A framework for understanding how preservice teachers notice students’ statistical reasoning about comparing groups

References

• Ben-Zvi, D. (2004). Reasoning about variability in comparing distributions. Statistics Education Research Journal, 3(2), 42–63.
   Google Scholar
• Ben-Zvi, D., & Garfield, J. (2004). Statistical literacy, reasoning, and thinking: Goals, definitions and challenges. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning, and thinking (pp. 79–95). Dordrecht: Kluwer.
   Google Scholar
• Ben-Zvi, D., & Garfield, J. (2008). Introducing the emerging discipline of statistics education. School Science and Mathematics, 108(8), 355–361. doi: 10.1111/j.1949-8594.2008.tb17850.x
   Google Scholar
• Biehler, R., Frischemeier, D., Reading, C., & Shaughnessy, J. M. (2018). Reasoning about data. In D. Ben-Zvi, J. Garfield, & K. Makar (Eds.), International handbook of research in statistics education (pp. 139–192). New York, NY: Springer.
   Google Scholar
• Callejo, M. L., & Zapatera, A. (2017). Prospective primary teachers’ noticing of students’ understanding of pattern generalization. Journal of Mathematics Teacher Education, 20(4), 309–333. doi: 10.1007/s10857-016-9343-1
   Web of Science ®Google Scholar
• Common Core State Standards Initiative. (2010). Common core state standards for mathematics. Retrieved from http://corestandards.org/asserts/CCSSI_Math%20Standards.pdf
   Google Scholar
• Corbin, J., & Strauss, A. (2015). Basics of qualitative research: Techniques and procedures for developing grounded theory (4th Ed.). Thousand Oaks, CA: Sage.
   Google Scholar
• Diamond, J. M., Kalinec-Craig, C. A., & Shih, J. C. (2018). The problem of Sunny’s pennies: A multi-institutional study about the development of elementary preservice teachers’ professional noticing. Mathematics Teacher Education & Development, 20(2), 114–132.
   Google Scholar
• Ding, L., & Domínguez, H. (2016). Opportunities to notice: Chinese prospective teachers noticing students’ ideas in a distance formula lesson. Journal of Mathematics Teacher Education, 19(4), 325–347. doi: 10.1007/s10857-015-9301-3
   Web of Science ®Google Scholar
• Fernández, C., Llinares, S., & Valls, J. (2012). Learning to notice students’ mathematical thinking through on-line discussions. ZDM, 44(6), 747–759. doi: 10.1007/s11858-012-0425-y
   Google Scholar
• Franklin, C., Bargagliotto, A., Case, C., Kader, G., Scheaffer, R., & Spangler, D. (2015). The statistical education of teachers. Alexandria, VA: American Statistical Association. Retrieved from http://www.amstat.org/education/SET/SET.pdf
   Google Scholar
• Garfield, J., & Ben-Zvi, D. (2009). Helping students develop statistical reasoning: Implementing a statistical reasoning learning environment. Teaching Statistics, 31(3), 72–77. doi: 10.1111/j.1467-9639.2009.00363.x
   Google Scholar
• Huang, R., & Li, Y. (2009). Pursuing excellence in mathematics classroom instruction through exemplary lesson development in China: A case study. ZDM, 41(3), 297–309. doi: 10.1007/s11858-008-0165-1
   Google Scholar
• Jacobs, J. K., Yoshida, M., Stigler, J. W., & Fernandez, C. (1997). Japanese and American teachers’ evaluations of mathematics lessons: A new technique for exploring beliefs. The Journal of Mathematical Behavior, 16(1), 7–24. doi: 10.1016/S0732-3123(97)90004-3
   Google Scholar
• Jacobs, V. R., & Ambrose, R. C. (2008). Making the most of story problems. Teaching Children Mathematics, 15(5), 260–266.
   Google Scholar
• Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202.
   Web of Science ®Google Scholar
• Konold, C. (2011). TinkerPlots^TM: Dynamic data exploration. Emeryville, CA: Key Curriculum Press.
   Google Scholar
• Konold, C., Pollatsek, A., Well, A., & Gagnon, A. (1997). Students analyzing data: Research of critical barriers. In J. B. Garfield & G. Burrill (Eds.), Research on the role of technology in teaching and learning statistics (pp. 151–167). Voorburg: International Statistical Institute.
   Google Scholar
• Lee, H. S., Hollebrands, K. F., & Wilson, P. H. (2015). Preparing to teach mathematics with technology: An integrated approach to data analysis and probability (3rd Ed.). Raleigh, NC: North Carolina State University. Retrieved from https://ptmt.fi.ncsu.edu
   Google Scholar
• Makar, K., & Confrey, J. (2002). Comparing two distributions: Investigating secondary teachers’ statistical thinking. In B. Phillips (Ed.), Proceedings of the 6th International Conference on teaching statistics: Developing a statistically literate society. Cape Town: International Statistical Institute.
