Advertisement

The significance of dealing with mistakes for student achievement and motivation: results of doubly latent multilevel analyses

  • Julia Käfer
  • Susanne Kuger
  • Eckhard Klieme
  • Mareike Kunter
Article

Abstract

From a constructivist perspective on learning, mistakes are seen as natural elements of learning processes. A supportive and constructive way of dealing with student mistakes has shown to affect students’ individual motivation and learning performances in a favorable way. In classroom settings, however, making mistakes is not just a personal but also a social event. Dealing with mistakes should therefore be considered as both student-level and classroom-level characteristic. This study investigates three aspects of dealing with mistakes and their relevance for students’ achievement and motivation in English as a foreign language by analyzing the aspects at student and classroom level. The aspects are (a) teacher attitude toward mistakes, (b) teacher response to student mistakes, and (c) students’ perception of mistakes as useful for learning. Analyzing data of 5266 students from 427 classes in German secondary schools, the results demonstrate that at student level, all three aspects of dealing with mistakes affect students’ individual achievement as well as motivation in English language class. At classroom level, none of the aspects affect student average achievement. Two aspects affect student average motivation at the classroom level, namely (a) teacher attitude toward mistakes and (c) students’ shared perception of the usefulness of mistakes for learning. Our results show that students’ individual and shared perception of dealing with mistakes affect students’ motivational and cognitive learning outcomes in different ways. Furthermore, our findings underline the relevance of teachers’ attitudes as well as students’ perceptions concerning mistakes for student learning and motivation in English as a foreign language class.

Keywords

Mistake culture Error management Classroom teaching and learning English as a foreign language Multilevel analysis 

Notes

Funding information

The present study is a result of the Thin Slices project, which is collaboratively conducted by researchers at the DIPF | Leibniz Institute for Research and Information in Education and the Goethe University Frankfurt. The preparation of this paper was financially supported by grants from the German Federal Ministry of Education and Research (BMBF, grant number 01LSA1501B).

