Appears in Computers and Graphics (January/February 1996),
vol. 20, no. 1, pages 177-80.
Student learning and the depth of the student's knowledge increase
when active and group learning methods are employed in the classroom.
Group learning has the additional benefit of preparing students
for professional environments. Active and group learning strategies
are discussed in general computer science course work and as applicable
in the graphics class. Difficulties with active learning and techniques
for dealing with these are also presented.
Active learning  gets students involved in an activity in the
classroom rather than passively listening to a lecture. This activity
can be reading, writing, discussing or solving a problem. This
is important, because student concentration declines after 10-15
minutes in a 50 minute lecture . Group work enhances this by
providing a formalized way for students to cooperate in the learning
process. In computer science and computer graphics, this usually
takes the form of programming assignments. Structured, in-class
group activities are an excellent way to combine both active and
group learning benefits.
The act of learning is not passive. As faculty, we learn actively.
In preparing lecture notes, we read, possibly from many sources,
compare what we have read with our experiences, synthesize the
information into coherent notes, and develop examples that illustrate
the concept. This leads to greater understanding of the material.
Unfortunately, we then use this understanding to lecture to our
students depriving them of this journey of discovery. By carefully
involving the students in this learning process, we can increase
student depth of understanding of the material, increase student
comfort with the material, and improve student confidence. In
most sciences, the value of active learning is already realized
and implemented through laboratories, or in computer science,
through programming projects. The ideas presented expand this
to include activities in the classroom that replace the lecture
or part of it.
If active and group learning is so successful, why is it not used
more frequently? This is because there is a perception that classroom
active and group learning has higher risks. There is fear that
to use active and group learning content will have to be taken
out, pre-class preparation time will be higher, and that it is
not appropriate for large classes. Perhaps the largest fear though
giving up control of the classroom -- a lecture lets the professor
decide what to say when, where student centered activities may
raise questions that the professor is not ready to answer.
These fears are real, but surmountable. To cover the content,
give students the responsibility for learning the factual material
so that they can apply it in the classroom discussion. I have
had students write on course evaluations that they didn't need
to read the book before class because I would tell them what they
needed to know from the chapter. To assure that students read
the material, they can be asked to prepare a short essay or begin
the class with a short quiz.
For faculty that re-use class notes year after year, developing
these strategies will take more time than pulling notes out of
a filing cabinet. In a field as rapidly changing as computer graphics,
notes need to be done frequently enough that this should not be
a concern. Further, as you develop ideas for active and group
learning, you will find that they can be applied across a number
of different courses.
Active learning strategies allow you to control the level of risk.
By selecting short, highly structured and well-planned activities,
the level of risk is fairly low. Involving students by asking
a series of questions about the current topic allows the teacher
to control the direction and content of the discussion but still
makes students active. Breaking the students into small groups,
and letting them independently solve a problem is a much higher
risk but can prove to be highly rewarding.
There is a common problem that faculty frequently have when asking
questions for immediate student response. They answer their own
question or rephrase it too quickly. Rowe  has found that teachers
at all levels typically wait less than one second before beginning
to speak again. Rowe further found that when the waiting time
was increased to three to five seconds, that students are more
likely to respond as well as respond more completely, support
their statements, and respond to each other. The number of student
generated questions also increased. So, it appears that the more
we restrain ourselves, the more our students will participate.
This is reasonable, since if we are talking, our students are
not likely to interrupt.
2. Active Learning in Computer Graphics
As mentioned above, strategies for the computer graphics classroom
are equally valid in many other computer science courses. The
strategies will be described generically and examples for the
graphics classroom will be given.
Modified Lecture 
As was mentioned, student attention begins to decline after 10-15
minutes of lecture. Further, we have all been in lectures where
something catches our attention, causing us to "miss"
part or all of the next point. A low risk strategy to handle both
of these is to lecture for 10-13 minutes and then take a 2-3 minute
pause. During the pause, students can discuss their notes with
the person next to them filling in gaps and correcting misunderstandings.
Posing a specific question for the students to answer can lead
to a classroom discussion. A good mechanism for this is "think-pair-share."
In this technique, a question is posed to the students who then
individually write an answer within a one to two minute time limit.
Students then "pair" up and discuss their answers, possibly
developing a new answer. The instructor can then lead the class
into a discussion by asking a few pairs to "share" their
answer with the class. A less risky method would be to pose a
question chosen to lead into the next lecture topic and then use
the shared answers as the bridge back to another mini-lecture.
In the graphics class, you could pose questions like:
What will happen to the highlights on this ball if we increase
the coefficient of reflection?
How will this shadow change if the light source moves closer?
Why is it important to reduce the number of multiplications and
divisions in graphics (or line drawing) algorithms?
There are obviously many other questions. The more concrete the
subject of a question, the quicker it can be answered and the
less risk it poses for the instructor. The more abstract the subject
of a question, the better it will be to lead into discussion and
the higher risk it poses. In all cases, the question should not
just require the recall of facts. To help the development of higher
order thinking, questions should ask for contrasts, comparison
or parallels between two ideas in a way that requires more than
the repetition of material from the lecture or readings.
Instead of tracing the execution of an algorithm in a lecture,
break the students into groups and have them trace the algorithm.
