PEP Conceptual Framework
UNIVERSITY OF WISCONSIN - STEVENS POINT
PROFESSIONAL EDUCATION PROGRAMS
CONCEPTUAL FRAMEWORK, WISCONSIN TEACHING STANDARDS, OVERARCHING ASSESSMENT PLAN, REFERENCES, and CONCEPTUAL FRAMEWORK CHART
MISSION
The basic mission of the University of Wisconsin – Professional Education Programs (UWSP - PEP) is to provide quality pre-service training to undergraduates in early childhood, elementary and secondary education and to provide quality graduate, credit and non-credit, learning opportunities to educators in Central Wisconsin. It is the vision of the Professional Education Programs that students of our programs will encounter rich multicultural experiences, varied and meaningful opportunities for experimentation within classrooms, a sound understanding of educational pedagogy and knowledge of the most current views regarding educational practices. Part of our vision for our students is that they become reflective practitioners, capable of anticipating future needs and changes within the professional arena, and capable of assuming roles of leadership.
The PEP faculty and staff are dedicated to the creation of new partnerships between the University and the schools in this service area to enable teachers, students and schools to meet or exceed world-class standards. To further these goals, the PEP will strive to use the most advanced concepts of distance learning, computer technology, and other innovations in technology to extend our campus into every district in Central Wisconsin.
These new partnerships, professional development alliances, will be embedded throughout the undergraduate program and will be a model of excellence for teacher certification programs. Implicit in this view of alliances is the vision of the educator (both public school and higher education faculty) as the professional who engages in life-long learning, professional development and personal growth.
Research supports this mission as follows:
Rich, Multicultural Experiences. According to Lynch and Hanson (1998) understanding of cultural beliefs and behavior changes, because culture is not static. Cultural beliefs, language, economic status, and degree of acculturation are continually influenced by sociopolitical boundaries and changing demographics. One of the important goals of multicultural education is to help all students to acquire the knowledge, attitudes and skills needed to function effectively in a pluralistic democratic society and to interact, negotiate, and communicate with peoples from diverse groups in order to create a civic and moral community that works for the common good (Banks, 1995). Based upon an examination of research related to the effects of multicultural education, an important implication that Banks notes “is that teachers must be provided with training and opportunities that will enable them to examine their feelings, attitudes and values, and helped to develop attitudes consistent with a democratic society” (1995).
Opportunities for Experimentation within Classrooms. Experimentation implies movement away from students merely functioning as passive recipients of information. At the core of the active learning argument is the idea that the students must act on information in particular ways in order to “make what they learn a part of themselves” (Cerbin, 1995, p.1). Active learning may be created through the application of collaborative and cooperative learning strategies. According to Gerlach (1994), effective collaborative strategies involve the teacher becoming a task setter, classroom manager and synthesizer. While collaborative learner activities vary widely, they are all centered on the students’ processes of investigation, discovery and application, not the teacher’s presentation (Smith & MacGregor, 1992). Knowledge and skills are of little use if a student cannot apply them in cooperative interactions with others. Smith (1985) believes the use of cooperative learning approximates more closely the activity of real world employment, found within many of the practicum offerings.
Understanding of Educational Pedagogy and Knowledge of Current Views of Educational Practices. We have long been aware of the importance of interaction between students and students and teacher in learning experiences. Dewey (1902) placed the learner at the center of the learning process and indicated the greater the depth of interaction with others the better the learning, and thus the experience. A synthesis of the literature on pedagogy and educational practices supports the following classroom strategies: 1) Allow students to write and discuss what they are learning; 2) Encourage teacher/student contact inside and outside the classroom; 3) Have students working with others on substantive tasks inside and outside of class; 4) Give prompt and frequent feedback to students; 5) Communicate high expectations; 6) Make standards and grading criteria explicit; 7) Help students achieve to their highest ability; 8) Respect diverse talents and ways of learning; 9) Motivate through posed problems, questions, means of inquiry, rather than merely content coverage; 10) Focus on assignments and help students successfully complete assignments (Astin 1985; Bonwell & Eison, 1991; Chickering &Gamson, 1987; Drummond, 1997; Erickson, 1984; Frost, 1991; Kurfiss, 1987; Light, 1992; McKeachie, 1986; Pascarella & Terenzini, 1991; Penrose, 1992.)
In 1987,Chickering & Gamson presented their widely accepted Seven Principles of Good Practice in Undergraduate Education for use in teaching and learning environments on campuses across the country. The Education Commission of the States (ECS) through the American Association of Higher Education (AAHE) expanded on these principles in developing the “ECS Dozen” (AAHE, 1996). The “ECS Dozen” is based on extensive research conducted in response to changing student needs. There is strong evidence indicating that colleges and universities systematically engaging in the employment of these practices demonstrating improved student performance and satisfaction (AAHE, 1996).
Becoming Reflective Practitioners Capable of Assuming Roles of Leadership. It has been said that all teachers, formally or informally, engage in the process of reflection. Specifically, reflection-in-action, reflection-of-action, and reflection-on-practice (Schon, 1983, 1987). Any type of reflection on practice, pedagogy, and process allows for teachers to continue to learn and grow as professionals and as people. This reflection may be purposeful or incidental but is typically ongoing and powerful. Ideally, reflection-on-action is a shared process that presents an opportunity for discussion of practice with peers. If reflection is a normal process for teachers, we need to teach pre-professionals to reflect critically on their teaching to continue to grow and learn about self, their students and the teaching profession. Brookfield (1995) believes many teachers fail to reflect critically on their teaching practices, not because of a lack of sincerity or a strong sense of purpose, but because they fail to fully understand the effect of their actions on their students. Critically reflective teachers regularly inquire into how students are perceiving the learning environment (Brookfield, 1995).
PEP Enabling Students to Meet World Class Standards. Wisconsin Model Academic Standards, which align with discipline-specific national standards, form a framework for content and pedagogical study within each certification area in UWSP Professional Education Programs. These standards are used in the creation of classroom lesson plans, consideration of appropriate learning strategies, examination of current discipline-specific research and practicum and student teaching experiences. See http://www.dpi.state.wi.us/dpi/dlsis/tel/index.html
PEP Using Advanced Concepts of Technology. Understanding the most effective use of distance education continues to evolve with its on-going usage. Many schools currently are using technology as an aide to accomplishing traditional prescriptive approaches. As we progress toward maturity with these new tools, a more constructivist approach involving collaboration, authentic methodologies and the development of higher level thinking skill development and problem solving is emerging through careful attention to broad ranging assessment technique. Researchers such as Hawkes (1996), Rowland et. al.(1996) emphasize the evaluation of program components by the faculty and students in order to determine further refinement and development. Therefore, the Professional Education Program makes alterations to their courses using varying distance education technologies.
