Formative assessment in mathematics from pre-service preparation to the first year of teaching: A longitudinal multiple-case study
PDF

Keywords

formative assessment
mathematics education
teacher preparation
teaching practice
pre-service elementary teachers

How to Cite

Kottová, T., & Jirotková, D. (2026). Formative assessment in mathematics from pre-service preparation to the first year of teaching: A longitudinal multiple-case study. Scientia in Educatione, 17(1), 2–18. https://doi.org/10.14712/18047106.5240

Abstract

This longitudinal multiple-case study investigates the development of formative assessment among five Czech pre-service primary mathematics teachers across university preparation and their first year of teaching after graduation. Using repeated interviews, lesson plan analysis, and video observations, the study examines how novices’ understanding and classroom enactment of a five-strategy formative assessment (FA) framework develop over time. Findings indicate that while initial teacher education successfully initiates a conceptual shift toward process-oriented assessment, classroom enactment remains highly uneven. Practices supporting discussion and peer learning were most visible, while structured routines for eliciting evidence strengthened over time but remained uneven; explicit work with learning goals, success criteria, and criteria-linked feedback remained weak across phases. Key facilitators included collegial and leadership support, observation of concrete practices, and structured reflection; major constraints included time pressure, grading demands, parental expectations, and the demands of interpreting pupils’ mathematical thinking in real time.

https://doi.org/10.14712/18047106.5240
PDF

References

Alarcón, C., & Lawn, M. (Eds.). (2018). Assessment cultures: Historical perspectives. Peter Lang.

Ayalon, M., & Wilkie, K. J. (2021). Investigating peer-assessment strategies for mathematics pre-service teacher learning on formative assessment. Journal of Mathematics Teacher Education, 24(4), 399–426. https://doi.org/10.1007/s10857-020-09465-1

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, 5–31. https://doi.org/10.1007/s11092-008-9068-5

Creswell, J.W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (4th ed.). Pearson.

Crooks, T. J. (1988). The impact of classroom evaluation practices on students. Review of Educational Research, 58(4), 438–481. https://doi.org/10.2307/1170281

Darling-Hammond, L., & Bransford, J. (Eds.). (2005). Preparing teachers for a changing world: What teachers should learn and be able to do. Jossey-Bass.

Derry, S. J. (2007). Guidelines for video research in education: Recommendations from an expert panel. Data Research and Development Center.

Farrell, T. S. C. (2012). Novice-service language teacher development: Bridging the gap between preservice and in-service education and development. TESOL Quarterly, 46(3), 435–449. https://doi.org/10.1002/tesq.36

Flick, U. (2009). An introduction to qualitative research (4th ed.). SAGE.

Goldman, R., Pea, R., Barron, B., & Derry, S. J. (Eds.). (2007). Video research in the learning sciences. Routledge.

Grossman, P., Hammerness, K., & McDonald, M. (2009). Redefining teaching, re-imagining teacher education. Teachers and Teaching, 15(2), 273–289. https://doi.org/10.1080/13540600902875340

Hattie, J., Fisher, D., Frey, N., Gojak, L. M., Delano Moore, S., & Mellman, W. (2017). Visible learning for mathematics, grades K–12: What works best to optimize student learning. Corwin.

Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81–112. https://doi.org/10.3102/003465430298487

Hendl, J. (2005). Kvalitativní výzkum: základní metody a aplikace [Qualitative research: Basic methods and applications]. Portál.

Hendl, J. (2016). Kvalitativní výzkum: základní teorie, metody a aplikace [Qualitative research: Basic theory, methods, and applications]. Portál.

Herbert, S., Vale, C., White, P., & Bragg, L. A. (2022). Engagement with a formative assessment rubric: A case of mathematical reasoning. International Journal of Educational Research, 111, Article 101899. https://doi.org/10.1016/j.ijer.2021.101899

Heritage, M. (2007). Formative assessment: What do teachers need to know and do? Phi Delta Kappan, 89(2), 140–145. https://doi.org/10.1177/003172170708900210

Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National council of teachers of Mathematics (pp. 65–97). Macmillan.

