• 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.

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 long-range;

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