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Development of student understanding of outcomes involving two or more dice


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Watson, JM and Kelly, BA 2007 , 'Development of student understanding of outcomes involving two or more dice' , International Journal of Science and Mathematics Education, vol. Online, no. Online , EJ .

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Data from 154 interviews with students in grades 3 to 13 were analyzed to
suggest a developmental progression of conceptual understanding associated with the
sample space for two ordinary six-sided dice tossed simultaneously. The model was then
considered in the light of responses to an extension task involving three six-sided dice
with four sides painted black and two white. Forty-five of the interviews were
longitudinal interviews of students 3 or 4 years after the original interviews, allowing
for analysis of change in levels of understanding across time. This study suggests some
of the intuitions and understandings that form the intermediate steps to a complete
understanding of outcomes for two dice, as well as documenting the conceptual
regression likely to occur when a more difficult task is encountered. Links to previous
research, including well-known misconceptions, and educational implications of the
model are among the discussion points.

Item Type: Article
Authors/Creators:Watson, JM and Kelly, BA
Keywords: cognitive development, dice, interview data, longitudinal data, probability, school students, statistics education
Journal or Publication Title: International Journal of Science and Mathematics Education
Publisher: Springer
ISSN: 1473-1774
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