Effects of formative assessment on intrinsic motivation in primary school mathematics instruction

Bandura, A. (1997). Self-efficacy: The exercise of control. Freeman. Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education: Principles, Policy & Practice, 5(1), 7–74. https://doi.org/10.1080/0969595980050102 Black, P., & Wiliam, D. (2009). Developing the theory of formative assessment. Educational Assessment, Evaluation and Accountability, 21(1), 5–31. https://doi.org/10.1007/s11092-008-9068-5 Blumberg, E. (2008). Multikriteriale Zielerreichung im naturwissenschaftsbezogenen Sachunterricht der Grundschule – Eine Studie zum Einfluss von Strukturierung in schülerorientierten Lehr-Lernumgebungen auf das Erreichen kognitiver, motivationaler und selbstbezogener Zielsetzungen [Multi-criterial goal attainment in elementary school science education] [Doctoral dissertation, University of Münster]. https://miami.uni-muenster.de/Record/d767660e-c351-46ca-9828-7075ef173a3c. Accessed 16 Nov 2023 Bokhove, C., & Drijvers, P. (2012). Effects of a digital intervention on the development of algebraic expertise. Computers & Education, 58(1), 197–208. https://doi.org/10.1016/j.compedu.2011.08.010 Bos, W., Lankes, E.-M., Prenzel, M., Schwippert, K., Valtin, R., Voss, R., & Walther, G. (2005). IGLU. Skalenhandbuch zur Dokumentation der Erhebungsinstrumente [IGLU. Scale manual for the documentation of the survey instruments]. Waxmann. Brühwiler, C., & Blatchford, P. (2011). Effects of class size and adaptive teaching competency on classroom processes and academic outcome. Learning and Instruction, 21(1), 95–108. https://doi.org/10.1016/j.learninstruc.2009.11.004 Bureau, J. S., Howard, J. L., Chong, J. X. Y., & Guay, F. (2022). Pathways to student motivation: A meta-analysis of antecedents of autonomous and controlled motivations. Review of Educational Research, 92(1), 46–72. https://doi.org/10.3102/00346543211042426 Century, J., & Cassata, A. (2016). Implementation research: Finding common ground on what, how, why, where, and who. Review of Research in Education, 40(1), 169–215. https://doi.org/10.3102/0091732X16665332 Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Erlbaum. https://doi.org/10.4324/9780203771587 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), 558–577. https://doi.org/10.1037/0021-843X.112.4.558 Deci, E. L., & Ryan, R. M. (1985). Intrinsic motivation and self-determination in human behavior. Plenum Press. https://doi.org/10.1007/978-1-4899-2271-7 Decristan, J., Hondrich, A. L., Büttner, G., Hertel, S., Klieme, E., Kunter, M., Lühken, A., Adl-Amini, K., Djakovic, S.-K., Mannel, S., Naumann, A., & Hardy, I. (2015). Impact of additional guidance in science education on primary students’ conceptual understanding. The Journal of Educational Research, 108(5), 358–370. https://doi.org/10.1080/00220671.2014.899957 Department for Education. (2013). The national curriculum in England. Key stages 1 and 2 framework document. https://assets.publishing.service.gov.uk/media/5a81a9abe5274a2e8ab55319/PRIMARY_national_curriculum.pdf. Accessed 10 Mar 2023. DiCiccio, T. J., & Efron, B. (1996). Bootstrap confidence intervals. Statistical Science, 11(3), 189–212. https://doi.org/10.1214/ss/1032280214 Drost, D. K., & Todorovich, J. R. (2017). Perceived competence and skill development in physical education: The effect of teacher feedback. Journal of Sports Science, 5(6), 291–304. https://doi.org/10.17265/2332-7839/2017.06.001 Eccles, J. S., & Wigfield, A. (2002). Motivational beliefs, values, and goals. Annual Review of Psychology, 53(1), 109–132. https://doi.org/10.1146/annurev.psych.53.100901.135153 Enders, C. K. (2001). A primer on maximum likelihood algorithms available for use with missing data. Structural Equation Modeling: A Multidisciplinary Journal, 8(1), 128–141. https://doi.org/10.1207/S15328007SEM0801_7 Faber, J. M., Luyten, H., & Visscher, A. J. (2017). The effects of a digital formative assessment tool on mathematics achievement and student motivation: Results of a randomized experiment. Computers & Education, 106, 83–96. https://doi.org/10.1016/j.compedu.2016.12.001 Fend, H. (1981). Theorie der Schule [School theory]. Urban & Schwarzenberg. Förster, N., & Souvignier, E. (2014). Learning progress assessment and goal setting: Effects on reading achievement, reading motivation and reading self-concept. Learning and Instruction, 32, 