A Framework for Characterizing Children's Statistical Thinking

Based on a review of research and a cognitive development model (Biggs & Collis, 1991), we formulated a framework for characterizing elementary children's statistical thinking and refined it through a validation process. The 4 constructs in this framework were describing, organizing, representing, and analyzing and interpreting data. For each construct, we hypothesized 4 thinking levels, which represent a continuum from idiosyncratic to analytic reasoning. We developed statistical thinking descriptors for each level and construct and used these to design an interview protocol. We refined and validated the framework using data from protocols of 20 target students in Grades 1 through 5. Results of the study confirm that children's statistical thinking can be described according to the 4 framework levels and that the framework provides a coherent picture of children's thinking, in that 80% of them exhibited thinking that was stable on at least 3 constructs. The framework contributes domain-specific theory for characterizing children's statistical thinking and for planning instruction in data handling.

[1]  Jane Watson,et al.  Longitudinal Development of Chance Measurement. , 1998 .

[2]  Cynthia W. Langrall,et al.  A framework for assessing and nurturing young children‘s thinking in probability , 1997 .

[3]  Students' Thinking and Writing in the Context of Probability , 1998 .

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

[5]  Cynthia W. Langrall,et al.  Students' Probabilistic Thinking in Instruction. , 1999 .

[6]  Frances R. Curcio,et al.  Early Childhood Corner: Exploring Data: Kindergarten Children Do It Their Way. , 1996 .

[7]  Lionel Pereira-Mendoza,et al.  Students' Concepts of Bar Graphs - Some Preliminary Findings , 1990 .

[8]  Bob Moon.  A Guide to the National Curriculum , 1991 .

[9]  S. Strauss,et al.  The Development of Children's Concepts of the Arithmetic Average. , 1988 .

[10]  Young Students’Informal Statistical Knowledge , 1999 .

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

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

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

[14]  Frances R. Curcio,et al.  Comprehension of Mathematical Relationships Expressed in Graphs. , 1987 .

[15]  David S. Moore,et al.  Statistics: Concepts and Controversies , 1979 .

[16]  C. KONOLD,et al.  STUDENTS ANALYZING DATA : RESEARCH OF CRITICAL BARRIERS , 1998 .

[17]  J. Shaughnessy.  Research in probability and statistics: Reflections and directions. , 1992 .

[18]  Thomas A. Romberg,et al.  Rational numbers : an integration of research , 1993 .

[19]  James E. Tarr,et al.  A framework for assessing middle school students’ thinking in conditional probability and independence , 1997 .

[20]  Susan Jo Russell,et al.  Children's Concepts of Average and Representativeness. , 1995 .

[21]  James M. Moser,et al.  The Acquisition of Addition and Subtraction Concepts in Grades One through Three. , 1984 .

[22]  Brenda Stones.  A guide to the National Curriculum , 1995 .

[23]  Susan B. Empson,et al.  A Longitudinal Study of Learning to Use Children's Thinking in Mathematics Instruction , 1996, Journal for Research in Mathematics Education.

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

[25]  Paul Cobb,et al.  Assessment of a problem-centered second-grade mathematics project. , 1991 .

[26]  Nancy K. Mack,et al.  Learning Fractions with Understanding: Building upon Informal Knowledge. , 1988 .

[27]  Ian Putt,et al.  A model for nurturing and assessing multidigit number sense among first grade children , 1994 .

[28]  A. Beaton.  Mathematics Achievement in the Primary School Years. IEA's Third International Mathematics and Science Study (TIMSS). , 1996 .

[29]  Richard T. White,et al.  Book Review: Evaluating the Quality of Learning: The SOLO Taxonomy (Structure of the Observed Learning Outcome) , 1983 .

[30]  Richard Lehrer,et al.  Exploring Children's Data Modeling , 1996 .

[31]  최영한,et al.  미국 NCTM의 Principles and Standards for School Mathematics에 나타난 수학과 교수,학습의 이론 , 2002 .

[32]  Lauren B. Resnick,et al.  Toward a Cognitive Theory of Instruction. , 1984 .

[33]  Martin A. Simon.  Reconstructing Mathematics Pedagogy from a Constructivist Perspective. , 1995 .

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

[35]  Ian Putt,et al.  Multidigit number sense: A framework for instruction and assessment , 1996 .