The American Association for the Advancement of Science suggests that teaching should be based on learning principles that are derived "from systematic research and from well-tested craft experience." [14] In keeping with the spirit of inquiry, teaching should begin with questions dealing with phenomena, not answers to be memorized or learned. Students should propose hypotheses and collect evidence. The instructional activities in the classroom should include designing investigations, using the processes of science and mathematics, and engaging in hands-on experiences. Creativity and curiosity should be encouraged and highly regarded, and students should work together as teams whenever possible.

The National Council of Teachers of Mathematics (Curriculum and Evaluation Standards for School Mathematics, 1989) [15] identifies as the central goal of teaching mathematics that of the development of mathematical power for all students.

Mathematical power includes the ability to explore, conjecture and reason logically; to solve nonroutine problems; to communicate about and through mathematics; and to connect ideas within mathematics and between mathematics and other intellectual activity. Mathematical power also involves the development of personal self-confidence and a disposition to seek, evaluate and use quantitative and spatial information in solving problems and in making decisions. Students' flexibility, perseverance, interest, curiosity, and inventiveness also affect the realization of mathematical power (p. 5). [16]

The NCTM also identifies needed changes:

• Toward classrooms as mathematical communities - away from classrooms as simply a collection of individuals within four walls.

• Toward logic and mathematical evidence as verification - away from the teacher as the sole authority for right answers.

• Toward mathematical reasoning - away from merely memorizing procedures.

• Toward conjecturing, inventing and problem solving - away from an emphasis on mechanistic answer-finding.

• Toward connecting mathematics, its ideas, and its applications - away from treating mathematics as a body of isolated concepts and procedures. [17]

While not prescribing an instructional model, these goals certainly point toward certain tasks, types of discourse, and school environments.

The National Middle School Association's task force on curriculum supports learning experiences that:

• Help young adolescents make sense of themselves and the world about them.

• Are genuinely responsive to students' intellectual, physical, social, emotional, and moral development.

• Are highly integrated, so that students see the connectedness of life.

• Address students' own questions and focus upon enduring issues and ideas.

• Open doors to new ideas, evoking curiosity, exploration, and at times, awe and wonder.

• Teach the full range of communication skills in functional contexts.

• Actively engage students in solving problems and a variety of experiential learning opportunities.

At the same time, the following conditions are counterproductive and should be de-emphasized in middle grades:

• A curriculum that consists chiefly of separate subjects and skills taught in isolation.

• A faculty that is organized in departments.

• Exploratory courses isolated from academic endeavors and viewed as less important.

• Judgment of learning by the content in isolation from the process by which it is learned.

• Instruction dominated by textbooks and worksheets.

• Lecturing, rote learning, and drill.

• The tendency to label and track students into rigid ability groups. [18]