This document provides an overview of an introductory course on 3D spatial visualization. The course aims to improve students' spatial skills, which are important for careers in engineering and technology. Students will complete pre- and post-testing using various spatial visualization tests and work through 10 instructional modules combining lecture, software exercises, and assignments. Grades will be based on quizzes, homework, attendance, and a final exam involving the Purdue Spatial Visualization Test: Rotations, Mental Cutting Test, and Mental Rotations Test.

1. Funded by a grant from the National Science Foundation. Any opinions, findings, conclusions or recommendations expressed
are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Pretest: Introduction to 3-D Spatial Visualization
Prepared by: Sheryl Sorby, Ph.D.
Amy Hamlin, Ph.D.
Norma Veurink

2. ENG1002: Introduction to 3-D
Spatial Visualization
● Instructor:
– Dr. Sheryl Sorby
● Teaching Assistant
– Morgan Hansen
● Office Hours:
– 9 am – 12 pm Tues or by appointment
● Text/Software – Introduction to 3D Spatial
Visualization – an active approach by Sorby and
Wysocki

3. Course Objective
● To improve spatial visualization skills

4. Why Spatial Visualization?
● Spatial Skills
- have been a topic for educational research for the past
100 years
- are considered to be one of the seven human
intelligences
- have been shown to be important to success in more
than 84 careers
– Spatial skills are particularly important for engineering and
technological careers
- are important to the design process

5. Spatial Skills Can Be Learned!

6. Spatial Skills: Stages of
Development
● Topological Skills
● Projective Skills
● Euclidean Skills

7. Spatial Skills: Stages of
Development
● Topological Skills
– 2-D skills, closeness of an object to other objects,
order in a group
– Usually acquired in early childhood if exposed to
spatial stimuli (drawing, puzzles, building blocks,
erector sets, video games, etc.)

8. Spatial Skills: Stages of
Development
● Projective Skills
– 3-D skills, determine what an object looks like from
another perspective
– Usually acquired by 18 years old, however, some
people may not have had the opportunity to fully
develop these skills

9. Spatial Skills: Stages of
Development
● Euclidean Skills
– 3-D in combination with concepts of measurement,
such as distance, area, volume
– Many individuals never acquire these skills

10. Developing Spatial Skills
● Skills are developed through practice
– Sketching has been found to be a key
– Working with hand-held or computer models has
been shown to be effective
● In this class, we will use all of these techniques to
help you develop your spatial skills

11. Course Structure
● Pre-testing first day, post-testing last day
● Ten instructional modules
– 15-20 minute lecture on topic for the day
– Student teams work through the software module
– Individual students work on assignment for day
● Two quiz days
– Students take an online test or work with puzzles or
games for extra credit points
– Quiz follows work with on-line test or puzzles
● Attendence = 10% of course grade

12. Grade Allocation
● Quizzes 30%
● Homework 40%
● Attendence 10%
● Final Exam 20%
A 92-100
AB88-91
B 82-87
BC 78-81
C 70-77
D 62-70
F <62

13. Spatial Tests
● Spatial pre- and post-tests administered to assess
student learning
– PSVT:R will be a part of your final exam for this course
– The Mental Cutting Test and the Mental Rotations Test
will be given as a pre-test and also as part of your final
exam for this course

14. Purdue Spatial Visualization Test:
Rotations (done during orientation week)
● Used at Michigan Tech to identify students who
have not fully developed spatial skills

15. Mental Rotations Test
(Two four minute tests)
● Five figures are given, with the figure on the left
the target figure. Two of the remaining four
figures are rotated versions of the target figure.
● Fill in the Scantron bubbles corresponding to the
two figures which are rotated versions of the
figure on the left.
● Test will be given in two segments.

16. Mental Cutting Test (20 Minutes)
● Part of a College Entrance Exam from the 1930s
and 40s
● An object is given with an imagined cutting plane
– Objective is to choose the resulting cross section

17. Next Time . . .
● Module 8: Surfaces and Solids of Revolution
● Bring your book to class!!!!