Formative assessment in mathematics: Mediated by feedback's perceived usefulness and students' self-efficacy
ARTICLE
Katrin Rakoczy, Petra Pinger, German Institute for International Educational Research, Germany ; Jan Hochweber, The University of Teacher Education, Switzerland ; Eckhard Klieme, German Institute for International Educational Research, Germany ; Birgit Schütze, The University of Münster, Germany ; Michael Besser, Leuphana University of Lüneburg, Germany
Learning and Instruction Volume 60, Number 1, ISSN 0959-4752 Publisher: Elsevier Ltd
Abstract
Although formative assessment is regarded as a promising way to improve teaching and learning, there is considerable need for research on precisely how it influences student learning. In this study we developed and implemented a formative assessment intervention for mathematics instruction and investigated whether it had effects on students' interest and achievement directly and via students' perception of the usefulness of the feedback and their self-efficacy. We conducted a cluster randomized field trial with pretest and posttest. The 26 participating classes were randomly assigned to a control group or the intervention group. Results of path analyses indicate that feedback was perceived as more useful in the formative assessment condition, self-efficacy was greater, and interest tended to increase; learning progress did not differ between the groups. The assumed indirect effects were partly confirmed: formative assessment showed an indirect effect on interest via its perceived usefulness.
Citation
Rakoczy, K., Pinger, P., Hochweber, J., Klieme, E., Schütze, B. & Besser, M. (2019). Formative assessment in mathematics: Mediated by feedback's perceived usefulness and students' self-efficacy. Learning and Instruction, 60(1), 154-165. Elsevier Ltd. Retrieved August 13, 2024 from https://www.learntechlib.org/p/208135/.
This record was imported from
Learning and Instruction
on March 15, 2019.
Learning and Instruction is a publication of Elsevier.
Keywords
References
View References & Citations Map- Andrade, H.L. (2010). Summing up and moving forward: Key challenges and future directions for research and development in formative assessment. Handbook of formative assessment, pp. 344-351. New York, NJ: Routledge.
- Asparouhov, T., & Muthén, B.O. (2010). Multiple imputation with Mplus. Available online: http://statmodel.com/download/Imputations7.pdf.
- Bandura, A. (1997). Self-efficacy: The exercise of control. New York: Freeman.
- Baron, R.M., & Kenny, D.A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic and statistical considerations. Journal of Personality and Social Psychology, 51, pp. 1173-1182. Available online: https://doi.org/10.1037/0022-3514.51.6.1173.
- Bennett, R.E. (2011). Formative assessment: A critical review. Assessment in Education: Principles, Policy & Practice, 18(1), pp. 5-25. Available online: https://doi.org/10.1080/0969594X.2010.513678.
- Besser, M., Blum, W., & Klimczak, M. (2012). Formative assessment in every-day teaching of mathematical modelling: Implementation of written and oral feedback to competency-oriented tasks. ICTMA-15 proceedings (469-478) New York: Springer.
- 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. 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. Vancouver, Canada: PME.
- Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education: Principles, Policy & Practice, 5(1), pp. 7-75. Available online: https://doi.org/10.1080/0969595980050102.
- Black, P., & Wiliam, D. (1998). Inside the Black Box: Raising standards through classroom assessment. Phi Delta Kappan, 80(2), pp. 139-144. Available online: https://dx.doi.org10.1177/003172171009200119.
- Black, P., & Wiliam, D. (1998). Inside the black box: Raising standards through classroom assessment. London: Kings College, London School of Education.
- Black, P., & Wiliam, D. (2009). Developing the theory of formative assessment. Educational Assessment, Evaluation and Accountability, 21(1), pp. 5-31. Available online: https://doi.org/10.1007/s11092-008-9068-5.
- Black, P., & Wiliam, D. (2012). Assessment for learning in the classroom. Assessment and learning, pp. 11-32. London [u.a.]: SAGE.
- Blum, W., & Leiss, D. (2007). Investigating quality mathematics teaching – the DISUM Project. Develobing and researching quality in mathematics teaching and learning, pp. 3-16. Linköping: SMDF.
- Briggs, D.C., Ruiz-Primo, M.A., Furtak, E., Shepard, L., & Yin, Y. (2012). Meta-analytic methodology and inferences about the efficacy of formative assessment. Educational Measurement: Issues and Practice, 31(4), pp. 13-17.
- Brookhart, S.M. (1997). A theoretical framework for the role of classroom assessment in motivating student effort and achievement. Applied Measurement in Education, 10(2), pp. 161-180. Available online: https://doi.org/10.1207/s15324818ame1002_4.
