ZDM

, Volume 48, Issue 1–2, pp 1–27 | Cite as

Teachers’ perception, interpretation, and decision-making: a systematic review of empirical mathematics education research

  • Rebekka Stahnke
  • Sven Schueler
  • Bettina Roesken-Winter
Survey Paper

Abstract

Research in mathematics education has investigated teachers’ professional knowledge in depth, comprising two different approaches: a cognitive and a situated perspective. Linking these two perspectives leads to addressing situation-specific skills such as perception, interpretation and decision-making, indicative of revealing a teacher’s knowledge while in the act of teaching. The aim of this study is to systematically review empirical research into mathematics teachers’ situation-specific skills. From the databases Eric, PsycINFO and MathEduc a total of 60 articles were included in the review, based on specific criteria. The studies were categorized with respect to theoretical frameworks used, designs and methods applied as well as the main findings of each study. Teachers’ noticing or teachers’ professional vision, and teachers’ (situated) professional knowledge were found to be the most frequent frameworks. Designs ranged from comprehensive case studies with a variety of methods to confirmatory studies testing a large sample with standardized instruments. The main findings suggest: (1) Teachers’ expertise and experience positively influence noticing and teachers’ noticing can be successfully fostered by (video-based) professional development programs. (2) Pre-service teachers struggle with perceiving and interpreting students’ work. Thereby, their mathematical knowledge plays an important role. (3) Teachers’ in-the-moment decision-making is influenced by their knowledge, beliefs and goals. (4) Teachers’ knowledge and belief facets predict their situation specific-skills which in turn correlate with aspects close to instructional practice. (5) Teachers have difficulties interpreting tasks and identifying their educational potential. Methods and implication of this systematic review are thoroughly discussed.

Keywords

Teacher professional knowledge Teacher cognition Situation-specific skills Perception Interpretation Decision-making 

