How do high school students solve probability problems? A mixed methods study on probabilistic reasoning

References

• Baker-Doyle, K. J. 2015. “Stories in Networks and Networks in Stories: A Tri-modal Model for Mixed-methods Social Network Research on Teachers.” International Journal of Research and Method in Education 38: 72–82. doi:10.1080/1743727X.2014.911838.
   Web of Science ®Google Scholar
• Batanero, C., and E. Sanchez. 2005. “What Is the Nature of High School Students’ Conceptions and Misconceptions about Probability?” In Exploring Probability in School. Challenges for Teaching and Learning, edited by G. A. Jones, 241–266. New York: Springer.
   Google Scholar
• Biesta, G. J. J. 2010. “Pragmatism and the Philosophical Foundations of Mixed Methods Research.” In Sage Handbook of Mixed Methods in Social and Behavioral Research, edited by A. Tashakkori and C. Teddlie, 2nd ed., 95–118. Thousand Oaks, CA: Sage.
   Google Scholar
• Brenner, M. E. 2006. “Interviewing in Educational Research.” In Handbook of Complementary Methods in Education Research, edited by J. L. Green, G. Camilli, and P. B. Elmore, 357–370. Mahwah, NJ: Lawrence Erlbaum.
   Google Scholar
• Castro Sotos, A., S. Vanhoof, W. Van Den Noortgate, and P. Onghena. 2007. “Students’ Misconceptions of Statistical Inference: A Review of the Empirical Evidence from Research on Statistics Education.” Educational Research Review 2: 98–113. doi:10.1016/j.edurev.2007.04.001.
   Google Scholar
• Cohen, S., G. Smith, R. A. Chechile, G. Burns, and F. Tsai. 1996. “Identifying Impediments to Learning Probability and Statistics from an Assessment of Instructional Software.” Journal of Educational and Behavioral Statistics 21: 35–54. doi:10.3102/10769986021001035.
   Web of Science ®Google Scholar
• Collins, K., A. Onwuegbuzie, and Q. Jiao. 2007. “A Mixed Methods Investigation of Mixed Methods Sampling Designs in Social and Health Science Research.” Journal of Mixed Methods Research 1: 267–294. doi:10.1177/1558689807299526.
   Web of Science ®Google Scholar
• Department of Education and Training. 2008. Education in Flanders: The Flemish Educational Landscape in a Nutshell. Brussels: Flemish Government.
   Google Scholar
• Feilzer, M. Y. 2010. “Doing Mixed Methods Research Pragmatically: Implications for the Rediscovery of Pragmatism as a Research Paradigm.” Journal of Mixed Methods Research 4: 6–16. doi:10.1177/1558689809349691.
   Web of Science ®Google Scholar
• Flick, U. 2009. An Introduction to Qualitative Research. 4th ed. London: Sage.
   Google Scholar
• Garfield, J. 2003. “Assessing Statistical Reasoning.” Statistics Education Research Journal 2: 22–38.
   Web of Science ®Google Scholar
• Garfield, J. B., and A. Ahlgren. 1988. “Difficulties in Learning Basic Concepts in Statistics: Implications for Research.” Journal for Research in Mathematics Education 19: 44–63. doi: 10.2307/749110
   Web of Science ®Google Scholar
• Garfield, J., and R. delMas. 2010. “A Web Site that Provides Resources for Assessing Students’ Statistical Literacy, Reasoning and Thinking.” Teaching Statistics 32: 2–7. doi:10.1111/j.1467-9639.2009.00373.x.
   Google Scholar
• Gillard, E., W. Van Dooren, W. Schaeken, and L. Verschaffel. 2009. “Dual Processes in the Psychology of Mathematics Education and Cognitive Psychology.” Human Development 52: 95–108. doi:10.1159/000202728.
   Web of Science ®Google Scholar
• Greene, J. C. 2005. “The Generative Potential of Mixed Methods Inquiry.” International Journal of Research and Method in Education 28: 207–211. doi:10.1080/01406720500256293.
   Google Scholar
• Greene, J. C. 2007. Mixed Methods in Social Inquiry. San Fransisco, CA: Jossey-Bass.
   Google Scholar
• Greene, J. C., V. J. Caracelli, and W. F. Graham. 1989. “Toward a Conceptual Framework for Mixed-Method Evaluation Designs.” Educational Evaluation and Policy Analysis 11: 255–274. doi:10.3102/01623737011003255.
