Formative Assessment in Mathematics Instruction: Theoretical Considerations and Empirical Results of the Co2CA Project

Methodology of Educational Measurement and Assessment

Volumn , Issue , 2017, Pages 447-467

  Rakoczy, Katrin ^a   Klieme, Eckhard ^a   Leiß, Dominik ^b   Blum, Werner ^c  

^a GERMAN INSTITUTE FOR INTERNATIONAL EDUCATIONAL RESEARCH   (Germany)

^b LEUPHANA UNIVERSITY OF LÜNEBURG   (Germany)

^c UNIVERSITY OF KASSEL   (Germany)

Author keywords

Feedback; Formative assessment; Implementation; Mathematics instruction; Transfer study

Indexed keywords

EID: 85151561650     PISSN: 2367170X     EISSN: 23671718     Source Type: Book Series    
DOI: 10.1007/978-3-319-50030-0_26     Document Type: Chapter

References (50)

1. Andrade, H. L. (2010). Summing up and moving forward: key challenges and future directions for research and development in formative assessment. In H. L. Andrade & G. J. Cizek (Eds.), Handbook of formative assessment (pp. 344–351). New York: Routledge.
2. Baumert, J., Kunter, M., Blum, W., Brunner, M., Dubberke, T., Jordan, & Tsai, Y. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47, 133–180. doi:10.3102/0002831209345157.
3. Bennett, R. E. (2010). Cognitively based assessment of, for, and as learning: A preliminary theory of action for summative and formative assessment. Measurement: Interdisciplinary Research and Perspectives, 8, 70–91. doi:10.1080/15366367.2010.508686.
4. Bennett, R. E. (2011). Formative assessment: A critical review. Assessment in Education: Principles, Policy & Practice, 18, 5–25. doi:10.1080/0969594X.2010.513678.
5. Besser, M., & Leiß, D. (2014). The influence of teacher-training on in-service teachers’ expertise: A teacher-training-study on formative assessment in competency-oriented mathematics. In S. Oesterle, P. Liljedahl, C. Nicol, & D. Allan (Eds.), Proceedings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics Education (Vol. 2, pp. 129– 136). PME: Vancouver.
6. Besser, M., Blum, W., & Klimczak, M. (2013). Formative assessment in every-day teaching of mathematical modelling: Implementation of written and oral feedback to competency-oriented tasks. In G. Stillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 469–478). New York: Springer.
7. 2CA project. In G. A. Stillman, M. S. Biembengut, & W. Blum (Eds.), Proceedings of ICTMA 16. New York: Springer.
8. Besser, M., Leiß, D., & Klieme, E. (2015b). Wirkung von Lehrerfortbildungen auf Expertise von Lehrkräften zu formativem Assessment im kompetenzorientierten Mathematikunterricht [Impact of teacher training on teachers‘ expertise on formative assessment in competenc-oriented instruction]. Zeitschrift für Entwicklungs-und Pädagogische Psychologie, 47, 110– 122. doi:10.1026/0049-8637/a000128.
9. Besser, M., Leiß, D., Harks, B., Rakoczy, K., Klieme, E., & Blum, W. (2010). Kompetenzorientiertes Feedback im Mathematikunterricht: Entwicklung und empirische Erprobung prozessbezo-gener, aufgabenbasierter Rückmeldesituationen [Competence-oriented feedback in mathematics instruction: Development and empirical test of process-oriented and task-based feedback situations]. Empirische Pädagogik, 24(4), 404–432.
10. Black, P., & Wiliam, D. (1998a). Assessment and classroom learning. Assessment in Education: Principles, Policy & Practice, 5, 7–75. doi:10.1080/0969595980050102.
11. Black, P., & Wiliam, D. (1998b). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan, 80, 139–148. doi:10.1177/003172171009200119.
12. Black, P., & Wiliam, D. (1998c). Inside the black box: Raising standards through classroom assessment. London: Kings College.
13. Black, P., & Wiliam, D. (2009). Developing the theory of formative assessment. Educational Assessment, Evaluation and Accountability, 21, 5–31. doi:10.1007/s11092-008-9068-5.
14. Blum, W. (2011). can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 15–30). New York: Springer.
15. Blum, W., & Leiß, D. (2007a). How do students and teachers deal with modelling problems? In C. Haines, W. Blum, P. Galbraith, & S. Khan (Eds.), Mathematical modelling (ICTMA 12): education, engineering and economics (pp. 222–231). Chichester: Horwood.
