Statistical problem posing, problem refining, and further reflection in grade 6

This report is based on an activity completed by 89 Grade 6 students carrying out a statistical investigation with a focus on posing an initial question given a context and then refining it for a chosen data set. Having reached a conclusion based on evidence from their data analysis, students were given additional information on the context and asked to reconsider their conclusions and degree of certainty associated with them. Data from student workbooks were used to assess students' capacity to engage in the extensions of a statistical investigation not usually encountered at the school level. Results showed approximately 70% of students were able to carry out the complete investigation and justify a meaningful decision.

[1]  Stephen I. Brown,et al.  The Art of Problem Posing , 1983 .

[2]  C. Hirsch.  Curriculum and Evaluation Standards for School Mathematics , 1988 .

[3]  Kari Augustine.  Mystery Three, Find It, and Treasure Hunt , 2006 .

[4]  Lyn D. English,et al.  STEM: Challenges and opportunities for mathematics education , 2015 .

[5]  Refractor.  Uncertainty , 2001, The Lancet.

[6]  Efi Paparistodemou,et al.  Developing students’ reasoning about samples and sampling in the context of informal inferences , 2015 .

[7]  Young-Ok Kim.  미국 Common Core State Standards for Mathematics 소개 , 2011 .

[8]  G. Pólya,et al.  How to Solve It. A New Aspect of Mathematical Method. , 1945 .

[9]  C. Radhakrishna Rao,et al.  Teaching of statistics at the secondary level- an interdisciplinary approach , 1975 .

[10]  Kevin F. Collis,et al.  Evaluating the Quality of Learning: The SOLO Taxonomy , 1977 .

[11]  Joan Ferrini-Mundy,et al.  Principles and Standards for School Mathematics: A Guide for Mathematicians , 2000 .

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

[13]  Jane Watson,et al.  Modelling with authentic data in sixth grade , 2017 .

[14]  Jane Watson,et al.  Introducing the practice of statistics: are we environmentally friendly? , 2015 .

[15]  J. Biggs,et al.  Multimodal Learning and the Quality of Intelligent Behavior , 1991 .

[16]  Andee Rubin,et al.  A FRAMEWORK FOR THINKING ABOUT INFORMAL STATISTICAL INFERENCE , 2009, STATISTICS EDUCATION RESEARCH JOURNAL.

[17]  L. Schauble,et al.  Design Experiments in Educational Research , 2003 .

[18]  Katie Makar,et al.  DEVELOPING PRIMARY STUDENTS' ABILITY TO POSE QUESTIONS IN STATISTICAL INVESTIGATIONS , 2010 .

[19]  Katherine K. Wallman,et al.  Enhancing Statistical Literacy: Enriching Our Society , 1993 .

[20]  Edward A. Silver,et al.  Problem-posing research in mathematics education: looking back, looking around, and looking ahead , 2013 .

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

[22]  Jane Watson,et al.  Exploring variation in measurement as a foundation for statistical thinking in the elementary school , 2015 .

[23]  Edward S. Mooney,et al.  Models of Development in Statistical Reasoning , 2004 .

[24]  Chris Reading,et al.  AN EMERGING HIERARCHY OF REASONING ABOUT DISTRIBUTION: FROM A VARIATION PERSPECTIVE5 , 2006 .

[25]  A. Su,et al.  The National Council of Teachers of Mathematics , 1932, The Mathematical Gazette.

[26]  Randall E. Groth.  High school students’ levels of thinking in regard to statistical study design , 2003 .

[27]  Chris Reading,et al.  Reasoning About Data , 2018 .

[28]  Susanne P. Lajoie,et al.  Statistical reasoning of middle school children engaged in survey inquiry , 2007 .

[29]  Jane Watson,et al.  Statistical Literacy in the Elementary School: Opportunities for Problem Posing , 2015 .

[30]  Jane Watson,et al.  Reaction Time in Grade 5: Data Collection within the Practice of Statistics. , 2017 .

[31]  Jane Watson,et al.  Statistical Literacy at School: Growth and Goals , 2006 .

[32]  Dani Ben-Zvi,et al.  The Reasoning Behind Informal Statistical Inference , 2011 .

[33]  Jane Watson,et al.  Development of probabilistic understanding in fourth grade , 2016 .

[34]  Florence Mihaela Singer,et al.  Mathematical Problem Posing , 2015 .