   Google Scholar
• Heyvaert, M., B. Maes, and P. Onghena. 2013. “Mixed Methods Research Synthesis: Definition, Framework, and Potential.” Quality and Quantity 47: 659–676. doi:10.1007/s11135-011-9538-6.
   Web of Science ®Google Scholar
• Humphrey, P. T., and J. Masel. Forthcoming. “Outcome Orientation. A Misconception of Probability that Harms Medical Research and Practice.” Physics Education. Retrieved from http://xxx.tau.ac.il/abs/1412.4604.
   Google Scholar
• Ivankova, N. V., J. W. Creswell, and S. L. Stick. 2006. “Using Mixed-Methods Sequential Explanatory Design: From Theory to Practice.” Field Methods 18: 3–20. doi:10.1177/1525822X05282260.
   Web of Science ®Google Scholar
• Jones, G. A. 2005. Exploring Probability in School: Challenges for Teaching and Learning. New York: Springer.
   Google Scholar
• Kahneman, D., P. Slovic, and A. Tversky. 1982. Judgment under Uncertainty: Heuristics and Biases. Cambridge: Cambridge University Press.
   Google Scholar
• Konold, C. 1991. “Understanding Students’ Beliefs about Probability.” In Radical Constructivism in Mathematics Education, edited by E. Von Glasersfeld, 139–156. Dordrecht: Kluwer.
   Google Scholar
• Konold, C. 1995. “Issues in Assessing Conceptual Understanding in Probability and Statistics.” Journal of Statistics Education 3 (1). http://www.amstat.org/publications/jse/v3n1/konold.htmllimo.libis.be. doi: 10.1080/10691898.1995.11910479
   Google Scholar
• Konold, C., A. Pollatsek, A. Well, J. Lohmeier, and A. Lipson. 1993. “Inconsistencies in Students’ Reasoning about Probability.” Journal for Research in Mathematics Education 24: 392–414. doi:10.2307/749150.
   Web of Science ®Google Scholar
• Lawrence, D. P. 1993. “Quantitative Versus Qualitative Evaluation: A False Dichotomy?” Environmental Impact Assessment Review 13: 3–11. doi:10.1016/0195-9255(93)90025-7.
   Google Scholar
• Lecoutre, M.-P. 1992. “Cognitive Models and Problem Spaces in ‘Purely Random’ Situations.” Educational Studies in Mathematics 23: 557–568. doi:10.1007/BF00540060.
   Google Scholar
• Leech, N. L., and A. J. Onwuegbuzie. 2009. “A Typology of Mixed Methods Research Designs.” Quality and Quantity 43: 265–275. doi:10.1007/s11135-007-9105-3.
   Web of Science ®Google Scholar
• Leron, U., and O. Hazzan. 2006. “The Rationality Debate: Application of Cognitive Psychology to Mathematics Education.” Educational Studies in Mathematics 62: 105–126. doi:10.1007/s10649-006-4833-1.
   Google Scholar
• Maxwell, J. A. 2016. “Expanding the History and Range of Mixed Methods Research.” Journal of Mixed Methods Research 10: 12–27. doi:10.1177/1558689815571132.
   Web of Science ®Google Scholar
• Morgan, D. L. 2007. “Paradigms Lost and Pragmatism Regained: Methodological Implications of Combining Qualitative and Quantitative Methods.” Journal of Mixed Methods Research 1: 48–76. doi:10.1177/2345678906292462.
   Web of Science ®Google Scholar
• Morsanyi, K., C. Primi, F. Chiesi, and S. Handley. 2009. “The Effects and Side-effects of Statistics Education: Psychology Students’ (Mis-)conceptions of Probability.” Contemporary Educational Psychology 34: 210–220. doi:10.1016/j.cedpsych.2009.05.001.
   Web of Science ®Google Scholar
• Newman, I. 2008. Mixed Methods Research: Exploring the Interactive Continuum. Carbondale: Southern Illinois University Press.
   Google Scholar
• Newman, I., and C. R. Benz. 1998. Qualitative-quantitative Research Methodology: Exploring the Interactive Continuum. Carbondale: Southern Illinois University Press.
   Google Scholar
• Onwuegbuzie, A. J., and N. L. Leech. 2005. “On Becoming a Pragmatic Researcher: The Importance of Combining Quantitative and Qualitative Research Methodologies.” International Journal of Social Research Methodology 8: 375–387. doi:10.1080/13645570500402447.