References

  1. Adams, R. J., & Wu, M. L. (2007). The mixed-coefficients logit model: A generalized form of the Rasch model. In M. v. Davier & C. H. Carstensen (Eds.), Multivariate and Mixture Distribution Rasch Models: Extensions and Applications (pp. 57–75). New York: Springer.CrossRefGoogle Scholar
  2. Ames, C., & Archer, J. (1988). Achievement Goals in the Classroom: Students’ Learning Strategies and Motivation Processes. Journal of Educational Psychology, 80(3), 260–267.  https://doi.org/10.1037/0022-0663.80.3.260.CrossRefGoogle Scholar
  3. Beck, B., Bundt, S., & Gomolka, J. (2008). Ziele und Anlage der DESI-Studie [Objectives and Layout of the DESI Study]. In DESI-Konsortium (Ed.), Unterricht und Kompetenzerwerb in Deutsch und Englisch: Ergebnisse der DESI-Studie (pp. 11–25). Beltz: Weinheim.Google Scholar
  4. Billett, S. (2012). Errors and Learning from Errors at Work. In J. Bauer & C. Harteis (Eds.), Professional and Practice-based Learning: Vol. 6. Human Fallibility: The Ambiguity of Errors for Work and Learning (pp. 17–32). Dordrecht: Springer.Google Scholar
  5. Black, P., & Wiliam, D. (2012). Assessment for Learning in the Classroom. In J. Gardner (Ed.), Assessment and Learning (pp. 11–32). London: SAGE Publications Ltd.  https://doi.org/10.4135/9781446250808.n2. CrossRefGoogle Scholar
  6. Bohnensteffen, M. (2010). Fehler-Korrektur: Lehrer- und lernerbezogene Untersuchungen zur Fehlerdidaktik im Englischunterricht der Sekundarstufe II [Mistake Correction: Teacher and Learner-Related Studies on Mistake Didactics in English at Upper Secondary School]. Europäische Hochschulschriften. Reihe XI, Pädagogik: Bd. 1001. Frankfurt am Main: Lang.Google Scholar
  7. Brookhart, S. M. (2008). How to give Effective Feedback to Your Students. Alexandria, VA: Association for Supervision and Curriculum Development.Google Scholar
  8. Deppe, M. (2017). Fehler als Stationen im Lernprozess: Eine kognitionswissenschaftliche Untersuchung am Beispiel Rechnungswesen [Mistakes as Stations in the Learning Process: A Cognitive Science Study on the Example of Financial Accounting]. Wirtschaft - Beruf - Ethik.Google Scholar
  9. DESI-Konsortium (Ed.). (2008). Unterricht und Kompetenzerwerb in Deutsch und Englisch: Ergebnisse der DESI-Studie [Teaching and Acquisition of Competencies in German and English: Results of the DESI Study]. Weinheim: Beltz.Google Scholar
  10. Dresel, M., Schober, B., Ziegler, A., Grassinger, R., & Steuer, G. (2013). Affektiv-motivational adaptive und handlungsadaptive Reaktionen auf Fehler im Lernprozess [Affective-Motivational Adaptive and Action-Adaptive Reactions on Mistakes in Learning Processes]. Zeitschrift für pädagogische Psychologie, 27(4), 255–271.  https://doi.org/10.1024/1010-0652/a000111. CrossRefGoogle Scholar
  11. Grotjahn, R. (2002). Konstruktion und Einsatz von C-Tests: Ein Leitfaden für die Praxis. In R. Grotjahn (Ed.), Der C-Test: Theoretische Grundlagen und praktische Anwendungen. [The C-Test: Theoretical Groundwork and Practical Applications] (pp. 211–225). Bochum: AKS.Google Scholar
  12. Harks, B., Rakoczy, K., Hattie, J., Besser, M., & Klieme, E. (2014). The effects of feedback on achievement, interest and self-evaluation: the role of feedback’s perceived usefulness. Educational Psychology, 34(3), 269–290.  https://doi.org/10.1080/01443410.2013.785384.CrossRefGoogle Scholar
  13. Harsch, C., & Schröder, K. (2007). Textrekonstruktion: C-Test. In B. Beck & E. Klieme (Eds.), Sprachliche Kompetenzen: Konzepte und Messung; DESI-Studie (Deutsch-Englisch-Schülerleistungen-International). [Language Competencies: Concepts and Evaluation; DESI-Study (Assessment of Student Achievement in German and English as a Foreign Language)] (pp. 212–225). Weinheim: Beltz.Google Scholar