References

  1. *Alsawaie, O. N., & Alghazo, I. M. (2010). The effect of video-based approach on prospective teachers’ ability to analyze mathematics teaching. Journal of Mathematics Teacher Education, 13(3), 223–241. doi:10.1007/s10857-009-9138-8.
  2. *Amador, J., & Weiland, I. (2015). What preservice teachers and knowledgeable others professionally notice during lesson study. Teacher Educator, 50(2), 109–126.Google Scholar
  3. Ball, D. L. (2000). Bridging practices intertwining content and pedagogy in teaching and learning to teach. Journal of Teacher Education, 51(3), 241–247.CrossRefGoogle Scholar
  4. Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple perspectives on the teaching and learning of mathematics (pp. 83–104). Westport, CT: Ablex.Google Scholar
  5. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching what makes it special? Journal of Teacher Education, 59(5), 389–407.CrossRefGoogle Scholar
  6. Baumert, J., & Kunter, M. (2006). Stichwort: Professionelle Kompetenz von Lehrkräften. Zeitschrift für Erziehungswissenschaft, 9(4), 469–520.CrossRefGoogle Scholar
  7. Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., et al. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133–180.CrossRefGoogle Scholar
  8. Berliner, D. C. (1992). The nature of expertise in teaching. In F. K. Oser, A. Dick & J.-L. Partry (Eds.), Effective and responsible teaching (pp. 227–248). San Franzisco, CA: Jossey-Bass.Google Scholar
  9. Berliner, D. C. (2001). Learning about and learning from expert teachers. International journal of educational research, 35(5), 463–482.CrossRefGoogle Scholar
  10. Blömeke, S., & Delaney, S. (2014). Assessment of teacher knowledge across countries: A review of the state of research. In S. Blömeke, F.-J. Hsieh, G. Kaiser, & W. H. Schmidt (Eds.), International perspectives on teacher knowledge, beliefs and opportunities to learn (pp. 541–585). Berlin: Springer.Google Scholar
  11. Blömeke, S., Gustafsson, J.-E., & Shavelson, R. J. (2015a). Beyond dichotomies: Competence viewed as a continuum. Zeitschrift für Psychologie, 223(1), 3–13. doi:10.1027/2151-2604/a000194.CrossRefGoogle Scholar
  12. *Blömeke, S., Hoth, J., Döhrmann, M., Busse, A., Kaiser, G., & König, J. (2015b). Teacher change during induction: Development of beginning primary teachers’ knowledge, beliefs and performance. International Journal of Science and Mathematics Education, 13(2), 287–308. doi:10.1007/s10763-015-9619-4.
  13. Blömeke, S., Kaiser, G., & Lehmann, R. (2010). TEDS-M 2008. Professionelle Kompetenz und Lerngelegenheiten angehender Primarstufenlehrkräfte im internationalen Vergleich. New York: Waxmann Verlag.Google Scholar
  14. Blömeke, S., Suhl, U., & Kaiser, G. (2011). Teacher education effectiveness: Quality and equity of future primary teachers’ mathematics and mathematics pedagogical content knowledge. Journal of Teacher Education, 62(2), 154–171.CrossRefGoogle Scholar
  15. Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. C. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily? Journal for Research in Mathematics Education, 23(3), 194–222CrossRefGoogle Scholar
  16. *Bruckmaier, G., Krauss, S., Blum, W., & Leiss, D. (2016). Measuring mathematical teachers’ professional competence by using video clips (COACTIV video). ZDM Mathematics Education, 48(1) (this issue).Google Scholar
  17. 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.CrossRefGoogle Scholar
  18. Chi, M. T. (2011). Theoretical perspectives, methodological approaches, and trends in the study of expertise. In Y. Li & G. Kaiser (Eds.), Expertise in mathematics instruction (pp. 17–39). New York: Springer.Google Scholar
  19. *Colestock, A., & Sherin, M. G. (2009). Teachers’ sense-making strategies while watching video of mathematics instruction. Journal of Technology and Teacher Education, 17(1), 7–29.Google Scholar
  20. *Cooper, S. (2009). Preservice teachers’ analysis of children’s work to make instructional decisions. School Science and Mathematics, 109(6), 355–362.Google Scholar
  21. 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.CrossRefGoogle Scholar
  22. *Derry, S. J., Wilsman, M. J., & Hackbarth, A. J. (2007). Using contrasting case activities to deepen teacher understanding of algebraic thinking and teaching. Mathematical Thinking and Learning: An International Journal, 9(3), 305–329.Google Scholar
  23. *Dreher, A., & Kuntze, S. (2015). Teachers’ professional knowledge and noticing: The case of multiple representations in the mathematics classroom. Educational Studies in Mathematics, 88(1), 89–114.Google Scholar
  24. *Dunekacke, S., Jenßen, L., & Blömeke, S. (2015). Effects of mathematics content knowledge on pre-school teachers’ performance: A video-based assessment of perception and planning abilities in informal learning situations. International Journal of Science and Mathematics Education, 13(2), 267–286.Google Scholar
