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

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Abstract
When studying a complex research phenomenon, a mixed methods design allows to answer a broader set of research questions and to tap into different aspects of this phenomenon, compared to a monomethod design. This paper reports on how a sequential equal status design (QUAN → QUAL) was used to examine students’ reasoning processes when solving probability problems. A select clustered sampling resulted in the inclusion of 168 high school students in a first, quantitative phase, in which a questionnaire was used to assess how they solved probability problems. This questionnaire included probability items that were based on the outcome orientation, the representativeness misconception, and the equiprobability bias. In a second, qualitative phase, 18 students who were purposefully sampled from the first research phase were interviewed in order to conduct an in-depth study of their probabilistic reasoning processes. In this paper, we illustrate and discuss how several mixed methods research purposes were realized throughout our study: development, expansion, and initiation.
Keywords
Mixed methods research, probabilistic reasoning, development, inititation, expansion

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MLA
Heyvaert, Mieke, Maarten Deleye, Lore Saenen, et al. “How Do High School Students Solve Probability Problems? A Mixed Methods Study on Probabilistic Reasoning.” INTERNATIONAL JOURNAL OF RESEARCH AND METHOD IN EDUCATION (2017): 1–23. Print.
APA
Heyvaert, Mieke, Deleye, M., Saenen, L., Van Dooren, W., & Onghena, P. (2017). How do high school students solve probability problems? A mixed methods study on probabilistic reasoning. INTERNATIONAL JOURNAL OF RESEARCH AND METHOD IN EDUCATION, 1–23.
Chicago author-date
Heyvaert, Mieke, Maarten Deleye, Lore Saenen, Wim Van Dooren, and Patrick Onghena. 2017. “How Do High School Students Solve Probability Problems? A Mixed Methods Study on Probabilistic Reasoning.” International Journal of Research and Method in Education: 1–23.
Chicago author-date (all authors)
Heyvaert, Mieke, Maarten Deleye, Lore Saenen, Wim Van Dooren, and Patrick Onghena. 2017. “How Do High School Students Solve Probability Problems? A Mixed Methods Study on Probabilistic Reasoning.” International Journal of Research and Method in Education: 1–23.
Vancouver
1.
Heyvaert M, Deleye M, Saenen L, Van Dooren W, Onghena P. How do high school students solve probability problems? A mixed methods study on probabilistic reasoning. INTERNATIONAL JOURNAL OF RESEARCH AND METHOD IN EDUCATION. Informa UK Limited; 2017;1–23.
IEEE
[1]
M. Heyvaert, M. Deleye, L. Saenen, W. Van Dooren, and P. Onghena, “How do high school students solve probability problems? A mixed methods study on probabilistic reasoning,” INTERNATIONAL JOURNAL OF RESEARCH AND METHOD IN EDUCATION, pp. 1–23, 2017.
@article{8509833,
  abstract     = {When studying a complex research phenomenon, a mixed methods design allows to answer a broader set of research questions and to tap into different aspects of this phenomenon, compared to a monomethod design. This paper reports on how a sequential equal status design (QUAN → QUAL) was used to examine students’ reasoning processes when solving probability problems. A select clustered sampling resulted in the inclusion of 168 high school students in a first, quantitative phase, in which a questionnaire was used to assess how they solved probability problems. This questionnaire included probability items that were based on the outcome orientation, the representativeness misconception, and the equiprobability bias. In a second, qualitative phase, 18 students who were purposefully sampled from the first research phase were interviewed in order to conduct an in-depth study of their probabilistic reasoning processes. In this paper, we illustrate and discuss how several mixed methods research purposes were realized throughout our study: development, expansion, and initiation.},
  author       = {Heyvaert, Mieke and Deleye, Maarten and Saenen, Lore and Van Dooren, Wim and Onghena, Patrick},
  issn         = {1743-727X},
  journal      = {INTERNATIONAL JOURNAL OF RESEARCH AND METHOD IN EDUCATION},
  keywords     = {Mixed methods research,probabilistic reasoning,development,inititation,expansion},
  language     = {eng},
  pages        = {1--23},
  publisher    = {Informa UK Limited},
  title        = {How do high school students solve probability problems? A mixed methods study on probabilistic reasoning},
  url          = {http://dx.doi.org/10.1080/1743727x.2017.1279138},
  year         = {2017},
}

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