title: Diagrams benefit symbolic problem-solving.
abstract: BACKGROUND
  The format of a mathematics problem often influences students' problem-solving performance. For example, providing diagrams in conjunction with story problems can benefit students' understanding, choice of strategy, and accuracy on story problems. However, it remains unclear whether providing diagrams in conjunction with symbolic equations can benefit problem-solving performance as well.
  
  
  OBJECTIVE
  We tested the impact of diagram presence on students' performance on algebra equation problems to determine whether diagrams increase problem-solving success. We also examined the influence of item- and student-level factors to test the robustness of the diagram effect.
  
  
  METHODS
  We worked with 61 seventh-grade students who had received 2 months of pre-algebra instruction.
  
  
  METHODS
  Students participated in an experimenter-led classroom session. Using a within-subjects design, students solved algebra problems in two matched formats (equation and equation-with-diagram).
  
  
  RESULTS
  The presence of diagrams increased equation-solving accuracy and the use of informal strategies. This diagram benefit was independent of student ability and item complexity.
  
  
  CONCLUSIONS
  The benefits of diagrams found previously for story problems generalized to symbolic problems. The findings are consistent with cognitive models of problem-solving and suggest that diagrams may be a useful additional representation of symbolic problems.
authors.affiliation: Department of Psychology, University of California San Diego, La Jolla, California, USA.
authors.forename: Junyi
authors.initials: J
authors.lastname: Chu
authors.affiliation: Department of Psychology and Human Development, Vanderbilt University, Nashville, Tennessee, USA.
authors.forename: Bethany
authors.initials: B
authors.lastname: Rittle-Johnson
authors.affiliation: Department of Psychological and Brain Sciences, Indiana University, Bloomington, Indiana, USA.
authors.forename: Emily R
authors.initials: ER
authors.lastname: Fyfe
mesh_terms: D000293:Adolescent; D002648:Child; D032882:Comprehension / Q000502:physiology; D005260:Female; D006801:Humans; D008297:Male; D008433:Mathematics; D011340:Problem Solving / Q000502:physiology*; D013663:Teaching; D013664:Teaching Materials
keywords: algebra equations; diagrams; external representations; mathematics problemsolving