Preservice teachers studying video narratives of student argumentation
DOI:
https://doi.org/10.30862/jhm.v6i2.443Keywords:
children’s argumentation, fraction comparisons, preservice teachers, reasoning, video narrativesAbstract
National Standards in the teaching of mathematics call for teachers to pay attention to the nature of student problem solving and argumentation in learning mathematics. In order to attend to student argumentation, resources are needed in which student argumentation can be observed. This paper reports the result of a preservice-teacher intervention study in which teachers described student argumentation in a video narrative before and after instruction, which included video narratives designed to highlight argumentation. Pre- and post-assessment of teachers’ identification of student argumentation used a mixed-methods analysis to investigate growth in noticing more of children’s argumentation across a video narrative that was created with 15 video clips that displayed student argumentation in the classroom. Results showed that growth occurred in cycles that described shorter argumentation stories within the longer narrative. On average, over 85% of the teachers consistently exhibited growth at the end of a cycle of 3 to 6 video clips that provided a complete story of several children’s argumentation, in contrast to growth on specific clips that showed a particular child’s argument. Results suggest the enhanced value of using video episodes that reveal complete stories of student argumentation in a classroom for teacher intervention.References
Agnew, G., Mills, C. M., & Maher, C. A. (2010). VMC analytic: Developing a collaborative video analysis tool for education faculty and practicing educators. In Proceedings of the Annual Hawaii International Conference on System Sciences. https://doi.org/10.1109/HICSS.2010.438
Akkus, M. (2016). The common core state standards for mathematics. International Journal of Research in Education and Science, 2(1), 49–54. https://doi.org/10.21890/ijres.61754
Ball, D. L., Hoyles, C., Jahnke, H. N., & Movshovitz-Hadar, N. (2002). The teaching of proof. In L. I. Tatsien (Ed.), In Proceedings of the International Congress of Mathematicians. Retrieved from https://doi.org/10.1007/978-3-031-04313-0_8
Berenson, S. B. (2012). Improving Teacher Practice with Action Learning. Teachers’ Life-cycle from Initial Teacher Education to Experienced Professional, 112.
Bieda, K. N. (2010). Enacting proof-related tasks in middle school mathematics: Challenges and opportunities. Journal for Research in Mathematics Education, 41(4), 351–382. https://doi.org/10.5951/jresematheduc.41.4.0351
Bieda, K. N., & Lepak, J. (2014). Are You Convinced? Middle-Grade Students' Evaluations of Mathematical Arguments. School Science and Mathematics, 114(4), 166-177. https://doi.org/10.5951/mathteacmiddscho.20.4.0212
Brunvand, S., & Fishman, B. (2006). Investigating the impact of the availability of scaffolds on preservice teacher noticing and learning from video. Journal of Educational Technology Systems, 35(2), 151-174. https://doi.org/10.2190/l353-x356-72w7-42l9
Conner, A., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014a). Identifying Kinds of Reasoning in Collective Argumentation. Mathematical Thinking and Learning, 16(3), 181-200. https://doi.org/10.1080/10986065.2014.921131
Conner, A., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014b). Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities. Educational Studies in Mathematics, 86(3), 401-429. https://doi.org/10.1007/s10649-014-9532-8
Derry, S. J. (2007). Guidelines for video research in education: Recommendations from an expert panel. Chicago: Data Research and Development Center, University of Chicago. Retrieved from http://drdc.uchicago.edu/what/video-research-guidelines.pdf
