If a student thinks, “I'm not a math person”, do preservice teachers notice?

Helene Rieche 1 * , Timo Leuders 2, Alexander Renkl 1
More Detail
1 Department of Educational and Developmental Psychology, University of Freiburg, Freiburg, Germany
2 Institute of Mathematics Education, University of Education Freiburg, Freiburg, Germany
* Corresponding Author
EUR J SCI MATH ED, Volume 7, Issue 1, pp. 32-49. https://doi.org/10.30935/scimath/9532
OPEN ACCESS   2359 Views   2653 Downloads
Download Full Text (PDF)

ABSTRACT

Students’ beliefs that mathematical abilities are fixed can cause long-standing problems with motivation and learning. Hence, teachers should notice such problematic beliefs about identity among their students and handle them adequately. We used written descriptions of classroom situations to determine whether preservice mathematics teachers (n = 80) noticed fixed beliefs about mathematical abilities and whether they had strategies for dealing with them. The qualitative data were coded and transformed into a score for noticing. We found that most of the preservice teachers did not notice problematic beliefs. Thereby, preservice teachers who believed that mathematical abilities are malleable were more likely to notice fixed beliefs among students. When describing beliefs, few participants referred to theoretical concepts. Hardly any preservice teachers suggested strategies for handling students’ beliefs. However, the strategies that were suggested mostly corresponded with findings from educational research. Our study provides first evidence that preservice teachers’ abilities to notice and handle belief-related problems may be insufficient. We discuss implications for teacher education as well as directions for future research.
Keywords: beliefs, identity, teacher noticing, professional vision, teacher education

CITATION

Rieche, H., Leuders, T., & Renkl, A. (2019). If a student thinks, “I'm not a math person”, do preservice teachers notice?. European Journal of Science and Mathematics Education, 7(1), 32-49. https://doi.org/10.30935/scimath/9532

