title: Developing procedural flexibility: are novices prepared to learn from comparing procedures?
abstract: BACKGROUND
  A key learning outcome in problem-solving domains is the development of procedural flexibility, where learners know multiple procedures and use them appropriately to solve a range of problems (e.g., Verschaffel, Luwel, Torbeyns, & Van Dooren, 2009). However, students often fail to become flexible problem solvers in mathematics. To support flexibility, teaching standards in many countries recommend that students be exposed to multiple procedures early in instruction and be encouraged to compare them.
  
  
  OBJECTIVE
  We experimentally evaluated this recommended instructional practice for supporting procedural flexibility during a classroom lesson, relative to two alternative conditions. The alternatives reflected the common instructional practice of delayed exposure to multiple procedures, either with or without comparison of procedures.
  
  
  METHODS
  Grade 8 students from two public schools (N= 198) were randomly assigned to condition. Students had not received prior instruction on multi-step equation solving, which was the topic of our lessons.
  
  
  METHODS
  Students learned about multi-step equation solving under one of three conditions in math class for about 3 hr. They also completed a pre-test, post-test, and 1-month-retention test on their procedural knowledge, procedural flexibility, and conceptual knowledge of equation solving.
  
  
  RESULTS
  Novices who compared procedures immediately were more flexible problem solvers than those who did not, even on a 1-month retention test. Although condition had limited direct impact on conceptual and procedural knowledge, greater flexibility was associated with greater knowledge of both types.
  
  
  CONCLUSIONS
  Comparing procedures can support flexibility in novices and early introduction to multiple procedures may be one important reason.
authors.affiliation: Department of Psychology and Human Development, Peabody College, Vanderbilt University, Nashville, Tennessee 37203, USA. johnson@vanderbilt.edu
authors.forename: Bethany
authors.initials: B
authors.lastname: Rittle-Johnson
authors.forename: Jon R
authors.initials: JR
authors.lastname: Star
authors.forename: Kelley
authors.initials: K
authors.lastname: Durkin
mesh_terms: D000293:Adolescent; D000704:Analysis of Variance; D003210:Concept Formation; D005260:Female; D005500:Follow-Up Studies; D006801:Humans; D007858:Learning; D008297:Male; D008433:Mathematics; D011340:Problem Solving; D012153:Retention, Psychology; D013334:Students / Q000523:psychology*; D013663:Teaching / Q000379:methods*; D014481:United States