  25. *Dunekacke, S., Jenßen, L., Eilerts, K., & Blömeke, S. (2016). Epistemological beliefs of prospective preschool teachers and their relation to knowledge, perception, and planning abilities in the field of mathematics: A process model. ZDM,. doi:10.1007/s11858-015-0711-6. (this issue).
  26. *Dyer, E. B., & Sherin, M. G. (2016). Instructional reasoning about interpretations of student thinking that supports responsive teaching in secondary mathematics. ZDM,. doi:10.1007/s11858-015-0740-1. (this issue).
  27. *Escudero, I., & Sánchez, V. (2007). How do domains of knowledge integrate into mathematics teachers’ practice? The Journal of Mathematical Behavior, 26(4), 312–327. doi:10.1016/j.jmathb.2007.11.002.
  28. *Fernández, C., Llinares, S., & Valls, J. (2013). Primary school teacher’s noticing of students’ mathematical thinking in problem solving. The Mathematics Enthusiast, 10(1/2), 441–467.Google Scholar
  29. *Gal, H. (2011). From another perspective-training teachers to cope with problematic learning situations in geometry. Educational Studies in Mathematics, 78(2), 183–203.Google Scholar
  30. *Galant, J. (2013). Selecting and sequencing mathematics tasks: Seeking mathematical knowledge for teaching. Perspectives in Education, 31(3), 34–48.Google Scholar
  31. Goodwin, C. (1994). Professional vision. American Anthropologist, 96(3), 606–633.CrossRefGoogle Scholar
  32. Hattie, J. C. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. London, New York: Routledge, Taylor & Francis Group.Google Scholar
  33. Helmke, A. (2009). Unterrichtsqualität und Lehrerprofessionalität: Diagnose, Evaluation und Verbesserung des Unterrichts [Instructional quality and teacher professionality: diagnosis, evaluation, and enhancement of instruction]. Seelze-Velber: Kallmeyer.Google Scholar
  34. *Hines, E., & McMahon, M. T. (2005). Interpreting middle school students’ proportional reasoning strategies: Observations from preservice teachers. School Science and Mathematics, 105(2), 88–105.Google Scholar
  35. *Ho, K. F., & Tan, P. (2013). Developing a professional vision of classroom practices of a mathematics teacher: Views from a researcher and a teacher. Teaching Education, 24(4), 415–426.Google Scholar
  36. *Hoth, J., Döhrmann, M., Kaiser, G., Busse, A., König, J., & Blömeke, S. (2016). Diagnostic competence of primary school mathematics teachers during classroom situations. ZDM Mathematics Education, 48(1) (this issue).Google Scholar
  37. *Houssart, J. (2000). Perceptions of mathematical pattern amongst primary teachers. Educational Studies, 26(4), 489–502.Google Scholar
  38. *Huang, R., & Li, Y. (2012). What matters most: A comparison of expert and novice teachers’ noticing of mathematics classroom events. School Science and Mathematics, 112(7), 420–432.Google Scholar
  39. *Ingram, J. (2014). Supporting student teachers in developing and applying professional knowledge with videoed events. European Journal of Teacher Education, 37(1), 51–62.Google Scholar
  40. *Jacobs, V. R., & Empson, S. B. (2016). Responding to children’s mathematical thinking in the moment: an emerging framework of teaching moves. ZDM,. doi:10.1007/s11858-015-0717-0. (this issue).
  41. *Jacobs, V. R., Lamb, L. L., & Philipp, R. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202.Google Scholar
  42. Jacobs, V. R., Lamb, L. C., Philipp, R., Schappelle, B., & Burke, A. (2007). Professional noticing by elementary school teachers of mathematics. Paper presented at the American Educational Research Association Annual Meeting, Chicago.Google Scholar
  43. *Jakobsen, A., Ribeiro, C., & Mellone, M. (2014). Norwegian prospective teachers’ MKT when interpreting pupils’ productions on a fraction task. Nordic Studies in Mathematics Education, 19(3–4), 135–150.Google Scholar
  44. 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.CrossRefGoogle Scholar
  45. Kaiser, G., Blömeke, S., Busse, A., Döhrmann, M., & König, J. Professional knowledge of (prospective) mathematics teachers—Its structure and its development. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), PME 38 and PME-NA 36, Vancouver, 2014 (Vol. 1, pp. 35–50). PME.Google Scholar
  46. *Kersting, N. (2008). Using video clips of mathematics classroom instruction as item prompts to measure teachers’ knowledge of teaching mathematics. Educational and Psychological Measurement, 68(5), 845–861. doi:10.1177/0013164407313369.
  47. *Kersting, N., Sutton, T., Kalinec-Craig, C., Stoehr, K. J., Heshmati, S., Lozano, G., et al. (2016). Further exploration of the classroom video analysis (CVA) instrument as a measure of usable knowledge for teaching mathematics: Taking a knowledge system perspective. ZDM,. doi:10.1007/s11858-015-0733-0. (this issue).
