff in K-12 school districts and departments of mathematics, science, and education at the collegiate level. What and how prospective teachers learn in the college setting must be applied and practiced within the classrooms of K-12 schools where field experiences take place. There must be a match philosophically and practically within and between the two settings, or mixed messages leading to confusion and disillusionment will be given to those about to enter the teaching profession. Evidence of this is cited in a study by Grissmer and Kirby (1987), who found that 30-50% of new teachers leave the profession within 3-5 years of entry. With the projected demand for 2 million new teachers within the next decade, this is an alarming statistic. All stakeholders in the preparation of teachers must strive to ensure a seamless continuity in the transition of prospective teachers from preservice preparation programs to teaching in K-12 classrooms.
K-12 schools and institutions of higher education must design and implement programs that foster the continuing professional development of teachers as they seek to extend their expertise in both mathematics and science content, sharpen and enrich their instructional strategies, and increase their knowledge of the learners in their classrooms. In this dynamic, ever-changing profession, matching the needs of teachers and school districts with the programs offered by the institutions of higher education requires continuous and active communication among all the stakeholders. Most teachers will seek to remain current in their field by pursuing a degree beyond the baccalaureate. Thus, graduate programs must sensitively respond to the articulated needs of teachers and administrators in the field.
To address the issues cited in the above paragraphs, many institutions
of higher education and local school districts have entered into agreements
to form professional development schools. These schools seek to eliminate
the barriers between school districts and teacher preparation institutions
for both the preservice and inservice development of teachers. The demarcation
lines blur and there is a continuous flow of personnel, resources, and
expertise between the two levels of education. College staff can be found
in K-12 schools and K-12 staff can be found in college classes as each
seek to extend their knowledge and expertise of the educational process
at different levels. Teachers at all levels, K-16, sharpen their skills
and knowledge. They learn new methods and strategies for teaching students
of all ages and abilities in important subject matter utilizing current
pedagogical practices.
These professional development schools serve as sites for the field
experiences of prospective teachers. Experienced teachers, recognized for
excellence in their craft, work with prospective teachers during their
field experiences while others serve as mentors to beginning teachers in
their induction to the profession. K-12 teachers may serve as adjunct faculty
at the college. In turn, college faculty do demonstration lessons in the
K-12 schools or conduct in-service experiences that address the needs of
both prospective teachers and current etachers. Action research projects
are jointly conducted to ascertain the effectiveness of instructional practices
or the appropriateness of certain content or modes of instruction for various
groups of students.
While professional development schools systematically combine these
practices into an integrated program that will enhance education at all
levels, many of these practices can be instituted on a more informal basis.
The reader is encouraged to look in the bibliography of this document for
resources on establishing the important linkages between K-12 schools and
institutions of higher education.
Breaking the Cycle of Blame
Educational reform is a critical issue in the United States today. More than a decade of reports discussing the shortcomings of the American educational system have precipitated unparalleled changes in educational programs. States have legislated standards and frameworks, made grants available for the design of more technology-based courses, increased science and mathematics requirements for high school graduation, and mandated testing of both students and teachers. But all of these efforts have failed to produce a substantial and sustained change. Data suggest that today's students do not have solid foundations in science and mathematics. Why is it that there are still gaps in children's understanding of mathematics and science concepts? Consider the following ... a system-wide cycle of blame.
Cycle of Blame
What is this system-wide cycle of blame? As students progress through each level of the educational system, teachers note that many students do not possess basic concept and skill foundations in mathematics and science. As a result, remediation of basic skills becomes the foremost task of teachers and professors.
Business people complain that their workers do not have the skills needed to be effective in their jobs and blame the colleges and high schools for not preparing students to meet adequately the demands of the work force. College professors blame high school teachers for not preparing students to meet the demands of intensive study. High school teachers blame middle school teachers and they, in turn, blame elementary school teachers for not providing students with a basic foundation in mathematics and science concepts. As the cycle continues, elementary school teachers blame early childhood educators and teachers at all levels blame parents for not supporting their children's education.
Each of the stakeholders in our educational system see themselves as
separate entities who must struggle with inadequacies caused by others.
Stakeholders do not see their roles as shareholders connected to one another,
helping all to achieve success.
Creating a system of support within our educational system is a requisite and key to true educational improvement. This is systemic reform. Parents, business people, educators at all levels, and students have important contributions to make. True educational improvement requires every stakeholder to do his or her part to improve the system rather than tear it down. Every person must realize that all constituencies within the system play an important role in the education of every child.
A key to the system of support is providing a mechanism to allow stakeholders
to come together and develop plans of action for unifying and strengthening
the entire system. Together, every level must look at the big picture and
discuss and debate what can be done to promote better mathematics and science
education.
What can be done at each level? As a community of life-long learners, the focus must be on collaboration, communication, reflection, and assessment. Colleges and universities must implement more rigorous mathematics and science content courses that also model good mathematics and science instruction. Businesses can join together in industry initiatives and form business/education partnerships. Preservice teachers at all levels can seek out a more in-depth study of science and mathematics and participate in effective induction programs.
There are currently many constituents involved in the educational process
and it is important to recognize and understand the similarities and differences
among them. If we are to engage in systemic reform, we must move beyond
both superficial programs and structural arrangements. Only within this
collaborative context can we hope to make substantive change in our educational
system.
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