Gomoll, A. S., Sigley, R., Winter, E., Hmelo-Silver, C., & Maher, C. (2015). Constructing multimedia artifacts with pre-service and in-service teachers: Problem solving in a heterogeneous technology learning environment. In CEUR Workshop Proceedings. Retrieved from https://ceur-ws.org/Vol-1411/paper-08.pdf
Hmelo-Silver, C. E., Maher, C. A., Agnew, G., Palius, M., & Derry, S. J. (2010). The video mosaic: design and preliminary research. In Proceedings of the 9th International Conference of the Learning Sciences, 2, 425-426. Retrieved from https://repository.isls.org/bitstream/1/2888/1/425-426.pdf
Hmelo-Silver, C. E., Maher, C. A., Alston, A., Palius, M. F., Agnew, G., Sigley, R., & Mills, C. (2013). Building multimedia artifacts using a cyber-enabled video repository: The VMCAnalytic. In 2013 46th Hawaii International Conference on System Sciences, 3078-3087. IEEE. https://doi.org/10.1109/hicss.2013.122
Hmelo-Silver, C. E., Maher, C. A., Palius, M. F., Sigley, R., & Alston, A. (2014). Showing what they know: Multimedia artifacts to assess learner understanding. In Proceedings of International Conference of the Learning Sciences,1, 410–417. Retrieved from https://repository.isls.org/bitstream/1/1143/1/410-417.pdf
Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education, 169-202. https://doi.org/10.5951/jresematheduc.41.2.0169
Krummheuer, G. (1995). The ethnography of argumentation. In Cobb, Paul, Bauersfeld, Heinrich (Eds). (1995). The emergence of mathematical meaning: Interaction in classroom cultures. Studies in mathematical thinking and learning series., (pp. 229-269). Hillsdale, NJ, England: Lawrence Erlbaum Associates, Inc, xi. ( https://doi.org/10.4324/9780203053140-11 )
Krummheuer, G. (2007). Argumentation and participation in the primary mathematics classroom: Two episodes and related theoretical abductions. The Journal of Mathematical Behavior, 26(1), 60-82. https://doi.org/10.1016/j.jmathb.2007.02.001
Maher, C. A. (2010). Children's reasoning: Discovering the idea of mathematical proof. In Teaching and learning proof across the grades (pp. 120-132). Routledge. https://doi.org/10.4324/9780203882009-7
Maher, C. A. (2011). Supporting the development of mathematical thinking through problem solving and reasoning. In Proceedings of 35th Conference of the International Group for the Psychology of Mathematics Education, 1, 85-90.
Maher, C. A., & Sigley, R. (2014). Task-based interviews in mathematics education. In Encyclopedia of Mathematics Education (pp. 579-582). Springer Netherlands. https://doi.org/10.1007/978-94-007-4978-8_147
Maher, C. A., & Yankelewitz, D. (2017). Children’s reasoning while building fraction ideas. Springer. https://doi.org/10.1007/978-94-6351-008-0
Maher, C. A., Landis, J., & Palius, M. F. (2010). Teachers attending to student reasoning: Using videos as tools. Journal of Mathematics Education, 3(2), 1–24.
Maher, C. A., Palius, M. F., & Mueller, M. (2010). Challenging beliefs about children’s mathematics learning through video study. In Proceedings of the 32nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 4, 885-992.
Maher, C. A., Palius, M. F., Maher, J. A., Hmelo-Silver, C. E., & Sigley, R. (2014). Teachers Can Learn to Attend to Students’ Reasoning Using Videos as a Tool. Issues in Teacher Education, 23(1), 31-47. Retrivied from https://www.itejournal.org/wp-content/pdfs-issues/spring-2014/07maheretal.pdf
Maher, C., & Martino, A. (1996). The development of the idea of mathematical proof: A 5-year case study. Journal of Research in Mathematics Education, 27 (2), 194-214. https://doi.org/10.5951/jresematheduc.27.2.0194
Martinez, M. V., Castro Superfine, A., Carlton, T., & Dasgupta, C. (2015). Examining the Impact of a Videocase-based Mathematics Methods Course on Secondary Preservice Teachers’ Skills at Analyzing Students’ Strategies. Journal of Research in Mathematics Education, 4(1), 52–79. https://doi.org/10.4471/redimat.2015.59
National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM.
National Council of Teachers of Mathematics (NCTM). (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NTCM.
