Abstract
Prospective elementary school teachers (PTs), at the completion of their mathematics content course, often feel that (1) they did not learn anything new in the course, (2) they “knew it all along,” and (3) they just needed a refresher. Thus, PTs often undervalue both their own learning in the mathematics content course and the complexity of the elementary mathematics content they learned. In this study, I replicate prior work in which I found that conducting a videotaped interview with PTs at the beginning of the course can help them recognize, before taking the course, that they have mathematics content to learn. I also extend that work by having PTs view their videotaped interviews at the end of the course. I argue that reviewing of the interview and thus remembering what they did not know before the course can help PTs recognize, after they have taken the course, that they have learned content. This remembering led the PTs not only to appreciate the content they learned but also to be aware of the complexity of elementary mathematics, an essential aspect of Mathematical Knowledge for Teaching.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Adler, J., & Davis, Z. (2006). Opening another black box: Researching mathematics for teaching in mathematics teacher education. Journal for Research in Mathematics Education, 37(4), 270–296.
Ball, D. (1988). Knowledge and reasoning in mathematical pedagogy: Examining what prospective teachers bring to teacher education. Doctoral dissertation (50 doctoral dissertation), Michigan State University, Ann Arbor.
Ball, D., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on mathematics teaching and learning (pp. 83–104). Westport, CT: Greenwood.
Ball, D., Charalambous, C., Thames, M., & Lewis, J. (2009). Teacher knowledge and teaching: Viewing a complex relationship from three perspectives. Paper presented at the Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education.
Ball, D., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.
Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.). (1999). How people learn. Washington, DC: National Academy Press.
Bransford, J. D., & Schwartz, D. L. (1999). Rethinking transfer: A simple proposal with multiple implications. Review of Research in Education, 24, 61–100.
Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101.
Bukszar, E., & Connolly, T. (1988). Hindsight bias and strategic choice: Some problems in learning from experience. Academy of Management Journal, 31(3), 628–641.
Chapman, O. (2007). Facilitating preservice teachers’ development of mathematics knowledge for teaching arithmetic operations. Journal of Mathematics Teacher Education, 10, 341–349.
Chi, M. T., Slotta, J. D., & De Leeuw, N. (1994). From things to processes: A theory of conceptual change for learning science concepts. Learning and Instruction, 4(1), 27–43.
Crespo, S., & Nicol, C. (2006). Challenging preservice teachers’ mathematical understanding: The case of division by zero. School Science and Mathematics, 106(2), 84–97.
Dweck, C. S. (2000). Self-theories: Their role in motivation, personality, and development. Philadelphia, PA: Psychology Press.
Dweck, C. S. (2006). Mindset: The new psychology of success. New York, NY: Random House.
Dweck, C. S. (2007). Boosting achievement with messages that motivate. Education Canada, 47(2), 6–10.
Fischhoff, B. (1975). Hindsight is not equal to foresight: The effect of outcome knowledge on judgment under uncertainty. Journal of Experimental Psychology: Human Perception and Performance, 1(3), 288–299.
Fischhoff, B., & Beyth, R. (1975). I knew it would happen: Remembered probabilities of once—Future things. Organizational Behavior and Human Performance, 13(1), 1–16.
Graeber, A. O. (1999). Forms of knowing mathematics: What preservice teachers should learn. Educational Studies in Mathematics, 38(1–3), 189–208.
Harkness, S. S., & Thomas, J. (2008). Reflections on “multiplication as original sin”: The implications of using a case to help preservice teachers understand invented algorithms. Journal of Mathematical Behavior, 27(2), 128–137.
Hawkins, S. A., & Hastie, R. (1990). Hindsight: Biased judgments of past events after the outcomes are known. Psychological Bulletin, 107(3), 311.
Hill, H., Rowan, B., & Ball, D. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.
Kaasila, R., Pehkonen, E., & Hellinen, A. (2010). Finnish pre-service teachers’ and upper secondary students’ understanding of division and reasoning strategies used. Educational Studies in Mathematics, 73(3), 247–261.
Kahneman, D. (2011). Thinking, fast and slow. New York, NY: Farrar, Straus and Giroux.
Khoury, H. A., & Zazkis, R. (1994). On fractions and non-standard representations: Pre-service teachers’ concepts. Educational Studies in Mathematics, 27(2), 191–204.
Loftus, E. F., & Loftus, G. R. (1980). On the permanence of stored information in the human brain. American Psychologist, 35(5), 409–420.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum.
Mason, J. (1998). Enabling teachers to be real teachers: Necessary levels of awareness and structure of attention. Journal of Mathematics Teacher Education, 1(3), 243–267. https://doi.org/10.1023/A:1009973717476
Menon, R. (2009). Preservice teachers’ subject matter knowledge of mathematics. The International Journal for Mathematics Teaching and Learning. Retrieved from www.cimtplymouth.ac.uk/jjournal/menon.pdf.