  14. Hartig, J., Jude, N., & Wagner, W. (2008). Methodische Grundlagen der Messung und Erklärung sprachlicher Kompetenzen [Method Foundations of Measuring and Explaining Language Competencies]. In DESI-Konsortium (Ed.), Unterricht und Kompetenzerwerb in Deutsch und Englisch: Ergebnisse der DESI-Studie (pp. 34–54). Weinheim: Beltz.Google Scholar
  15. Heinze, A., & Reiss, K. (2007). Mistake-handling activities in the mathematics classroom: Effects of an in-service teacher training on students’ performance in geometry. In H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 31 st Conference of the International Group for the Psychology of Mathematics Education (pp. 9–16).Google Scholar
  16. Heinze, A., Ufer, S., Rach, S., & Reiss, K. (2012). The student perspective on dealing with errors in mathematics class. In E. Wuttke & J. Seifried (Eds.), Research in vocational education: Vol. 1. Learning from Errors at School and at Work (pp. 65–80). Opladen: Budrich.Google Scholar
  17. Helmke, A., Helmke, T., Schrader, F.-W., Wagner, W., Klieme, E., Nold, G., & Schröder, K. (2008). Wirksamkeit des Englischunterrichts [Efficacy of English Language Education]. In DESI-Konsortium (Ed.), Unterricht und Kompetenzerwerb in Deutsch und Englisch: Ergebnisse der DESI-Studie (pp. 382–397). Weinheim: Beltz.Google Scholar
  18. Helmke, A. (2006). Was wissen wir über guten Unterricht? Über die Notwendigkeit der Rückbesinnung auf den Unterricht als dem „Kerngeschäft“ der Schule [What Do We Know About Good Teaching? About the Necessity of Refocusing on Teaching as the “core business” of School]. Pädagogik und Schulalltag, 58, 42–45.Google Scholar
  19. Hesketh, B. (1997). Dilemmas in Training for Transfer and Retention. Applied Psychology, 46(4), 317–339.  https://doi.org/10.1111/j.1464-0597.1997.tb01234.x.CrossRefGoogle Scholar
  20. Hochweber, J., & Vieluf, S. (2016). Gender differences in reading achievement and enjoyment of reading: The role of perceived teaching quality. The Journal of Educational Research, 111(3), 268–283.  https://doi.org/10.1080/00220671.2016.1253536.CrossRefGoogle Scholar
  21. Klieme, E. (2006). Empirische Unterrichtsforschung: Aktuelle Entwicklungen, theoretische Grundlagen und fachspezifische Befunde [Empirical Educational Research: Recent Developments, Theoretical Basis and Domain-Specific Results]. Zeitschrift für Pädagogik, 52(6), 765–773.Google Scholar
  22. Klieme, E., Lipowsky, F., Rakoczy, K., & Ratzka, N. (2006). Qualitätsdimensionen und Wirksamkeit von Mathematikunterricht: Theoretische Grundlagen und ausgewählte Ergebnisse des Projekts „Pythagoras“ [Quality Dimensions and Efficacy of Mathematical Education. Theoretical Basis and Selected Results of the Project “Pythagoras”]. In M. Prenzel (Ed.), Untersuchungen zur Bildungsqualität von Schule: Abschlussbericht des DFG-Schwerpunktprogramms: BIQUA (pp. 127–146). Münster: Waxmann.Google Scholar
  23. Klieme, E., Pauli, C., & Reusser, K. (2009). The Pythagoras Study: Investigating effects of teaching and learning in Swiss and German mathematics classrooms. In J. Tomáš & T. Seidel (Eds.), The Power of Video Studies in Investigating Teaching and Learning in the Classroom (pp. 137–160). Münster: Waxmann.Google Scholar
  24. Kapur, M. (2010). Productive failure in mathematical problem solving. Instructional Science, 38(6), 523–550.  https://doi.org/10.1007/s11251-009-9093-x.CrossRefGoogle Scholar
  25. Kapur, M. (2012). Productive Failure in Learning Math. Cognitive Science, 38(5), 1008–1022.  https://doi.org/10.1111/cogs.12107. CrossRefGoogle Scholar
