Learning from Erroneous Examples: When and How Do Students Benefit from Them?

We investigate whether erroneous examples in the domain of fractions can help students learn from common errors of other students presented in a computer-based system. Presenting the errors of others could spare students the embarrassment and demotivation of confronting their own errors. We conducted lab and school studies with students of different grade levels to measure the effects of learning with erroneous examples. We report results that compare the learning gains of three conditions: a control condition, an experimental condition in which students were presented with erroneous examples without help, and an experimental condition in which students were provided with additional error detection and correction help. Our results indicate significant metacognitive learning gains of erroneous examples for lower-grade students, as well as cognitive and conceptual learning gains for higher-grade students when additional help is provided with the erroneous examples, but not for middle-grade students.

[1]  F. Paas,et al.  Variability of Worked Examples and Transfer of Geometrical Problem-Solving Skills: A Cognitive-Load Approach , 1994 .

[2]  Raffaělla Borasi.  Capitalizing on Errors as "Springboards for Inquiry": A Teaching Experiment. , 1994 .

[3]  Stellan Ohlsson,et al.  Learning from Performance Errors. , 1996 .

[4]  Alexander Renkl,et al.  Learning from Worked-Out-Examples: A Study on Individual Differences , 1997, Cogn. Sci..

[5]  F. Oser,et al.  Lernen aus Fehlern Zur Psychologie des „negativen“ Wissens , 1999 .

[6]  R. Siegler.  Microgenetic Studies of Self-Explanation , 2002 .

[7]  F. Paas,et al.  Cognitive Load Theory and Instructional Design: Recent Developments , 2003 .

[8]  John D. Hey,et al.  AN EXPERIMENTAL ANALYSIS , 2004 .

[9]  Fred Paas,et al.  Process-Oriented Worked Examples: Improving Transfer Performance Through Enhanced Understanding , 2004 .

[10]  S. Vosniadou,et al.  The development of students’ understanding of the numerical value of fractions , 2004 .

[11]  Erica Melis.  Design of Erroneous Examples for ACTIVEMATH , 2005, AIED.

[12]  P. Tsamir,et al.  In-Service Elementary Mathematics Teachers' Views of Errors in the Classroom , 2005 .

[13]  Paul Libbrecht,et al.  Semantic-aware components and services of ActiveMath , 2006, Br. J. Educ. Technol..

[14]  Lieven Verschaffel,et al.  A Teaching Experiment , 2007 .

[15]  Alexander Renkl,et al.  Finding and fixing errors in worked examples: Can this foster learning outcomes? ☆ , 2007 .

[16]  V. Kopp,et al.  Fostering diagnostic knowledge through computer‐supported, case‐based worked examples: effects of erroneous examples and feedback , 2008, Medical education.

[17]  R. Siegler,et al.  Differentiation and integration: guiding principles for analyzing cognitive change. , 2008, Developmental science.

[18]  K. Newton.  An Extensive Analysis of Preservice Elementary Teachers’ Knowledge of Fractions , 2008 .

[19]  Kenneth R. Koedinger,et al.  When and how often should worked examples be given to students? New results and a summary of the current state of research , 2008 .

[20]  Erica Melis,et al.  Erroneous Examples: A Preliminary Investigation into Learning Benefits , 2009, EC-TEL.

[21]  Ulrike Cress,et al.  Learning in the Synergy of Multiple Disciplines, 4th European Conference on Technology Enhanced Learning, EC-TEL 2009, Nice, France, September 29 - October 2, 2009, Proceedings , 2009, EC-TEL.

[22]  N. Granott,et al.  Microdevelopment: Transition Processes in Development and Learning , 2009 .