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  • Author or Editor: Cynthia W. Langrall x
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Graham A. Jones, Cynthia W. Langrall, Carol A. Thornton and A. Timothy Mogill

In this study we evaluated the thinking of 3rd-grade students in relation to an instructional program in probability. The instructional program was informed by a research- based framework that included a description of students' probabilistic thinking. Both an early- and a delayed-instruction group participated in the program. Qualitative evidence from 4 target students revealed that overcoming a misconception in sample space, applying both part-part and part-whole reasoning, and using invented language to describe probabilities were key patterns in producing growth in probabilistic thinking. Moreover, 51% of the students exhibited the latter 2 learning patterns by the end of instruction, and both groups displayed significant growth in probabilistic thinking following the intervention.

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Graham A. Jones, Cynthia W. Langrall and Carol A. Thornton

Karen and Leon had been constructing their booth for the school fair. They had made a “pull the strings” game in which half the strings had one end painted red and the other half of the strings had one end painted blue. The strings are randomly placed over a board with the colored end hidden. After the first string is pulled, it is replaced to a random location so that ten strings are available for the second pull. A prize would be given whenever two strings of the same color were pulled. Leon was concerned that the game was not fair.