   Google Scholar
• Makar, K., & Confrey, J. (2004). Secondary teachers’ reasoning about comparing two groups. In D. Ben-Zvi & J. Garfield (Eds.), The challenges of developing statistical literacy, reasoning, and thinking (pp. 353–373). Dordrecht: Kluwer Academic Publishers.
   Google Scholar
• Males, L. M. (2017). Using video of Peer teaching to examine grades 6–12 preservice teachers’ noticing. In E. O. Schack, M. H. Fisher, & J. A. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 91–109). New York, NY: Springer International Publishing.
   Google Scholar
• Mason, J. (2002). Researching your own practice: The discipline of noticing. London: Routledge-Falmer.
   Google Scholar
• Miller, K. (2011). Situating awareness in teaching. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 51–65). New York, NY: Routledge.
   Google Scholar
• Miller, K., & Zhou, X. (2007). Learning from classroom video: What makes it compelling and what makes it hard. In R. Goldman, R. Pea, B. Barron, & S. J. Deny (Eds.), Video research in the learning sciences (pp. 321–334). Mahwah, NJ: Erlbaum.
   Google Scholar
• Mitchell, R. N., & Marin, K. A. (2015). Examining the use of a structured analysis framework to support prospective teacher noticing. Journal of Mathematics Teacher Education, 18(6), 551–575. doi: 10.1007/s10857-014-9294-3
   Web of Science ®Google Scholar
• National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematics success for all. Reston, VA: Author.
   Google Scholar
• Noll, J., & Shaughnessy, J. M. (2012). Aspects of students’ reasoning about variation in empirical sampling distributions. Journal for Research in Mathematics Education, 43(5), 509–556. doi: 10.5951/jresematheduc.43.5.0509
   Web of Science ®Google Scholar
• Reaburn, R. (2012). Strategies used by students to compare two data sets. In J. Dindyal, L. P. Cheng, & S. F. Ng (Eds.), Proceedings of the 35th annual conference of the mathematics education research group of Australasia (pp. 633–639). Singapore: MERGA.
   Google Scholar
• Santagata, R., Zannoni, C., & Stigler, J. W. (2007). The role of lesson analysis in pre-service teacher education: An empirical investigation of teacher learning from a virtual video-based field experience. Journal of Mathematics Teacher Education, 10(2), 123–140. doi: 10.1007/s10857-007-9029-9
   Google Scholar
• Sánchez-Matamoros, G., Fernández, C., & Llinares, S. (2015). Developing pre-service teachers’ noticing of students’ understanding of the derivative concept. International Journal of Science and Mathematics Education, 13(6), 1305–1329. doi: 10.1007/s10763-014-9544-y
   Web of Science ®Google Scholar
• Schack, E. O., Fisher, M. H., Thomas, J. N., Eisenhardt, S., Tassell, J., & Yoder, M. (2013). Prospective elementary school teachers’ professional noticing of children’s early numeracy. Journal of Mathematics Teacher Education, 16(5), 379–397. doi: 10.1007/s10857-013-9240-9
   Google Scholar
• Sherin, M. G., & van Es, E. A. (2009). Effects of video club participation on teachers’ professional vision. Journal of Teacher Education, 60(1), 20–37. doi: 10.1177/0022487108328155
   Web of Science ®Google Scholar
• 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. doi: 10.1007/s10857-007-9063-7
   Google Scholar
• van den Bogert, N., van Bruggen, J., Kostons, D., & Jochems, W. (2014). First steps into understanding teachers’ visual perception of classroom events. Teaching and Teacher Education, 37, 208–216. doi: 10.1016/j.tate.2013.09.001
   Web of Science ®Google Scholar
• van den Kieboom, L. A., Magiera, M. T., & Moyer, J. C. (2017). Learning to notice student thinking about the equal sign: K-8 preservice teachers’ experiences in a teacher preparation program. In E. O. Schack, M. H. Fisher, & J. A. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 141–159). New York, NY: Springer International Publishing.
   Google Scholar
• van Es, E. A. (2011). A framework for learning to notice student thinking. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 134–151). New York, NY: Routledge.
   Google Scholar
• Walkoe, J. (2015). Exploring teacher noticing of student algebraic thinking in a video club. Journal of Mathematics Teacher Education, 18(6), 523–550. doi: 10.1007/s10857-014-9289-0
   Web of Science ®Google Scholar
• Watson, J. M., & Moritz, J. B. (1998). The beginning of statistical inference: Comparing two data sets. Educational Studies in Mathematics, 37(2), 145–168. doi: 10.1023/A:1003594832397
   Google Scholar
• Wilson, P. H., Lee, H. S., & Hollebrands, K. F. (2011). Understanding prospective mathematics teachers’ processes for making sense of students’ work with technology. Journal for Research in Mathematics Education, 42(1), 39–64. doi: 10.5951/jresematheduc.42.1.0039
   Web of Science ®Google Scholar