Vision of the Professional Engaging in Life-long Learning, Professional Development and Personal Growth Every person is a product of his/her life experiences. These life experiences play heavily in shaping and determining an individual style of teaching. Developmental psychology, cognitive psychology and motivation research have been examined to better understand forces that shape development of a preferred style of teaching (Bain, 1998; Shrank, 1998). Not surprisingly, professional development training and practices are more beneficial for people with a high self-esteem (Riordan, 1993; Lindley, 1993; Kalivoda, 1995; and Showers, Joyce and Bennett, 1987). In many cases, much of what we learn is incidental through either observation and/or trial and error, making it difficult to describe, understand and/or appreciate (Marsick & Watkins, 1990).
A great deal of research has been done to better understand conditions essential for the successful implementation of any professional development plan or strategy for improvement of teaching practices. (Borko & Putnam, 1995; Hargreaves & Dawes, 1989; Kahn, 1993; Eraut, 1994; Schon, 1983, 1987; Brookfield, 1995; Shulman, 1993; Smylie, 1995; Guskey, 1995; Harnish & Wild, 1994; Quinlan, 1995; Zeichner, 1993.)
WISCONSIN TEACHING STANDARDS
1. The teacher understands the central concepts, tools of inquiry, and structures of the disciplines he or she teaches and can create learning experiences that make these aspects of subject matter meaningful for pupils.
(NOTE: See Wisconsin DPI Content Guidelines for each certification program for Knowledge, Skills and Dispositions related to subject knowledge. Web-site: http://www.uwsp.edu/education
2. The teacher understands how children with broad ranges of ability learn and provides instruction that supports their intellectual, social and personal development.
Knowledge:
Teacher candidate describes theoretical frameworks for understanding and identifying patterns of intellectual, social and personal development.
Skills:
Teacher candidate plans learning experiences that consider patterns of pupils’ individual and group development.
Dispositions:
Teacher candidate values, accepts, and honors diverse personalities, abilities, socio-economic, cultural/religious, and gender differences.
3. The teacher understands how pupils differ in their approaches to learning and the barriers that impede learning and can adapt instruction to meet the diverse needs of pupils, including those with disabilities and exceptionalities.
Knowledge:
Teacher candidate identifies a variety of learning approaches for pupils with diverse needs.
Skills:
Teacher candidate designs, selects and implements instructional strategies to accommodate specific pupil needs.
Dispositions:
Teacher candidate believes all pupils can learn.
4. The teacher understands and uses a variety of instructional strategies, including the use of technology to encourage children’s development of critical thinking, problem solving, and performance skills.
Knowledge:
Teacher candidate defines and applies elements in critical thinking, problem solving, and performance.
Teacher candidate identifies various instructional strategies appropriate to his/her discipline and instructional context.
Skills:
Teacher candidate selects appropriate instructional strategies to meet curricular goals and pupils’ needs.
Teacher candidate appropriately utilizes technology in his/her instruction.
Teacher candidate effectively incorporates a variety of learning strategies to support performance skills, problem solving and critical thinking.
Dispositions:
Teacher candidate values a wide range of strategies for meeting instructional goals and needs of pupils.
Teacher appreciates the importance of using a variety of classroom techniques to encourage pupils to think critically and deeply.
5. The teacher uses an understanding of individual and group motivation and behavior to create a learning environment that encourages positive social interaction, active engagement in learning, and self-motivation.
Knowledge:
Teacher candidate describes the influence of the learning environment to pupil achievement.
Teacher candidate identifies developmental influences and differences among pupils.
Teacher candidate identifies techniques and pedagogical practices to accommodate learner differences.
Teacher candidate describes the principles of effective group structure and dynamics.
Skills:
Teacher candidate creates a learning environment that supports social interaction, active engagement, and pupil achievement.
Teacher candidate creates materials to accommodate diverse learning needs.
Teacher candidate demonstrates effective group facilitation.
Teacher candidate varies tempo and pacing of instruction.
Dispositions:
Teacher candidate values teaching as a craft.
Teacher candidate appreciates change, modifications and adaptations.
6. The teacher uses effective verbal and nonverbal communication techniques as well as instructional media and technology to foster active inquiry, collaboration and supportive interaction in the classroom.
Knowledge:
Teacher candidate identifies instructional media to foster an interactive classroom.
Teacher candidate describes strategies that create a supportive environment.
Skills:
Teacher candidate demonstrates ability to foster a respectful, safe, supportive instructional environment.
Teacher candidate creates classroom activities that support discussions, open-ended questions, collaboration, communication and active inquiry.
Teacher candidate uses a variety of instructional techniques, media and technology to foster and support discovery/authentic learning.
Dispositions:
Teacher candidate values the importance and role of collaborative and interactive learning.
Teacher values the importance of verbal and non-verbal communication in establishing an interactive classroom.
Teacher candidate realizes that, as a teacher, listening is often more important than speaking.
7. The teacher organizes and plans systematic instruction based upon knowledge of subject matter, pupils, the community and curriculum goals.
Knowledge:
Teacher candidate identifies the Wisconsin Model Academic Standards.
Skills:
Teacher candidate integrates trends and research that impact curriculum reform into instructional design.
Teacher candidate writes lessons that align with the Wisconsin Model Academic Standards.
Teacher candidate designs instruction consistent with the nature of the specific discipline.
Dispositions:
Teacher candidate values the importance of building school and community collaborations.
Teacher candidate appreciates student interests and parental and community values and concerns.
8. The teacher understands and uses formal and informal assessment strategies to evaluate and ensure the continuous intellectual, social, and physical development of the pupil.
Knowledge:
Teacher candidate identifies a variety of formal and informal assessment strategies.
Teacher candidate describes and explains how assessment is effectively used to monitor pupil progress and instruction.
Skills:
Teacher candidate creates and uses both formal and informal assessments.
Teacher candidate creates assessment criteria for evaluating knowledge and performance.
Teacher candidate interprets data for use in decision-making about instruction and pupil learning.
Teacher candidate creates, utilizes, explains and modifies assessment measures such as: checklists, rubrics, performance tasks, problem solving exercises and simulations.
