REASONING ABOUT DATA ANALYSIS

OVERVIEW The purpose of this chapter is to describe and analyze the ways in which middle school students begin to reason about data and come to understand exploratory data analysis (EDA). The process of developing reasoning about data while learning skills, procedures, and concepts is described. In addition, the students are observed as they begin to adopt and exercise some of the habits and points of view that are associated with statistical thinking. The first case study focuses on the development of a global view of data and data representations. The second case study concentrates on design of a meaningful EDA learning environment that promotes statistical reasoning about data analysis. In light of the analysis, a description of what it may mean to learn to reason about data analysis is proposed and educational and curricular implications are drawn.

[1]  Cindy E. Hmelo-Silver,et al.  Problem-based Learning: A Research Perspective on Learning Interactions , 2000 .

[2]  Andrew C. Gross,et al.  Statistics in the 21st Century , 1996 .

[3]  Rolf Biehler,et al.  Software for Learning and for Doing Statistics , 1997 .

[4]  H. J. Arnold.  Introduction to the Practice of Statistics , 1990 .

[5]  D. Schifter,et al.  A research companion to Principles and standards for school mathematics , 2003 .

[6]  Jeremy Kilpatrick,et al.  International handbook of mathematics education , 1997 .

[7]  Janet Ainley.  Re-viewing Graphing: Traditional and Intuitive Approaches , 1995 .

[8]  W. Cleveland.  The elements of graphing data , 1986 .

[9]  L. Resnick.  Treating Mathematics as an Ill-Structured Discipline. , 1988 .

[10]  D. S. Moore,et al.  Mathematics, statistics, and teaching , 1997 .

[11]  D. S. Moore,et al.  New Pedagogy and New Content: The Case of Statistics , 1997 .

[12]  Joan Garfield,et al.  How students learn statistics , 1995 .

[13]  E. Ziegel.  Introduction to the Practice of Statistics (2nd ed.) , 1994 .

[14]  Robert B. Davis,et al.  Constructivist Views on the Teaching and Learning of Mathematics , 1990 .

[15]  Edward A. Silver,et al.  The teaching and assessing of mathematical problem solving , 1988 .

[16]  Neville Hunt.  Teaching Statistical Concepts Using Spreadsheets , 1996 .

[17]  Douglas A. Grouws,et al.  Handbook of research on mathematics teaching and learning , 1992 .

[18]  G. Brousseau.  Theory of didactical situations in mathematics , 1997 .

[19]  Dani Ben-Zvi,et al.  TOWARDS A CHARACTERIZATION AND UNDERSTANDING OF STUDENTS' LEARNING IN AN INTERACTIVE STATISTICS ENVIRONMENT , 1998 .

[20]  David Green,et al.  Data Handling , 1994 .

[21]  Sue Willis,et al.  A national statement on mathematics for Australian schools , 1991 .

[22]  Rolf Biehler,et al.  Software Tools and Mathematics Education: The Case of Statistics , 1993 .

[23]  P. Cobb,et al.  Sociomathematical Norms, Argumentation, and Autonomy in Mathematics. , 1996 .

[24]  Dani Ben-Zvi,et al.  Junior high school students' construction of global views of data and data representations , 2001 .

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

[26]  Frederick Mosteller,et al.  Data Analysis and Regression , 1978 .

[27]  Sharon Price Bonham,et al.  Education and Employment , 1971 .

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

[29]  D. Ben-Zvi.  Toward Understanding the Role of Technological Tools in Statistical Learning , 2000 .

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

[31]  Dani Ben-Zvi.  SEVENTH GRADE STUDENTS' SENSE MAKING OF DATA AND DATA REPRESENTATIONS , 2002 .

[32]  Lyn D. English,et al.  Handbook of International Research in Mathematics Education , 2002 .

[33]  A. Schoenfeld.  Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics (Reprint) , 2009 .

[34]  Joan Garfield,et al.  Curricular goals and assessment challenges in statistics education , 1997 .

[35]  John W. Tukey,et al.  Exploratory Data Analysis. , 1979 .

[36]  Magdalene Lampert,et al.  When the Problem Is Not the Question and the Solution Is Not the Answer: Mathematical Knowing and Teaching , 1990 .

[37]  G. S. Monk.  Students' Understanding of Functions in Calculus Courses. , 1994 .

[38]  Alan Graham,et al.  Statistical investigations in the secondary school , 1987 .

[39]  Paul Cobb,et al.  Individual and Collective Mathematical Development: The Case of Statistical Data Analysis. , 1999 .

[40]  Michal Yerushalmy,et al.  Mathematical problem posing: Implications for facilitating student inquiry in classrooms , 1990 .

[41]  L. Vygotsky.  Mind in Society: The Development of Higher Psychological Processes: Harvard University Press , 1978 .

[42]  Joan Garfield,et al.  The Assessment Challenge in Statistics Education , 1997 .