National Research Council (Ed.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
Pintrich, P. R. (2002). The role of metacognitive knowledge in learning, teaching, and assessing. Theory into Practice, 41(4), 219–225. https://doi.org/10.1207/s15430421tip4104_3
Roese, N. J., & Vohs, K. D. (2012). Hindsight bias. Perspectives on Psychological Science, 7(5), 411–426.
Silverman, J., & Thompson, P. (2008). Toward a framework for the development of mathematical knowledge for teaching. Journal of Mathematics Teacher Education, 11(6), 499–511. https://doi.org/10.1007/s10857-008-9089-5
Simon, M. (1993). Prospective elementary teachers’ knowledge of division. Journal for Research in Mathematics Education, 24(3), 233–254.
Simon, M., & Blume, G. W. (1992). Mathematization as a component of the concept of ratio-as-measure: A study of prospective elementary teachers. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco, CA. Retrieved from http://stats.lib.pdx.edu/proxy.php?url=http://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=ED349175&site=ehost-live.
Tanner, K. D. (2012). Promoting student metacognition. CBE-Life Sciences Education, 11(2), 113–120.
Thanheiser, E. (2009). Preservice elementary school teachers’ conceptions of multidigit whole numbers. Journal for Research in Mathematics Education, 40(3), 251–281.
Thanheiser, E. (2010). Investigating further preservice teachers’ conceptions of multidigit whole numbers: Refining a framework. Educational Studies in Mathematics, 75(3), 241–251. https://doi.org/10.1007/s10649-010-9252-7
Thanheiser, E. (2015). Developing prospective teachers’ conceptions with well-designed tasks: Explaining successes and analyzing conceptual difficulties. Journal of Mathematics Teacher Education, 18(2), 141–172. https://doi.org/10.1007/s10857-014-9272-9
Thanheiser, E. (2018). Brief report: The effects of preservice elementary school teachers’ accurate self-assessments in the context of whole number. Journal for Research in Mathematics Education, 49(1), 39–56.
Thanheiser, E., Browning, C., Edson, A. J., Lo, J., Whitacre, I., Olanoff, D., & Morton, C. (2014). Prospective elementary mathematics teacher content knowledge: What do we know, what do we not know, and where do we go? The Mathematics Enthusiast, 11(2), 433–448.
Thanheiser, E., Philipp, R., Fasteen, J., Strand, K., & Mills, B. (2013). Preservice-teacher interviews: A tool for motivating mathematics learning. Mathematics Teacher Educator, 1(2), 137–147. https://doi.org/10.5951/mathteaceduc.1.2.0137
Thanheiser, E., Whitacre, I., & Roy, G. (2014). Mathematical content knowledge for teaching elementary mathematics: A focus on whole-number concepts and operations. The Mathematics Enthusiast, 11(2), Article 4.
Veenman, M. V., Van Hout-Wolters, B. H., & Afflerbach, P. (2006). Metacognition and learning: Conceptual and methodological considerations. Metacognition and Learning, 1(1), 3–14. https://doi.org/10.1007/s11409-006-6893-0
Von Glasersfeld, E. (1995). A constructivist approach to teaching. In L. P. Steffe & J. E. Gale (Eds.), Constructivism in education. New York, NY: Lawrence Erlbaum.
Vosniadou, S., & Verschaffel, L. (2004). Extending the conceptual change approach to mathematics learning and teaching. Learning and Instruction, 14(5), 445–451.
Wang, M. C., Haertel, G. D., & Walberg, H. J. (1990). What influences learning? A content analysis of review literature. The Journal of Educational Research, 84(1), 30–43. https://doi.org/10.1080/00220671.1990.10885988
Zazkis, R., & Campbell, S. (1996). Divisibility and multiplicative structure of natural numbers: Preservice teachers’ understanding. Journal for Research in Mathematics Education, 27, 540–563.
Zazkis, R., & Khoury, H. A. (1993). Place value and rational number representations: Problem solving in the unfamiliar domain of non-decimals. Focus on Learning Problems in Mathematics, 15(1), 38–51.
Acknowledgement
I would like to thank Krista Strand and Briana Mills who accompanied me through the beginnings of this work and Jodi Fasteen who tirelessly coded this data with me.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Thanheiser, E. (2021). How Do I Know I Learned Something? Reflecting on Learning by Using Video-Recorded Interviews to Battle Hindsight (“I-Knew-It-All-Along”) Bias. In: Li, Y., Howe, R.E., Lewis, W.J., Madden, J.J. (eds) Developing Mathematical Proficiency for Elementary Instruction. Advances in STEM Education. Springer, Cham. https://doi.org/10.1007/978-3-030-68956-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-68956-8_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-68955-1
Online ISBN: 978-3-030-68956-8
eBook Packages: EducationEducation (R0)