91–100. https://doi.org/10.1016/j.learninstruc.2014.02.002 Förster, N., & Souvignier, E. (2015). Effects of providing teachers with information about their students’ reading progress. School Psychology Review, 44(1), 60–75. https://doi.org/10.17105/SPR44-1.60-75 Fuchs, D., & Fuchs, L. S. (2019). On the importance of moderator analysis in intervention research: An introduction to the special issue. Exceptional Children, 85(2), 126–128. https://doi.org/10.1177/0014402918811924 Gottfried, A. E. (1990). Academic intrinsic motivation in young elementary school children. Journal of Educational Psychology, 82(3), 525–538. https://doi.org/10.1037/0022-0663.82.3.525 Goudas, M., Biddle, S., Fox, K., & Underwood, M. (1995). It ain’t what you do, it’s the way that you do it! Teaching style affects children’s motivation in track and field lessons. The Sport Psychologist, 9(3), 254–264. https://doi.org/10.1123/tsp.9.3.254 Guay, F., Vallerand, R. J., & Blanchard, C. (2000). On the assessment of situational intrinsic and extrinsic motivation: The situational motivation scale (SIMS). Motivation and Emotion, 24(3), 175–213. https://doi.org/10.1023/A:1005614228250 Hardy, I., Hertel, S., Kunter, M., Klieme, E., Warwas, J., Büttner, G., & Lühken, A. (2011). Adaptive Lerngelegenheiten in der Grundschule. Merkmale, methodisch-didaktische Schwerpunktsetzungen und erforderliche Lehrerkompetenzen [Adaptive learning opportunities in elementary school]. Zeitschrift Für Pädagogik, 57(6), 819–833. https://doi.org/10.25656/01:8783 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 Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81–112. https://doi.org/10.3102/003465430298487 Hebbecker, K., Förster, N., Forthmann, B., & Souvignier, E. (2022). Data-based decision-making in schools: Examining the process and effects of teacher support. Journal of Educational Psychology, 114(7), 1695–1721. https://doi.org/10.1037/edu0000530 Hebbecker, K., & Souvignier, E. (2018). Formatives assessment im Leseunterricht der Grundschule – Implementation und Wirksamkeit eines modularen, materialgestützten Konzepts [Formative assessment in third-grade reading instruction—Implementation and effectiveness of a modular concept including prepared teaching-material]. Zeitschriftf ür Erziehungswissenschaft, 21(4), 735–765. https://doi.org/10.1007/s11618-018-0834-y Helmke, A. (2003). Unterrichtsqualität: Erfassen, Bewerten, Verbessern [Teaching quality: Assessment, evaluation, improvement]. Kallmeyer. Hondrich, A. L., Decristan, J., Hertel, S., & Klieme, E. (2018). Formative assessment and intrinsic motivation: The mediating role of perceived competence. Zeitschrift für Erziehungswissenschaft, 21(4), 717–734. https://doi.org/10.1007/s11618-018-0833-z Hondrich, A. L., Hertel, S., Adl-Amini, K., & Klieme, E. (2016). Implementing curriculum-embedded formative assessment in primary school science classrooms. Assessment in Education: Principles, Policy & Practice, 23(3), 353–376. https://doi.org/10.1080/0969594X.2015.1049113 Howard, J. L., Bureau, J., Guay, F., Chong, J. X. Y., & Ryan, R. M. (2021). Student motivation and associated outcomes: A meta-analysis from self-determination theory. Perspectives on Psychological Science, 16(6), 1300–1323. https://doi.org/10.1177/1745691620966789 Jamshidian, M., & Jalal, S. (2010). Tests of homoscedasticity, normality, and missing completely at random for incomplete multivariate data. Psychometrika, 75(4), 649–674. https://doi.org/10.1007/s11336-010-9175-3 Jamshidian, M., Jalal, S., & Jansen, C. (2014). MissMech: An R package for testing homoscedasticity, multivariate normality, and missing completely at random (MCAR). Journal of Statistical Software, 56(6), 1–31. https://doi.org/10.18637/jss.v056.i06 Käpnick, F. (2016). Mathe für kleine Asse: Empfehlungen zur Förderung mathematisch interessierter und begabter Kinder im ersten und zweiten Schuljahr [Math for little aces: Recommendations for the support of mathematically interested and gifted children in the first and second school year]. Cornelsen. Kingston, N., & Nash, B. (2011). Formative assessment: A meta-analysis and a call for research. Educational Measurement: Issues and Practice, 30(4), 28–37. https://doi.org/10.1111/j.1745-3992.2011.00220.x Klute, M., Apthorp, H., Harlacher, J., & Reale, M. (2017). Formative assessment and elementary school student academic achievement: A review of the evidence. REL 