  26. Kreutzmann, M., Zander, L., & Hannover, B. (2014). Versuch macht kluch/g?! Der Umgang mit Fehlern auf Klassen- und Individualebene.: Zusammenhänge mit Selbstwirksamkeit, Anstrengungsbereitschaft und Lernfreude von Schülerinnen und Schülern [Learning by Doing? Managing Mistakes on the Class and Individual Level: Interrelations with Students’ Self-efficacy, Effort Investment, and Joy of Learning]. Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie, 46(2), 101–113.  https://doi.org/10.1026/0049-8637/a000103. CrossRefGoogle Scholar
  27. Link, M. (2012). Learning from errors: Strategies for accounting lessons - Outline of a research project. In E. Wuttke & J. Seifried (Eds.), Research in vocational education: Vol. 1. Learning from Errors at School and at Work (pp. 49–64). Opladen: Budrich.Google Scholar
  28. Lipowsky, F., Rakoczy, K., Pauli, C., Drollinger-Vetter, B., Klieme, E., & Reusser, K. (2009). Quality of geometry instruction and its short-term impact on students’ understanding of the Pythagorean Theorem. Learning and Instruction, 19(6), 527–537.  https://doi.org/10.1016/j.learninstruc.2008.11.001.CrossRefGoogle Scholar
  29. Lüdtke, O., Marsh, H. W., Robitzsch, A., & Trautwein, U. (2011). A 2x2 taxonomy of multilevel latent contextual models: Accuracy-bias trade-offs in full and partial error-correction models. Psychological Methods, 16, 444–467.CrossRefGoogle Scholar
  30. Lüdtke, O., Marsh, H. W., Robitzsch, A., Trautwein, U., Asparouhov, T., & Muthén, B. (2008). The multilevel latent covariate model: A new, more reliable approach to group-level effects in contextual studies. Psychological Methods, 13, 203–229.CrossRefGoogle Scholar
  31. Lüdtke, O., Robitzsch, A., Trautwein, U., & Kunter, M. (2009). Assessing the impact of learning environments: How to use student ratings of classroom or school characteristics in multilevel modelling. Contemporary Educational Psychology, 34(2), 120–131.  https://doi.org/10.1016/j.cedpsych.2008.12.001.CrossRefGoogle Scholar
  32. Lüdtke, O., Trautwein, U., Kunter, M., & Baumert, J. (2006). Analyse von Lernumwelten: Ansätze zur Bestimmung der Reliabilität und Übereinstimmung von Schülerwahrnehmungen [Analysis of Learning Environments: Approaches to Determining Reliability and Consistency with Student Perceptions]. Zeitschrift für pädagogische Psychologie, 20(1/2), 85–96.CrossRefGoogle Scholar
  33. Marsh, H. W., Lüdtke, O., Nagengast, B., Trautwein, U., Morin, A. J., Abduljabbar, A. S., & Köller, O. (2012). Classroom Climate and Contextual Effects: Conceptual and Methodological Issues in the Evaluation of Group-Level Effects. Educational Psychologist, 47(2), 106–124.CrossRefGoogle Scholar
  34. Marsh, H. W., Lüdtke, O., Robitzsch, A., Trautwein, U., Asparouhov, T., Muthén, B., & Nagengast, B. (2009). Doubly-Latent Models of School Contextual Effects: Integrating Multilevel and Structural Equation Approaches to Control Measurement and Sampling Error. Multivariate Behavioral Research, 44, 764–802.  https://doi.org/10.1080/00273170903333665.CrossRefGoogle Scholar
  35. Mindnich, A., Wuttke, E., & Seifried, J. (2008). Aus Fehlern wird man klug? Eine Pilotstudie zur Typisierung von Fehlern und Fehlersituationen [Learning from Mistakes? A Pilot Study on the Typification of Mistakes and Mistake Situations]. In E.-M. Lankes (Ed.), Pädagogische Professionalität als Gegenstand empirischer Forschung (pp. 153–163). Münster: Waxmann.Google Scholar
  36. Morin, A. J. S., Marsh, H. W., Nagengast, B., & Scalas, L. F. (2014). Doubly Latent Multilevel Analyses of Classroom Climate: An Illustration. The Journal of Experimental Education, 82(2), 143–167.  https://doi.org/10.1080/00220973.2013.769412.CrossRefGoogle Scholar