Dispositions:
Teacher candidate appreciates the need for continuous, on-going assessment to modify instruction to meet pupil needs.
9. The teacher is a reflective practitioner who continually evaluates the effect of his or her choices and actions on pupils, parents, professionals in the learning community and others and who actively seeks out opportunities to grow professionally.
Knowledge:
Teacher candidate explains the impact of his/her choices, beliefs and actions on pupils.
Teacher candidate identifies resources for professional development in the school, community and beyond.
Skills:
Teacher candidate critically evaluates lessons and make necessary adjustments.
Teacher candidate critiques and modifies teaching based on reflections.
Teacher candidate identifies personal and professional strengths and builds on them.
Dispositions:
Teacher candidate appreciates the importance of reflection to improve the teaching and instructional environment.
Teacher candidate values professional growth and development.
Teacher candidate values and seeks advice and direction of others.
10. The teacher fosters relationships with school colleagues, parents, and agencies in the larger community to support pupil learning and well being and who acts with integrity, fairness and in an ethical manner.
Knowledge:
Teacher candidate describes the importance of the community’s political structure or climate.
Teacher candidate identifies the impact of home and community on pupil learning and performance.
Teacher candidate identifies relevant community resources, agencies and issues.
Skills:
Teacher candidate examines the relationship between community characteristics and the functioning of the school.
Teacher candidate develops positive relationships with students, parents, colleagues and community members.
Dispositions:
Teacher candidate views the school within its larger community context.
Teacher candidate understands the importance of building effective relationships within the community.
Teacher candidate honors his/her position as a role model.
Teacher candidate values behaving with integrity, fairness and in an ethical manner.
Teacher candidate values and seeks positive relationships with the community.
OVERARCHING ASSESSMENT PLAN
Stage in Program of Study |
Requirement |
Task |
Entrance to UWSP |
· Graduation from recognized high school · High School GPA 3.0 or above
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Pre-Admission Coursework
Pre-Admission Coursework (cont’d) |
|
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Admission to Professional Education Program |
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Completion of Professional Education Coursework |
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Completion of Content Area Course of Study |
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Admission to Student Teaching |
· Minimum GPA of 2.75 in major/minor, teacher education, and overall GPA
· Completion of all teaching methods courses
|
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Prior to UWSP Recommendation for Certification and Licensure
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· Successful completion of student teaching as documented by UWSP Supervisor
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· Minimum GPA of 2.75 in major/minor, teacher education, and overall GPA
· Completion of Professional Development Portfolio to include specified performance tasks as evidence of proficiency in 10 Wisconsin Teaching Standards and evidence related to subject knowledge |
REFERENCES
Rich Multicultural Experiences
Banks, J.A. (1995) Multicultural Education: Historical Development, Dimensions, and Practice, Pp. 3-24 In Handbook of Research on Multicultural Education. Banks J.A. (ed.) Macmillan, New York.
Lynch, E. W., & Hanson, M. J. (1998). Developing cross-cultural competence: A guide for working with children and their families. Baltimore: Paul H. Brookes.
Experimentation Within Classrooms
Astin, A. (1985). Involvement: the cornerstone of excellence. Change, 17 (4) 35-39.
Bonwell, C.C. & Eison, J.A. (1991). Active learning: Creating excitement in the classroom. ASHE-ERIC Higher Education Report #1, Washington D.C.
Gerlach, J.M. (1994). Is this collaboration? New Directions for teaching and Learning #59. San Francisco: Jossey-bass, Inc.
Kurfiss, J. (1987). Critical thinking. ASHE-ERIC Higher Education Report #1. Washington, D.C. p.88-97.
McKeachie, W. (1986). Teaching Tips, 8th edition. Lexington, MA: Heath & Co.
Pascarella, E. T., & Terenzini, P. T. (1991). How College Effects Students. San Francisco, Jossey-Bass.
Penrose, A.M. (1992). To write or not to write: Effects of task and task interpretation on learning through writing. Written Communication, 9, 465-500.
Smith, B. & MacGregor, J. (1992). What is collaborative learning? In A. Goodsell and others (eds), Collaborative Learning: A Sourcebook for Higher Education. University Park, PA: National Center on Postsecondary Teaching and Learning Assessment.
Smith, K.A. (1985). Cooperative learning groups. N S. Schomberg (Ed.) Strategies for Active Teaching and Learning in University Classrooms, Minneapolis: University of Minnesota.
Sound Understanding of Educational Pedagogy
American Association of Higher Education, (April, 1996). What Research Says About Improving Undergraduate Education 5-8.
Bain, K. (1998). What Do the Best Teachers Do? Searle Center for Teaching Excellence, Northwestern University. Evanston, Illinois.
Borko, H. & Putnam, R. T. (1995). Expanding a teacher’s knowledge base: A cognitive psychological perspective on professional development. In T. R. Guskey & M. Huberman (Eds.) Professional Development in Education. New York: Teachers College Press.
Cerbin, W. (1995). Teaching Students to Use Their Minds Well: The Nature of Thoughtful Learning. Paper presented at the UW System Faculty College, Marinette, WI.
Chickering, A.W. & Gamson, Z. F. (March, 1987). Seven principles for good practice in undergraduate education. AAHE Bulletin.
Chickering, A.W. & Gamson, Z. F. (1991). Applying the seven principles for good practice in undergraduate education. New Directions For Teaching and Learning 47, San Francisco: Jossey-Bass.
Dewey, J. (1902). The Child and the Curriculum: the School and Society, Chicago: University of Chicago Press.
Drummond, T. (1997). A brief summary of the best practice in college teaching, Prodigy: Web Browser (http:/nssux.sccd.ctc.edu/~eceprog/bstprac.html).
Guskey, T. R. (1995). Professional development in education. In T. R. Guskey and M. Huberman (Eds.), Professional Development in Education, New York: Teacher College Press.
Hargreaves, A. & Dawe, R. (1989). Paths of professional development: Contrived collegiality, collaborative culture, and the case of peer coaching. Teaching and Teacher Education, 6 (3), 227-241.
Harnish, D. & Wild, L. A. (1994). Mentoring strategies for faculty development. Studies in Higher Education 19, (2), 191-201.
Hawkes, Mark (1996). Evaluating School-Based Distance Education Programs: Some Thoughts about Methods. v80 n582 26-33 Oct 1996
Kahn, S. (1993). Better teaching through better evaluation: A guide for faculty and institutions. To Improve the Academy 12, 111-126.
