LEARNING TO THINK SPATIALLY: WHAT DO STUDENTS ‘SEE’ IN NUMERACY TEST ITEMS?

Learning to think spatially in mathematics involves developing proficiency with graphics. This paper reports on 2 investigations of spatial thinking and graphics. The first investigation explored the importance of graphics as 1 of 3 communication systems (i.e. text, symbols, graphics) used to provide information in numeracy test items. The results showed that graphics were embedded in at least 50 % of test items across 3 year levels. The second investigation examined 11 – 12-year-olds’ performance on 2 mathematical tasks which required substantial interpretation of graphics and spatial thinking. The outcomes revealed that many students lacked proficiency in the basic spatial skills of visual memory and spatial perception and the more advanced skills of spatial orientation and spatial visualisation. This paper concludes with a reaffirmation of the importance of spatial thinking in mathematics and proposes ways to capitalize on graphics in learning to think spatially.

[1]  Carmel M. Diezmann,et al.  The role of fluency in a mathematics item with an embedded graphic: interpreting a pie chart , 2009 .

[2]  Carmel M. Diezmann,et al.  National Numeracy Tests: A Graphic Tells a Thousand Words , 2009 .

[3]  J. Mathewson Visual-spatial thinking: An aspect of science overlooked by educators , 1999 .

[4]  Steve Cunningham,et al.  Visualization in teaching and learning mathematics , 1991 .

[5]  M. G. McGee Human spatial abilities: psychometric studies and environmental, genetic, hormonal, and neurological influences. , 1979, Psychological bulletin.

[6]  Robert L. Harris,et al.  Information Graphics: A Comprehensive Illustrated Reference , 1996 .

[7]  Carmel M. Diezmann,et al.  Primary students’ spatial visualization and spatial orientation: An evidence base for instruction , 2009 .

[8]  Carmel M. Diezmann,et al.  Solving Graphics Problems: Student Performance in Junior Grades , 2007 .

[9]  Jock D. Mackinlay,et al.  Automating the design of graphical presentations of relational information , 1986, TOGS.

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

[11]  Bernard Parzysz,et al.  Representation of space and students' conceptions at high school level , 1991 .

[12]  I. Macfarlane Smith,et al.  Spatial ability : its educational and social significance , 1965 .

[13]  T. Mueller Learning to Think Spatially , 2006 .

[14]  Alan J. Bishop Spatial abilities and mathematics education—A review , 1980 .

[15]  A. Frank Counting Skills--A Foundation for Early Mathematics. , 1989 .

[16]  Ben Shneiderman,et al.  Readings in information visualization - using vision to think , 1999 .

[17]  Raymond W. Kulhavy,et al.  Comprehension of Graphics , 2011 .

[18]  William Winn,et al.  Chapter 1 Contributions of Perceptual and Cognitive Processes to the Comprehension of Graphics , 1994 .

[19]  N. Newcombe Picture This: Increasing Math and Science Learning by Improving Spatial Thinking. , 2010 .

[20]  A. Gagatsis,et al.  The Effects of Different Modes of Representation on Mathematical Problem Solving. , 2004 .

[21]  Carmel M. Diezmann,et al.  An instrument for assessing primary students’ knowledge of information graphics in mathematics , 2009 .

[22]  Á. Gutiérrez,et al.  Handbook of research on the psychology of mathematics education: past, present and future , 2006 .

[23]  N. Presmeg Research on Visualization in Learning and Teaching Mathematics: Emergence from Psychology , 2006 .

[24]  Susan Goldin-Meadow,et al.  Nonverbal Communication: The Hand's Role in Talking and Thinking , 2007 .

[25]  Michel-Ange Amorim,et al.  "What is my avatar seeing?": The coordination of "out-of-body" and "embodied" perspectives for scene recognition across views , 2003 .

[26]  Alessandra Lee Michelle Torres,et al.  OUT OF BODY , 2006 .

[27]  T. P. Carpenter,et al.  Cognitively Guided Instruction: A Knowledge Base for Reform in Primary Mathematics Instruction , 1996, The Elementary School Journal.

[28]  I. Sigel,et al.  HANDBOOK OF CHILD PSYCHOLOGY , 2006 .