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Developing Problem Solving Skills in Elementary School

The Case of Data Analysis, Statistics, and Probability

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Proficiency and Beliefs in Learning and Teaching Mathematics

Part of the book series: Mathematics Teaching and Learning ((MTAL))

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Abstract

If somebody asked us to address the merits of Alan Schoenfeld and Günter Törner for mathematics education in a single sentence we would probably argue that they are mathematicians and mathematics educators who are able to think mathematically in both contexts and to share their way of thinking with both communities.

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References

  • Bullock, M., & Ziegler, A. (1999). Scientific thinking: Development and individual differences. In F. E. Weinert & W. Schneider (Eds.), Individual development from 3 to 12 (pp. 38–54). New York, NY: Cambridge University Press.

    Google Scholar 

  • Bullock, M., Sodian, B., & Koerber, S. (2009). Doing experiments and understanding science: Development of scientific reasoning from childhood to adulthood. In W. Schneider & M. Bullock (Eds.), Human development from early childhood to early adulthood. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Common Core State Standards Initiative (CCSSI) (2010). Common Core State Standards for Mathematics. Retrieved 2011/11/15 from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf.

  • Duncker, K. (1935). Zur Psychologie des produktiven Denkens. Berlin: Springer.

    Google Scholar 

  • Fischbein, E. (1987). Intuition in science and mathematics. Dordrecht: Reidel.

    Google Scholar 

  • Fischbein, E., & Schnarch, D. (1997). The evolution with age of probabilistic intuitively based misconceptions. Journal for Research in Mathematics Education, 28, 96–105.

    Article  Google Scholar 

  • Green, D. R. (1982). Probability concepts in 11–16 year old pupils. University of Technology, Loughborough, England Report of Research, CAMET.

    Google Scholar 

  • Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence.New York, NY: Basic Books.

    Google Scholar 

  • Koerber, S., Sodian, B., Kropf, N., Mayer, D., & Schwippert, K. (2011). Die Entwicklung des wissenschaftlichen Denkens im Grundschulalter. Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie, 43(1), 16–21.

    Article  Google Scholar 

  • Koerber, S., Sodian, B., Thoermer, C., & Nett, U. (2005). Scientific reasoning in young children. Preschoolers’ ability to evaluate covariation evidence. Swiss Journal of Psychology, 64, 141–152.

    Article  Google Scholar 

  • Kuhn, D. (2011). What is scientific thinking and how does it develop? In U. Goswami (Ed.), The Wiley-Blackwell handbook of childhood cognitive development. West Sussex: BlackWell Publishers.

    Google Scholar 

  • Kuhn, D., & Pearsall, S. (2000). Developmental origins of scientific thinking. Journal of Cognition and Development, 1, 113–129.

    Article  Google Scholar 

  • Kultusministerkonferenz (KMK). (2004). Bildungsstandards im Fach Mathematik für den Primarbereich. Beschluss der Kultusministerkonferenz vom 15.10.2004. München: Luchterhand.

    Google Scholar 

  • Lindmeier, A., Reiss, K., Ufer, S., Barchfeld, P., & Sodian, B. (2011). Umgang mit wissenschaftlicher Evidenz in den Jahrgangsstufen 2, 4 und 6: Stochastische Basiskonzepte und Kontingenztafelanalyse. In R. Haug & L. Holzäpfel (Eds.), Beiträge zum Mathematikunterricht 2011. Münster: WTM.

    Google Scholar 

  • McKenzie, C. R. M. (1994). The accuracy of intuitive judgment strategies: Covariation assessment and bayesian inference. Cognitive Psychology, 26(3), 209–239.

    Article  Google Scholar 

  • National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: NCTM.

    Google Scholar 

  • Reiss, K., & Winkelmann, H. (2008). Kompetenzstufenmodelle für das Fach Mathematik im Primarbereich. In D. Granzer, O. Köller, A. Bremerich-Vos, K. Reiss, & G. Walther (Eds.), Bildungsstandards Deutsch und Mathematik. Leistungsmessung in der Grundschule (pp. 120–141). Weinheim: Beltz.

    Google Scholar 

  • Reiss, K., Barchfeld, P., Lindmeier, A.M., Sodian, B., & Ufer, S. (2011). Interpreting scientific evidence: Primary student’s understanding of base rates and contingency tables. In B. Ubuz (Ed.), Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (pp. 33-40). Ankara (Turkey): PME.

    Google Scholar 

  • Reiss, K., Hellmich, F., & Thomas, J. (2002). Individuelle und schulische Bedingungsfaktoren für Argumentationen und Beweise im Mathematikunterricht. In M. Prenzel & J. Doll. (Eds.), Bildungsqualität von Schule: Schulische und außerschulische Bedingungen mathematischer, naturwissenschaftlicher und überfachlicher Kompetenzen. 45. Beiheft der Zeitschrift für Pädagogik (pp. 51–64). Weinheim: Beltz.

    Google Scholar 

  • Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic Press.

    Google Scholar 

  • Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334-370). New York, NY: MacMillan.

    Google Scholar 

  • Schoenfeld, A. H. (1999). Looking toward the 21st century: Challenges of educational theory and practice. Educational Researcher, 28(7), 4–14.

    Article  Google Scholar 

  • Schoenfeld, A. H. (2011). How we think. A theory of goal-oriented decision making and its educational applications. New York: Routledge.

    Google Scholar 

  • Shtulman, A., & Carey, S. (2007). Improbable or impossible? How children reason about the possibility of extraordinary events. Child Development, 78, 1015–1032.

    Article  Google Scholar 

  • Sodian, B., & Bullock, M. (2008). Scientific reasoning – Where are we now? Cognitive Development, 23(4), 431–434.

    Article  Google Scholar 

  • Sodian, B., Zaitchik, D., & Carey, S. (1991). Young cildren’s differentiation of hypothetical beliefs from evidence. Child Development, 62, 753–766.

    Article  Google Scholar 

  • Törner, G. (2004). Mathematische Weltbilder und ihr Einfluss auf Bildung. Wissenschaftler und Verantwortung – Mitteilungen der Gesellschaft für Verantwortung in der Wissenschaft (GVW), 12(3), 15–29.

    Google Scholar 

  • Törner, G. (2009). Mathematical problem solving around the world: Patterns and trends. Paper presented at the EARLI conference, August 2009, Amsterdam (the Netherlands).

    Google Scholar 

  • Törner, G., & Zielinski, U. (1992). Problemlösen als integraler Bestandteil des Mathematikunterrichts – Einblicke und Konsequenzen. Journal für Mathematikdidaktik, 13, 253–270.

    Google Scholar 

  • Törner, G., Schoenfeld, A. H., & Reiss, K. (2007). Problem solving around the world: Summing up the state of the art. ZDM – The International Journal on Mathematics Education, 39, 353.

    Google Scholar 

  • Zimmerman, C. (2007). The development of scientific thinking skills in elementary and middle school. Developmental Review, 27, 172–223.

    Article  Google Scholar 

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Reiss, K., Lindmeier, A.M., Barchfeld, P., Sodian, B. (2013). Developing Problem Solving Skills in Elementary School. In: Li, Y., Moschkovich, J.N. (eds) Proficiency and Beliefs in Learning and Teaching Mathematics. Mathematics Teaching and Learning. SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6209-299-0_4

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