Kalivoda, P. (Winter,1995). Exemplary senior faculty at research universities: Their guiding principles for balancing teaching and research. Innovative Higher Education, 20 (2), 95-116.
Light, R. (1992). The Harvard assessment seminars: Second report. Cambridge, Mass: The Harvard University School of Education.
Lindley, D. A. (1993). This Rough Magic: The Life of Teaching. Westport, CT: Bergin & Garvey.
Marsik, V. J, Watkins, K.E., Informal and incidental learning in the workplace. London; New York: Routledge, 1990.
Quinlan, K. M. (1995). Faculty perspectives on peer review. The NEA Higher Education Journal 11, 5-22.
Riordan, T. (1993). Beyond the debate: The nature of teaching. Paper presented at Alverno College, March, 1993.
Rowlands, Mark; And Others (1996). A Case Study of Students Teachers’ Science Placements. Assessment & Evaluation in Higher Education v21 n1 91-98 Mar 1996
Showers, B., Joyce, B., & Bennett, B. (1987, November). Synthesis of research on staff development: A framework for future study and a state-of-the-art analysis. Educational Leadership, 75-87.
Shrank, R. (1998). How do people learn? Paper presented at the Searle Center for Teaching Excellence, Northwestern University, June.
Shulman, L.S. (1993, November/December). Teaching as community property. Change, 25, 6-7.
Smylie, M. A., (1995). Teacher learning in the workplace. In T. R. Guskey and M. Huberman (Eds.), Professional Development in Education, New York; Teachers College Press.
Zeichner, K. M. & Gore, J. M. (1990). Teacher socialization. In N. Brouwer (Ed.) Participants in Teacher Education. New York: Teachers College Press
Reflective Practitioners
Brookfield. S.D. (1995). Becoming a Critically Reflective Teacher. San Francisco: Jossey-Bass.
Schon, D.A. (1983). The Reflective Practitioner: How Professionals Think in Action. New York: Basic Books.
Schon, D.A. (1987). Educating the Reflective Practitioner: Towards a New Design fir Teaching and Learning in the Professions. San Francisco, Jossey-Bass.
Capable of Assuming the Roles of Leadership
Eraut, M. (1994). Developing Professional Knowledge and Competence. Bristol, PA, the Falmer Press.
TABLE OF CONTENTS
ADMINISTRATION
ATHLETICS AND CO-CURRICULAR PROGRAMS COORDINATOR
CHILDREN AT RISK COORDINATOR
DEAN OF STUDENTS
DIRECTOR OF INSTRUCTION
DIRECTOR OF SPECIAL EDUCATION & PUPIL SERVICES
EDUCATION FOR EMPLOYMENT COORDINATOR
GIFTED AND TALENTED COORDINATOR
INSTRUCTIONAL LIBRARY MEDIA SUPERVISOR
INSTRUCTIONAL TECHNOLOGY COORDINATOR
LOCAL VOCATIONAL EDUCATION COORDINATOR
PERSONNEL COORDINATOR
PRINCIPALS
PUBLIC RELATIONS COORDINATOR
READING SPECIALIST
RESEARCH COORDINATOR
SCHOOL BUSINESS ADMINISTRATOR
SCHOOL DISTRICT ADMINISTRATOR OR SUPERINTENDENT
SCHOOL NETWORK ADMINISTRATOR
SCHOOL TO WORK COORDINATOR
STANDARDS AND ASSESSMENT COORDINATOR
TITLE 1 COORDINATOR
PUPIL SERVICES
SCHOOL COUNSELOR
SCHOOL PSYCHOLOGIST
SCHOOL SOCIAL WORK
SPECIAL EDUCATION
COGNITIVE DISABILITIES
CROSS CATEGORICAL SPECIAL EDUCATION
DEAF OR HARD OF HEARING
EARLY CHILDHOOD SPECIAL EDUCATION
EMOTIONAL DISTURBANCE/EMOTIONAL BEHAVIORAL DISABILITY
LEARNING DISABILITIES
SPEECH–LANGUAGE PATHOLOGY
VISUAL IMPAIRMENT
GENERAL EDUCATION
AGRICULTURE EDUCATION
ART
BROADFIELD LANGUAGE ARTS
BROADFIELD SCIENCE
BROADFIELD SOCIAL STUDIES
BUSINESS EDUCATION
COMPUTER SCIENCE
DANCE
EARLY CHILDHOOD
EARLY CHILDHOOD THROUGH MIDDLE CHILDHOOD
EARTH AND SPACE SCIENCE
ECONOMICS
ENGLISH AS A SECOND LANGUAGE
ENGLISH LITERATURE AND COMPOSITION
ENVIRONMENTAL SCIENCE
FAMILY AND CONSUMER EDUCATION
FOREIGN LANGUAGE
GEOGRAPHY
HEALTH
HISTORY
JOURNALISM
LIFE & ENVIRONMENTAL SCIENCE INCLUDING BIOLOGY AND ENVIRONMENTAL STUDIES
MARKETING EDUCATION
MATHEMATICS
MIDDLE CHILDHOOD THROUGH EARLY ADOLESCENCE
MUSIC
PHYSICAL EDUCATION
PHYSICAL SCIENCE INCLUDING CHEMISTRY
PHYSICAL SCIENCE INCLUDING PHYSICS
POLITICAL SCIENCE and CITIZENSHIP
PSYCHOLOGY
SOCIOLOGY
SPEECH COMMUNICATION
TECHNOLOGY EDUCATION
THEATRE
SUPPLEMENTARY PROGRAMS
ADAPTIVE EDUCATION
ADAPTIVE PHYSICAL EDUCATION
ASSISTIVE TECHNOLOGY
BILINGUAL-BICULTURAL EDUCATION
GIFTED AND TALENTED
INSTRUCTIONAL LIBRARY MEDIA SPECIALIST
READING TEACHERS
ADMINISTRATION
ATHLETICS AND CO-CURRICULAR PROGRAMS COORDINATOR
CONTENT GUIDELINES FOR
CHILDREN AT RISK COORDINATOR
A Children At Risk Coordinator will demonstrate knowledge of and skills in:
