Every classroom relies on an implicit 'contract' between the teacher and the students, defining what each expects of the other � the patterns of behavior, the range of roles, etc. Traditionally, the teacher with the textbook explains and demonstrates, while the students imitate; if the student makes mistakes the teacher explains again. This procedure is not effective in preventing the development of misconceptions or in removing pre-existing ones. It cannot be used for teaching students to solve non-routine problems. Thus, improving learning and achievement for all students depends on establishing a more effective classroom contract. What are the essential changes?

Non-routine problem solving, and much else, depends on the student taking more responsibility for their own understanding, being willing and able to articulate their own lines of thought and to discuss them in class and with their peers. Thus, students need to move to:

• work more independently, moving beyond mainly imitative learning
• work on more substantial problems, developing longer chains of reasoning
• explain their thinking and discuss it with others � and through this
• detect and correct their own misunderstandings and mistakes
• take broader responsibility for their work.

The teacher is a facilitator of this process rather than the expected source of all understanding. Thus, teachers need to move to:

• give students more substantial problems, and enough time to struggle with them
• encourage discussion, in groups or with the whole class, taking the role of chair
• move away from providing correct answers
• expect students to present and explain their solutions for discussion.

Achieving these substantial changes in the classroom contract is not easy. It takes time and a systematic approach. The tools listed provide effective support for teachers and students in this important area.