- Bullock, J.G., Green, D.P., & Ha, S.E. (2015). Yes, but what's the mechanism? (Don't expect an easy answer). Journal of Personality and Social Psychology, 98, pp. 550-558. Available online: https://doi.org/10.1037/a0018933.
- Bürgermeister, A., Klieme, E., Rakoczy, K., Harks, B., & Blum, W. (2014). Formative Leistungsbeurteilung im Unterricht: Konzepte, Praxisberichte und ein neues Diagnoseinstrument für das Fach Mathematik. Lernverlaufsdiagnostik. Tests und Trends [Formative assessment. Tests and trends], Vol. 12, pp. S41-S60. Göttingen: Hogrefe.
- Carver, C.S., & Scheier, M.F. (1998). On the self-regulation of behavior. New York, Cambridge: University Press.
- Clark, I. (2012). Formative assessment: Assessment is for self-regulated learning. Educational Psychology Review, 24, pp. 205-249.
- Cole, D.A., & Maxwell, S.E. (2003). Testing mediational models with longitudinal data: Questions and tips in the use of structural equation modeling. Journal of Abnormal Psychology, 112(4), pp. 558-577. Available online: https://doi.org/10.1037/0021-843X.112.4.558.
- Collins, L.M., Schafer, J.L., & Kam, C.-M. (2001). A comparison of inclusive and restrictive strategies in modern missing data procedures. Psychological Methods, 6(4), pp. 330-351. Available online: https://doi.org/10.1037/1082-989X.6.4.330.
- Dresel, M., & Ziegler, A. (2002). Failure as an element of adaptive learning. Paper presented at the eighth biennial conference of the European association for research on adolescence UK: Oxford.
- 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), pp. 1-11.
- Educational Testing Service (2009). Research rationale for the keeping learning on track program. Princeton: Author.
- Fast, L.A., Lewis, J.L., Bryant, M.J., Bocian, K.A., Cardullo, R.A., & Rettig, M. (2010). Does math self-efficacy mediate the effect of the perceived classroom environment in standardized math test performance?. Journal of Educational Psychology, 102, pp. 729-740. Available online: https://doi.org/10.1037/a0018863.
- Furtak, E.M., Ruiz-Primo, M.A., Shemwell, J.T., Ayala, C.C., Brandon, P.R., & Shavelson, R.J. (2008). On the fidelity of implementing embedded formative assessments and its relation to student learning. Applied Measurement in Education, 21(4), pp. 360-389. Available online: https://doi.org/10.1080/08957340802347852.
- Gielen, S., Peeters, E., Dochy, F., Onghena, P., & Struyven, K. (2010). Improving the effectiveness of peer feedback for learning. Learning and Instruction, 20, pp. 304-315. Available online: https://doi.org/10.1016/j.learninstruc.2009.08.007.
- Goetz, T., Frenzel, A.C., Stoeger, H., & Hall, N.C. (2010). Antecedents of everyday positive emotions: An experience sampling analysis. Motivation and Emotion, 34, pp. 49-62. Available online: https://doi.org/10.1007/s11031-009-9152-2.
- Graham, J.W., Olchowski, A.E., & Gilreath, T.D. (2007). How many imputations are really needed? Some practical clarifications of multiple imputation theory. Prevention Science, 8(3), pp. 206-213. Available online: https://doi.org/10.1007/s11121-007-0070-9.
- Harks, B., Klieme, E., Hartig, J., & Leiß, D. (2014). Separating cognitive and content domains in mathematical competence. Educational Assessment, 19(4), pp. 243-266.
- 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(4), pp. 269-290. Available online: https://doi.org/10.1080/01443410.2013.785384.
- Hattie, J. (2003). Formative and summative interpretations of assessment information. Available online: http://web.auckland.ac.nz/uoa/fms/default/education/staff.
- Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), pp. 81-112. Available online: https://doi.org/10.3102/003465430298487.
- Heritage, M. (2007). Formative assessment: What do teachers need to know and do?. Phi Delta Kappan, 89, pp. 140-145. Available online: https://doi.org/10.1177/003172170708900210.
- Hiebert, J., Gallimore, R., Garnier, H., Givvin, K.B., Hollingsworth, H., Jacobs, J., (2003). Teaching mathematics in seven countries: Results from the TIMSS 1999 Video Study. Washington, DC: National Center for Education Statistics.
- Jiang, Y., Song, J., Lee, M., & Bong, M. (2014). Self-efficacy and achievement goals as motivational links between perceived contexts and achievement. Educational Psychology, 34(1), pp. 92-117. Available online: https://doi.org/10.1080/01443410.2015.999417.