1. Diversity as identified in PI 34.15.
2. Wisconsin Children At-Risk legislation and Administrative codes.
3. Children At-Risk program and budget management.
4. School and student level performance reports.
5. Research related to student risk factors and strategies to overcome risks.
6. Advocacy role and strategies for serving at-risk students in school/community.
7. Contracting and monitoring strategies for at-risk students’ performance.
8. School and community support services.
9. Communication with school staff, parents/guardians and community agencies.
10. Empathy for working with at-risk students.
11. Commitment to at-risk students’ success in school and community.
12. Persistence in working with at-risk students, community and families.
13. Entrepreneurial approach to services design.
Draft 8/17/01
CONTENT GUIDELINES FOR
DEAN OF STUDENTS
CONTENT GUIDELINES FOR
DIRECTOR OF INSTRUCTION
A Director of Instruction will demonstrate knowledge of and skills in:
1. Minority group relations as identified in PI 34.15(4)(c).
2. The organization and operation of public schools at all levels.
3. The governance of education at the national, state and local levels.
4. Supervision of instruction.
5. Evaluation of personnel.
6. School finance and taxation.
7. School business administration.
8. School law including those related to pupils, special education and employee contracts.
9. School and community relations.
10. The politics of education.
11. Educational leadership including participatory management, long-range strategic planning and change agent processes.
12. Human growth and development from birth through adult.
13. Oral and written communication.
14. Coordination of co-curricular and extra-curricular programs including organization structure, program planning and evaluation, policy formation, and curriculum development at both the school and district levels.
15. Test and measurements including norm-referenced and teacher constructed testing.
16. Curriculum development at the early childhood – middle childhood, middle childhood – early adolescence, and early adolescence – adolescence levels.
17. The role, function, and responsibility of a director of instruction through a supervised practicum, internship or documented work experience in a school setting.
CONTENT GUIDELINES FOR
DIRECTOR OF SPECIAL EDUCATION & PUPIL SERVICES
The Director of Special Education and Pupil Services will demonstrate knowledge of and skills in:
1. Historical, theoretical and legal foundations of special education and pupil services including:
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Historical and evolving special education laws, regulations, and policies and procedures that effect the lives of children with disabilities and their families.
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Models, theories and philosophies that provide the basis for general and special educational systems.
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Organizational and systems theory including political and economic issues that effect policy development within state and local education agencies and across other service systems.
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Federal, state, and local education reform initiatives and their requirements for both general and special education.
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Legal responsibility with regard to school-based counseling, psychological, social work, and nursing services including the children’s code under Wis. Stats., Chapter 48.
2. The characteristics of learners including:
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Theories of child and adolescent development and principles of learning and how they relate to children at risk and children with disabilities.
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Differential learning characteristics of students with and without disabilities and the implications for development of programs and service
3. Assessment and diagnosis practices including:
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Current legal and policy issues surrounding assessment and accountability related to children at risk and children with disabilities.
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Characteristics, appropriate use, and interpretation of various types of education-related assessments, including but not limited to norm-referenced, informal, and performance-based portfolio.
4. Instructional content and practice including:
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General education curriculum theory, models, and implications for children at risk and children with disabilities.
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General education curriculum theory, instruction, and how special education and related services support student access to the general education curricul
5. Planning and managing the educator and learning environment including:
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Research methods and knowledge about issues and trends to improve practice in schools and classrooms.
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Coordination of curriculum and instructional programs and practice strategies that facilitate the seamless movement of students from early childhood into K-12 environments and from school to post-secondary settings.
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Organization, development and management of collaborative and mutually supportive pupil services and special education programs within educational settings.
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Program evaluation models, processes and accountability systems.
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Leadership and human resources management including recruitment, personnel assistance and development, on-going supervision and evaluation of personnel, sites and district services related to learning outcomes for all students.
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Federal, state and local fiscal and taxation policies related to education and other social and health agencies.
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The educator standards under s. PI 34.02.
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Minority group relations under s. PI 34.15(4)(c).
6. Managing student behavior and social skills/interactions including:
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Federal, state and local policies and procedures governing the discipline of all students and the implications for children at risk and children with disabilities.
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Knowledge of legal and ethical issues surrounding use of various forms of behavior and social skills management procedures for children at risk and children with disabilities.
7. Communication and collaboration partnerships including:
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Interacting successfully with students, parents, educators, employers, and community support systems such as juvenile justice, public health, vocational rehabilitation, human services, and early childhood and adult education.
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Approaches for involving parents, family, and community members in educational planning, implementation, and evaluation.
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The roles of parents and various advocacy organizations as they support children at risk and children with disabilities and their families.
8. Professional and ethical practices including:
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The professional ethics and social behaviors appropriate for school and community.
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Interpersonal communication, intergroup communication, and public communication both oral and written.
CONTENT GUIDELINES FOR
EDUCATION FOR EMPLOYMENT COORDINATOR
(Career and Technical Education Coordinator)
An Education for Employment Coordinator will demonstrate knowledge of and skills in:
1. developing policies, long-rang plans and advocacy for career and technical education based on current research, federal and state requirements and best practices.
2. understanding and promotion of the concept of comprehensive programs in career and technical education which includes teaching the academic disciplines of marketing education, business education, health sciences occupations, agriculture education, technology education, and family and consumer sciences education.
3. understanding and promoting the concept of comprehensive programs in career and technical education which includes co-curricular career and technical student organizations related to each of the disciplines.
4. understanding and promotion of the concept of comprehensive programs in career and technical education which includes planning, coordinating and evaluating work based learning as a strategy for career development.
5. developing and implementing on-going evaluation plans for career and technical education and using the results for program improvement.
6. developing school, business and community relations that support the goals of career and technical education. (create advisory committees, serve on economic development committees, etc.)
7. developing and managing budgets and grants.
8. gathering, analyzing and disseminating data related to career and technical education, including local, state and national labor market information.
9. personnel selection and supervisory practices according to accepted personnel standards.
10. assessing staff development needs and providing quality staff development opportunities in career and technical education. (in-services, workshops/meetings, sharing research and best practices)
11. strategic planning, group facilitation, conflict resolution and mediation, and continuous improvement practices.
12. understanding the Wisconsin Developmental Guidance Model and the Education for Employment Standards, especially the relationship between comprehensive career development and career and technical education.
13. providing leadership in the understanding and promotion of postsecondary options for students especially in technical areas. (articulation, Tech Prep, Youth Options, nontraditional opportunities)
14. the integration of career and technical education model academic standards into K-12 curricula and assessment.
15. understanding the roles and responsibilities of working in a profit-making business environment. (through externships, work experience, volunteer experiences, etc.)
