Geometry Education for Developing Spatial Visualisation Abilities of Engineering Students

1. Geometry Education for Developing Spatial Visualisation Abilities of Engineering Students Cornelie LeopoldUniversity of Kaiserslautern, Germany Faculty of Architecture, Urban and Environmental Planning, Civil Engineering www.uni-kl.de/AG-Leopold 1. Historical Notes on the Role of Geometry Education 2. The Importance and Measurement of Spatial Visualisation Abilities 3. Developing Spatial Visualisation Abilities 4. Consequences for Geometry Education

2. 1 Historical Notes on the Role of Geometry Education Geometry education: special importance for engineering education in the 18th century 'École polytechnique' new basic discipline 'Descriptive Geometry' Gaspard Monge (1746-1818) 'Descriptive Geometry' was given the role to deal with the representation of technical objects in the design process practical demand of drawing 3-D objects critique of the literal humanistic traditional education system technical and practical relevance http://www.engineering.auckland.ac.nz/mechanical/MechEng232/

3. Descriptive Geometry • communication about spatial objects • method of research • development of spatial visualisation abilities • break with the old pedagogic ideal of reproducing things

4. 2 New Developments of Geometry Education for Engineering Students The applied understanding of descriptive geometry that had been a positive aspect in Monge's time led today to an understanding of geometry education as a simply drawing discipline. Misunderstanding: descriptive geometry = drawing techniques Consequence: Development of computer technologies and CAD-systems Training of CAD-systems instead of descriptive geometry wrong development!!! • Requests of today: • spatial translation process between 3-D and 2-D • geometry of the creation of forms and transformations • communication processes

5. 3 The Importance and Measurement of Spatial Visualisation Abilities Well developed spatial visualisation abilities are important conditions for all engineering studies that deal with 3-D reality Students mostly enter our universities with low spatial visualisation abilities Today: visual competence is even more important for an understanding of various digital representations

6. Standardised tests to assess a person's spatial ability mostly used at University of Kaiserslautern since 1994: Mental Rotation Test (MRT) by Vandenberg and Kuse Mental Cutting Test (MCT) - Sub-set of CEEB Special Aptitude Test in Spatial Relations, entrance exam USA

7. MRT and MCT test results between 1996 and 2004 Mean Scores of right answers of men Mean Scores of right answers of women In most cases students entered our university 2003/2004 with less spatial visualisation abilities than in 1996/1997

8. men women

9. 4 Developing Spatial Visualisation Abilities • International research showed that it is possible to develop spatial visualisation abilities • also in our research: • significant predictors of success on the spatial tests • playing with construction toys • previous drafting and work experience • type of secondary education • results by pre- and post-tests: • descriptive geometry course has an positive impact • results by questionnaire: • drawing examples by hand, solved independently by the students and touchable models are most helpful

10. 5 Consequences for Geometry Education Most important elements of geometry education for architecture and civil engineering: 5.1 Hand Drawing and Sketching Examples Example of a first project in descriptive geometry: creating spatial ideas out of a 2-D image G. Fruhtrunk "Pour Jear Arp et Marguerite Hagenbach" - derived spatial configurations to the theme "living" by first semester students 2001

11. creation process: 1. Step: sketching 2. Step: drawing the spatial configuration in three orthographic views 3. Step: two kind of axonometries to get a visual representation

12. 5.2 Creating and Using Touchable Models Helpful for students with low spatial abilities: starting with creation of 3-D touchable models not with drawings To support the 2-D to 3-D thinking process: 2-D collages with given geometric figures 3-D models multiview drawings and axonometric drawings comparing model and drawings

13. Creation of Surfaces and Solids by model and drawing example: hyperbolic paraboloid

14. Models and axonometric drawings in lectures and labs for explaining the spatial thinking process when solving a spatial problem by 2-D drawings Example: Cutting point of a line and a plane Activities with the models support the spatial thinking process while drawing

15. 5.3 Supporting the Learning Process in Consecutive Steps Geometry course consists of three parts: lectures, labs and homework projects Lectures: theoretical background with examples, theory illustrated by touchable and virtual models, axonometries and photos of built architecture Example: cone cutting

16. Labs: transferring the basic ideas to more complex problems with support Homework Projects:working independently by the students on applied problems with the possibility to ask for tutoring Example: cone cutting, intersection and development Ferry Terminal in Nagasaki, Japan, designed by Takamatsu and Lahyani

17. 5.4 Combining Geometry with 3-D Modelling CAD-Programs and Digital Visualisations Working by hand and working with the computer parallel By transferring the geometric knowledge about space, representation of space, forms and combinations between forms to the digital working process with a 3-D modelling software, the spatial visualisation ability can be enhanced. • Examples: • 3-D modelling of spatial configuration • Boolean operations

18. By visualising different variants of the spatial objects from various viewpoints and by getting aware of the parameters of the used representation method, we achieve a better understanding of the forms and the representation methods. Examples:perspective representation by photomontage and various perspectives as elements of an animation

19. REFERENCES [1] CEEB. Special Aptitude Test in Spatial Relations (MCT). Developed by the College Entrance Examination Board, USA, 1939 [2] Gòrska, R. / Sorby, S. / Leopold, C.: Gender Differences in Visualization Skills - An International Perspective. The Engineering Design Graphics Journal. Autumn 1998, Volume 62, Number 3, 9-18 [3] Leopold, C. / Gòrska, R / Sorby, S., International Experiences in Developing the Spatial Visualization Abilities of Engineering Students. Journal for Geometry and Graphics, Volume 5 (2001), No. 1, 81 - 91 [4] Leopold, C., Geometrische Grundlagen der Architekturdarstellung. Kohlhammer Verlag Stuttgart 1999. ISBN 3-17-015216-5 [5] Leopold, C., Principles of a Geometry Program for Architecture - Experiences, Examples, and Evaluations. Proceedings of the 10th International Conference on Geometry and Graphics, 2002, Kiev, Ukraine, Volume 2, 67-71, ISBN: 966-96185-2-5 and Journal for Geometry and Graphics, Volume 7 (2003), No. 1, 101-110

20. [6] Paul, M., Gaspard Monges 'Géométrie Descriptive' und die Ecole Polytechnique ­ Eine Fallstudie über den Zusammenhang von Wissenschafts­ und Bildungsprozeß. Materialien und Studien, Band 17. Institut für Didaktik der Mathematik der Universität Bielefeld, 1980 [7] Sorby, S. / Gòrska, R., The Effect of Various Courses and Teaching Methods on the Improvement of Spatial Ability. Proceedings of the 8th International Conference on Engineering Design Graphics and Descriptive Geometry, 1998, Austin, Texas, USA, Volume 1, 252-256 [8] Suzuki, K., Evaluation of Students' Spatial Abilities by a Mental Cutting Test – Review of the Surveys in the Past Decade. Proceedings of the 11th International Conference on Geometry and Graphics, August, 2004, Guangzhou, China, 15-21, ISBN: 5-8037-0184 [9] Vandenberg, S.G.; Kuse, A.R., Mental Rotations, a Group Test of Threedimensional Spatial Visualization. Perceptual and Motor Skills. 47 (1978), 599-604 [10] http://encyclopedia.laborlawtalk.com/Monge English translation of the introduction of G. Monge "Géométrie Descriptive" [11] http://www.getty.edu/art/exhibitions/geometry/timeline.html