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Worked examples

See also: teaching, teaching-mathematics, teaching-digital-technologies

Worked examples (Eiriksdottir & Catrambone, 2011)

  • typically associated with well-structured domains; and
  • consist of a problem statement, one or more solution steps, and the final solution to the problem.
  • illustrate how a domain problem is solved through a sequence of steps/statements without explanation why these actions are performed

Main advantage is that worked examples reduce cognitive load. Learner does not have to focus on both the process of solving the problem, and finding the correct answer.

Explanation#

Arising out of cognitive load theory demonstrates the steps required to complete a task. Benefit arises from the explanations of each step taken and then learners using self-explanations to describe the steps.

Effectiveness reduces as the learner gains increased expertise. An approach perhaps best applied to algorithmic skill domains where there a single correct solutions.

Zhu & Simon (1987) demonstrate how worked examples can be used to replace lectures and direct instruction.

Fortunately for the feasibility of students' learning to factor, these rules are easier to understand in the context of examples and problems than they are when thus stated in prose (Zhu & Simon, 1987)

Designing effective worked examples#

Source Neelen & Kirschner's series on "Designing winning worked examples"

Three factors to consider

  • Intra-example features - how the example is designed and presented

    • Integrate text and diagrams
    • Integrate aural and visual information
    • Avoid the redundancy effect
    • Integrating steps and subgoals

  • Inter-example features - relationships among multiple examples and practice problems within a session

    • Multiple examples - required for complex tasks to increase the chance of transfer
    • Variability in surface stories - i.e. to limit misconceptions based on surface features
    • Varying problems within sessions/lessons - aka interleaving
    • Example-problem pairs

  • Individual differences - the way learners process examples

    • Fostering self-explanations through structural manipulations
      • Subgoal labelling
      • Incomplete examples followed by feedback
      • Integrated examples
    • Training self-explanations
    • Use of social incentives

Resources#

References#

Atkinson, R. K., Derry, S. J., Renkl, A., & Wortham, D. (2000). Learning from Examples: Instructional Principles from the Worked Examples Research. Review of Educational Research, 70(2), 181--214. https://doi.org/10.2307/1170661

Eiriksdottir, E., & Catrambone, R. (2011). Procedural Instructions, Principles, and Examples: How to Structure Instructions for Procedural Tasks to Enhance Performance, Learning, and Transfer. Human Factors, 53(6), 749--770. https://doi.org/10.1177/0018720811419154

Renkl, A. (2014). Toward an Instructionally Oriented Theory of Example-Based Learning. Cognitive Science, 38(1), 1--37. https://doi.org/10.1111/cogs.12086

Zhu, X., & Simon, H. A. (1987). Learning Mathematics From Examples and by Doing. Cognition and Instruction, 4(3), 137--166. https://doi.org/10.1207/s1532690xci0403_1