7/02/01
CONTENT GUIDELINES FOR
GIFTED AND TALENTED COORDINATOR
CONTENT GUIDELINES FOR
INSTRUCTIONAL LIBRARY MEDIA SUPERVISOR
An Instructional Library Media Supervisor will demonstrate knowledge of and skills in:
Educational administration/leadership:
The candidate can:
· Articulate the principles of school administration and apply them to the school district's library media program
· Build consensus and motivate different people
· Monitor, assess, and employ existing and emerging technologies for instructional and management applications
School personnel management:
The candidate can:
· Apply a knowledge of human relations to the direction of library media program personnel
· Recruit, hire, train, assign, supervise, evaluate, and provide leadership for school library media specialists and other staff in the school district's library media programs
Supervision of instruction:
The candidate can:
· Apply knowledge of adult learning theory, program planning and evaluation, and curriculum development at the elementary, middle and secondary levels
· Apply appropriate research findings to improve teaching and learning throughout the school district and specifically within the library media program
· Participate in district-wide instructional leadership efforts
· Provide leadership in planning and using existing and emerging instructional and informational technologies in all aspects of the school district's educational program
· Assess needs, and develop and implement a program of inservice education that incorporates information and technology literacy and its integration into the curriculum
District level library media program supervision:
The candidate can:
· Apply effective management principles to the administration of the district level library media program
· Work with faculty, administrators, instructional technology staff, and other library media professionals to establish library media program goals that are an integral part of the educational program in the district
· Initiate and direct activities involving faculty, administrators, and other library media professionals to meet the library media program goals
· Design, establish, and communicate district wide policies and procedures to meet the library media program goals
· Articulate and promote the library media program goals, activities, and policies, to appropriate individuals and groups
· Prepare, justify, and administer the district level library media program budget based on instructional program needs
· Develop proposals to secure funding from grant programs and other sources
· Evaluate in collaboration with faculty, administrators, instructional technology staff, and other library media professionals the instructional effects of the library media program.
· Advocate, initiate, and implement formal and informal agreements providing for increased availability and accessibility of information through interlibrary cooperation and resource sharing.
· Conduct research to assist in the development and operation of exemplary district level library media programs throughout the school district
· Facilitate the efforts of the district level library media advisory committee that includes administrators, teachers, library media staff, instructional technology staff, students, parents, and other representatives of the community
· Understand the principles and support the practice of free inquiry and access to information
· Model and promote ethical use of information and technology and respect and comply with intellectual property rights, laws, and guidelines
· Demonstrate awareness of laws and regulations that affect school library media programs
· Design school library media centers and other instructional facilities that support the instructional program and facilitate learning
· Support and develop a library media program that provides for equitable and flexible access to information, ideas, resources, and services both within and beyond the district
March 17, 2000
Professional Development Standard D:
Professional development programs for teachers of science must be coherent and integrated. Quality preservice and inservice programs are characterized by
· Clear, shared goals based on a vision of science learning, teaching, and teacher development congruent with the National Science Education Standards.
· Integration and coordination of the program components so that understanding and ability can be built over time, reinforced continuously, and practiced in a variety of situations.
· Options that recognize the developmental nature of teacher professional growth and individual and group interests, as well as the needs of teachers who have varying degrees of experience, professional expertise, and proficiency.
· Collaboration among the people involved in programs, including teachers, teacher educators, teacher unions, scientists, administrators, policy makers, members of professional and scientific organizations, parents, and business people, with clear respect for the perspectives and expertise of each.
· Recognition of the history, culture, and organization of the school environment.
· Continuous program assessment that captures the perspectives of all those involved, uses a variety of strategies, focuses on the process and effects of the program, and feeds directly into program improvement and evaluation..
Biology – Part 1
The information to follow was developed as a result of Wisconsin’s Model Academic Standards for Science and based on the National Science Education Teaching Standards.
PI 34 Standard 1. Teachers know the subjects they are teaching.
The teacher understands the central concepts, tools of inquiry, and structures of the disciplines he/she teaches and can create learning experiences that make these aspects of subject matter meaningful for students.
Teachers of science shall demonstrate knowledge and understandings sufficient to teach subject matter science to students (ages 10-21) in the following areas:
1) Science classroom safety standards, practices, and procedures
2) The interconnectedness of science, science connections
3) Science as inquiry
4) Physical science including physics and chemistry
5) Life science including biology and environmental science
6) Earth and space science
7) Science and technology
8) Science in personal and social perspectives
9) History and nature of science
Teachers of science shall demonstrate abilities to:
1) Understand the central concepts, tool of inquiry, and structures of the discipline he/she teaches
2) Create learning experiences that make the subject matter meaningful for students.
3) Select science content consistent with the Wisconsin’s Model Academic Standards in Science and adapt and design curricula to meet the interests, knowledge, understandings, abilities, and experiences of students.
4) Encourage and model the skills of scientific inquiry, as well as curiosity, openness to new ideas and data, and skepticism.
5) Plan inquiry based science programs.
Biology – Part 2:
The following content has been taken from Wisconsin’s Model Academic Standards for Science and provide guidelines for a license in biology.
Teachers must have sufficient background content knowledge in order to teach biology or life science by knowing about
v The characteristics of organisms,
v Life cycles of organisms,
v Organisms and their environment,
v Structure and function of living things,
v Reproduction and heredity,
v Regulation and behavior,
v Populations and ecosystems,
v Diversity and adaptations of organisms,
v The cell,
v The molecular basis of heredity,
v Biological evolution,
v The interdependence of organisms,
v Matter, energy, and organization in living systems, and
v The behavior of organisms.
PI 34 Standard 2. Teachers know how children grow.
The teacher understands how children learn and develop and can provide learning opportunities that support their intellectual, social, and personal development.
Teachers of science shall demonstrate abilities to:
1) Understand how student learn and develop
2) Provide learning opportunities that support student intellectual, social, and personal development.
PI 34 Standard 3. Teachers understand that children learn differently.
The teacher understands how students differ in their approaches to learning and creates instructional opportunities that are adapted to diverse learners, including students with disabilities.
Teachers of science shall demonstrate abilities to:
1) Understand how students differ in their approaches to learning
2) Creates instructional opportunities that are adapted to diverse learners, including students with disabilities.
3) Recognize and respond to student diversity and encourage all students to participate fully in science learning.
PI 34 Standard 4. Teachers know how to teach.
The teacher understands and uses a variety of instructional strategies, including the use of technology, to encourage students’ development of critical-thinking, problem-solving, and performance skills.
Teachers of science shall demonstrate abilities to:
1) Understand and use a variety of instructional strategies, including the use of technology, to encourage students’ development of critical thinking, problem solving, and performance skills.
