Electronic Proceedings of the 12th Asian Technology Conference in Mathematics


Abstract for 12729

Transfer of spatial visualization: Training with discrete, composite

transformations in USA, Taiwan and Turkey

Authors: Helen Gerretson, Glenn Smith, Yuan Yuan, Sinan Olkun

Affiliations: University of South Florida, Chung Yuan Christian

University, Ankara University



Problem: The learning and transfer of spatial skills, such as

spatial visualization (SV) and mental rotation (MR), although

important to mathematics, remain resistant to educators and

researchers best efforts to teach them. Through re-testing and

practice, people improve spatial skills within a narrow context, but

such context-specific improvements have not transferred globally to

other contexts.


Research question: We investigated whether: a) composition of

discrete transformations (mental rotation, reflection, dilation, and

translation), b) in multiple contexts, c) using multiple

interventions could affect transfer to MR and SV. We also

investigated how such spatial learning played out in different



Method: The study investigated whether six weekly sessions involving

interactive software could aid female pre-service elementary

teachers in the USA, Taiwan, and Turkey in the transfer of MR and

SV, as measured by two standardized tests: Flags test of mental

rotation and the Differential Aptitude Test (DAT) space relations

subset (surface development). The study employed a pretest,

intervention, posttest design with experimental and control groups

to compare pre to post improvements in spatial skills between groups

within each country. The intervention consisted of six weekly

sessions (approximately 15 minutes each) of structured activities,

in the computer lab, that used interactive computer programs

involving composition of discrete spatial transformations (e.g. 90

degrees of rotation, dilations a factor of two, etc.): NCTM

Illuminations applets, Copycat and Mathmagic. All students were

enrolled in the second of a two-course sequence of mathematics

methods, however the US course involved geometry content, while the

Turkish and Taiwanese courses did not.


Results: At this writing, data from USA and Turkey are in, but not

from Taiwan. See figures 1 and 2. All participants improved on MR

from pre to post, but the intervention did not make a difference for

MR. For the Turkish students, the training made a significant

positive difference for SV.


Table 1: Flags Mental Rotation test pre to post differences

Country Within subjects (all groups) Between groups/between subjects

USA SIG., .0001, t = 6.33 Not sig.

Turkey SIG., .02, t = 2.47 Not sig.


Table 2: DAT Spatial Visualization test pre to post differences

Country Within subjects (all groups) Between groups/between subjects

USA Not sig. Not sig.

Turkey SIG., .001, t = 3.7 SIG., .05 (.04), F = 4.65


Implications: Consistent with most prior studies, re-testing, but

not training, improved MR. However, based on the significant

between-group differences in improvements on the DAT for the Turkish

(who were not yet exposed to geometric transformation content),

training with composition of discrete transformations may improve

multi-step SV and effect transfer.