16. Blum, W., & Leiß, D. (2007b). Investigating quality mathematics teaching—the DISUM project. In C. Bergsten & B. Grevholm (Eds.), Developing and Researching Quality in Mathematics Teaching and Learning: Proceedings of MADIF 5 (pp. 3–16). Linköping: SMDF.
17. Bromme, R. (2008). Lehrerexpertise [Teacher’s skill]. In W. Schneider & M. Hasselhorn (Eds.), Handbuch der Pädagogischen Psychologie (pp. 159–167). Göttingen: Hogrefe.
18. Brookhart, S. M. (1997). A theoretical framework for the role of classroom assessment in motivating student effort and achievement. Applied Measurement in Education, 10, 161–180. doi:10.1207/s15324818ame1002_4.
19. Bürgermeister, A. (2014). Leistungsbeurteilung im Mathematikunterricht: Bedingungen und Effekte von Beurteilungspraxis und Beurteilungsgenauigkeit [Performance assessment in mathematics instruction: Conditions and effects of judgement practice and judgement accu-racy]. Münster: Waxmann.
20. 2CA) [Documentation of the intervention study questionnaires in the project “Conditions and Consequences of Classroom Assessment”]. Frankfurt am Main: DIPF.-URN: urn:nbn:de:0111-opus-35284.
21. Bürgermeister, A., Klieme, E., Rakoczy, K., Harks, B., & Blum, W. (2014). Formative Leistungsbeurteilung im Unterricht [Formative assessment in instruction]. In M. Hasselhorn, W. Schneider, & U. Trautwein (Eds.), Lernverlaufsdiagnostik (pp. 41–60). Göttingen: Hogrefe.
22. Dunn, K. E., & Mulvenon, S. W. (2009). A critical review of research on formative assessment: The limited scientific evidence of the impact of formative assessment in education. Practical Assessment, Research and Evaluation, 14(7), 1–11.
23. Furtak, E. M., Ruiz-Primo, M. A., Shemwell, J. T., Ayala, C. C., Brandon, P. R., Shavelson, R. J., & Yin, Y. (2008). On the fidelity of implementing embedded formative assessments and its relation to student learning. Applied Measurement in Education, 21, 360–389. doi:10.1080/08957340802347852.
24. Harks, B. (2013). Kompetenzdiagnostik und Rückmeldung: zwei Komponenten formativen Assessments [Diagnostic of competencies and feedback: two components of formative assess-ment]. Doctoral Dissertation. Frankfurt/Main, Germany.
25. Harks, B., Klieme, E., Hartig, J., & Leiß, D. (2014a). Separating cognitive and content domains in mathematical competence. Educational Assessment, 19, 243–266. doi:10.1080/10627197.201 4.964114.
26. Harks, B., Rakoczy, K., Hattie, J., Besser, M., & Klieme, E. (2014b). The effects of feedback on achievement, interest, and self-evaluation: The role of feedback’s perceived usefulness. Educational Psychology, 34, 269–290. doi:10.1080/01443410.2013.785384.
27. Harks, B., Rakoczy, K., Klieme, E., Hattie, J., & Besser, M. (2014c). Indirekte und moderierte Effekte von Rückmeldung auf Leistung und Motivation [Indirect and moderated effects of feedback on achievement and motivation]. In H. Ditton & A. Müller (Eds.), Feedback und Rückmeldungen: Theoretische Grundlagen, empirische Befunde, praktische Anwendungsfelder (pp. 163–194). Münster: Waxmann.
28. Hattie, J. (2003). Formative and summative interpretations of assessment information. Retrieved from https://cdn.auckland.ac.nz/assets/education/hattie/docs/formative-and-summative-assessment-%282003%29.pdf.
29. Kingston, N., & Nash, B. (2011). Formative assessment: A meta-analysis and a call for research. Educational Measurement: Issues and Practice, 30(4), 28–37. doi:10.1111/j.1745-3992.2011.00220.x.
30. Klieme, E., Bürgermeister, A., Harks, B., Blum, W., Leiß, D., & Rakoczy, K. (2010). Leistungsbeurteilung und Kompetenzmodellierung im Mathematikunterricht [Assesment and modeling of competencies in mathematics instruction]. Zeitschrift für Pädagogik, Beiheft, 56, 64–74.
31. Klieme, E., Pauli, C., & Reusser, K. (2009). The Pythagoras study. In T. Janik & T. Seidel (Eds.), The power of video studies in investigating teaching and learning in the classroom (pp. 137– 160). Münster: Waxmann.