  37. Muthén, B. O., & Asparouhov, T. (2011). Beyond multilevel regression modeling: Multilevel analysis in a general latent variable framework. In J. Hox & J. K. Roberts (Eds.), Handbook of advanced multilevel analysis (pp. 15–40). New York: Taylor and Francis.Google Scholar
  38. Muthén, L. K., & Muthén, B. O. (1998–2013). Mplus: Statistical analysis with latent variables: User’s guide. Version 7.11.Google Scholar
  39. Nold, G., & Rossa, H. (2007). Hörverstehen. In B. Beck & E. Klieme (Eds.), Sprachliche Kompetenzen: Konzepte und Messung; DESI-Studie (Deutsch-Englisch-Schülerleistungen-International). [Language Competencies: Concepts and Evaluation; DESI-Study (Assessment of Student Achievement in German and English as a Foreign Language)] (pp. 174–192). Weinheim: Beltz.Google Scholar
  40. Oser, F., Hascher, T., & Spychiger, M. B. (1999). Lernen aus Fehlern: Zur Psychologie des „negativen“ Wissens [Learning from Mistakes: On the Psychology of „Negative“ Knowledge]. In W. Althof (Ed.), Fehlerwelten: Vom Fehlermachen und Lernen aus Fehlern. Beiträge und Nachträge zu einem interdisziplinären Symposium aus Anlaß des 60. Geburtstags von Fritz Oser (pp. 11–41). Wiesbaden: Springer.Google Scholar
  41. Oser, F., & Spychiger, M. B. (2005). Lernen ist schmerzhaft: Zur Theorie des negativen Wissens und zur Praxis der Fehlerkultur [Learning is Painful: On the Theory of Negative Knowledge and the Practice of Mistake Culture]. Beltz-Pädagogik. Weinheim: Beltz.Google Scholar
  42. Pianta, R. C., & Hamre, B. K. (2009). Conceptualization, Measurement, and Improvement of Classroom Processes: Standardized Observation Can Leverage Capacity. Educational Researcher, 38(2), 109–119.CrossRefGoogle Scholar
  43. Praetorius, A.-K., Vieluf, S., Saß, S., Bernholt, A., & Klieme, E. (2016). The same in German as in English? Investigating the subject-specificity of teaching quality. Zeitschrift für Erziehungswissenschaft, 19(1), 191–209.  https://doi.org/10.1007/s11618-015-0660-4.CrossRefGoogle Scholar
  44. Rach, S., Ufer, S., & Heinze, A. (2013). Learning from errors: effects of teachers’ training on students’ attitudes towards and their individual use of errors. PNA, 8(1), 21–30.Google Scholar
  45. Rakoczy, K., Harks, B., Klieme, E., Blum, W., & Hochweber, J. (2013). Written feedback in mathematics: Mediated by students’ perception, moderated by goal orientation. Learning and Instruction, 27, 63–73.  https://doi.org/10.1016/j.learninstruc.2013.03.002.CrossRefGoogle Scholar
  46. Rakoczy, K., Klieme, E., Bürgermeister, A., & Harks, B. (2008). The Interplay Between Student Evaluation and Instruction: Grading and Feedback in Mathematics Classrooms. Zeitschrift für Psychologie, 216(2), 111–124.  https://doi.org/10.1027/0044-3409.216.2.111.CrossRefGoogle Scholar
  47. Rakoczy, K., Pinger, P., Hochweber, J., Klieme, E., Schütze, B., & Besser, M. (2018). Formative assessment in mathematics: Mediated by feedback's perceived usefulness and students' self-efficacy. Learning and Instruction.  https://doi.org/10.1016/j.learninstruc.2018.01.004.
  48. Reusser, K. (1999). Schülerfehler – die Rückseite des Spiegels [Student Mistakes – the Other Side of the Mirror]. In W. Althof (Ed.), Fehlerwelten: Vom Fehlermachen und Lernen aus Fehlern. Beiträge und Nachträge zu einem interdisziplinären Symposium aus Anlaß des 60. Geburtstags von Fritz Oser (pp. 203–231). Wiesbaden: Springer.CrossRefGoogle Scholar
  49. Rheinberg, F., & Wendland, M. (2001). Veränderung der Lernmotivation in Mathematik und Physik: Eine Komponentenanalyse und der Einfluss elterlicher sowie schulischer Kontextfaktoren. DFG-Bericht zum Projekt „Förderung von Motivationskomponenten“ [Changes of Motivation for Learning in Mathematics and Physical Science: A Component Analysis and the Influence of Parental and School Context Factors. DFG-Report on the Project “Promoting Motivational Components”].Google Scholar
