Teachers’ reflection on PISA items and why they are so hard for students in Serbia

• Autores: Jelena Radisic, Aleksander Baucal
• Localización: European journal of psychology of education, ISSN-e 1878-5174, ISSN 0256-2928, Vol. 33, Nº 3, 2018 (Ejemplar dedicado a: Promoting teaching, learning and informed decision-making through the lenses of international large-scale assessment / coord. por Roger Säljö, Jelena Radisic), págs. 445-466
• Idioma: inglés
• DOI: 10.1007/s10212-018-0366-0
• Texto completo no disponible (Saber más ...)
• Resumen

  • The study explores how teachers perceive and go about students’ thinking in connection to particular mathematical content and how they frame the notion of applied mathematics in their own classrooms. Teachers’ narratives are built around two released PISA 2012 mathematics items, the ‘Drip rate’ and ‘Climbing Mount Fuji’ (will be referred to as the Fuji item). Teachers show concordance as to the reasons that could make either of the items difficult for students and are able to provide more examples justifying their reasoning for the ‘Fuji’ item. Suggestions linked to making the items more familiar to the students mostly relate to de-contextualization of the items’ content towards a more formal mathematical record. The teachers agree that students need only basic mathematical knowledge, at a level learned during elementary school, in order to solve these problems. Yet, at the same time, many teachers have difficulty clearly verbalising which procedures students are expected to follow to be able to solve the tasks. Disagreement among the teachers is noticeable when labelling the most difficult part(s) of each of the selected items. Mathematics teachers show openness for learning on how to create math problems we examined in this study, but question the purpose and meaning in incorporating more such problems in their own teaching.