32. Klimczak, M., & Rakoczy, K. (2010). Richtlinien zur Aufzeichnung von Unterrichtsvideos im Projekt “Conditions and Consequences of Classroom Assessment” (Co2CA) [Guidelines to videotape instruction in the project “Conditions and Consequences of Classroom Assessment”]. Unpublished manuscript.
33. Krauss, S., Blum, W., Brunner, M., Neubrand, M., Baumert, J., Kunter, M., et al. (2011). Konzeptualisierung und Testkonstruktion zum fachbezogenen Professionswissen von Mathematiklehrkräften [Conceptualisation and test construction of content-related knowledge of mathematics teachers]. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss, & M. Neubrand (Eds.), Professionelle Kompetenz von Lehrkräften: Ergebnisse des Forschungsprogramms COACTIV (pp. 135–161). Waxmann: Münster.
34. Kulhavy, R. W., White, M. T., Topp, B. W., Chan, A. L., & Adams, J. (1985). Feedback complexity and corrective efficiency. Contemporary Educational Psychology, 10, 285–291. doi:10.1016/0361-476X(85)90025-6.
35. Leiß, D. (2010). Adaptive Lehrerinterventionen beim mathematischen Modellieren: empirische Befunde einer vergleichenden Labor-und Unterrichtsstudie [Adaptive teacher interventions for mathematical modeling: empirical results of a comparative experimental and field study]. JMD, 31, 197–226. doi:10.1007/s13138-010-0013-z.
36. Leiß, D., Schukajlow, S., Blum, W., Messner, R., & Pekrun, R. (2010). The role of the situation model in mathematical modelling: task analyses, student competencies, and teacher interventions. JMD, 31, 119–141. doi:10.1007/s13138-010-0006-y.
37. Muthén, L. K., & Muthén, B. O. (1998–2012). Mplus (Version 7) [Computer Software]. Los Angeles: Muthen & Muthen.
38. Narciss, S., & Huth, K. (2006). Fostering achievement and motivation with bug-related tutoring feedback in a computer-based training for written subtraction. Learning and Instruction, 16, 310–322. doi:10.1016/j.learninstruc.2006.07.003.
39. Pinger, P., Rakoczy, K., Besser, M., Klieme, E. (2016). Implementation of formative assessment: Effects of quality of program delivery on students’ mathematics achievement and interest. Assessment in Education: Principles, Policy and Practice. Advance online publication. doi:10.1080/0969594X.2016.117066.
40. Preacher, K. J., Zyphur, M. J., & Zhang, Z. (2010). A general multilevel SEM framework for assessing multilevel mediation. Psychological Methods, 15, 209–233. doi:10.1037/a0020141.
41. 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. doi:10.1016/j.learninstruc.2013.03.002.
42. Rakoczy, K., Pinger, P., Harks, B., Besser, M., Klieme, E. (under revision). Formative assessment in mathematics instruction: Mediated by feedback’s perceived usefulness and students’ self-efficacy? Learning and Instruction.
43. Sadler, R. (1998). Formative assessment: Revisiting the territory. Assessment in Education, 5, 77–84. doi:10.1080/0969595980050104.
44. Shavelson, R. J., Young, D. B., Ayala, C. C., Brandon, P. R., Furtak, E. M., Ruiz-Primo, M. A., et al. (2008). On the impact of curriculum-embedded formative assessment on learning: A collaboration between curriculum and assessment developers. Applied Measurement in Education, 21, 295–314. doi:10.1080/08957340802347647.
45. Shuell, T. J. (1996). Teaching and learning in a classroom context. In D. C. Berliner & R. Calfee (Eds.), Handbook of educational psychology (pp. 726–764). New York: Macmillan.
46. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. doi:10.3102/0013189X015002004.
47. Shute, V. (2008). Focus on formative feedback. Review of Educational Research, 78, 153–189. doi:10.3102/0034654307313795.
48. Stiggins, R. (2006). Assessment for learning: A key to motivation and achievement. Edge, 2(2), 3–19.
49. Wiliam, D., & Thompson, M. (2008). Integrating Assessment with Learning: What will it take to make it work? In C. A. Dwyer (Ed.), The future of assessment: Shaping teaching and learning (pp. 53–84). New York: Lawrence Erlbaum.
50. Wu, M. L., Adams, R. J., & Wilson, M. R. (1998). ConQuest: Generalised item response modelling software. Camberwell: Australian Council for Educational Research.