Informal Formative Assessment Conversations in Mathematics: Focusing on Preservice Teachers’ Initiation, Response and Follow-up Sequences in the Classroom
More details
Hide details
College of Education, Texas Tech University, USA
Publication date: 2020-07-30
EURASIA J. Math., Sci Tech. Ed 2020;16(10):em1884
This study highlighted the characteristics and patterns of preservice teachers’ informal formative assessment conversations woven into mathematics classrooms. Participants were four preservice teachers from an elementary mathematics methods course whose videotaped lessons were analyzed using an analytic framework based on Initiation, Response and Follow-up (IRF) sequences. Findings indicated that the patterns of IRF sequence were varied across the preservice teachers, although they taught the same topic. We also found common patterns in their IRF sequences in that preservice teachers mainly initiated and drove classroom conversations of mathematics, while students’ roles were passive. In addition, they used frequent follow-up questions; however, most of them were closed questions intended to guide students to quickly give correct responses. Regarding feedback, their feedback were mostly made to affirm or elaborate on what students said or to clarify meanings of statements, not to explore students’ initial ideas or reasoning processes.
Association of Mathematics Teacher Educators. (2017). Standards for Preparing Teachers of Mathematics. Retrieved from
Baird, J. R., & Northfield, J. R. (Eds.). (1992). Learning from the PEEL experience. Melbourne, Australia: Monash University Printing.
Bamberger, H. J., Oberdorf, C., Schultz-Ferrell, K., & Leinwand, S. (2011). Math misconceptions, prek-grade 5: From misunderstanding to deep understanding. Portsmouth, NH: Heinemann.
Black, P. J., Harrison, C., Lee, C., Marshall, B., & Wiliam, D. (2002). Working inside the black box: Assessment for learning in the classroom. London, UK: King’s College London School of Education.
Cai, J. and Wang, T. (2006). U.S. and Chinese teachers’ conceptions and constructions of presentations: A case of teaching ratio concept. International Journal of Science and Mathematics Education, 4, 145-186.
Chin, C. (2006). Classroom Interaction in Science: Teacher questioning and feedback to students’ responses. International Journal of Science Education, 28(11), 1315-1346.
Chin, C. (2007). Teacher questioning in science classrooms: approaches that stimulate productive thinking. Journal of Research in Science Teaching, 44(6), 815-843.
Cobb, P., Boufi, A., McClain, K., & Whitenack, J. (1997). Reflective discourse and collective reflection. Journal for research in mathematics education, 18(3), 258-277.
Council of Chief State School Officers & National Governors Association. (2010). Common core state standards-mathematics. Retrieved from
Duschl, R. A., & Gitomer, D. H. (1997). Strategies and challenges to changing the focus of assessment and instruction in science classrooms. Educational Assessment, 4(1), 37-73.
Edwards, D., & Mercer, N. (1987). Common knowledge: the development of understanding in the classroom. New York, NY, US: Methuen.
English, L. D., & Halford, G. S. (1995). Mathematics Education: Models and Processes. Hillsdale, NJ: Lawrence Erlbaum.
Fazio, L., & Siegler, R. (2011). Teaching Fractions. Educational Practices Series-22. UNESCO International Bureau of Education. Retrieved from
Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning to elicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60(4), 380-392.
Furtak, E. M., & Ruiz‐Primo, M. A. (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.
Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81-112.
Isiksal, M., & Cakiroglu, E. (2011). The nature of prospective mathematics teachers’ pedagogical content knowledge: The case of multiplication of fractions. Journal of Mathematics Teacher Education, 14, 213-230.
Izsák, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26(1), 95-143.
Jiang, Y. (2014). Exploring Teacher Questioning as a Formative Assessment Strategy. RELC Journal, 45(3), 287-304.
Kawanaka, T., & Stigler, J. W. (1999). Teachers’ use of questions in eighth-grade mathematics classrooms in Germany, Japan, and the United States. Mathematical Thinking and Learning, 1(4), 255-278.
Kreide, A. N. I. T. A., Turner, C. E., & Tomlinson, A. (2015). Pre-service teachers development of questioning skills through common core aligned exemplar videotaped math lessons. In Hawaii University International Conferences, June (pp. 13-15).