REFERENCES

  • Aronson, E. (1999). The power of self-persuasion. American Psychologist, 54(11), 875–884. https://doi.org/10.1037/h0088188
  • Bandura, A. (1993). Perceived self-efficacy in cognitive development and functioning. Educational Psychologist, 28(2), 117–148. https://doi.org/10.1207/s15326985ep2802_3
  • Blackwell, L. S., Trzesniewski, K. H., & Dweck, C. S. (2007). Implicit theories of intelligence predict achievement across an adolescent transition: A longitudinal study and an intervention. Child Development, 78(1), 246–263. https://doi.org/10.1111/j.1467-8624.2007.00995.x
  • Blömeke, S., Gustafsson, J.-E., & Shavelson, R. J. (2015). Beyond dichotomies. Zeitschrift Für Psychologie, 223(1), 3–13. https://doi.org/10.1027/2151-2604/a000194
  • Blömeke, S., Hoth, J., Döhrmann, M., Busse, A., Kaiser, G., & König, J. (2015). Teacher change during induction: Development of beginning primary teachers’ knowledge, beliefs and performance. International Journal of Science and Mathematics Education, 13(2), 287–308. https://doi.org/10.1007/s10763-015-9619-4
  • Boaler, J. (2015). Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. New York, NY: Wiley.
  • Borkowski, J. G., Weyhing, R. S., & Carr, M. (1988). Effects of attributional retraining on strategy-based reading comprehension in learning-disabled students. Journal of Educational Psychology, 80(1), 46–53. https://doi.org/10.1037/0022-0663.80.1.46
  • Bruder, R., Hefendehl-Hebeker, L., Schmidt-Thieme, B., & Weigand, H.-G. (2015). Handbuch der Mathematikdidaktik (2015th ed.). Berlin Heidelberg: Springer Spektrum.
  • Burkley, M., Parker, J., Paul Stermer, S., & Burkley, E. (2010). Trait beliefs that make women vulnerable to math disengagement. Personality and Individual Differences, 48(2), 234–238. https://doi.org/10.1016/j.paid.2009.09.002
  • Burnette, J. L., O’Boyle, E. H., VanEpps, E. M., Pollack, J. M., & Finkel, E. J. (2013). Mind-sets matter: A meta-analytic review of implicit theories and self-regulation. Psychological Bulletin, 139(3), 655–701. https://doi.org/10.1037/a0029531
  • Burnette, J. L., Russell, M. V., Hoyt, C. L., Orvidas, K., & Widman, L. (2017). An online growth mindset intervention in a sample of rural adolescent girls. British Journal of Educational Psychology. https://doi.org/10.1111/bjep.12192
  • Butler, R. (2000). Making judgments about ability: the role of implicit theories of ability in moderating inferences from temporal and social comparison information. Journal of Personality and Social Psychology, 78(5), 965–978. https://doi.org/10.1037/0022-3514.78.5.965
  • Carter, K., Cushing, K., Sabers, D., Stein, P., & Berliner, D. (1988). Expert-Novice Differences in Perceiving and Processing Visual Classroom Information. Journal of Teacher Education, 39(3), 25–31. https://doi.org/10.1177/002248718803900306
  • Cooper, S. (2009). Preservice teachers’ analysis of children’s work to make instructional decisions. School Science and Mathematics, 109(6), 355–362. https://doi.org/10.1111/j.1949-8594.2009.tb18105.x
  • Depaepe, F., Verschaffel, L., & Kelchtermans, G. (2013). Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research. Teaching and Teacher Education, 34, 12–25. https://doi.org/10.1016/j.tate.2013.03.001
  • Dreher, A., & Kuntze, S. (2014). Teachers’ professional knowledge and noticing: the case of multiple representations in the mathematics classroom. Educational Studies in Mathematics, 88(1), 89–114. https://doi.org/10.1007/s10649-014-9577-8
  • Dweck, C. S. (2000). Self-theories: Their role in motivation, personality, and development. Philadelphia, PA: Psychology Press.
  • Friesen, M., & Kuntze, S. (2016). Teacher students analyse texts, comics and video-based classroom vignettes regarding the use of representations - does format matter? In Proceedings of the 30th Annual Conference of the International Group for the Psychology of Mathematics Education (pp. 259–266). Szeged, Hungary.
  • Furner, J. M., & Berman, B. T. (2003). Review of research: Math anxiety: Overcoming a major obstacle to the improvement of student math performance. Childhood Education, 79(3), 170–174. https://doi.org/10.1080/00094056.2003.10522220
  • Georgiou, S. N. (2008). Beliefs of experienced and novice teachers about achievement. Educational Psychology, 28(2), 119–131. https://doi.org/10.1080/01443410701468716
  • Grootenboer, P., Smith, T., & Lowrie, T. (2006). Researching identity in mathematics education: The lay of the land. Identities, Cultures and Learning Spaces, 2, 612–615.
  • Grossman, P., Compton, C., Igra, D., Ronfeldt, M., Shahan, E., & Williamson, P. (2009). Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055–2100.
  • Hand, V. (2012). Seeing culture and power in mathematical learning: Toward a model of equitable instruction. Educational Studies in Mathematics, 80(1–2), 233–247. https://doi.org/10.1007/s10649-012-9387-9
  • Harr, N., Eichler, A., & Renkl, A. (2015). Integrated learning: ways of fostering the applicability of teachers’ pedagogical and psychological knowledge. Educational Psychology, 738. https://doi.org/10.3389/fpsyg.2015.00738
  • Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77(1), 81–112. https://doi.org/10.3102/003465430298487
  • Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202.
  • Jonsson, A.-C., Beach, D., Korp, H., & Erlandson, P. (2012). Teachers’ implicit theories of intelligence: influences from different disciplines and scientific theories. European Journal of Teacher Education, 35(4), 387–400. https://doi.org/10.1080/02619768.2012.662636
  • Kaiser, G., Busse, A., Hoth, J., König, J., & Blömeke, S. (2015). About the complexities of video-based assessments: Theoretical and methodological approaches to overcoming shortcomings of research on teachers’ competence. International Journal of Science and Mathematics Education, 13(2), 369–387. https://doi.org/10.1007/s10763-015-9616-7
  • Kalinec-Craig, C. (2017). “Everything matters”: Mexican-American prospective elementary teachers noticing issues of status and participation while learning to teach mathematics. In Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks (pp. 215–229). New York, NY: Springer. https://doi.org/10.1007/978-3-319-46753-5_13
  • Kelley, H. H. (1973). The processes of causal attribution. American Psychologist, 28(2), 107–128. https://doi.org/10.1037/h0034225
  • Kersting, N. B., Givvin, K. B., Thompson, B. J., Santagata, R., & Stigler, J. W. (2012). Measuring usable knowledge: Teachers’ analyses of mathematics classroom videos predict teaching quality and student learning. American Educational Research Journal, 49(3), 568–589. https://doi.org/10.3102/0002831212437853
  • König, J., & Kramer, C. (2016). Teacher professional knowledge and classroom management: on the relation of general pedagogical knowledge (GPK) and classroom management expertise (CME). ZDM, 48(1–2), 139–151. https://doi.org/10.1007/s11858-015-0705-4
  • Krauss, S., & Brunner, M. (2011). Schnelles Beurteilen von Schülerantworten: Ein Reaktionszeittest für Mathematiklehrer/innen. Journal für Mathematik-Didaktik, 32(2), 233. https://doi.org/10.1007/s13138-011-0029-z
  • Kuntze, S. (2012). Pedagogical content beliefs: Global, content domain-related and situation-specific components. Educational Studies in Mathematics, 79(2), 273–292. https://doi.org/10.1007/s10649-011-9347-9
  • Leahy, W., & Sweller, J. (2011). Cognitive load theory, modality of presentation and the transient information effect. Applied Cognitive Psychology, 25(6), 943–951. https://doi.org/10.1002/acp.1787
  • Lee, M. Y., & Cross Francis, D. (2017). Investigating the relationships among elementary teachers’ perceptions of the use of students’ thinking, their professional noticing skills, and their teaching practices. The Journal of Mathematical Behavior. https://doi.org/10.1016/j.jmathb.2017.11.007
  • Lerman, S. (Ed.). (2014). Encyclopedia of mathematics education. Dordrecht: Springer.
  • Louie, N. L. (2017). Culture and ideology in mathematics teacher noticing. Educational Studies in Mathematics, 1–15. https://doi.org/10.1007/s10649-017-9775-2
  • Louie, N. L. (2018). Culture and ideology in mathematics teacher noticing. Educational Studies in Mathematics, 97(1), 55–69. https://doi.org/10.1007/s10649-017-9775-2
  • Lowe, R. K. (2003). Animation and learning: Selective processing of information in dynamic graphics. Learning and Instruction, 13(2), 157–176. https://doi.org/10.1016/S0959-4752(02)00018-X
  • Marsh, H. W. (1990). A multidimensional, hierarchical model of self-concept: Theoretical and empirical justification. Educational Psychology Review, 2(2), 77–172. https://doi.org/10.1007/BF01322177
  • Marsh, H. W., & Craven, R. (1997). Academic self-concept: Beyond the dustbowl. In G. D. Phye (Ed.), Handbook of classroom assessment: Learning, achievement, and adjustment. San Diego, CA: Academic Press.
  • Martino, P. D., & Zan, R. (2010). ‘Me and maths’: Towards a definition of attitude grounded on students’ narratives. Journal of Mathematics Teacher Education, 13(1), 27–48. https://doi.org/10.1007/s10857-009-9134-z
  • Meschede, N., Fiebranz, A., Möller, K., & Steffensky, M. (2017). Teachers’ professional vision, pedagogical content knowledge and beliefs: On its relation and differences between pre-service and in-service teachers. Teaching and Teacher Education, 66, 158–170. https://doi.org/10.1016/j.tate.2017.04.010
  • Meyer, W.-U. (1982). Indirect communications about perceived ability estimates. Journal of Educational Psychology, 74(6), 888–897. https://doi.org/10.1037/0022-0663.74.6.888
  • Mueller, C. M., & Dweck, C. S. (1998). Praise for intelligence can undermine children’s motivation and performance. Journal of Personality and Social Psychology, 75(1), 33–52. https://doi.org/http://dx.doi.org/10.1037/0022-3514.75.1.33
  • OECD. (2013). PISA 2012 Results: Ready to learn. Students’ engagement, drive and self-beliefs. Paris: OECD Publishing.
  • Pankow, L., Kaiser, G., Busse, A., König, J., Blömeke, S., Hoth, J., & Döhrmann, M. (2016). Early career teachers’ ability to focus on typical students errors in relation to the complexity of a mathematical topic. ZDM, 48(1–2), 55–67. https://doi.org/10.1007/s11858-016-0763-2
