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

            Keywords:

 

            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

            countries.

 

            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.