- Kingston, N., & Nash, B. (2011). Formative assessment: A meta-analysis and a call for research. Educational Measurement: Issues and Practice, 30(4), pp. 28-37. Available online: https://doi.org/10.1111/j.1745-3992.2011.00220.
- 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. Journal für Mathematikdidaktik, 31(1), pp. 119-141. Available online: https://doi.org/10.1007/s13138-010-0006-y.
- MacKinnon, D.P., Lockwood, C.M., & Williams, J. (2004). Confidence limits for the indirect effect: Distribution of the product and resampling methods. Multivariate Behavioral Research, 39(1), pp. 99-128. Available online: https://doi.org/10.1207/s15327906mbr3901_4.
- McMillan, J.H., Venable, J.C., & Varier, D. (2013). Studies of the effect of formative assessment on student achievement: So much more is needed. Practical Assessment, Research and Evaluation, 18(2) Available online: http://pareonline.net/getvn.asp?v=18&n=2.
- Morin, A.J.S., Marsh, H.W., Nagengast, B., & Scalas, L.F. (2014). Doubly latent multilevel analyses of classroom climate: An illustration. Journal of Experimental Education, 82, pp. 143-167. Available online: https://doi.org/10.1080/00220973.2013.769412.
- Mouratidis, A., Vansteenkiste, M., & Lens, W. (2010). How you provide corrective feedback makes a difference: The motivating role of communicating in an autonomy-supporting way. Journal of Sport & Exercise Psychology, 32, pp. 619-637. Available online: https://doi.org/10.1123/jsep.32.5.619.
- Muthén, L.K., & Muthén, B.O. (n.d.). Mplus user's guide (version 7.4). Los Angeles, CA: Muthén & Muthén.
- Narciss, S. (2008). Feedback strategies for interactive learning tasks. Handbook of research on educational communications and technology, pp. 125-144. Mahwah, NJ: Lawrence Erlbaum Associates.
- Nicol, D.J., & Macfarlane-Dick, D. (2006). Formative assessment and self-regulated learning: A model and seven principles of good feedback practice. Studies in Higher Education, 31(2), pp. 199-218. Available online: https://doi.org/10.1080/03075070600572090.
- Olkin, I., & Finn, J.D. (1995). Correlations redux. Psychological Bulletin, 118, pp. 155-164. Available online: https://doi.org/10.1037/0033-2909.118.1.155.
- Pajares, F. (1996). Self-efficacy beliefs in achievement settings. Review of Educational Research, 66, pp. 543-578. Available online: https://doi.org/10.3102/00346543066004543.
- Panadero, E., & Jonsson, A. (2013). The use of scoring rubrics for formative assessment purposes revisited: A review. Educational Research Review, 9, pp. 129-144. Available online: https://doi.org/10.1016/j.edurev.2013.01.002.
- Panadero, E., Jonsson, A., & Botella, J. (2017). Effects of self-assessment on self-regulated learning and self-efficacy: Four meta-analyses. Educational Research Review, 22, pp. 74-98. Available online: https://doi.org/10.1016/j.edurev.2017.08.004.
- Pellegrino, J.W., Chudowsky, N., & Glaser, R. (2001). Knowing what students know: The science and design of educational assessment. Washington, DC: National Academy Press.
- Perrenoud, P. (1998). From formative evaluation to a controlled regulation of learning. Towards a wider conceptual field. Assessment in Education: Principles, Policy & Practice, 5(1), pp. 85-102. Available online: https://doi.org/10.1080/0969595980050105.
- 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 & Practice Available online: https://doi.org/10.1080/0969594X.2016.1170665.
- Preacher, K.J. (2015). Advances in mediation analysis: A survey and synthesis of new developments. Annual Review of Psychology, 66, pp. 825-852. Available online: https://doi.org/10.1146/annurev-psych-010814-015258.
- Preacher, K.J., & Hayes, A.F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40, pp. 879-891. Available online: https://doi.org/10.3758/BRM.40.3.879.
- 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, pp. 63-73. Available online: https://doi.org/10.1016/j.learninstruc.2013.03.002.
- Rakoczy, K., Klieme, E., Leiß, D., & Blum, W. (2017). Formative assessment in mathematics in-struction: Theoretical considerations and empirical results of the Co 2 CA project. Competence assessment in education: Research, models, and instruments, pp. 447-467. Berlin: Springer.
- Rotondi, M.A. (2015). Sample size estimation functions for cluster randomized trials (Version 1.0). Available online: https://cran.r-project.org/web/packages/CRTSize/CRTSize.pdf.
- Sadler, R. (1998). Formative assessment: Revisiting the territory. Assessment in Education, 5(1), pp. 77-84. Available online: https://doi.org/10.1080/0969595980050104.
