Appendix C
Overview of Teaching Standards from the National Science Education Standards and the Principles and Standards for School Mathematics
Science Teaching Standards
(From the National Science Education Standards, National Research Council, 1996a, excerpted from pages 2753)
The standards for science teaching are grounded in five assumptions.

The vision of science education described by the Standards requires changes throughout the entire system.

What students learn is greatly influenced by how they are taught.

The actions of teachers are deeply influenced by their perceptions of science as an enterprise and as a subject to be taught and learned.

Student understanding is actively constructed through individual and social processes.

Actions of teachers are deeply influenced by their understanding of and relationships with students.
TEACHING STANDARD A:
Teachers of science plan an inquirybased science program for their students. In doing this, teachers

Develop a framework of yearlong and shortterm goals for students.

Select science content and adapt and design curricula to meet the interest, 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 selfassessment.

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 the, 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.
From the Principles and Standards for School Mathematics
(National Council of Teachers of Mathematics, 2000, excerpted from pages 2567).
Standard 1. Worthwhile Mathematical Tasks
The teacher of mathematics should pose tasks that are based on—

Sound and significant mathematics;

Knowledge of students’ understandings, interests, and experiences;

Knowledge of the range of ways that diverse students learn mathematics;
And that

Engage students’ intellect;

Develop students’ mathematical understandings and skills;

Stimulate students to make connections and develop a coherent framework for mathematical ideas;

Call for problem formulation, problem solving, and mathematical reasoning;

Promote communication about mathematics;

Represent mathematics as an ongoing human activity;

Display sensitivity to, and draw on, students’ diverse background experiences and dispositions;

Promote the development of all students’ dispositions to do mathematics
Standard 2. The Teacher’s Role in Discourse
The teacher of mathematics should orchestrate discourse by—

Posing questions and tasks that elicit, engage, and challenge each student’s thinking;

Listening carefully to students’ ideas;

Asking students to clarify and justify their ideas orally and in writing;

Deciding what to pursue in depth from among the ideas that students bring up during a discussion;

Deciding when and how to attach mathematical notation and language to students’ ideas;

Deciding when to provide information, when to clarify and issue, when to model, when to lead, and when to let a student struggle with a difficulty;

Monitoring students’ participation in discussions and deciding when and how to encourage each student to participate.
Standard 3. Students’ Role in Discourse
The teacher of mathematics should promote classroom discourse in which students—

Listen to, respond to, and question the teacher and one another;

Use a variety of tools to reason, make connections, solve problems, and communicate;

Initiate problems and question;

Make conjectures and present solutions;

Explore examples and counterexamples to investigate a conjecture;

Try to convince themselves and one another of the validity of particular representations, solutions, conjectures, and answers;

Rely on mathematical evidence and argument to determine validity.
Standard 4. Tools for Enhancing Discourse
The teacher of mathematics, in order to enhance discourse, should encourage and accept the use of—

Computers, calculators, and other technology;

Concrete materials used as models;

Pictures, diagrams, tables, and graphs;

Invented and conventional terms and symbols

Metaphors, analogies, and stories;

Written hypotheses, explanations, and arguments;

Oral presentations and dramatizations.
Standard 5. Learning Environment
The teacher of mathematics should create a learning environment that fosters the development of each student’s mathematical power by—

Providing and structuring the time necessary to explore sound mathematics and grapple with significant ideas and problems;

Using the physical space and materials in ways that facilitate students’ learning of mathematics;

Providing a context that encourages the development of mathematical dispositions;
And by consistently expecting and encouraging students to—

Work independently or collaboratively to make sense of mathematics;

Take intellectual risks by raising questions and formulating conjectures;

Display a sense of mathematical competence by validating and supporting ideas with mathematical argument.
Standard 6. Analysis of Teaching and Learning
The teacher of mathematics should engage in ongoing analysis of teaching and learning by—

Observing, listening to, and gathering other information about students to assess what they are learning;

Examining effects of the tasks, discourse, and learning environment on students’ mathematical knowledge, skills, and dispositions;
In order to—

Ensure that every student is learning sound and significant mathematics and is developing a positive disposition toward mathematics;

Challenge and extend students’ ideas;

Adapt or change activities while teaching; make plans, both short and longrange;

Describe and comment on each student’s learning to parents and administrators, as well as to the students themselves.