Formative Assessment Practices in a Mathematics Classroom
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Abstract
Formative assessment plays a pivotal role in promoting student achievement, particularly in mathematics education, where it supports conceptual understanding, procedural fluency, and problem-solving skills. Despite its known benefits, consistent implementation remains a challenge. This qualitative instrumental case study examines how junior high school mathematics teachers implement formative assessment strategies in mathematics classrooms. Three case studies were conducted in a private Philippine secondary school involving classroom observations. Findings reveal the integration of diagnostic questioning, Claim-Evidence-Reasoning (CER) strategies, technology-enhanced assessments, and reflection practices are commonly used as formative assessments by the teachers. The study identifies patterns in teacher actions and student responses, underscores the benefits of formative assessment, and highlights challenges such as time constraints and professional development needs. Recommendations are provided to enhance formative assessment implementation across mathematics classrooms.
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References
Andrade, H., & Valtcheva, A. (2009). Promoting learning and achievement through self-assessment. Theory Into Practice, 48(1), 12-19.
Bell, B., & Cowie, B. (2001). Formative assessment and science education. Kluwer Academic Publishers.
Bennett, R. E. (2011). Formative assessment: A critical review. Assessment in Education: Principles, Policy & Practice, 18(1), 5–25.
Bernardo, A. B. I. (2010). Extending the Vygotskian concept of the zone of proximal development to the discussion of pedagogical assumptions in language and education. Asia Pacific Education Review, 11(1), 58–67.
Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education: Principles, Policy & Practice, 5(1), 7–74.
Black, P., & Wiliam, D. (2018). Assessment for learning in the mathematics classroom. Mathematics Teaching, 245, 32–38. https://doi.org/10.1080/0969595980050202
Boaler, J. (2008). Promoting 'relational equity' and high mathematics achievement through an innovative mixed-media curriculum. The Journal of Educational Research, 102(2), 129–142.
Clark, I. (2012). Formative assessment: Assessment is for self-regulated learning. Educational Psychology Review, 24(2), 205–249.
David, A., & Dizon, L. (2017). Formative assessment in large mathematics classes: Challenges and strategies. Philippine Educational Research Journal, 3(2), 21-34.
Dayal, H. C. (2021). How Teachers Use Formative Assessment Strategies during Teaching: Evidence from the Classroom. Australian Journal of Teacher Education, 46(7).
Department of Education. (2015). K to 12 Assessment Guidelines (DepEd Order No. 8, s. 2015). https://www.deped.gov.ph.
Derivita, R. A. (2023). Assessment in learning 1: An outcomes-based approach. Lorimar Publishing, Inc.
Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool: Instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213–234. https://doi.org/10.1007/s10649-010-9254-5.
Furtak, E. M., Kunter, M., & Klusmann, U. (2012). The relationship between formative assessment and student achievement: A meta-analysis. Educational Psychology Review, 24(3), 469-497.
Gay, G. (2000). Culturally responsive teaching: Theory, research, and practice. Teachers College Press.
Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81–112.
Heritage, M. (2010). Formative assessment: Making it happen in the classroom. Corwin Press.
Heritage, M. (2019). Formative assessment in mathematics: Teacher knowledge and student learning outcomes. Journal of Mathematics Teacher Education, 22(4), 383–405. https://doi.org/10.1007/s10857-018-9403-x.
Humes, A. (2021). Formative Assessment and Technology in the Mathematics Classroom. Master's Thesis, Northwestern College, Iowa.
Kenney, R. H., Shoffner, M. B., & Lin, P. (2023). Strengthening formative assessment practices in mathematics through qualitative synthesis. Journal of Mathematics Teacher Education, 26(1), 25–45. https://doi.org/10.1007/s10857-022-09557-3.
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. National Academy Press.
Kingston, N., & Nash, B. (2011). Formative assessment: A meta-analysis and a call for research. Educational Measurement: Issues and Practice, 30(4), 28–37.
Kültür, Y. Z., & Kutlu, M. O. (2021). The effect of formative assessment on high school students' mathematics achievement and attitudes 7. Journal of Pedagogical Research, 5(4), 155-171 1. https://doi.org/10.33902/JPR.2021474302 1.