Otto, J. J., & Ralston, S. L. (2012). Disseminating equine research and teaching videos through the institutional repository: A collaboration. Journal of Agricultural & Food Information, 13(1), 64-77. https://doi.org/10.1080/10496505.2012.638247
Palius, M. F., & Maher, C. A. (2011). Teacher education models for promoting mathematical thinking. In Proceedings of 35th Conference of the International Group for the Psychology of Mathematics Education, 1, 321-328.
Palius, M. F., & Maher, C. A. (2013). Teachers learning about student reasoning through video study. Mediterranean Journal for Research in Mathematics Education, 12(1-2), 39-55. Retrieved from https://www.cymsjournal.com/
Pedemonte, B. (2007). How can the relationship between argumentation and proof be analysed. Educational Studies in Mathematics, 66(1), 23-41. https://doi.org/10.1007/s10649-006-9057-x
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
Schwarz, B. B. (2009). Argumentation and learning. Argumentation and education: Theoretical foundations and practices, 91-126. https://doi.org/10.1007/978-0-387-98125-3_4
Sherin, M. G., & Van Es, E.A. (2005). Using video to support teachers’ ability to notice classroom interactions. Journal of Technology and Teacher Education, 13(3), 475–491. Retrieved from file:///Users/maryloutardif/Dropbox/Articles_Textes/Mendeley/2005/Journal
Sigley, R., & Wilkinson, L. C. (2015). Ariel's cycles of problem solving: An adolescent acquires the mathematics register. The Journal of Mathematical Behavior, 40, 75- 87. https://doi.org/10.1016/j.jmathb.2015.03.001
Sriraman, B., & Umland, K. (2020). Argumentation in mathematics education. Encyclopedia of Mathematics Education, 63-66. https://doi.org/10.1007/978-3-030-15789-0_11
Star, J. R., & Strickland, S. K. (2008). Learning to observe: Using video to improve preservice mathematics teachers’ ability to notice. Journal of Mathematics Teacher Education, 11(2), 107-125. https://doi.org/10.1007/s10857-007-9063-7
Tall, D., Yevdokimov, O., Koichu, B., Whiteley, W., Kondratieva, M., & Cheng, Y. H. (2012). Cognitive development of proof. In Proof and proving in mathematics education (pp. 13-49). Springer, Dordrecht.Thompson, D. R. (1996). Learning and Teaching Indirect Proof. Mathematics Teacher, 89(6), 474-82. https://doi.org/10.1007/978-94-007-2129-6_2
Toulmin, S. (1958). The uses of argument. United Kingdom: Cambridge University Press. https://doi.org/10.1017/s0008197300003937
Toulmin, S. E. (2003). The uses of argument. Cambridge University Press. https://doi.org/10.1017/cbo9780511840005 Pedemonte, B. (2007). How can the relationship between argumentation and proof be analysed. Educational Studies in Mathematics, 66(1), 23-41. https://doi.org/10.1007/s10649-006-9057-x
Towers, J. (2007). Using video in teacher education. Canadian Journal of Learning and Technology/La revue canadienne de l’apprentissage et de la technologie, 33(2). https://doi.org/10.21432/t2dg6t
Van Es, E. A., & Sherin, M. G. (2002). Learning to Notice : Scaffolding New Teachers ’ Interpretations of Classroom Interactions. Journal of Technology and Teacher Education, 10, 571–596.
