title: Iterating between lessons on concepts and procedures can improve mathematics knowledge.
abstract: BACKGROUND
  Knowledge of concepts and procedures seems to develop in an iterative fashion, with increases in one type of knowledge leading to increases in the other type of knowledge. This suggests that iterating between lessons on concepts and procedures may improve learning.
  
  
  OBJECTIVE
  The purpose of the current study was to evaluate the instructional benefits of an iterative lesson sequence compared to a concepts-before-procedures sequence for students learning decimal place-value concepts and arithmetic procedures.
  
  
  METHODS
  In two classroom experiments, sixth-grade students from two schools participated (N=77 and 26).
  
  
  METHODS
  Students completed six decimal lessons on an intelligent-tutoring systems. In the iterative condition, lessons cycled between concept and procedure lessons. In the concepts-first condition, all concept lessons were presented before introducing the procedure lessons.
  
  
  RESULTS
  In both experiments, students in the iterative condition gained more knowledge of arithmetic procedures, including ability to transfer the procedures to problems with novel features. Knowledge of concepts was fairly comparable across conditions. Finally, pre-test knowledge of one type predicted gains in knowledge of the other type across experiments.
  
  
  CONCLUSIONS
  An iterative sequencing of lessons seems to facilitate learning and transfer, particularly of mathematical procedures. The findings support an iterative perspective for the development of knowledge of concepts and procedures.
authors.affiliation: Department of Psychology and Human Development, Vanderbilt University, Nashville, Tennessee 37203, USA. bethany.rittle-johnson@vanderbilt.edu
authors.forename: Bethany
authors.initials: B
authors.lastname: Rittle-Johnson
authors.forename: Kenneth
authors.initials: K
authors.lastname: Koedinger
mesh_terms: D000124:Achievement; D002648:Child; D003194:Computer-Assisted Instruction; D003210:Concept Formation; D003479:Curriculum; D005260:Female; D006801:Humans; D008297:Male; D008433:Mathematics; D012984:Software; D013663:Teaching; D014163:Transfer, Psychology