   Google Scholar
• Osman, M. 2004. “An Evaluation of Dual-process Theories of Reasoning.” Psychonomic Bulletin and Review 11: 988–1010. doi:10.3758/BF03196730.
   PubMed Web of Science ®Google Scholar
• Patton, M. Q. 1990. Qualitative Evaluation and Research Methods. 2nd ed. Beverly Hills, CA: Sage.
   Google Scholar
• Piaget, J., and B. Inhelder. 1965. The Origin of the Idea of Chance in Children. London: Routledge and Kegan Paul.
   Google Scholar
• Plano Clark, V. L. 2010. “The Adoption and Practice of Mixed Methods: US Trends in Federally Funded Health-related Research.” Qualitative Inquiry 16: 428–440. doi:10.1177/1077800410364609.
   Web of Science ®Google Scholar
• Pratt, D. 2000. “Making Sense of the Total of Two Dice.” Journal for Research in Mathematics Education 31: 602–625. doi:10.2307/749889.
   Google Scholar
• Reams, P., and D. Twale. 2008. “The Promise of Mixed Methods: Discovering Conflicting Realities in the Data.” International Journal of Research and Method in Education 31: 133–142. doi:10.1080/17437270802124509.
   Google Scholar
• Shaughnessy, J. M. 1977. “Misconceptions of Probability: An Experiment with a Small-group, Activity-based, Model Building Approach to Introductory Probability at the College Level.” Educational Studies in Mathematics 8: 295–316. doi:10.1007/BF00385927.
   Google Scholar
• Sloman, S. A. 1996. “The Empirical Case for Two Systems of Reasoning.” Psychological Bulletin 119: 3–22. doi:10.1037/0033-2909.119.1.3.
   Web of Science ®Google Scholar
• Stanovich, K. E., and R. F. West. 2000. “Individual Differences in Reasoning: Implications for the Rationality Debate.” Behavioral and Brain Sciences 23: 645–665. doi: 10.1017/S0140525X00003435
   PubMed Web of Science ®Google Scholar
• Stanovich, K. E., and R. F. West. 2008. “On the Relative Independence of Thinking Biases and Cognitive Ability.” Journal of Personality and Social Psychology 94: 672–695. doi:10.1037/0022-3514.94.4.672.
   PubMed Web of Science ®Google Scholar
• Tashakkori, A., and C. Teddlie. 1998. Mixed Methodology. Combining Qualitative and Quantitative Approaches. Thousand Oaks, CA: Sage.
   Google Scholar
• Teddlie, C., and F. Yu. 2007. “Mixed Methods Sampling: A Typology with Examples.” Journal of Mixed Methods Research 1: 77–100. doi:10.1177/2345678906292430.
   Web of Science ®Google Scholar
• Tversky, A., and D. Kahneman. 1974. “Judgment under Uncertainty: Heuristics and Biases.” Science 185: 1124–1131. doi:10.1126/science.185.4157.1124.
   PubMed Web of Science ®Google Scholar
• Van Dooren, W., D. De Bock, D. Weyers, and L. Verschaffel. 2004. “The Predictive Power of Intuitive Rules: A Critical Analysis of the Impact of ‘More A-More B’ and ‘Same A-Same B.’” Educational Studies in Mathematics 56: 179–207. doi:10.1023/B:EDUC.0000040379.26033.0d.
   Google Scholar
• Vanhoof, S., A. Castro Sotos, L. Verschaffel, and P. Onghena. 2009. “Vragenlijst Statistisch Redeneren.” Wiskunde en Onderwijs 35: 305–319.
   Google Scholar
• Vanhoof, S., P. Onghena, L. Verschaffel, W. Van Dooren, W. Van Den Noortgate, and A. Castro Sotos. 2006. “Attitudes Towards Statistics and their Relationship with Short- and Long-term Exam Results.” Journal of Statistics Education 14 (3). http://www.amstat.org/publications/jse/v14n3/vanhoof.html. doi: 10.1080/10691898.2006.11910588
   Google Scholar
• Walsh, K. 2012. “Quantitative vs Qualitative Research: A False Dichotomy.” Journal of Research in Nursing 17: 9–11. doi:10.1177/1744987111432053.
   Google Scholar
• Watson, J. M. 2006. Statistical Literacy at School: Growth and Goals. Mahwah, NJ: Lawrence Erlbaum Associates.
   Google Scholar