  50. Rjosk, C., Richter, D., Hochweber, J., Lüdtke, O., & Stanat, P. (2015). Classroom composition and language minority students’ motivation in language lessons. Journal of Educational Psychology, 107(4), 1171–1185.  https://doi.org/10.1037/edu0000035.CrossRefGoogle Scholar
  51. Rutkowski, L., & Svetina, D. (2014). Assessing the Hypothesis of Measurement Invariance in the Context of Large-Scale International Surveys. Educational and Psychological Measurement, 74(1), 31–57.  https://doi.org/10.1177/0013164413498257.CrossRefGoogle Scholar
  52. Santagata, R. (2004). “Are you joking or are you sleeping?” Cultural beliefs and practices in Italian and U.S. teachers’ mistake-handling strategies. Linguistics and Education, 15(1-2), 141–164.  https://doi.org/10.1016/j.linged.2004.12.002.CrossRefGoogle Scholar
  53. Santagata, R. (2005). Practices and beliefs in mistake-handling activities: A video study of Italian and US mathematics lessons. Teaching and Teacher Education, 21(5), 491–508.  https://doi.org/10.1016/j.tate.2005.03.004.CrossRefGoogle Scholar
  54. Schoy-Lutz, M. (2005). Fehlerkultur im Mathematikunterricht: Theoretische Grundlegung und evaluierte unterrichtspraktische Erprobung anhand der Unterrichtseinheit „Einführung in die Satzgruppe des Pythagoras“. [Mistake Culture in Mathematics: Theoretical Basis and Evaluated Practical Trial in Class for the Teaching Unit “Introduction to the Pythagorean Theorem”]. Texte zur mathematischen Forschung und Lehre: Vol. 39. Hildesheim: Franzbecker.Google Scholar
  55. Seidel, T., Kobarg, M., & Rimmele, R. (2003). Aufbereitung der Videodaten [Preparation of Video Data]. In T. Seidel, M. Prenzel, R. Duit, and M. Lehrke (Eds.), Technischer Bericht zur Videostudie „Lehr-Lern-Prozesse im Physikunterricht“. Kiel: IPN.Google Scholar
  56. Seidel, T., & Prenzel, M. (2004). Muster unterrichtlicher Aktivitäten im Physikunterricht [Patterns of Teaching Activities in Physics]. In J. Doll & M. Prenzel (Eds.), Bildungsqualität von Schule: Lehrerprofessionalisierung, Unterrichtsentwicklung und Schülerförderung als Strategien der Qualitätsverbesserung. Münster: Waxmann.Google Scholar
  57. Spychiger, M. B. (2003). Fehler als Fenster auf den Lernprozess: Zur Entwicklung einer Fehlerkultur in der Praxisausbildung [Mistakes as Windows to the Learning Process: On the Development of a Mistake Culture in Teaching Practices]. Journal für LehrerInnenbildung, 3(2), 31–38.Google Scholar
  58. Spychiger, M. B., Kuster, R., & Oser, F. (2006). Dimensionen von Fehlerkultur in der Schule und deren Messung: Der Schülerfragebogen zur Fehlerkultur im Unterricht für Mittel- und Oberstufe [Dimensions of Mistake Culture in School and their Measurement: The Student Questionnaire on Mistake Culture in Secondary School Classes]. Schweizerische Zeitschrift für Bildungswissenschaften, 28(1), 87–110.Google Scholar
  59. Spychiger, M. B., Mahler, F., Hascher, T., & Oser, F. (1998). Fehlerkultur aus der Sicht von Schülerinnen und Schülern: Der Fragebogen S-UFS. Entwicklung und erste Ergebnisse [Mistake Culture as Viewed by Students: The S-UFS Questionnaire. Development and First Results]. Lernen Menschen aus Fehlern? Zur Entwicklung einer Fehlerkultur in der Schule: Vol. 4. Freiburg, Schweiz: Pädagogisches Institut der Universität Freiburg.Google Scholar