- Sadler, T.D. (2011). Socio-scientific issues in the classroom: Teaching, learning and research. Contemporary trends and issues in science education: v. 39. Dordrecht, New York: Springer.
- Schafer, J.L., & Graham, J.W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7(2), pp. 147-177. Available online: https://doi.org/10.1037/1082-989X.7.2.147.
- Schunk, D.H. (1995). Self-efficacy and education and instruction. Self-efficacy, adaptation, and adjustment: Theory, research, and applications, pp. 281-303. New York: Plenum.
- Schunk, D.H., & Pajares, F. (2009). Self-efficacy theory. Handbook of motivation at school, pp. 35-53. New York: Routledge.
- Schunk, D.H., & Swartz, C.W. (1993). Goals and progress feedback: Effects on self-efficacy and writing achievement. Contemporary Educational Psychology, 18(3), pp. 337-354. Available online: https://doi.org/10.1006/ceps.1993.1024.
- Shute, V.J. (2008). Focus on formative feedback. Review of Educational Research, 78(1), pp. 153-189. Available online: https://doi.org/10.3102/0034654307313795.
- Stiggins, R. (2006). Assessment for learning: A key to motivation and achievement. Edge, 2(2), pp. 3-19.
- Strijbos, J.W., Narciss, S., & Dünnebier, K. (2010). Peer feedback content and sender's competence level in academic writing revision tasks: Are they critical for feedback perceptions and efficiency?. Learning and Instruction, 20, pp. 291-303. Available online: https://doi.org/10.1016/j.learninstruc.2009.08.008.
- Televantou, I., Marsh, H.W., Kyriakides, L., Nagengast, B., Fletcher, J., & Malmberg, L.-E. (2015). Phantom effects in school composition research: Consequences of failure to control biases due to measurement error in traditional multilevel models. School Effectiveness and School Improvement, 26, pp. 75-101. Available online: https://doi.org/10.1080/09243453.2013.871302.
- Tulis, M. (2013). Error management behavior in classrooms: Teachers' responses to students' mistakes. Teaching and Teacher Education, 33, pp. 56-68. Available online: https://doi.org/10.1016/j.tate.2013.02.003.
- Tulis, M., Steuer, G., & Dresel, M. (2016). Learning from errors: A model of individual processes. Frontline Learning Research, 4(2), pp. 12-26. Available online: https://doi.org/10.14786/flr.v4i2.168.
- Tymms, P. (2004). Effect sizes in multilevel models. But what does it mean? The use of effect sizes in educational research, pp. 55-66. Slough: NFER.
- Tymms, P., Merrell, C., & Henderson, B. (1997). The first year at school: A quantitative investigation of the attainment and progress of pupils. Educational Research and Evaluation, 3, pp. 101-118. Available online: https://doi.org/10.1080/1380361970030201.
- Van Zundert, M., Sluijsmans, D., & van Merriënboer, J. (2010). Effective peer assessment processes: Research findings and future directions. Learning and Instruction, 20, pp. 270-279.
- Wigfield, A., Eccles, J.S., & Rodriguez, D. (1998). The development of children's motivation in school contexts. Review of research in education, Vol. 23, pp. 73-118. Washington DC: American Educational Research Association.
- Wiliam, D., Lee, C., Harrison, C., & Black, P. (2004). Teachers developing assessment for learning: Impact on student achievement. Assessment in Education: Principles, Policy & Practice, 11(1), pp. 49-65. Available online: https://doi.org/10.1080/0969594042000208994.
- Wiliam, D., & Thompson, M. (2008). Integrating Assessment with Learning: What will it take to make it work?. The future of assessment. Shaping teaching and learning, pp. 53-84. New York: Lawrence Erlbaum Associates.
- Wilson, M.R., & Sloane, K. (2008). From principles to practice: An embedded assessment system. Student assessment and testing, 3, pp. 87-112. Los Angeles, London, New Delhi, Singapore: SAGE.
- Wu, M.L., Adams, R.J., & Wilson, M.R. (1998). ConQuest: Generalised item response modelling software. Camberwell: Australian Council for Educational Research.
- Yin, Y., Shavelson, R.J., Ayala, C.C., Ruiz-Primo, M.A., Brandon, P., & Furtak, E.M. (2008). On the impact of formative assessment on student motivation, achievement, and conceptual change. Applied Measurement in Education, 21(4), pp. 335-359. Available online: https://doi.org/10.1080/08957340802347845.
These references have been extracted automatically and may have some errors. Signed in users can suggest corrections to these mistakes.
Suggest Corrections to References