Maine's Curriculum Framework for Mathematics & Science
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  SECTION III

Contents

Current Page

• Looking Ahead
  
  
• Part 1: Entering the Profession
  
  
  • Preparation in Science Content and Skills
    
    
  • Preparation in Mathematics Content and Skills
    
    
  • Preparation in Science and Mathematics Pedagogy

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Following Pages

• Essential Preservice Instruction and Experiences
  • Modeling Best Practice In All Environments
  • Contact with Student Learners
  • Reflecting on Practice
  • Developing Other Skills
  • Connecting to Resources
• Certification
  • Mathematics Content
  • Science Content
  • Alternatives to Traditional Certification
• Part 2: Growing in the Profession
  • Expanding Teacher's Expertise in Content Knowledge, Skills and Pedagogy
  • Supervision and Evaluation
    • Self and Peer Supervision and Evaluation
    • Administrative Supervision and Evaluation
• References

Introduction

In Maine and the nation, the teaching profession needs the most highly-qualified candidates it can attract. High schools, colleges, universities and professional organizations must encourage fine student mathematicians and scientists to pursue teaching careers.

Excellent, even inspirational mathematics and science teaching can propagate itself at least in part by power of example. The work of skillful, passionate, curious teachers at all levels creates not only the next crop of researchers and technicians, but also the next generation of mathematics and science teachers.

Other ways to attract talented new teachers include presentations on teaching careers in mathematics and science, opportunities for potential teachers to engage in activities with younger learners, university- and school-sponsored presentations on certification programs, and scholarships for qualified candidates. The Maine Department of Education can support development of such candidates by collaborating with colleges and professional organizations in determining certification requirements and procedures.

Learning to teach well is a continual challenge, beginning long before teachers enter their first classrooms and unfolding throughout their careers. Excellent graduate or undergraduate preservice preparation can be considered an opening chapter of professional development. Fine teachers of mathematics and science, whether entering the profession through traditional teacher preparation programs or less traditional routes, need frequent, engaging opportunities to continue learning as practitioners. Certification simply marks an early stage in a career-long process of developing and refining a repertoire of teaching skills and strategies.

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Looking Ahead

Framework Section III: Professional Standards considers both early and continuing teacher development. The first part, "Entering the Profession," outlines essential preservice preparation for teachers, while the second part, "Growing in the Profession," discusses teachers' continued professional development. This section can serve as a guide for prospective teachers, those who prepare or hire teacher candidates, and those who plan inservice teacher learning activities.

PART 1:

Entering the Profession

This part, which embodies Framework standards for student learning, describes preservice experiences and activities, certification procedures, and hiring practices for teachers of mathematics and science. It examines essential preparation of prospective teachers in mathematics and science content, skills and pedagogy. Suggesting important university and field experiences in both traditional and alternative paths to mathematics and science teaching, this section also explores certification options.

Preparation in Science Content and Skills

Those preparing to teach science should learn science content using inquiry methods because inquiry-based courses provide learners direct contact with scientific tools, methods and habits of mind. In teacher preparation programs meeting the spirit of this Framework, preservice teachers acquire skills necessary to support scientific investigations: skill in using technology, mathematical analysis, the laboratory and the field. Individually and in research groups they regularly engage in data gathering, analysis and interpretation, exploring and discussing open-ended, practical problems. To gain an understanding of science beyond the scope of isolated investigations, preservice teachers learn best by actively investigating phenomena, reading scientific papers and developing critical thinking skills. Prospective teachers of science must be able to make personal sense of findings which either are consistent with or which challenge currently accepted scientific understanding. Courses preparing future teachers should examine the implications of science and technology on community and world issues.

At all levels (K-12), teachers of science should possess this knowledge and these competencies:

• Fundamental facts aned concepts.
  Understand the fundamental facts and concepts of the life sciences, physical sciences, environmental science and earth/space science, as they are necessary to support the Content Standards of the Maine Curriculum Framework for Mathematics and Science.
  
  
• Nature and skills of scientific inquiry.
  Understand the nature and skills of scientific inquiry and be able to apply the skills and processes of inquiry to pose questions; design ways to investigate those questions; use measurement and observation tools such as microscopes, telescopes, electronic probes, and analytical balances to collect data; analyze data qualitatively and quantitatively (using computer and mathematical methods); and interpret data.
  
  
• Connections.
  Make conceptual connections among the sciences, with mathematics and other disciplines, and with everyday phenomena and problems.
  
  
• Science, technology, society.
  Understand past and present relationships among science, technology, society, human issues and cultural values.
  
  
• Responsible laboratory practices.
  Understand and use procedures for safe handling of materials and equipment. Learn and practice safe laboratory techniques. Know how to dispose of materials safely, handle living things ethically and use the environment thoughtfully.

More specific information about what teachers should know and be able to do in order to teach science at primary, intermediate, middle and secondary levels appear in the Performance Indicators listed for each Content Standard in Framework Section II and under Certification in this section.

