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.