  • Patterson, M. M., Kravchenko, N., Chen-Bouck, L., & Kelley, J. A. (2016). General and domain-specific beliefs about intelligence, ability, and effort among preservice and practicing teachers. Teaching and Teacher Education, 59, 180–190. https://doi.org/10.1016/j.tate.2016.06.004
  • Rattan, A., Good, C., & Dweck, C. S. (2012). “It’s ok — Not everyone can be good at math”: Instructors with an entity theory comfort (and demotivate) students. Journal of Experimental Social Psychology, 48(3), 731–737. https://doi.org/10.1016/j.jesp.2011.12.012
  • Rattan, A., Savani, K., Naidu, N. V. R., & Dweck, C. S. (2012). Can everyone become highly intelligent? Cultural differences in and societal consequences of beliefs about the universal potential for intelligence. Journal of Personality and Social Psychology, 103(5), 787–803. https://doi.org/10.1037/a0029263
  • Renkl, A., Mandl, H., & Gruber, H. (1996). Inert knowledge: Analyses and remedies. Educational Psychologist, 31(2), 115–121. https://doi.org/10.1207/s15326985ep3102_3
  • Saylan, A., Armagan, F. Ö., & Bektas, O. (2016). The Relationship between Pre-Service Science Teachers’ Epistemological Beliefs and Preferences for Creating a Constructivist Learning Environment. European Journal of Science and Mathematics Education, 4(2), 251–267.
  • Schmidt, J. A., Shumow, L., & Kackar-Cam, H. Z. (2017). Does Mindset Intervention Predict Students’ Daily Experience in Classrooms? A Comparison of Seventh and Ninth Graders’ Trajectories. Journal of Youth and Adolescence, 46(3), 582–602. https://doi.org/10.1007/s10964-016-0489-z
  • Schneider, J., Bohl, T., Kleinknecht, M., Rehm, M., Kuntze, S., & Syring, M. (2016). Unterricht analysieren und reflektieren mit unterschiedlichen Fallmedien: Ist Video wirklich besser als Text? Unterrichtswissenschaft, 44(4), 474–489.
  • Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of “well-taught” mathematics courses. Educational Psychologist, 23(2), 145–166. https://doi.org/http://dx.doi.org/10.1207/s15326985ep2302_5
  • Seidel, T., & Prenzel, M. (2007). Wie Lehrpersonen Unterricht wahrnehmen und einschätzen - Erfassung pädagogisch-psychologischer Kompetenzen mit Videosequenzen. In M. Prenzel, I. Gogolin, & H.-H. Krüger (Eds.), Kompetenzdiagnostik (pp. 201–216). Wiesbaden: VS Verlag für Sozialwissenschaften.
  • Seidel, T., & Stürmer, K. (2014). Modeling and measuring the structure of professional vision in preservice teachers. American Educational Research Journal, 51(4), 739–771. https://doi.org/10.3102/0002831214531321
  • Shavelson, R. J., Hubner, J. J., & Stanton, G. C. (1976). Self-concept: Validation of construct interpretations. Review of Educational Research, 46(3), 407–441. https://doi.org/10.3102/00346543046003407
  • 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. https://doi.org/10.1177/0022487108328155
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004
  • Spinath, B., & Schöne. (2003). Subjektive Überzeugungen zu Bedingungen von Erfolg in Lern- und Leistungskontexten und deren Erfassung. In J. Stiensmeier-Pelster & F. Rheinberg (Eds.), Diagnostik von Motivation und Selbstkonzept (pp. 15–27). Göttingen: Hogrefe.
  • Stahnke, R., Schueler, S., & Roesken-Winter, B. (2016). Teachers’ perception, interpretation, and decision-making: A systematic review of empirical mathematics education research. ZDM, 48(1–2), 1–27. https://doi.org/10.1007/s11858-016-0775-y
  • Teuscher, D., Leatham, K. R., & Peterson, B. E. (2017). From a Framework to a Lens: Learning to Notice Student Mathematical Thinking. In Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks (pp. 31–48). Springer, Cham. https://doi.org/10.1007/978-3-319-46753-5_3
  • Tuijl, C. van, & Molen, J. H. W. van der. (2015). Study choice and career development in STEM fields: An overview and integration of the research. International Journal of Technology and Design Education, 26(2), 159–183. https://doi.org/10.1007/s10798-015-9308-1
  • 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(4), 571–596.
  • Voss, T., Kunter, M., & Baumert, J. (2011). Assessing teacher candidates’ general pedagogical/psychological knowledge: Test construction and validation. Journal of Educational Psychology, 103(4), 952–969. https://doi.org/10.1037/a0025125
  • Wager, A. A. (2014). Noticing children’s participation: Insights into teacher positionality toward equitable mathematics pedagogy. Journal for Research in Mathematics Education, 45(3), 312–350. https://doi.org/10.5951/jresematheduc.45.3.0312
  • Whitehead, A. N. (1929). The aims of education. New York, NY: Macmillan.
  • Wood, R., & Bandura, A. (1989). Impact of conceptions of ability on self-regulatory mechanisms and complex decision making. Journal of Personality and Social Psychology, 56(3), 407–415. https://doi.org/10.1037/0022-3514.56.3.407
  • Woolfolk, A. (2012). Educational Psychology (12 edition). Boston: Pearson.
  • Yeager, D. S., & Walton, G. M. (2011). Social-psychological interventions in education: They’re not magic. Review of Educational Research, 81(2), 267–301. https://doi.org/10.3102/0034654311405999