Preparation in Mathematics Content and Skills

Those preparing to teach mathematics should be actively engaged in doing mathematics. They should have experiences in problem-solving, communicating mathematical concepts and procedures in mathematical language, reasoning, and exploring various connections in mathematics: connections between mathematical concepts, how those concepts are related to other disciplines, and how the concepts are applied in the world outside of school. The application of mathematical methods in scientific investigations is one such connection.

The mathematics preparation of teachers should incorporate preparation in content, skills and preservice experiences as suggested in the NCTM Curriculum and Evaluation Standards for School Mathematics, NCTM Professional Standards for Teaching Mathematics and Framework Content Standards. Teacher candidates should understand and use tools for learning mathematics, including calculators, graphing calculators, computers and other tools that provide images for conceptual understanding.

The preparation of future mathematics teachers should foster the disposition to do mathematics, the confidence to learn mathematics independently, and fluency in the language and symbolism of mathematics.


At all K-12 levels, teachers of mathematics should possess this knowledge and these competencies:

• Fundamental concepts and skills.
  Understand the concepts and have the mathematical skills described in Framework Content Standards (Section II).
  
  
• Nature and skills of mathematical inquiry.
  Understand the nature, skills and processes of mathematical inquiry (pattern recognition, conjecture, induction, deduction and the role of proof) to reason mathematically and support decision making through problem identification, analysis and interpretation. Use the tools of mathematics (physical models, manipulatives, calculators, computers, measuring tools and design tools) to develop conceptual understanding and solve problems.
  
  
• Connections.
  Make connections among mathematics concepts, with mathematics and other disciplines, and with everyday phenomena and problems.
  
  
• Mathematics in society.
  Understand mathematics as an ongoing human enterprise and be able to describe the role of mathematics in past and present societal endeavors.

More specific information about what teachers should know and be able to do in order to teach mathematics at primary, intermediate, middle and secondary levels appears in the Performance Indicators listed for each Content Standard in Framework Section II and in Certification in this section.

Preparation in Science and Mathematics Pedagogy

In addition to content knowledge, teachers of mathematics and science need pedagogical knowledge, including understanding of how children learn and knowledge of recent research and best teaching practices. It is especially important that post-secondary science and mathematics faculty model these practices because research in learning to teach suggests that teachers frequently teach as they have been taught. Future teachers must also develop the analytical skills necessary to translate educational and scientific research into good classroom practice. Furthermore, they need practice in action research - learning to examine their classroom experiences in search of findings which can be used to improve teaching.

Future mathematics and science teachers should be prepared to:

• Respond to the learning needs of all students.
  
  Effective teachers are able to design activities which match their students' developmental levels. They can develop short-term and year-long goals with and for learners, prepare lessons that are designed for a variety of learning styles, and provide experiences that consider students' diverse cultural and social backgrounds, gender, and special needs.
  
  
• Promote active, engaging, experiential learning.
  Effective teachers provide students with "hands-on, minds-on" scientific and mathematical experiences whenever appropriate. Structuring lessons that promote active involvement of all students, these teachers skillfully design learning tasks based on problem-solving and/or inquiry. They use a variety of techniques to support student inquiry and construction of knowledge, and they know how to help students take increased responsibility for their own learning.
  
  
• Assess student achievement and readiness for learning. Effective teachers use a variety of methods, including both alternative and traditional assessment tools, to assess student progress and performance. They encourage and support student self-assessment as well. They know how to use the results of formative and summative assessment in productive ways to guide teaching and improve student learning.
  
  
• Create a positive learning environment in the classroom. Effective teachers provide a physically and emotionally safe environment for all learners. By supporting students in constructive risk-taking, they help learners build confidence and a sense of personal worth.
  
  
• Support collaboration in learning.
  Effective teachers create learning environments in which students can work cooperatively and collaboratively. These teachers model collaborative learning by learning with and from their students, showing that learning is a valuable shared enterprise in which individuals are responsible for their own learning and for the learning of a group or team.
• Help students communicate in mathematics and science. Effective teachers provide frequent opportunities for students to use the language of mathematics and science by using and encouraging oral and written discourse in the classroom.
  
  
• Connect mathematics and science to the student's world. Effective teachers draw from the students' experiences to create relevant learning situations that involve practical problem-solving. This can include grappling with community problems or issues which lead students to generate hypotheses, investigate problems, collect data, interpret results and draw conclusions. Teachers drive home the relevance of science and mathematics learning by finding and using community resources to support class activities. This includes contact with practicing mathematicians and scientists from diverse backgrounds and information about the range of possible careers in mathematics and science.
  
  
• Use tools and technology for instruction in mathematics and science.
  Effective teachers use a variety of tools such as calculators, computers, and digital probes - not only as audiovisual aids, but also for collecting and interpreting data. Using physical models, visual aids and multimedia resources to demonstrate concepts, these teachers encourage students to use tools and technology to construct knowledge and develop understanding.
  
• Use multiple resources to aid instruction and support student learning.
  Effective teachers locate and use a variety of print resources, both as primary sources as well as reference sources, in their classrooms. They also use a variety of multimedia technology to support auditory, visual and kinesthetic learners. Such teachers forge connections for their students: to resources in the local community through integrating the work of volunteer scientists and mathematicians in the life of the classroom, and to the global community through telecommunications technology.