problems, and communicate mathematics effectively at different levels of formality;

And, in addition develop their perspectives on—

• The nature of mathematics, the contributions of different cultures toward the development of mathematics, and the role of mathematics in culture and society;

• The changes in the nature of mathematics and the way we teach, learn, and do mathematics resulting from the availability of technology;

• School mathematics within the discipline of mathematics;

• The changing nature of school mathematics, its relationships to other school subjects, and its applications in society.

The preservice and continuing education of teachers of mathematics should provide multiple perspectives on students as learners of mathematics by developing teachers’ knowledge of—

• Research on how students learn mathematics;

• The effects of students’ age, abilities, interests, and experience on learning mathematics;

• The influences of students’ linguistic, ethnic, racial, and socioeconomic backgrounds and gender on learning mathematics;

• Ways to affirm and support full participation and continued study of mathematics by all students.

The preservice and continuing education of teachers of mathematics should develop teachers’ knowledge of and ability to use and evaluate—

• Instructional materials and resources, including technology;

• Ways to represent mathematics concepts and procedures;

• Instructional strategies and classroom organizational models;

• Ways to promote discourse and foster a sense of mathematical community;

• Means for assessing student understanding of mathematics.

The preservice and continuing education of teachers of mathematics should provide them with opportunities to—

• Examine and revise their assumptions about the nature of mathematics, how it should be taught, and how students learn mathematics;