  48. *Klymchuk, S., & Thomas, M. O. J. (2011). The influence of attention on mathematical knowledge of teachers and lecturers: A comparison. International Journal of Mathematical Education in Science and Technology, 42(7), 1011–1020.Google Scholar
  49. *Knievel, I., Lindmeier, A. M., & Heinze, A. (2015). Beyond knowledge: measuring primary teachers’ subject-specific competences in and for teaching mathematics with items based on video vignettes. International Journal of Science and Mathematics Education, 13(2), 309–329. doi:10.1007/s10763-014-9608-z.
  50. König, J., Blömeke, S., Paine, L., Schmidt, W., & Hsieh, F.-J. (2014). Teacher education effectiveness: Quality and equity of future primary and future lower secondary teachers’ general pedagogical knowledge. In S. Blömeke, F.-J. Hsieh, G. Kaiser, & W. H. Schmidt (Eds.), International perspectives on teacher knowledge, beliefs and opportunities to learn (pp. 187–206). Berlin: Springer.Google Scholar
  51. Kunter, M., Klusmann, U., Baumert, J., Richter, D., Voss, T., & Hachfeld, A. (2013). Professional competence of teachers: Effects on instructional quality and student development. Journal of Educational Psychology, 105(3), 805–820. doi:10.1037/a0032583.CrossRefGoogle Scholar
  52. *Lande, E., & Mesa, V. (2016). Instructional decision making and agency of community college mathematics faculty. ZDM,. doi:10.1007/s11858-015-0736-x. (this issue).
  53. *Lee, J.-E., & Kim, K.-T. (2005). Elementary school teacher candidates’ perceptions of good problems. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1, 1–13.Google Scholar
  54. Li, Y., & Kaiser, G. (2011). Expertise in mathematics instruction: Advancing research and practice from an international perspective. Berlin: Springer.CrossRefGoogle Scholar
  55. Lindmeier, A. M., Heinze, A., & Reiss, K. (2013). Eine Machbarkeitsstudie zur Operationalisierung aktionsbezogener Kompetenz von Mathematiklehrkräften mit videobasierten Maßen. Journal für Mathematik-Didaktik, 34(1), 99–119.CrossRefGoogle Scholar
  56. *Magiera, M. T., van den Kieboom, L. A., & Moyer, J. C. (2013). An exploratory study of pre-service middle school teachers’ knowledge of algebraic thinking. Educational Studies in Mathematics, 84(1), 93–113.Google Scholar
  57. *Nickerson, S. D., & Masarik, D. K. (2010). Assessing teachers’ developing interpretive power: analysing student thinking. Mathematics Teacher Education and Development, 12(1), 19–29.Google Scholar
  58. *Norton, A., McCloskey, A., & Hudson, R. A. (2011). Prediction assessments: Using video-based predictions to assess prospective teachers’ knowledge of students’ mathematical thinking. Journal of Mathematics Teacher Education, 14(4), 305–325. doi:10.1007/s10857-011-9181-0.
  59. *Osmanoglu, A., Isiksal, M., & Koc, Y. (2015). Getting ready for the profession: Prospective teachers’ noticing related to teacher actions. Australian Journal of Teacher Education, 40(2), 29–51.Google Scholar
  60. *Pankow, L., Kaiser, G., Busse, A., König, J., Hoth, J., Döhrmann, M., et al. (2016). Early career teachers’ ability to focus on typical students errors in relation to the complexity of a mathematical topic. ZDM Mathematics Education, 48(1) (this issue).Google Scholar
  61. *Paterson, J., Thomas, M., & Taylor, S. (2011). Decisions, decisions, decisions: What determines the path taken in lectures? International Journal of Mathematical Education in Science and Technology, 42(7), 985–995.Google Scholar
  62. Petticrew, M. (2015). Time to rethink the systematic review catechism? Moving from ‘what works’ to ‘what happens’. Systematic reviews, 4(1), 36.CrossRefGoogle Scholar
  63. Petticrew, M., & Roberts, H. (2008). Systematic reviews in the social sciences: A practical guide. New York: Wiley. Google Scholar
  64. Putnam, R. T., & Borko, H. (2000). What do new views of knowledge and thinking have to say about research on teacher learning? Educational researcher, 29(1), 4–15.CrossRefGoogle Scholar
  65. *Roth McDuffie, A., Foote, M. Q., Bolson, C., Turner, E. E., Aguirre, J. M., Bartell, T. G., et al. (2014). Using video analysis to support prospective K-8 teachers’ noticing of students’ multiple mathematical knowledge bases. Journal of Mathematics Teacher Education, 17(3), 245–270.Google Scholar
  66. Rowland, T., & Ruthven, K. (2011). Mathematical knowledge in teaching (Vol. 50). Berlin: Springer.CrossRefGoogle Scholar
  67. *Sánchez-Matamoros, G., Fernández, C., & Llinares, S. (2014). 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.
  68. *Santagata, R. (2009). Designing video-based professional development for mathematics teachers in low-performing schools. Journal of Teacher Education, 60(1), 38–51.Google Scholar
  69. *Santagata, R., & Yeh, C. (2016). The role of perception, interpretation, and decision making in the development of beginning teachers’ competence. ZDM,. doi:10.1007/s11858-015-0737-9. (this issue).
  70. *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.Google Scholar
