Informal Formative Assessment Conversations in Mathematics: Focusing on Preservice Teachers’ Initiation, Response and Follow-up Sequences in the Classroom

Mihwa Park; Minju Yi; Raymond Flores; Bangtam Nguyen

doi:10.29333/ejmste/8436

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Mihwa Park ¹ ^* , Minju Yi ¹, Raymond Flores ¹, Bangtam Nguyen ¹

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¹ College of Education, Texas Tech University, USA^* Corresponding Author

Abstract

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.

Keywords

assessment conversation
informal formative assessment
mathematics
preservice teacher education

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 16, Issue 10, October 2020, Article No: em1884

https://doi.org/10.29333/ejmste/8436

Publication date: 30 Jul 2020

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Article Downloads: 2597

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References

Association of Mathematics Teacher Educators. (2017). Standards for Preparing Teachers of Mathematics. Retrieved from www.amte.net/standards
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. https://doi.org/10.1177/003172170408600105
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. https://doi.org/10.1007/s10763-005-9006-7
Chin, C. (2006). Classroom Interaction in Science: Teacher questioning and feedback to students’ responses. International Journal of Science Education, 28(11), 1315-1346. https://doi.org/10.1080/09500690600621100
Chin, C. (2007). Teacher questioning in science classrooms: approaches that stimulate productive thinking. Journal of Research in Science Teaching, 44(6), 815-843. https://doi.org/10.1002/tea.20171
Cobb, P., Boufi, A., McClain, K., & Whitenack, J. (1997). Reflective discourse and collective reflection. Journal for research in mathematics education, 18(3), 258-277. https://doi.org/10.2307/749781
Council of Chief State School Officers & National Governors Association. (2010). Common core state standards-mathematics. Retrieved from http://www.corestandards.org/Math
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. https://doi.org/10.1207/s15326977ea0401_2
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. https://doi.org/10.4324/9780203052884
Fazio, L., & Siegler, R. (2011). Teaching Fractions. Educational Practices Series-22. UNESCO International Bureau of Education. Retrieved from http://www.ibe.unesco.org/fileadmin/user_upload/Publications/Educational_Practices/EdPractices_22.pdf
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. https://doi.org/10.1177/0022487109339906
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. https://doi.org/10.1002/tea.20163
Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81-112. https://doi.org/10.3102/003465430298487
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. https://doi.org/10.1007/s10857-010-9160-x
Izsák, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26(1), 95-143. https://doi.org/10.1080/07370000701798529
Jiang, Y. (2014). Exploring Teacher Questioning as a Formative Assessment Strategy. RELC Journal, 45(3), 287-304. https://doi.org/10.1177/0033688214546962
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. https://doi.org/10.1207/s15327833mtl0104_1
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. https://doi.org/10.12973/eurasia.2016.1298a
Mehan, H. (1979). Learning lessons. Cambridge, MA: Harvard University Press. https://doi.org/10.4159/harvard.9780674420106
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. https://doi.org/10.1023/A:1021251912775
Myhill, D., & Dunkin, F. (2005). Questioning learning. Language and Education, 19(5), 415-427. https://doi.org/10.1080/09500780508668694
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. https://doi.org/10.3102/0002831208320851
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. https://doi.org/10.1207/s15326985ep4001_3
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. https://doi.org/10.1016/j.stueduc.2011.04.003
Sadler, D. R. (1989). Formative assessment and the design of instructional systems. Instructional science, 18(2), 119-144. https://doi.org/10.1007/BF00117714
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. https://doi.org/10.1007/s10857-008-9071-2
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. https://doi.org/10.1007/1-4020-3673-6_31
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. https://doi.org/10.1080/09500693.2016.1274921
Shute, V. J. (2008). Focus on Formative Feedback. Review of Educational Research, 78(1), 153-189. https://doi.org/10.3102/0034654307313795
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. https://doi.org/10.1016/j.tate.2012.04.005
Stafylidou, S. & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503-518. https://doi.org/10.1016/j.learninstruc.2004.06.015
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 https://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2017072
Texas Education Agency. (2013). Introduction to the Revised Mathematics TEKS: Vertical Alignment Chart Kindergarten - Grade 6. Austin, TX: Texas Education Agency Retrieved from http://jukebox.esc13.net/PSgateway/vertical_alignment/docs/GatewayK6VAChart.pdf
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. https://doi.org/10.1080/03055690903148639
Van Zee, E., & Minstrell, J. (1997). Using questioning to guide student thinking. The Journal of the Learning Sciences, 6(2), 227-269. https://doi.org/10.1207/s15327809jls0602_3
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. https://doi.org/10.1007/s10763-013-9402-3
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. https://doi.org/10.1016/j.cedpsych.2006.02.001

How to cite this article

APA

Park, M., Yi, M., Flores, R., & Nguyen, B. (2020). Informal Formative Assessment Conversations in Mathematics: Focusing on Preservice Teachers’ Initiation, Response and Follow-up Sequences in the Classroom. Eurasia Journal of Mathematics, Science and Technology Education, 16(10), em1884. https://doi.org/10.29333/ejmste/8436

Vancouver

Park M, Yi M, Flores R, Nguyen B. Informal Formative Assessment Conversations in Mathematics: Focusing on Preservice Teachers’ Initiation, Response and Follow-up Sequences in the Classroom. EURASIA J Math Sci Tech Ed. 2020;16(10):em1884. https://doi.org/10.29333/ejmste/8436

AMA

Park M, Yi M, Flores R, Nguyen B. Informal Formative Assessment Conversations in Mathematics: Focusing on Preservice Teachers’ Initiation, Response and Follow-up Sequences in the Classroom. EURASIA J Math Sci Tech Ed. 2020;16(10), em1884. https://doi.org/10.29333/ejmste/8436

Chicago

Park, Mihwa, Minju Yi, Raymond Flores, and Bangtam Nguyen. "Informal Formative Assessment Conversations in Mathematics: Focusing on Preservice Teachers’ Initiation, Response and Follow-up Sequences in the Classroom". Eurasia Journal of Mathematics, Science and Technology Education 2020 16 no. 10 (2020): em1884. https://doi.org/10.29333/ejmste/8436

Harvard

Park, M., Yi, M., Flores, R., and Nguyen, B. (2020). Informal Formative Assessment Conversations in Mathematics: Focusing on Preservice Teachers’ Initiation, Response and Follow-up Sequences in the Classroom. Eurasia Journal of Mathematics, Science and Technology Education, 16(10), em1884. https://doi.org/10.29333/ejmste/8436

MLA

Park, Mihwa et al. "Informal Formative Assessment Conversations in Mathematics: Focusing on Preservice Teachers’ Initiation, Response and Follow-up Sequences in the Classroom". Eurasia Journal of Mathematics, Science and Technology Education, vol. 16, no. 10, 2020, em1884. https://doi.org/10.29333/ejmste/8436