Preservice Elementary Teachers' Conceptual and Procedural Knowledge of Mean, Median, and Mode

This article describes aspects of the statistical content knowledge of 46 preservice elementary school teachers. The preservice teachers responded to a written item designed to assess their knowledge of mean, median, and mode. The data produced in response to the written item were examined in light of the Structure of the Observed Learning Outcome (SOLO) taxonomy (Biggs & Collis, 1982, 1991) and Ma's (1999) conception of Profound Understanding of Fundamental Mathematics (PUFM). The article describes 4 levels of thinking in regard to comparing and contrasting mean, median, and mode. Several different categories of written definitions for each measure of central tendency are also described. Connections to previous statistical thinking literature are discussed, implications for teacher education are given, and directions for further research are suggested.

[1]  Richard S. Prawat,et al.  Teaching Mathematics for Understanding: Discussing Case Studies of Four Fifth-Grade Teachers , 1992, The Elementary School Journal.

[2]  Helen Chick,et al.  Cognition in the formal modes: Research mathematics and the SOLO taxonomy , 1998 .

[3]  James Hiebert,et al.  A Cognitive Approach to Meaningful Mathematics Instruction: Testing a Local Theory Using Decimal Numbers. , 1988 .

[4]  Zemira R. Mevarech.  A deep structure model of students' statistical misconceptions , 1983 .

[5]  Jane Watson,et al.  The Beginning of Statistical Inference: Comparing two Data Sets , 1998 .

[6]  Jane Watson,et al.  The Longitudinal Development of Understanding of Average , 2000 .

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

[8]  S. D. Lima,et al.  Concept or computation: Students' understanding of the mean , 1981 .

[9]  H. Borko,et al.  A Conceptual Framework for Learning to Teach Secondary Mathematics: A Situative Perspective , 2004 .

[10]  Richard Lehrer,et al.  New Habits of Mind@@@Designing Learning Environments for Developing Understanding of Geometry and Space , 2000 .

[11]  Ian Putt,et al.  A Framework for Characterizing Children's Statistical Thinking , 2000 .

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

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

[14]  Alexander Pollatsek,et al.  Data Analysis as the Search for Signals in Noisy Processes. , 2002 .

[15]  John Biggs,et al.  Matriculation, Degree Structures, and Levels of Student Thinking , 1983 .

[16]  Edward S. Mooney,et al.  A Framework for Characterizing Middle School Students' Statistical Thinking , 2002 .

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

[18]  William Edward Christilles,et al.  Mathematical Education for Teachers , 1962 .

[19]  Pearla Nesher.  Are Mathematical Understanding and Algorithmic Performance Related , 1986 .

[20]  L. Shulman.  Knowledge and Teaching: Foundations of the New Reform , 1987 .

[21]  Roger Howe,et al.  Knowing and Teaching Elementary Mathematics@@@Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States , 1999 .

[22]  T. P. Carpenter,et al.  Learning and teaching with understanding. , 1992 .

[23]  Understanding and representing the arithmetic averaging algorithm: an analysis and comparison of US and Chinese students' responses , 2000 .

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

[25]  James P. Byrnes,et al.  Role of Conceptual Knowledge in Mathematical Procedural Learning , 1991 .

[26]  G. Boulton‐Lewis.  Teaching for quality learning at university , 2008 .

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

[28]  David Kirshner,et al.  Interference of Instrumental Instruction in Subsequent Relational Learning , 2000 .

[29]  Jane Watson,et al.  Volume measurement and intellectual development. , 1992 .

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

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

[32]  Leon W. Cohen,et al.  Conference Board of the Mathematical Sciences , 1963 .

[33]  Roni Jo Draper,et al.  Symbolizing and Communicating in Mathematics Classrooms: Perspectives on Discourse, Tools, and Instructional Design , 2003 .

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

[35]  Edward A. Silver,et al.  Results from the Seventh Mathematics Assessment of the National Assessment of Educational Progress , 2000 .

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

[37]  J. Hiebert,et al.  Conceptual and Procedural Knowledge in Mathematics: An Introductory Analysis , 1986 .

[38]  Richard E. Morehouse,et al.  Beginning Qualitative Research: A Philosophical and Practical Guide , 1994 .

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

[40]  Graham A. Jones,et al.  Using students' statistical thinking to inform instruction , 2000 .

[41]  R. Skemp.  The psychology of learning mathematics , 1979 .

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

[43]  Leslie P. Steffe,et al.  Teaching experiment methodology: Underlying principles and essential elements , 2000 .

[44]  L. Alcock,et al.  Semantic and Syntactic Proof Productions , 2004 .

[45]  Teachers’ multimodal functioning in relation to the concept of average , 1997 .

[46]  John Pegg,et al.  Interpreting Student Understanding in Geometry: A Synthesis of Two Models , 2007 .