  71. *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.Google Scholar
  72. Schoenfeld, A. H. (1998). Toward a theory of teaching-in-context. Issues in Education, 4(1), 1–94.CrossRefGoogle Scholar
  73. Schoenfeld, A. H. (2010). How we think: A theory of goal-oriented decision making and its educational applications. London: Routledge.Google Scholar
  74. Schoenfeld, A. H., & Kilpatrick, J. (2008). Toward a theory of proficiency in teaching mathematics. International handbook of mathematics teacher education, 2, 321–354.Google Scholar
  75. Sherin, M. G., Jacobs, V., & Philipp, R. (2011a). Situating the study of teacher noticing. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers eyes (pp. 3–14). London: Routledge.Google Scholar
  76. Sherin, M. G., Russ, R. S., & Colestock, A. (2011b). Accessing mathematics teachers’ in-the-moment noticing. In M. G. Sherin, V. R. Jacobs, & R. A. Philipp (Eds.), Mathematics teacher noticing; seeing through teachers eyes (pp. 79–94). London: Routledge.Google Scholar
  77. *Sherin, M. G., Russ, R. S., Sherin, B. L., & Colestock, A. (2008). Professional vision in action: An exploratory study. Issues in Teacher Education, 17(2), 27–46.Google Scholar
  78. *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.Google Scholar
  79. *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.Google Scholar
  80. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4–14CrossRefGoogle Scholar
  81. *Sleep, L. (2012). The work of steering instruction toward the mathematical point: A decomposition of teaching practice. American Educational Research Journal, 49(5), 935–970.Google Scholar
  82. *Son, J.-W. (2013). How preservice teachers interpret and respond to student errors: Ratio and proportion in similar rectangles. Educational Studies in Mathematics, 84(1), 49–70.Google Scholar
  83. *Son, J.-W., & Kim, O.-K. (2015). Teachers’ selection and enactment of mathematical problems from textbooks. Mathematics Education Research Journal, 27(4), 491–518. doi:10.1007/s13394-015-0148-9.
  84. *Son, J.-W., & Sinclair, N. (2010). How preservice teachers interpret and respond to student geometric errors. School Science and Mathematics, 110(1), 31–46. doi:10.1111/j.1949-8594.2009.00005.x.
  85. Sowder, J. T. (2007). The mathematical education and development of teachers. In F. K. Lester (Ed.), Second handbook on research of mathematics teaching and learning (pp. 157–223). Charlotte: Information Age Inc.Google Scholar
  86. *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.Google Scholar
  87. *Stockero, S. L. (2008). Using a video-based curriculum to develop a reflective stance in prospective mathematics teachers. Journal of Mathematics Teacher Education, 11(5), 373–394.Google Scholar
  88. *Stockero, S. L., & Van Zoest, L. R. (2013). Characterizing pivotal teaching moments in beginning mathematics teachers’ practice. Journal of Mathematics Teacher Education, 16(2), 125–147.Google Scholar
  89. *Thomas, M., & Yoon, C. (2014). The impact of conflicting goals on mathematical teaching decisions. Journal of Mathematics Teacher Education, 17(3), 227–243.Google Scholar
  90. *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.Google Scholar
  91. *van Es, E. A., & Sherin, M. G. (2006). How different video club designs support teachers in “learning to notice”. Journal of Computing in Teacher Education, 22(4), 125–135.Google Scholar
  92. *van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers’ “learning to notice” in the context of a video club. Teaching and Teacher Education: An International Journal of Research and Studies, 24(2), 244–276.Google Scholar
  93. *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.Google Scholar
  94. *Weiland, I. S., Hudson, R. A., & Amador, J. M. (2014). Preservice formative assessment interviews: The development of competent questioning. International Journal of Science and Mathematics Education, 12(2), 329–352.Google Scholar
  95. Weinert, F. E. (2001). Competencies and key competencies: Educational perspective. In N. J. Smelser, & P. B. Baltes (Eds.), International encyclopedia of the social and behavioral sciences (pp. 2433–2436). Amsterdam: Elsevier.Google Scholar
  96. *Zahner, W., Velazquez, G., Moschkovich, J., Vahey, P., & Lara-Meloy, T. (2012). mathematics teaching practices with technology that support conceptual understanding for Latino/a students. Journal of Mathematical Behavior, 31(4), 431–446.Google Scholar
  97. *Zimmerman, A. (2015). The simultaneity of beginning teachers’ practical intentions. Mid-Western Educational Researcher, 27(2), 100–116.Google Scholar

Copyright information

© FIZ Karlsruhe 2016

Authors and Affiliations

  • Rebekka Stahnke
    • 1
  • Sven Schueler
    • 1
  • Bettina Roesken-Winter
    • 1
  1. 1.Humboldt-Universität zu BerlinBerlinGermany

Personalised recommendations