Kyriacou, C. and Issitt, J. (2007) Teacher-pupil dialogue in mathematics lessons. In Küchemann, D. (ed) Proceedings of the British Society for Research into Learning Mathematics (BSRLM) Day Conference held at the University of Northampton, 17 November 2007 (pp. 61-65). London: BSRLM.
Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629-667). Charlotte, NC: Information Age.
Li, N., Cao, Y., & Mok, I, A, C. (2016). A framework for teacher verbal feedback: Lessons from chinese mathematics classrooms. Eurasia Journal of Mathematics, Science & Technology Education, 12(9), 2465-2480.
Mehan, H. (1979). Learning lessons. Cambridge, MA: Harvard University Press.
Mortimer, E. F., & Scott, P. H. (2003). Meaning making in secondary science classrooms. Maidenhead: Open University Press.
Moyer, P. S. & Milewicz, E. (2002). Learning to question: Categories of questioning used by preservice teachers during diagnostic mathematics interviews. Journal of Mathematics Teacher Education, 5, 293-315.
Myhill, D., & Dunkin, F. (2005). Questioning learning. Language and Education, 19(5), 415-427.
National Council of Teachers of Mathematics (NCTM). 2014. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: NCTM.
Newton, K. J. (2008). An extensive analysis of preservice elementary teachers’ knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110.
Ni, Y., & Zhou, Y. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27-52.
Ong, E. G., Lim, C. S., & Ghazali, M. (2010). Examining the changes in novice and experienced mathematics teachers’ questioning techniques through the lesson study process. Journal of Science and Mathematics Education in Southeast Asia, 33(1), 86-109.
Ruiz-Primo, M. A. (2011). Informal formative assessment: The role of instructional dialogues in assessing students’ learning. Studies in Educational Evaluation, 37(1), 15-24.
Sadler, D. R. (1989). Formative assessment and the design of instructional systems. Instructional science, 18(2), 119-144.
Sahin, A., & Kulm, G. (2008). Sixth grade mathematics teachers’ intentions and use of probing, guiding, and factual questions. Journal of mathematics teacher education, 11(3), 221-241.
Scott, P., & Mortimer, E. (2005). Meaning making in high school science classrooms: A framework for analysing meaning making interactions. In Research and the quality of science education (pp. 395-406). Springer, Dordrecht.
Sezen-Barrie, A., & Kelly, G. J. (2017). From the teacher’s eyes: facilitating teachers noticings on informal formative assessments (IFAs) and exploring the challenges to effective implementation. International Journal of Science Education, 39(2), 181-212.
Shute, V. J. (2008). Focus on Formative Feedback. Review of Educational Research, 78(1), 153-189.
Sinclair, J., & Coulthard, M. (1975). Towards an analysis of discourse. London, UK: Oxford University Press.
Sleep, L., & Boerst, T. A. (2012). Preparing beginning teachers to elicit and interpret students’ mathematical thinking. Teaching and Teacher Education, 28(7), 1038-1048.
Stafylidou, S. & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503-518.
Taie, S., Goldring, R., & Spiegelman, M. (2017). Characteristics of Public Elementary and Secondary School Teachers in the United States: Results from the 2015–16 National Teacher and Principal Survey First Look (NCES 2017-072). U.S. Department of Education. Washington, DC: National Center for Education Statistics. Retrieved from
Texas Education Agency. (2013). Introduction to the Revised Mathematics TEKS: Vertical Alignment Chart Kindergarten - Grade 6. Austin, TX: Texas Education Agency Retrieved from
Van Steenbrugge, H., Valcke, M., & Desoete, A. (2010). Mathematics learning difficulties in primary education: Teachers’ professional knowledge and the use of commercially available learning packages. Educational Studies, 36(1), 59-71.
Van Zee, E., & Minstrell, J. (1997). Using questioning to guide student thinking. The Journal of the Learning Sciences, 6(2), 227-269.
Weiland, I. S., Hudson, R. A., & Amador, J. M. (2013). Preservice formative assessment interview: The development of competent questioning. International Journal of Science and Mathematics Education 12(2), 329-352.
Wilen, W. W. (1991). Questioning skills, for teachers. What research says to the teachers. Washington, DC: National Education Association.
Zhou, Z., Peverly, S. T., & Xin, T. (2006). Knowing and teaching fractions: A cross-cultural study of American and Chinese mathematics teachers. Contemporary educational psychology, 31(4), 438-457.
Journals System - logo
Scroll to top