Kynigos, C. (2015). Constructionism: Theory of learning or theory of design? In S. J. Cho (Ed.), The proceedings of the 12th International Congress on Mathematical Education (pp. 417–436). Springer. https://doi.org/10.1007/978-3-319-17187-6_24.
Labrador, S. R. (2022). Individualized feedback strategies in Philippine math classrooms. Mathematics Education Review, 14(1), 23–34.
Ladson-Billings, G. (1994). The Dreamkeepers: Successful teachers of African American Children. Jossey-Bass.
Manalo, M. (2019). Teacher perspectives on formative assessment in mathematics classrooms: Balancing curriculum demands and student engagement. Philippine Journal of Education, 95(1), 45–60.
Mayer, R. E. (2009). Multimedia learning (2nd ed.). Cambridge University Press.
McMillan, J. H., & Hearn, J. (2008). Student self-assessment: The key to stronger student motivation and higher achievement. Educational Horizons, 87(1), 40–49.
McNeill, K. L., Lizotte, D. J., Krajcik, J., & Marx, R. W. (2006). Supporting students’ construction of scientific explanations by fading scaffolds in instructional materials. The Journal of the Learning Sciences, 15(2), 153–191. https://doi.org/10.1207/s15327809jls1502_1.
Mendoza, R. (2020). The role of formative assessment in student engagement in the Philippine context. Education Quarterly, 67(3), 123–135.
Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017-1054.
National Council of Teachers of Mathematics. (2018). Catalyzing change in high school mathematics: Initiating critical conversations. Reston, VA: Author.
Nicol, D., & 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), 199–218.
Ocampo, D. (2017). Educational reform and the Philippine K to 12 curriculum. Philippine Journal of Development, 44(2), 1–20.
Piaget, J. (1977). The development of thought: Equilibration of cognitive structures. Viking Press.
Polya, G. (1957). How to solve it: A new aspect of mathematical method (2nd ed.). Princeton University Press.
Popham, W. J. (2008). Transformative assessment. ASCD.
Puentedura, R. R. (2006). Transformation, technology, and education. Retrieved from http://hippasus.com/resources/tte/.
Rathje, A. (2018). A qualitative case study of mathematics teachers’ formative assessment feedback [Doctoral dissertation, Concordia University Chicago].
Ruiz-Primo, M. A., & Furtak, E. M. (2007). Exploring teachers’ informal formative assessment practices and students’ understanding in the context of scientific inquiry. Journal of Research in Science Teaching, 44(1), 57–84. https://doi.org/10.1002/tea.20163.
Sadler, D. R. (1989). Formative assessment and the design of instructional systems. Instructional Science, 18(2), 119–144. https://doi.org/10.1007/BF00117714.
Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press.
Schoenfeld, A. H. (2013). Mathematical problem solving. Mathematics and Cognition, 3(1), 335-359.
Schoenfeld, A. H. (2013). Reflections on problem-solving and metacognition. ZDM Mathematics Education, 45(2), 211–213. https://doi.org/10.1007/s11858-012-0453-1.
Shute, V. J. (2008). Focus on formative feedback. Review of Educational Research, 78(1), 153–189. https://doi.org/10.3102/0034654307313795.
Sison, A. (2014). Formative assessment practices in Philippine secondary schools. Philippine Journal of Education, 93(1), 34–48.
Stroup, W. M., Ares, N., Hurford, A., & Wilensky, U. (2017). The evolution of integrated assessment in project-based curricula. International Journal of STEM Education, 4(1), 1–15.
Sweller, J. (1988). Cognitive load during problem-solving: Effects on learning. Cognitive Science, 12(2), 257–285.
Tanyag, R. M., & Garcia, J. M. (2021). Impact of formative assessment on math performance. Asian Journal of Education and Learning, 12(3), 111–124.
Wiggins, G., & McTighe, J. (2000). Understanding by design. ASCD.
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press.
Wiliam, D. (2011). Embedded formative assessment. Solution Tree Press.
Wiliam, D., & Thompson, M. (2017). Integrating formative assessment in mathematics classrooms: A framework for increasing student learning outcomes. Educational Assessment, Evaluation and Accountability, 29(1), 5–25. https://doi.org/10.1007/s11092-016-9257-3.