  60. Spychiger, M. B., Oser, F., Hascher, T., & Mahler, F. (1999). Zur Entwicklung einer Fehlerkultur in der Schule [On the Development of a Mistake Culture in School]. In W. Althof (Ed.), Fehlerwelten: Vom Fehlermachen und Lernen aus Fehlern. Beiträge und Nachträge zu einem interdisziplinären Symposium aus Anlaß des 60. Geburtstags von Fritz Oser (pp. 43–70). Wiesbaden: Springer.CrossRefGoogle Scholar
  61. Stapleton, L. M., Yang, J. S., & Hancock, G. R. (2016). Construct Meaning in Multilevel Settings. Journal of Educational and Behavioral Statistics, 41(5), 481–520.  https://doi.org/10.3102/1076998616646200.CrossRefGoogle Scholar
  62. Steuer, G. (2014). Fehlerklima in der Klasse: Zum Umgang mit Fehlern im Mathematikunterricht [Mistake Climate in Class: About Dealing with Mistakes in Mathematics]. Dordrecht: Springer.CrossRefGoogle Scholar
  63. Steuer, G., & Dresel, M. (2015). A constructive error climate as an element of effective learning environments. Psychological Test and Assessment Modeling, (57), 262–275.Google Scholar
  64. Steuer, G., Rosentritt-Brunn, G., & Dresel, M. (2013). Dealing with errors in mathematics classrooms. Structure and relevance of perceived error climate. Contemporary Educational Psychology, 38(3), 196–210.CrossRefGoogle Scholar
  65. Tulis, M. (2013). Error management behavior in classrooms: Teachers‘ responses to student mistakes. Teaching and Teacher Education, 33, 56–68.CrossRefGoogle Scholar
  66. Tulis, M., & Fulmer, S. M. (2013). Students’ motivational and emotional experiences and their relationship to persistence during academic challenge in mathematics and reading. Learning and Individual Differences, 27, 35–46.  https://doi.org/10.1016/j.lindif.2013.06.003.CrossRefGoogle Scholar
  67. Türling, J. M., Seifried, J., & Wuttke, E. (2012). Teachers’ knowledge about domain specific student errors. In E. Wuttke & J. Seifried (Eds.), Research in vocational education: Vol. 1. Learning from Errors at School and at Work (pp. 95–110). Opladen: Budrich.Google Scholar
  68. Van de Vijver, F. J. R., van Hemert, D. A., & Poortinga, Y. H. (2008). Conceptual issues in multilevel models. In F. J. R. van de Vijver, D. A. van Hemert, & Y. H. Poortinga (Eds.), Multilevel Analysis of Individuals and Cultures (pp. 3–26). New York: Psychology Press.Google Scholar
  69. VanLehn, K., Siler, S., Murray, C., Yamauchi, T., & Baggett, W. B. (2003). Why Do Only Some Events Cause Learning During Human Tutoring? Cognition and Instruction, 21(3), 209–249.  https://doi.org/10.1207/S1532690XCI2103_01.CrossRefGoogle Scholar
  70. Vosniadou, S., & Brewer, W. F. (1987). Theories of Knowledge Restructuring in Development. Review of educational research, 57(1), 51–67.CrossRefGoogle Scholar
  71. Warm, T. A. (1989). Weighted Likelihood Estimation of Ability in Item Response Theory. Psychometrika, 54, 427–450.CrossRefGoogle Scholar
  72. Wu, M. L., Adams, R. J., & Wilson, M. R. (1998). ConQuest: Multi-aspect test software [Computer Software]. Camberwell: Australian Council for Educational Research.Google Scholar
  73. Zander, L., Kreutzmann, M., & Wolter, I. (2014). Constructive handling of mistakes in the classroom: The conjoint power of collaborative networks and self-efficacy beliefs. Zeitschrift für Erziehungswissenschaften, 17, 205–223.CrossRefGoogle Scholar

Copyright information

© Instituto Superior de Psicologia Aplicada, Lisboa, Portugal and Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Departem ent of Educaitonal Quality and EvaluationDIPF | Leibniz Institute for Research and Information in EducationFrankfurt am MainGermany
  2. 2.Department of Social Monitoring and MethodologyGerman Youth InstituteMunichGermany
  3. 3.Faculty of Psychology and Sports Sciences, Department for Educational PsychologyGoethe University FrankfurtFrankfurt am MainGermany

Personalised recommendations