2017-259. Regional Educational Laboratory Central. Koedinger, K. R., McLaughlin, E. A., & Heffernan, N. T. (2010). A quasi-experimental evaluation of an on-line formative assessment and tutoring system. Educational Computing Research, 43(4), 489–510. https://doi.org/10.2190/EC.43.4.d Krajewski, K., Dix, S., & Schneider, W. (2004). DEMAT 2+. Deutscher Mathematiktest für zweite Klassen [DEMAT 2+. German mathematics test for second grade]. Hogrefe. Krijgsman, C., Mainhard, T., van Tartwijk, J., Borghouts, L., Vansteenkiste, M., Aelterman, N., & Haerens, L. (2019). Where to go and how to get there: Goal clarification, process feedback and students’ need satisfaction and frustration from lesson to lesson. Learning and Instruction, 61, 1–11. https://doi.org/10.1016/j.learninstruc.2018.12.005 Kunter, M. (2005). Multiple Ziele im Mathematikunterricht [Multiple goals in mathematics instrcution]. Waxmann. Kunter, M., Baumert, J., & Köller, O. (2007). Effective classroom management and the development of subject-related interest. Learning and Instruction, 17(5), 494–509. https://doi.org/10.1016/j.learninstruc.2007.09.002 Lane, R., Parrila, R., Bower, R., Bull, R., Cavanagh, M., Forbes, A., Jones, T., Leaper, D., Khosronejad, M., Pellicano, L., Powell, S., Ryan, M., & Skrebneva, I. (2019). Literature review: Formative assessment evidence and practice. In Australian Institute for Teaching and School Leadership (AITSL). https://www.lpofai.edu.au/media/u5ahfia0/literature-review.pdf. Accessed 21 Apr 2023 Lee, H., Chung, H. Q., Zhang, Y., Abedi, J., & Warschauer, M. (2020). The effectiveness and features of formative assessment in US K-12 education: A systematic review. Applied Measurement in Education, 33(2), 124–140. https://doi.org/10.1080/08957347.2020.1732383 Leenknecht, M., Wijnia, L., Köhlen, M., Fryer, L., Rikers, R., & Loyens, S. (2020). Formative assessment as practice: The role of students’ motivation. Assessment & Evaluation in Higher Education, 46(2), 236–255. https://doi.org/10.1080/02602938.2020.1765228 Lemos, M. S., & Veríssimo, L. (2014). The relationships between intrinsic motivation, extrinsic motivation, and achievement, along elementary school. Procedia - Social and Behavioral Sciences, 112, 930–938. https://doi.org/10.1016/j.sbspro.2014.01.1251 Linnenbrink-Garcia, L., Patall, E. A., & Pekrun, R. (2016). Adaptive motivation and emotion in education: Research and principles for instructional design. Policy Insights from the Behavioral and Brain Sciences, 3(2), 228–236. https://doi.org/10.1177/2372732216644450 Lüdtke, O., Robitzsch, A., Trautwein, U., & Köller, O. (2007). Umgang mit fehlenden Werten in der psychologischen Forschung [Handling of missing data in psychological research: Problems and solutions]. Psychologische Rundschau, 58(2), 103–117. https://doi.org/10.1026/0033-3042.58.2.103 Mandinach, E. B. (2012). A perfect time for data use: Using data-driven decision making to inform practice. Educational Psychologist, 47(2), 71–85. https://doi.org/10.1080/00461520.2012.667064 Miller, D., & Lavin, F. (2007). ‘But now I feel I want to give it a try’: Formative assessment, self-esteem and a sense of competence. The Curriculum Journal, 18(1), 3–25. https://doi.org/10.1080/09585170701292109 Pat-El, R., Tillema, H., & van Koppen, S. W. M. (2012). Effects of formative feedback on intrinsic motivation: Examining ethnic differences. Learning and Individual Differences, 22(4), 449–454. https://doi.org/10.1016/j.lindif.2012.04.001 Praetorius, A.-K., Klieme, E., Herbert, B., & Pinger, P. (2018). Generic dimensions of teaching quality: The German framework of three basic dimensions. ZDM, 50(3), 407–426. https://doi.org/10.1007/s11858-018-0918-4 Prast, E. J., van de Weijer-Bergsma, E., Kroesbergen, E. H., & van Luit, J. E. H. (2018). Differentiated instruction in primary mathematics: Effects of teacher professional development on student achievement. Learning and Instruction, 54, 22–34. https://doi.org/10.1016/j.learninstruc.2018.01.009 Preacher, K. J. (2015). Advances in mediation analysis: A survey and synthesis of new developments. Annual Review of Psychology, 66, 825–852. https://doi.org/10.1146/annurev-psych-010814-015258 Prenzel, M., Kristen, A., Dengler, P., Ettle, R., & Beer, T. (1996). Selbstbestimmt motiviertes und interessiertes Lernen in der kaufmännischen Erstausbildung [Self-determined motivated and interested learning in the initial commercial training]. In K. Beck & H. Heid (Eds.), Lehr-Lern-Prozesse in der kaufmännischen Erstausbildung: Wissenserwerb, Motivierungsgeschehen und Handlungskompetenzen: Zeitschrift für Berufs- und Wirtschaftspädagogik (13th ed., pp. 108–127). Steiner. R Core Team. (2022). R: A language and environment for statistical computing [Computer software]. R Foundation for Statistical Computing. Vienna. https://www.R-project.org/. Accessed 28 May 2023. 