Expectation versus Variation: Students’ Decision Making in a Chance Environment

Abstract This study explores school students’ understanding of variation within a probabilistic setting involving spinners. Sixty‐six students in Grades 3 to 9 answered survey questions involving a single 50/50 spinner and then were interviewed using a protocol involving compound events with different types of spinners (50/50 and 25/75). Of interest in interviews were students’ initial responses and changes in response and reasoning that occurred after experimentation with the spinners. Because there was the possibility of variation occurring in the experiments that could be considered contrary to expectation, responses following experimentation were analysed based on their appropriateness in terms of the observed experimental outcome. Data were used to determine a developmental progression among the students in the study and data from survey responses were considered in relation to the interview data. Differences were found between primary and secondary students. The outcomes of the study lead to suggest...

[1]  Alexander Pollatsek,et al.  Inconsistencies in Students' Reasoning about Probability. , 1993 .

[2]  Jane Watson,et al.  Variation in a Chance Sampling Setting: The Lollies Task , 2002 .

[3]  Jane Watson,et al.  Development of understanding of sampling for statistical literacy , 2000 .

[4]  Jane Watson,et al.  Development of the concept of statistical variation: An exploratory study , 2000 .

[5]  C. Wild,et al.  Statistical Thinking in Empirical Enquiry , 1999 .

[6]  D. Vere-Jones,et al.  Proceedings of the Second International Conference on Teaching Statistics , 1989 .

[7]  A. Tversky,et al.  BELIEF IN THE LAW OF SMALL NUMBERS , 1971, Pediatrics.

[8]  Jane Watson,et al.  The measurement of school students' understanding of statistical variation , 2003 .

[9]  A. Tversky,et al.  Subjective Probability: A Judgment of Representativeness , 1972 .

[10]  Rob Torok.  Putting the Variation into Chance and Data. , 2000 .

[11]  Jane Watson,et al.  The development of chance measurement , 1997 .

[12]  John B. Biggs.  Modes of learning, forms of knowing, and ways of schooling , 2005 .

[13]  Kathleen E. Metz.  Emergent Understanding and Attribution of Randomness: Comparative Analysis of the Reasoning of Primary Grade Children and Undergraduates. , 1998 .

[14]  Lynn Arthur Steen,et al.  On the shoulders of giants: new approaches to numeracy , 1990 .

[15]  D. Green.  A Longitudinal Study of Pupils' Probability Concepts , 1990 .

[16]  Maxine Pfannkuch,et al.  Statistical Thinking: One Statistician's Perspective , 1997 .

[17]  Maxine Pfannkuch,et al.  How Faithful Is Old Faithful? Statistical Thinking: A Story of Variation and Prediction , 2002 .

[18]  Matthew B. Miles,et al.  Qualitative Data Analysis: An Expanded Sourcebook , 1994 .

[19]  J. Shaughnessy,et al.  Secondary Students' Performance on Data and Chance in the 1996 NAEP , 1999 .

[20]  Barbara J. Dougherty,et al.  Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education , 2020 .

[21]  Chris Reading,et al.  Reasoning About Variation , 2004 .

[22]  Matthew Ciancetta,et al.  STUDENTS' UNDERSTANDING OF VARIABILITY IN A PROBABILITY ENVIRONMENT , 2002 .

[23]  C. Konold,et al.  Informal Conceptions of Probability , 1989 .

[24]  Joan Garfield,et al.  The challenge of developing statistical literacy, reasoning and thinking , 2004 .

[25]  Elizabeth C. Hirschman,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[26]  Jane Watson,et al.  Reasoning and Expressing Probability in Students' Judgements of Coin Tossing , 2000 .

[27]  Jane Watson,et al.  Emerging Concepts in Chance and Data , 2002 .