Mathematically Accountable Talk
Excerpts from an article by Lauren Resnick
From: 
Making America Smarter: A Century's Assumptions About Innate 
Ability Give Way to a Belief in the Power of Effort
 Resnick, Lauren B. (1999, June 16).  Education Week, 
38-40.
Click here for full article
 
....
Effort-Based Education and Learnable Intelligence: 
Principles for Teaching and Learning
....
For several years, the Institute for Learning at the University of
Pittsburgh has been working with school systems across the country to
set students -- and whole school faculties -- on the upward,
getting-smarter spiral.  A core set of principles guides this work,
principles that educators have found both inspiring and practical. 
These principles, which can be illustrated in multiple examples of
specific school and classroom practice, are based on cognitive
research and research on learning organizations.  Here they are in a
nutshell:
....
    -  Accountable Talk. 
 - Talking with others about ideas and 
    work is fundamental to learning. But not all talk sustains learning or 
    creates intelligence. For classroom talk to promote learning, it must have 
    certain characteristics that make it accountable. Accountable talk 
    seriously responds to and further develops what others in the group have 
    said. It puts forth and demands knowledge that is accurate and relevant to 
    the issue under discussion. Accountable talk uses evidence in ways 
    appropriate to the discipline (for example, proofs in mathematics, data 
    from investigations in science, textual details in literature, documentary 
    sources in history). Finally, it follows established norms of good 
    reasoning. Accountable talk sharpens students' thinking by reinforcing 
    their ability to use knowledge appropriately.  As such, it helps develop 
    the skills and habits of mind that constitute intelligence-in-practice. 
    Teachers can intentionally create the norms and skills of accountable talk 
    in their classrooms.
    
 -  Socializing Intelligence. 
 - Intelligent habits of mind are 
    learned through the daily expectations placed on the learner. By calling on 
    students to use the skills of intelligent thinking and accountable talk, 
    and by holding them responsible for doing so, educators can "teach" 
    intelligence. This is what teachers normally do with students they expect 
    much from; it should be standard practice with all students.