Hošpesová, A. (2018). Formative assessment in inquiry-based elementary mathematics. In G. Kaiser, H. Forgasz, M. Graven, A. Kuzniak, E. Simmt, & B. Xu (Eds.), Invited Lectures from the 13th International congress on mathematical education. ICME-13 Monographs (pp. 249–268). Springer. https://doi.org/10.1007/978-3-319-72170-5 15

Husu, J., Toom, A., & Patrikainen, S. (2008). Guided reflection as a means to demonstrate and develop student teachers’ reflective competencies. Reflective Practice, 9(1), 37–51. https://doi.org/10.1080/14623940701816642

Hsieh, H. F., & Shannon, S. E. (2005). Three approaches to qualitative content analysis. Qualitative Health Research, 15(9), 1277–1288. https://doi.org/10.1177/1049732305276687

Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202. https://doi.org/10.5951/jresematheduc.41.2.0169

Jönsson, A. (2020). Definitions of formative assessment need to make a distinction between a psychometric understanding of assessment and “evaluative judgment.” Frontiers in Education, 5, Article 2. https://doi.org/10.3389/feduc.2020.00002

Koenka, A. C., Linnenbrink-Garcia, L., Moshontz, H., Atkinson, K.M., Sanchez, C. E., & Cooper, H. (2021). A meta-analysis on the impact of grades and comments on academic motivation and achievement: A case for written feedback. Educational Psychology, 41(7), 922–947. https://doi.org/10.1080/01443410.2019.1659939

Kvale, S., & Brinkmann, S. (2009). InterViews: Learning the craft of qualitative research interviewing (2nd ed.). Sage Publications.

Leahy, S., Lyon, C., Thompson, M., & Wiliam, D. (2005). Classroom assessment: Minute by minute, day by day. Educational Leadership, 63(3), 18–24. https://www.ascd.org/el/articles/classroom-assessment-minute-by-minute-day-by-day

Maskos, K., Schulz, A., Oeksuez, S. S., & Rakoczy, K. (2025). Formative assessment in mathematics education: A systematic review. ZDM–Mathematics Education, 57(4), 679–693. https://doi.org/10.1007/s11858-025-01696-x

Ministerstvo školství, mládeže a tělovýchovy. (2020). Strategie vzdělávací politiky ČR do roku 2030+ [Strategy for the education policy of the Czech Republic up to 2030+]. https://www.msmt.cz/vzdelavani/skolstvi-v-cr/strategie-2030

Ministerstvo školství, mládeže a tělovýchovy. (2023). Kompetenční rámec absolventa a absolventky učitelství [Competence framework for teacher education graduates]. https://www.msmt.cz/uploads/kompetencni ramec absolventa 2023 10.pdf

OECD. (2005). Formative assessment: Improving learning in secondary classrooms. OECD. https://www.oecd.org/education/ceri/35661078.pdf

Popham, W. J. (2008). Classroom assessment: What teachers need to know. Prentice Hall.

Powell, A. B., Francisco, J. M., & Maher, C. A. (2003). An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. The Journal of Mathematical Behavior, 22(4), 405–435. https://doi.org/10.1016/j.jmathb.2003.09.002

Schildkamp, K., van der Kleij, F. M., Heitink, M. C., Kippers, W. B., & Veldkamp, B. P. (2020). Formative assessment: A systematic review of critical teacher prerequisites for classroom practice. International Journal of Educational Research, 103, Article 101602. https://doi.org/10.1016/j.ijer.2020.101602

Schmidt, W. H., Wang, H. C., & McKnight, C. C. (2005). Curriculum coherence: An examination of US mathematics and science content standards from an international perspective. Journal of Curriculum Studies, 37(5), 525–559. https://doi.org/10.1080/0022027042000294775

Starý, K., & Laufková, V. (2016). Formativní hodnocení ve výuce [Formative assessment in teaching]. Portál. Suurtamm, C., Thompson, D. R., Kim, R. Y., Diaz Moreno, L., Sayac, N., Schukajlow, S., Silver, E., Ufer, S., & Vos, P. (2016). Assessment in mathematics education: Large-scale assessment and classroom assessment. Springer. https://doi.org/10.1007/978-3-319-32394-7

Van Orman, D. S. J., Gotch, C. M., & Carbonneau, K. J. (2025). Preparing teacher candidates to assess for learning: A systematic review. Review of Educational Research, 95(3), 427–463. https://doi.org/10.3102/00346543241233015

Whalen, C., Majocha, E., & Van Nuland, S. (2019). Novice teacher challenges and promoting novice teacher retention in Canada. European Journal of Teacher Education, 42(5), 591–607. https://doi.org/10.1080/02619768.2019.1652906

Wiliam, D., & Leahy, S. (2015). Embedding formative assessment: Practical techniques for K–12 classrooms. Learning Sciences International.

Wisniewski, B., Zierer, K., & Hattie, J. (2020). The power of feedback revisited: A meta-analysis of educational feedback research. Frontiers in Psychology, 10, Article 3087. https://doi.org/10.3389/fpsyg.2019.03087

Yan, Z., Li, Z., Panadero, E., Yang, M., Yang, L., & Lao, H. (2021). A systematic review on factors influencing teachers’ intentions and implementations regarding formative assessment. Assessment in Education: Principles, Policy & Practice, 28(3), 228–260. https://doi.org/10.1080/0969594X.2021.1884042

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Copyright (c) 2026 Tereza Kottová, Darina Jirotková