• Referencias bibliográficas
  • Anić, I., & Pavlović Babić, D. (2015). How we can support success in solving mathematical problems? Teaching Innovations, 28(3), 36–49.
  • Ball, D. L. (1997). What do students know? Facing challenges of distance, context, and desire in trying to hear children. In B. Biddle, T....
  • Ball, D. L. (2001). Teaching, with respect to mathematics and students. Beyond classical pedagogy: Teaching elementary school mathematics...
  • Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching: who knows mathematics well enough to teach third grade,...
  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: what makes it special? Journal of Teacher Education,...
  • Baucal, A., & Pavlović Babić, D. (2010). PISA 2009 u Srbiji: prvi rezultati. Nauči me da mislim, nauči me da učim. Institut za psihologiju...
  • Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., et al. (2010). Teachers’ mathematical knowledge, cognitive activation...
  • Black, P., Harrison, C., Lee, C., Marshall, B., & Wiliam, D. (2003). Assessment for learning: Putting it into practice. Maidenhead: McGraw-Hill...
  • Blömeke, S., Gustafsson, J. E., & Shavelson, R. (2015). Beyond dichotomies: Viewing competence as a continuum. Zeitschrift für Psychologie,...
  • Borg, M. (2001). Key concepts: teachers’ beliefs. ELT Journal, 55(2), 186–188.
  • Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3, 77–101.
  • Cai, J., & Ding, M. (2017). On mathematical understanding: perspectives of experienced Chinese mathematics teachers. Journal of Mathematics...
  • Clarke, B. (2008). A framework of growth points as a powerful teacher development tool. In D. Tirosh & T. Wood (Eds.), International handbook...
  • Clements, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81–89.
  • Cobb, P., Wood, T., Yackel, E., & McNeal, E. (1993). Mathematics as procedural instructions and mathematics as meaningful activity: the...
  • Crespo, S. (2000). Seeing more than right and wrong answers: prospective teachers’ interpretations of students’ mathematical work. Journal...
  • Didis, M. G., Erbas, A. K., Cetinkaya, B., Cakiroglu, E., & Alacaci, C. (2016). Exploring prospective secondary mathematics teachers’...
  • Doabler, C. T., Baker, S. K., Kosty, D. B., Smolkowski, K., Clarke, B., Miller, S. J., & Fien, H. (2015). Examining the association between...
  • Doyle, W. (1983). Academic work. Review of Educational Research, 53, 159–199.
  • Dyer, E. B., & Sherin, M. G. (2016). Instructional reasoning about interpretations of student thinking that supports responsive teaching...
  • Ellis, M. V., & Berry, R. Q. (2005). The paradigm shift in mathematics education: explanations and implications of reforming conceptions...
  • Empson, S. B., & Jacobs, V. R. (2008). Learning to listen to children’s mathematics. In D. Tirosh & T. Wood (Eds.), The international...
  • Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching...
  • Fennema, E., Carpenter, T. P., Franke, M. L., Levi, L., Jacobs, V. R., & Empson, S. B. (1996). A longitudinal study of learning to use...
  • Fives, H., & Buehl, M. M. (2012). Spring cleaning for the “messy” construct of teachers’ beliefs: what are they? Which have been examined?...
  • Fives, H., & Gregoire-Gill, M. (2014). International handbook of research on teachers’ beliefs. New York: Routledge.
  • Furtak, E. M., Kiemer, K., Kizil Circi, R., Swanson, R., de Leon, V., Morrison, D., & Heredia, S. H. (2016). Teachers’ formative assessment...
  • Hattie, J. (2008). Visible learning: a synthesis of over 800 meta-analyses relating to achievement. London: Routledge.
  • Hattikudur, S., Sidney, P. G., & Alibali, M. W. (2016). Does comparing informal and formal procedures promote mathematics learning? The...
  • Hill, H. C., Blunck, M. L., Charalambos, Y. C., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for...
  • Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research...
  • Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: helping children learn mathematics. Washington, D.C.: National...
  • König, J., Blömeke, S., Klein, P., Suhl, U., Busse, A., & Kaiser, G. (2014). Is teachers’ general pedagogical knowledge a premise for...
  • Krstić, K. (2015). Attachment in the student-teacher relationship as a factor of school achievement. Teaching Innovation, 28(3), 167–188.
  • Leinhardt, G. (1986). Expertise in mathematics teaching. Educational Leadership, 43, 28–33.
  • Li, Y., & Kaiser, G. (2011). Expertise in mathematics instruction: advancing research and practice from an international perspective....
  • Merriam, S. R. (1998). Qualitative research and case study applications in education. San Francisco: Jossey Bass.
  • Mincu, M. E. (2009). Myth, rhetoric and ideology in eastern European education. European Education, 41(1), 55–78.
  • Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2016). TIMSS 2015 international results in mathematics. Retrieved from Boston...
  • OECD. (2013). PISA 2012 assessment and analytical framework: mathematics, reading, science, problem solving and financial literacy. Paris:...
  • OECD. (2016). PISA 2015 results (volume I): excellence and equity in education. Paris: OECD Publishing.
  • Palm, T. (2008). Impact of authenticity on sense making in word problem solving. Educational Studies in Mathematics, 67(1), 37–58.
  • Pavlović Babić, D., & Baucal, A. (2013). Inspiriši me, podrži me, PISA 2012 u Srbiji: prvi rezultati. Beograd: Institut za psihologiju.
  • Pepin, B. E. U., Xu, B., Trouche, L., & Wang, C. (2016). Developing a deeper understanding of mathematics teaching expertise: an examination...
  • Pešić, J., & Stepanović, I. (2004). Škola kao sredina za učenje-učenička percepcija i njihove strategije [School as a learning space—Students’...
  • Pierson, J. L. (2008). The relationship between patterns of classroom discourse and mathematics learning (unpublished dissertation). Austin:...
  • Radišić, J., & Baucal, A. (2015). Portret nastavnika matematike u srednjoj školi: kritička analiza dominantne prakse. Primenjena psihologija....
  • Radišić, J., & Baucal, A. (2016). "What about when the majority is excluded?": A Critical Eye on Language and Math Classrooms...
  • Radišić, J., Baucal, A., & Videnović, M. (2014). Unfolding the assessment process in a whole class mathematics setting. Psihološka istraživanja,...
  • Richland, L. E., Stigler, J. W., & Holyoak, K. J. (2012). Teaching the conceptual structure of mathematics. Educational Psychologist,...
  • Rittle-Johnson, B. (2017). Developing mathematics knowledge. Child Development Perspectives, 0(0), 1–7.
  • Romberg, T. A. (1992). Perspectives on scholarship and research methods. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching...
  • Säljö, R. (2009). Learning, theories of learning, and units of analysis in research. Educational Psychologist, 44(3), 202–208.
  • Santagata, R., & Yeh, C. (2016). The role of perception, interpretation, and decision making in the development of beginning teachers’...
  • Schneider, M., Rittle-Johnson, B., & Star, J. R. (2011). Relations among conceptual knowledge, procedural knowledge, and procedural flexibility...
  • Schoenfeld, A. H. (1992). Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In D. A. Grouws...
  • Schoenfeld, A. H. (2014). Mathematical problem solving. London: Academic Press.
  • Schoenfeld, A. H., & Kilpatrick, J. (2008). Toward a theory of proficiency in teaching mathematics. In T. Wood & D. Tirosh (Eds.),...
  • Sherin, M. G., & van Es, E. A. (2009). Effects of video club participation on teachers’ professional vision. Journal of Teacher Education,...
  • Sherin, M. G., Jacobs, V. R., & Philipp, R. A. (Eds.). (2011). Mathematics teacher noticing: seeing through teachers’ eyes. New York:...
  • Shulman, L. (1987). Knowledge and teaching: foundations of the new reform. Harvard Educational Review, 57, 1–22.
  • Smith, M. S. (2001). Practice-based professional development for teachers of mathematics. Reston: National Council of Teachers of Mathematics.
  • Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: an analysis of...
  • Teuscher, D., Moore, K. C., & Carlson, M. P. (2016). Decentering: a construct to analyze and explain teacher actions as they relate to...
  • Verschaffel, V., Greer, B., & de Corte, E. (Eds.). (2000). Making sense of word problems. Heereweg: Swets & Zeitlinger.
  • Verschaffel, L., Depaepe, F., & Van Dooren, W. (2015). Individual differences in word problem solving, The Oxford Handbook of Numerical...
  • Wijaya, A., van den Heuvel-Panhuizen, M., Doorman, M., & Robitzsch, A. (2014). Difficulties in solving context-based PISA mathematics...
  • Wyndhamn, J., & Säljö, R. (1997). Word problems and mathematical reasoning—a study of children’s mastery of reference and meaning in textual...