2) Orchestrate discourse among students about scientific ideas.
3) Challenge students to accept and share responsibility for their own learning in science.
4) Create a setting for student work that is flexible and supportive of science inquiry.
5) Nurture collaboration among students.
6) Structure and facilitate ongoing formal and informal discussions based on shared understanding of rules of scientific discourse.
7) Model and emphasize the skill, attitudes, and values of scientific inquiry.
8) Focus and support inquiry while interacting with students.
PI 34 Standard 5. Teachers know how to manage a classroom.
The teacher uses an understanding of individual and group motivation and behavior to create a learning environment that encourages positive social interaction, active engagement in learning, and self-motivation.
Teachers of science shall demonstrate abilities to:
1) Understand individual and group motivation and behavior to create a learning environment that encourages positive social interaction, active engagement in learning and self-motivation.
2) Develop a framework of year long and short-term science learning goals for students.
3) Plan a school science program.
4) Ensure a safe science classroom
5) Structure the time available so students can engage in extended investigations.
6) Create a setting for student work that is flexible and supportive of science inquiry
7) Manage science tools, materials, media, and technological resources.
8) Identify and use resources outside the school.
9) Engage students in designing a learning environment.
PI 34 Standard 6. Teachers communicate well.
The teacher uses knowledge of effective verbal and nonverbal communication techniques as well as instructional media and technology to foster active inquiry, collaboration, and supportive interaction in the classroom.
Teachers of science shall demonstrate abilities to:
Use knowledge of effective verbal and nonverbal communication techniques as well as instructional media and technology to foster active inquiry, collaboration, and supportive interaction in the classroom.
PI 34 Standard 7. Teachers are able to plan different kinds of lessons.
The teacher plans instruction based upon knowledge of subject matter, students, the community, and curriculum goals.
Teachers of science shall demonstrate abilities to:
1) Plan instruction based on knowledge subject matter, students, the community, and curriculum goals.
2) Use Wisconsin Model Academic Standards in Science in the development of lessons.
3) Engage students in designing the learning environment.
PI 34 Standard 8. Teachers know how to test for student progress.
The teacher understands and uses formal and informal assessment strategies to evaluate and ensure the continuous intellectual, social, and physical development of the learner.
Teachers of science shall demonstrate abilities to:
1) Understand and use formal and informal assessment strategies to evaluate and ensure the continuous intellectual, social, and physical development of the learner.
2) Select assessment strategies that support development of student understanding.
3) Use multiple methods to assess student understanding and ability.
4) Systematically gather and analyze assessment data to guide teaching.
5) Guide students in self-assessment.
PI 34 Standard 9. Teachers are able to evaluate themselves.
The teacher is a reflective practitioner who continually evaluates the effects of his/her choices and actions on others (students, parents, and other professionals in the learning community) and who actively seeks out opportunities to grow professionally.
Teachers of science shall demonstrate abilities to:
1) Be a reflective practitioner who continually evaluates the effectiveness of his/her choices and actions on others (students, parents, and other professionals in the learning community) and who actively seeks out opportunities to grow professionally.
2) Use student data, observations of teaching, and interactions with colleagues to reflect on and improve teaching practice.
3) Plan and implement professional growth and development strategies.
PI 34 Standard 10. Teachers are connected with other teachers and the community.
The teacher fosters relationships with school colleagues, parents, and agencies in the larger community to support students’ learning and well-being.
Teachers of science shall demonstrate abilities to:
1) Foster relationships with school colleagues, parents, and agencies in the larger community to support students’ learning and well being.
2) Use student data, observations of teaching, and interactions with colleagues to report student achievement and opportunities to learn to students, teachers, parents, policy makers, and the general public.
3) Work with colleagues within and across disciplines and grade levels.
Note: The above science teaching abilities were adapted from the National Science Education Teaching Standards, pages 27 through 53 and reprinted here:
Teaching Standard A:
Teachers of science plan an inquiry-based science program for their students. In doing this, teachers
· Develop a framework of yearlong and short-term goals for students.
· Select science content and adapt and design curricula to meet the interests, knowledge, understanding, abilities, and experiences of students.
· Select teaching and assessment strategies that support the development of student understanding and nurture a community of science learners.
· Work together as colleagues within and across disciplines and grade levels.
Teaching Standard B:
Teachers of science guide and facilitate learning. In doing this, teachers
· Focus and support inquiries while interacting with students.
· Orchestrate discourse among students about scientific ideas.
· Challenge students to accept and share responsibility for their own learning.
· Recognize and respond to student diversity and encourage all students to participate fully in science learning.
· Encourage and model the skills of scientific inquiry, as well as the curiosity, openness to new ideas and data, and skepticism that characterize science.
Teaching Standard C:
Teachers of science engage in ongoing assessment of their teaching and of student learning. In doing this, teachers
· Use multiple methods and systematically gather data about student understanding and ability.
· Analyze assessment data to guide teaching.
· Guide students in self-assessment.
· Use student data, observations of teaching, and interactions with colleagues to reflect on and improve teaching practice.
· Use student data, observations of teaching, and interactions with colleagues to report student achievement and opportunities to learn to students, teachers, parents, policy makers, and the general public.
Teaching Standard D:
Teachers of science design and manage learning environments that provide students with the time, space, and resources needed for learning science. In doing this, teachers
· Structure the time available so that students are able to engage in extended investigations.
· Create a setting for student work that is flexible and supportive of science inquiry.
· Ensure a safe working environment.
· Make the available science tools, materials, media, and technological resources accessible to students.
· Identify and use resources outside the school.
· Engage students in designing the learning environment.
Teaching Standard E:
Teachers of science develop communities of science learners that reflect the intellectual rigor of scientific inquiry and the attitudes and social values conducive to science learning. In doing this, teachers
· Display and demand respect for the diverse ideas, skills, and experiences of all students.
· Enable students to have a significant voice in decisions about the content and context of their work and require students to take responsibility for the learning of all members of the community.
· Nurture collaboration among students.
· Structure and facilitate ongoing formal and informal discussion based on a shared understanding of rules of scientific discourse.
· Model and emphasize the skills, attitudes, and values of scientific inquiry.
Teaching Standard F:
Teachers of science actively participate in the ongoing planning and development of the school science program. In doing this, teachers
· Plan and develop the school science program.
· Participate in decisions concerning the allocation of time and other resources to the science program.
