Geometry Education for Developing Spatial Visualisation Abilities of Engineering Students

Cornelie Leopold University of Kaiserslautern, GermanyFaculty of Architecture, Urban and Environmental Planning, Civil Engineering www.uni-kl.de/AG-Leopold

1. Historical Notes on the Role of Geometry Education2. The Importance and Measurement of Spatial Visualisation Abilities3. Developing Spatial Visualisation Abilities4. Consequences for Geometry Education

2

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

1 Historical Notes on the Role of Geometry Education

http://www.engineering.auckland.ac.nz/mechanical/MechEng232/

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Descriptive Geometry

• communication about spatial objects

• method of research

• development of spatial visualisation abilities

• break with the old pedagogic ideal of reproducing things

4

Misunderstanding: descriptive geometry = drawing techniques

Consequence:

Development of computer technologies and CAD-systems

Training of CAD-systems instead of descriptive geometry

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.

wrong development!!!

Requests of today:

• spatial translation process between 3-D and 2-D

• geometry of the creation of forms and transformations

• communication processes

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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

3 The Importance and Measurement of Spatial Visualisation Abilities

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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

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Mean Scores of right answers of men

Mean Scores of right answers of women

MRT and MCT test results between 1996 and 2004

0

10

20

30

40

50

60

70

80

90

1996 1997 2003 2004

mea

ns in

per

cent

ages

MCT - men Arch.MCT - men Civil Eng.MRT - men Arch.MRT - men Civil Eng.

0

10

20

30

40

50

60

70

80

90

1996 1997 2003 2004m

eans

in p

erce

ntag

es

MCT - women Arch.MCT - women Civil Eng.MRT - women Arch.MRT - women Civil Eng.

In most cases students entered our university 2003/2004 with less spatial visualisation abilities than in 1996/1997

8

years men MCT MRTstudies means std dev cases means std dev cases

1996

1997

2003

2004

Arch.Civil Eng.

Arch.Civil Eng.

Arch.Civil Eng.

Arch.Civil Eng.

71,4362,54

74,5062,18

69,6366,59

68,6956,22

19,5719,20

20,2020,08

20,4621,00

21,0913,41

4274

4833

2717

3518

59,7573,49

63,9774,77

71,3979,56

78,7165,88

17,3415,62

20,5117,45

26,0324,40

13,2420,02

2043

4633

2717

3517

years women MCT MRTstudies means std dev cases means std dev cases

1996

1997

2003

2004

Arch.Civil Eng.

Arch.Civil Eng.

Arch.Civil Eng.

Arch.Civil Eng.

59,8353,09

60,9358,77

59,3551,56

53,0053,54

22,7919,68

20,4521,06

21,5514,89

19,5816,13

4822

4313

379

4413

51,7054,17

50,3063,27

63,4558,33

66,1452,31

19,4726,98

22,0018,07

22,8915,76

18,6520,53

259

4113

379

4413

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

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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

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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

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5.2 Creating and Using Touchable Models

Helpful for students with low spatial abilities:

starting with creation of 3-D touchable models not with drawingsTo support the 2-D to 3-D thinking process:

2-D collages with given geometric figures 3-D modelsmultiview drawings and axonometric drawings

comparing model and drawings

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Creation of Surfaces and Solids by model and drawing

example: hyperbolic paraboloid

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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

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5.3 Supporting the Learning Process in Consecutive StepsGeometry 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

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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

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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

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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

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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

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[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