High school students took part in a series of pilot studies on the variables involved in step size and sequencing in programed instruction. Programed learning materials of the University of Illinois Committee on School Mathematics (UICSM) were varied as to covert and overt trial sequences, use of teachers, type of prior practice, order of frames,…

Widespread agreement exists that U.S. teachers need improved mathematics knowledge for teaching. Over the past decade, policymakers have funded a range of professional development efforts designed to address this need. However, there has been little success in determining whether and when teachers develop mathematical knowledge from professional…