· Participate fully in planning and implementing professional growth and development strategies for themselves and their colleagues..
Wisconsin’s Model Academic Standards for Science Content Standards
- Science Connections
CONTENT STANDARD
Students in Wisconsin will understand that among the science disciplines there are unifying themes: systems, order, organization, and interactions; evidence, models, and explanations; constancy, change, and measurement; evolution, equilibrium, and energy; and form and function.
These themes relate and interconnect the Wisconsin science standards to one another. Each theme is further defined in the glossary following the science standards.
- Nature of Science
CONTENT STANDARD
Students in Wisconsin will understand that science is ongoing and inventive, and that scientific understandings have changed over time as new evidence is found.
- Science Inquiry
CONTENT STANDARD
Students in Wisconsin will investigate questions using scientific methods and tools, revise their personal understanding to accommodate knowledge, and communicate these understandings to others.
- Physical Science
CONTENT STANDARD
Students in Wisconsin will demonstrate an understanding of the physical and chemical properties of matter, the forms and properties of energy, and the ways in which matter and energy interact.
- Earth and Space Science
CONTENT STANDARD
Students in Wisconsin will demonstrate an understanding of the structure and systems of the earth and other bodies in the universe and their interactions.
- Life and Environmental Science
CONTENT STANDARD
Students in Wisconsin will demonstrate an understanding of the characteristics and structures of living things, the processes of life, and how living things interact with one another and their environment.
- Science Applications
CONTENT STANDARD
Students in Wisconsin will demonstrate an understanding of the relationship between science and technology and the ways in which that relationship influences human activities.
- Science in Social and Personal Perspectives
CONTENT STANDARD
Students in Wisconsin will use scientific information and skills to make decisions about themselves, Wisconsin, and the world in which they live.
CONTENT GUIDELINES FOR
MARKETING EDUCATION
A Marketing Education teacher will demonstrate knowledge of and skills in:
1. Developing entrepreneurial ventures within the free enterprise system; understanding the challenges that are inherent in beginning a new business and maintaining an existing small business; applying marketing concepts in creating goods, services and idea for consumers; understanding entrepreneurship begins with the attitudes and unique talents associated with that of a risk-taker.
2. Understanding marketing within our free enterprise system; applying economic concepts in developing a competitive advantage in the global economy.
3. Applying marketing concepts and practices in a global economy; understanding that interdependence between nations has created the need to market products, services and ideas effectively to different countries/cultures throughout the world; developing fundamentals necessary to interact comfortably, productively and responsibly with various countries and cultures around the world.
4. Applying and actually experiencing the functions of marketing - distribution, financing, product/service management, marketing information management, pricing, promotion, risk management and selling - in a variety of business settings such as retailing, wholesaling, manufacturing and service industries; understanding that marketing touches the lives of people on a daily basis as family members, consumers and workers; understanding that marketing occupations are found in every segment of our economy.
5. Developing problem solving skills that involve critical and creative thinking; applying these skills to investigate, process, organize and reach conclusions regarding complex issues in the world of work and life; solve marketing related problems as well as creating new and innovative marketing applications.
6. Applying and actually experiencing marketing concepts/activities in specific fields of marketing; participating in current work-based and school based enterprises that provide real-life applications of marketing.
7. Exploring, analyzing and defining how talents, traits and abilities can best be applied to work and life; investigating lifework options; understanding the importance of planning and experience to ensure proper growth and development toward full potential as a worker, family member, and citizen in a democratic system; understand the vast career opportunities related to marketing.
8. Applying appropriate technology to assist in marketing related processes; selecting and using technology processes that lead to informed and quality decision making.
9. Applying the principles of leadership in school, community and marketing-related settings; understanding that marketing activities require a working climate that fosters creative thought, high employee morale and motivation, sustained cooperation and participation of diverse individuals; understanding the characteristics of organizational leadership; applying concepts and principles of human resource management.
10. Understanding the philosophy, principles, trends, issues, and methods of marketing education at K-12, technical college and collegiate levels.
11. Planning, coordinating, evaluating and administering an occupationally orientated program; planning and conducting advisory committees; coordinating work-based learning, understanding state and federal legislation that impacts marketing education; understanding new and emerging educational programs or initiatives that can affect marketing education programs.
12. Establishing and maintaining the Marketing Education Career and Technical Student Organization, DECA.
13. Understanding the philosophy and objectives of career and technical education (formerly known as vocational education) at all levels.
14. Creating an applied and integrated marketing curriculum for grades K-12; applying and integrating communication skills, social sciences, mathematics and science as they relate to marketing education; understanding the relationship of learning styles to instructional methods and student assessment; developing post-secondary articulation plans.
15. Understanding the importance of involvement in related professional associations such as MEA, WMEA, DECA, and ACTE; demonstrating professional and ethical behavior; understanding the importance of continual participation in professional development activities.
Draft 9-20-2000
CONTENT GUIDELINES FOR
MATHEMATICS
The Mathematics teacher will demonstrate knowledge of and skill in:
1. The structures within the discipline, the historical roots and evolving nature of mathematics, and the interaction between technology and the discipline.
2. Facilitating the building of student conceptual and procedural understanding.
3. Helping all students build understanding of the discipline including:
· Confidence in their abilities to utilize mathematical knowledge.
· Awareness of the usefulness of mathematics.
· The economic implications of fine mathematical preparation.
4. Exploring, conjecturing, examining and testing all aspects of problem solving.
5. Formulating and posing worthwhile mathematical tasks, solving problems using several strategies, evaluating results, generalizing solutions, using problem solving approaches effectively, and applying mathematical modeling to real-world situations.
6. Making convincing mathematical arguments, framing mathematical questions and conjectures, formulating counter-examples, constructing and evaluating arguments, and using intuitive, informal exploration and formal proof.
7. Expressing ideas orally, in writing, and visually; using mathematical language, notation, and symbolism; translating mathematical ideas between and among contexts.
8. Connecting the concepts and procedures of mathematics, drawing connections between mathematical strands, between mathematics and other disciplines, and with daily life.
9. Selecting appropriate representations to facilitate mathematical problem solving and translating between and among representations to explicate problem-solving situations.
10. Mathematical processes including:
· Problem solving.
· Communication.
· Reasoning and formal and informal argument.
· Mathematical connections.
· Representations.
· Technology.
11. Number operations and relationships from both abstract and concrete perspectives, identifying real world applications, and representing and connecting mathematical concepts and procedures including:
· Number sense.
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