The role of visual representations in the learning of mathematics

Visualization, as both the product and the process of creation, interpretation and reflection upon pictures and images, is gaining increased visibility in mathematics and mathematics education. This paper is an attempt to define visualization and to analyze, exemplify and reflect upon the many different and rich roles it can and should play in the learning and the doing of mathematics. At the same time, the limitations and possible sources of difficulties visualization may pose for students and teachers are considered.

[1]  Luis Rico Romero,et al.  Intuition in Science and Mathematics: an educational approach , 1988 .

[2]  Reed Stevens,et al.  Disciplined perception: Learning to see in technoscience: Studies of teaching and learning , 1998 .

[3]  A. Arcavi Symbol Sense: Informal Sense-Making in Formal Mathematics. , 1994 .

[4]  J. Hadamard,et al.  The Psychology of Invention in the Mathematical Field. , 1945 .

[5]  Andra A. DiSessa Inventing Graphing: Meta­ Representational Expertise in Children , 1991 .

[6]  Elizabeth M. Markham Proof without Words , 1992 .

[7]  B Francis,et al.  Power play. , 1989, Advancing clinical care : official journal of NOAADN.

[8]  P. Fayers,et al.  The Visual Display of Quantitative Information , 1990 .

[9]  Rafi Nachmias,et al.  What Is Your Family Name, Ms. Function? Exploring Families of Functions with a Non-Congenital Representation. , 1993 .

[10]  Herbert A. Simon,et al.  Why a Diagram is (Sometimes) Worth Ten Thousand Words , 1987, Cogn. Sci..

[11]  Walter Zimmermann,et al.  Editors' introduction: What is mathematical visualization? , 1991 .

[12]  Anna Sfard A Mathematician’s View of Research in Mathematics Education: An Interview with Shimshon A. Amitsur , 1998 .

[13]  Sharon Beder,et al.  Power play. , 1994, Nursing standard (Royal College of Nursing (Great Britain) : 1987).

[14]  Tommy Dreyfus,et al.  On the reluctance to visualize in mathematics , 1991 .

[15]  Y Groner,et al.  The Weizmann Institute of Science , 1962, Nature.

[16]  R. Hershkowitz,et al.  Reflections on the status and nature of visual reasoning - the case of the matches , 2001 .

[17]  R. Adams,et al.  Principles of Neurology , 1996 .

[18]  Alan Bell,et al.  The Interpretation of Graphs Representing Situations. , 1981 .

[19]  The World of Blind Mathematicians , 2002 .

[20]  Ricardo Nemirovsky,et al.  On Mathematical Visualization and the Place Where We Live , 1997 .

[21]  R. H. Eddy Proof without Words , 1992 .

[22]  B. Marx The Visual Display of Quantitative Information , 1985 .

[23]  F. J. Anscombe,et al.  Graphs in Statistical Analysis , 1973 .

[24]  R. Hershkowitz Mathematics and Cognition: Psychological Aspects of Learning Geometry , 1990 .

[25]  J. Kilpatrick,et al.  Mathematics Education as a Research Domain: A Search for Identity , 1998 .

[26]  Yves Chevallard,et al.  La transposition didactique : du savoir savant au savoir enseigné / , 1985 .

[27]  Michael T. Battista,et al.  Spatial Visualization, Formal Reasoning, and Geometric Problem-Solving Strategies of Preservice Elementary Teachers. , 1989 .

[28]  A. Bishop Review of Research on Visualization in Mathematics Education. , 1989 .

[29]  Padma Reddy,et al.  Visualization in Scientific Computing. , 1996 .

[30]  Norma C. Presmeg,et al.  Visualisation in High School Mathematics. , 1986 .

[31]  J. Barwise,et al.  Visual information and valid reasoning , 1991 .

[32]  Kenneth R. Koedinger,et al.  Emergent Properties and Structural Constraints: Advantages Diagrammatic Representations for Reasoning and Learning , 1992 .

[33]  Edward R. Tufte,et al.  The Visual Display of Quantitative Information , 1986 .

[34]  Abraham Arcavi,et al.  A visual approach to some elementary number theory , 1995, The Mathematical Gazette.

[35]  J. Hadamard,et al.  The Psychology of Invention in the Mathematical Field. , 1945 .

[36]  Josh H. McDermott,et al.  Visual Learning , 1968 .

[37]  Robert B. Davis Learning Mathematics: The Cognitive Science Approach to Mathematics Education , 1984 .