Worked Examples and Learner-Generated Representations: A Study in the Calculus Domain

Open Access
Author:
Shaw, Charlyn Welch
Graduate Program:
Educational Psychology
Degree:
Master of Education
Document Type:
Master Thesis
Date of Defense:
March 28, 2014
Committee Members:
  • Rayne Audrey Sperling, Thesis Advisor
Keywords:
  • Worked Examples
  • Learner-Generated Representations
  • Multiple Representations
  • Calculus
  • Conceptual Knowledge
  • Related Rates
Abstract:
Research repeatedly demonstrates the effectiveness of pairing practice problems with similar worked examples to improve student performance on problem-solving tasks. However, missing from the research is how these “example-problem pairs” can be designed to improve pervasive conceptual deficiencies in the calculus domain. The current study addressed the effectiveness of example-problem pairs in the content area of related rates. Of special interest were visual representations and student-generated representations with worked examples on several outcome measures. A pre-posttest experimental design was used with three conditions: conventional problem-solving (CP), worked examples with mathematical representations (WE-M), and worked examples with mathematical and visual representations (WE-V). Participants included undergraduate students in introductory calculus courses. Findings did not reveal statistically significant differences among the conditions on procedural performance, mental effort, conceptual understanding, or drawing. However, further analyses suggested prior knowledge and use of drawings were significant factors contributing to the effectiveness of the worked example format. Limitations of the current study and suggestions for future research are provided.