PROFESSIONAL DEVELOPMENT STANDARDS

    KNOWING MATHEMATICS AND SCIENCE

    Effective professional development provides all teachers of mathematics and science with opportunities to develop a broad understanding of content and a deep understanding of the specific concepts appropriate to their grade level. This understanding includes the ways of knowing, communicating, and the characteristic attitudes of the respective disciplines.

    Knowledge of both the content and nature of mathematics and science is an essential component of teacher preparation. Teachers' comfort with and confidence in their own knowledge of mathematics and science affect both what they teach and how they teach. The knowledge, skills, and attitudes teachers develop as a result of their study of the respective disciplines shape their choice of worthwhile mathematical and scientific tasks, the kinds of learning environments they create, and the discourse in their classrooms.

    Effective preservice and inservice education of mathematics and science teachers helps them develop their knowledge of mathematics and science, including:

    • significant mathematical and scientific concepts and the connections among them­within each discipline and across disciplines,
    • effectively conducting inquiry, reasoning, problem solving, and communicating,
    • multiple representations of mathematical and scientific concepts and procedures,
    • contributions of different cultures toward the development of mathematics and science,
    • changes in mathematics and science and the ways educators teach, learn, and do mathematics and science because of emerging technology,
    • school mathematics and school science within the disciplines of mathematics and science, their relationships to other school subjects, and their applications in society,
    • skills enabling them to broaden their own understanding of mathematics and science.

    The depth of understanding of mathematics and science required of teachers varies by grade level. Judgments regarding what constitutes sufficient understanding should be tied to the expectations for students in their classrooms. Teachers should have an understanding of the respective disciplines deep enough to guide student inquiries, assess student learning, and further the achievement of mathematical and scientific literacy. Teachers must be able to use their knowledge of content, teaching, and learning to use student questions as a starting point to design and guide inquiry, so that students are able to make the conceptual connections necessary for intellectual growth.

    This understanding is not developed in isolation. Learning to identify, define, and discuss concepts and processes, to understand the connections among them, and to appreciate the relationships of mathematics and science to other disciplines all take place at the same time. Effective teachers understand and use the techniques and perspectives of inquiry, reasoning, and problem solving. They are also able to communicate their understanding to others in a logical and accurate manner. A solid understanding of the content and the skills to conduct discourse lead teachers to greater confidence in their own abilities. There are common experiences that should be ingredients in the ways teachers of mathematics and science build and extend their knowledge. Regardless of the context, the following are prominent in these experiences:

    • problem solving,
    • communicating,
    • reasoning,
    • developing connections (both within the discipline and to their uses in the world around us),
    • building the confidence to learn mathematics and science independently,
    • developing and applying mathematical and scientific language and symbols,
    • developing a view of mathematics as a study of patterns and relationships, ·
    • perspectives on the nature of mathematics and science through a historical and cultural approach.

    Developing abilities in reasoning and problem solving are essential to becoming skilled in doing mathematics and science. Reasoning involves an interplay between intuition, informal and formal exploration, and logical argument. The struggles, the false starts, and the informal investigations that lead to a reasonable solution are frequently missing. Opportunities to construct mathematics and science for themselves and to interact with others to pose and solve problems in order to develop problem-solving strategies are an important part of professional development.

    Central to the preparation for teaching mathematics and science is the development of a deep understanding of the mathematics and science in the school curriculum and how they fit within the respective disciplines. Opportunities to revisit school mathematics and science content in ways that will allow teachers to develop deeper understandings of the ideas and relationships that are involved between and among concepts are an important part of professional development. Such opportunities include developing broad understandings of significant mathematics and science concepts and how they are related to other parts of the curriculum. This includes opportunities to develop an overview of the mathematics and science curricula. At all levels, effective teachers see the big picture of their discipline across the elementary and secondary school years. Computers, communication, and other technologies have become vital forces in learning, teaching and doing mathematics and science. They provide new approaches for solving problems and influence the kinds of questions to be investigated, as well as the pedagogical strategies that enhance and extend mathematics and science learning and teaching. Understanding technology and its applications is a significant component of understanding the disciplines of mathematics and science in the school setting.