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 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 Rakoczy, K., Klieme, E., & Pauli, C. (2008). Die Bedeutung der wahrgenommenen Unterstützung motivationsrelevanter Bedürfnisse und des Alltagsbezugs im Mathematikunterricht für die selbstbestimmte Motivation [The impact of the perceived support of basic psychological needs and of the perceived relevance of contents on students’ self-determined motivation in mathematics instruction]. Zeitschrift Für Pädagogische Psychologie, 22(1), 25–35. https://doi.org/10.1024/1010-0652.22.1.25 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, 154–165. https://doi.org/10.1016/j.learninstruc.2018.01.004 Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1–36. https://doi.org/10.18637/jss.v048.i02 Rosseel, Y., Jorgensen, T. D., Rockwood, N., Oberski, D., Byrnes, J., Vanbrabant, L., Savalei, V., Merkle, E., Hallquist, M., Rhemtulla, M., Katsikatsou, M., Barendse, M., Scharf, F., & Du, H. (2022). Latent variable analysis: Package “lavaan”. https://lavaan.ugent.be/. Accessed 28 Apr 2023. Roy, A., Guay, F., & Valois, P. (2015). The big-fish–little-pond effect on academic self-concept: The moderating role of differentiated instruction and individual achievement. Learning and Individual Differences, 42, 110–116. https://doi.org/10.1016/j.lindif.2015.07.009 Ryan, R. M., & Deci, E. L. (2000). Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being. American Psychologist, 55(1), 68–78. https://doi.org/10.1037/0003-066X.55.1.68 Ryan, R. M., & Deci, E. L. (2002). An overview of self-determination theory: An organismic-dialectical perspective. In E. L. Deci & R. M. Ryan (Eds.), Handbook of self-determination research (pp. 3–33). The University of Rochester Press. Schütze, B., Rakoczy, K., Klieme, E., Besser, M., & Leiss, D. (2017). Training effects on teachers’ feedback practice: the mediating function of feedback knowledge and the moderating role of self-efficacy. ZDM Mathematics Education, 49(3), 475–489. https://doi.org/10.25656/01:17042 Shute, V. J. (2008). Focus on formative feedback. Review of Educational Research, 78(1), 153–189. https://doi.org/10.3102/0034654307313795 Souvignier, E., Förster, N., Hebbecker, K., & Schütze, B. (2021). Using digital data to support teaching practice – quop: An effective web-based approach to monitor student learning progress in reading and mathematics in entire classrooms. In A. Wilmers & S. Jornitz (Eds.), International perspectives on school settings, education policy and digital strategies. A transatlantic discourse in education research (pp. 283–298). Barbara Budrich. https://doi.org/10.2307/j.ctv1gbrzf4.20 Vansteenkiste, M., Lens, W., & Deci, E. L. (2006). Intrinsic versus extrinsic goal contents in self-determination theory: Another look at the quality of academic motivation. Educational Psychologist, 41(1), 19–31. https://doi.org/10.1207/s15326985ep4101_4 Visscher, A. J. (2021). On the value of data-based decision making in education: The evidence from six intervention studies. Studies in Educational Evaluation, 69, 100899. https://doi.org/10.1016/j.stueduc.2020.100899 Wigfield, A., & Eccles, J. S. (2000). Expectancy–value theory of achievement motivation. Contemporary Educational Psychology, 25(1), 68–81. https://doi.org/10.1006/ceps.1999.1015 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. 53–82). Erlbaum. https://doi.org/10.4324/9781315086545-3 Wisniewski, B., Zierer, K., & Hattie, J. (2019). The power of feedback revisited: A meta-analysis of educational feedback research. Frontiers in Psychology, 10, 3087. https://doi.org/10.3389/fpsyg.2019.03087 Yin, Y., Shavelson, R. J., Ayala, C. C., Ruiz-Primo, M. A., Brandon, P. R., Furtak, E. M., Tomita, M. K., & Young, D. B. (2008). On the impact of formative assessment on student motivation, achievement, and conceptual change. Applied Measurement in Education, 21(4), 335–359. https://doi.org/10.1080/08957340802347845