Van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers’ “learning to notice” in the context of a video club. Teaching and teacher education, 24(2), 244-276. https://doi.org/10.1016/j.tate.2006.11.005
Van Ness, C. K. (2015a) Eighth Grader Stephanie’s Argumentation about Meaning for the Square of a Binomial using Algebraic Reasoning. [video]. Retrieved from http://dx.doi.org/doi:10.7282/T3FN180C
Van Ness, C. K. (2015b) Eighth Grader Stephanie’s Argumentation about Meaning for the Square of a Binomial using Geometric Reasoning. [video]. Retrieved from http://dx.doi:10.7282/T3QZ2CRF
Van Ness, C. K. (2015c). Fourth graders’ argumentation about the density of fractions between 0 and 1. [video]. Retrieved from http://dx.doi.org/doi:10.7282/T39K4CZC
Van Ness, C. K. (2016). Creating and Using Video Narratives for Secondary Preservice Teachers' Studying of Argumentation. In R. Huang and M. Strutchens (Co-chairs), Preservice mathematics education of secondary teachers. Topic Study Group 48 conducted at the 13th International Congress on Mathematical Education, Hamburg, Germany. https://doi.org/10.1007/978-3-319-62597-3_75
Van Ness, C. K. (2017). Creating and using VMCAnalytics for Preservice Teachers’ Studying of Argumentation. [Unpublished doctoral dissertation]. Rutgers The State University of New Jersey, School of Graduate Studies. Retrieved from https://rucore.libraries.rutgers.edu/rutgers-lib/52283/PDF/1/
Van Ness, C. K., & Alston, A. S. (2017). Justifying the Choice of the Unit. In C. A. Maher & D. Yankelewitz (Eds.). Children’s Reasoning While Building Fraction Ideas (pp. 83-94). Rotterdam, The Netherlands: Sense Publishers. https://doi.org/10.1007/978-94-6351-008-0_9
Van Ness, C. K., & Maher, C. A. (2019). Analysis of the argumentation of nine-year-olds engaged in discourse about comparing fraction models. The Journal of Mathematical Behavior, 53, 13-41. https://doi.org/10.1016/j.jmathb.2018.04.004
Wagner, P. A., Smith, R. C., Conner, A., Singletary, L. M., & Francisco, R. T. (2014). Using Toulmin's Model to Develop Prospective Secondary Mathematics Teachers' Conceptions of Collective Argumentation. Mathematics Teacher Educator, 3(1), 8-26. https://doi.org/10.5951/mathteaceduc.3.1.0008
Weber, K., Maher, C., Powell, A., & Lee, H. S. (2008). Learning opportunities from group discussions: Warrants become the objects of debate. Educational Studies in Mathematics, 68(3), 247-261. https://doi.org/10.1007/s10649-008-9114-8
Whitenack, J., & Yackel, E. (2002). Making mathematical arguments in the primary grades: The importance of explaining and justifying ideas. Teaching Children Mathematics, 8(9), 524. https://doi.org/10.5951/tcm.8.9.0524
Wilson, M. C., & Jantz, R. C. (2011). Building value-added services for institutional repositories (IRs): Modeling the Rutgers experience. Social Science Libraries: A Bridge to Knowledge for Sustainable Development, 0–18. Retrieved from http://hdl.handle.net/2142/25875
Yackel, E. (2002). What we can learn from analyzing the teacher’s role in collective argumentation. The Journal of Mathematical Behavior, 21(4), 423-440. https://doi.org/10.1016/s0732-3123(02)00143-8
Yankelewitz, D. (2009). The Development of Mathematical Reasoning in Elementary Schools’ Exploration of Fraction Ideas. [Unpublished doctoral dissertation]. Rutgers The State University of New Jersey, School of Graduate Studies. Retrieved from https://rucore.libraries.rutgers.edu/rutgers-lib/28410/PDF/1/play/
Zack, V. (1997). “You have to prove us wrong”: proof at the elementary school level. 21st Conference of the International Group for the Psychology of Mathematics Education, 4(1982), 291–298.
Downloads
Published
How to Cite
Issue
Section
License
License and Copyright Agreement
In submitting the manuscript to the journal, the authors certify that:
- They are authorized by their co-authors to enter into these arrangements.
- The work described has not been formally published before, except in the form of an abstract or as part of a published lecture, review, thesis, or overlay journal. Please also carefully read Journal of Honai Math Posting Your Article Policy at http://journalfkipunipa.org/index.php/jhm/about
- That it is not under consideration for publication elsewhere,
- That its publication has been approved by all the author(s) and by the responsible authorities – tacitly or explicitly – of the institutes where the work has been carried out.
- They secure the right to reproduce any material that has already been published or copyrighted elsewhere.
- They agree to the following license and copyright agreement.
Copyright
Authors who publish with Journal of Honai Math agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY-NC-SA 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