For example, to compare the DDA and Bresenham algorithms for lines,
break up the class into groups of four students each. Assign one
student as the algorithm tracer, one to keep track of the variable
values, another to record the number of additions/multiplications
performed, and the last to record the visual output. By providing
each team with transparencies (with permanent grids) and markers,
teams can compare the results of the two algorithms, and easily
display their answers to the rest of the class.
To understand computer graphics, one must understand the physical
processes that it is stimulating. Though we look at things all
the time, we do not tend to carefully look and analyze what we
are seeing. This is probably especially true of students and probably
much less true of computer graphics faculty. My attention will
be captivated by light and shadows that are cast on a wall if
the light source is not obvious. I find myself mesmerized by the
relative positions of objects, shadows, lights, and reflective
surface as I try to figure the complex path the light might be
taking. The same is true of many other lighting effects.
Instead of explaining how lighting works, it would be more instructive
to describe the types of reflections and refractions and then
provide the students with flashlights (torches) and different
types of objects and let them try to recreate the effects. This
type of exercise is especially important because it will also
get the student to begin visualizing particular effects and critically
analyzing physical and computer generated images.
It is extremely important to develop the ability of students to
mentally visualize three-dimensional objects, and their spatial
relationship. Without this ability, students cannot determine
whether the images their software creates correctly match their
Dino Schweitzer  has developed a series of demonstration programs
that can be used in the classroom and are available through the
ACM SIGGRAPH Computer Graphics Courseware Repository (via ftp
from cgcr.gsu.edu, login:cgcr, password:cgcr). The topics covered
include line clipping, color maps, boundary fill algorithm, line
drawing, shading, 2-D and 3-D transformations and projections.
G. Scott Owen  has developed a system called "Hyper Graph"
that is a hypermedia system he uses in place of a graphics textbook.
This system includes not only written descriptions but also images
and animations that the user can interact with.
Dividing the students into groups, you can ask them to predict
what will happen to an image based on some process (e.g. scale
followed by a rotation) or ask them what is necessary to cause
a particular effect (e.g. shadow an object by repositioning a
light source). Then in a laboratory or a classroom (with a projection
unit) running demonstration software, the professor has a powerful
tool to have students directly interact with the ideas of computer
graphics. This set up also allows students to formulate "what
if" questions as they are trying to understand an idea. For
example, students trying to understand the rendering equation,
with the proper software, can alter parameters and watch as the
object(s) change appearance.
Care must be taken in any exercise where students are directly
manipulating a demonstration program. The instructor must make
sure that students think before using the program. The educational
value of this exercise will be lost if the students just "hack"
at the software until they find the answer. This exercise will
not develop higher order thinking if students do not analyze the
question, propose an answer, produce a result using the software,
and then think about the relationship between their answer and
the result. Repeated iterations of this process will further enhance
3. Group Considerations
Most active learning exercises that go beyond Socratic questioning
of students or use of the "think-pair-share" technique
require groups. Group exercises pose an extra challenge in that
group interactions add a level of complexity over which the instructor
has only indirect influence.
There are measures that the instructor can take to positively
influence group interactions. Studies have been done on group
work, and  is an example. This section draws on this research
and personal experience to develop recommendations that help groups
succeed (or at least not completely fail).
When you use active and group learning, you need to fully inform
your students of the value of these methods, what you expect them
to do, and that their involvement will provide them with beneficial
results. You need to develop an atmosphere of cooperation between
you and your students, as well as among them.
I find that letting my students know that I am taking risks for
them and that this does not reduce my work (though it appears
to) seems to help set the right tone. I go so far as to list myself
as "Instructor/Guide" or "Instructor/Coach"
on the syllabus. I further make it clear that I see examinations
as the way for them to show me what they have learned rather than
for me to show them what they haven't.
Students will also need some help in organizing their groups.
I will usually give guidelines that, if followed, assure reasonable
levels of participation by all. I will also frequently suggest
roles (e.g., leader, time keeper, reporter/recorder) that the
students should rotate through that should help the group process.
The point is to share whatever strategies you feel will help.
I form groups. Allowing students to form their own groups has
two effects: it isolates students who have no friends in the class,
and creates groups with low peer pressure. Even though it might
seem that a group of friends might be more willing to work harder,
the reality is that friends will cover for those not working,
will be unwilling to discuss the problem with their instructor,
and will not want to risk the friendship by pressuring a friend
to work. In selecting groups, I will try and balance groups by
grade point average (most important), gender, race, age, and major
(in "service" courses). I will sometimes do a survey
of student interests and create groups based on similarities to
help group bonding.
Group size is important as well. Studies show that groups of between
four and six are best. Smaller groups break down into factions
or suffer if someone is absent. Larger groups do not allow enough
individual participation and pose scheduling problems for outside
Groups will take at least one half of the semester to become cohesive.
For this reason, my groups are static and students only get out
of a group by getting out of the course.
Students need early and regular feedback. In discussions, good
answers should be praised and incorrect ones should be questioned,
analyzed for misunderstandings, or critically evaluated. But if
discussion is to be encouraged, the student shouldn't feel attacked
by the professor. If a student answers incorrectly, I will ask
him/her for elaboration with a simple, "why?", or ask
the class for reactions to the answer. If it is partially correct,
I will praise the correct portion before questioning the incorrect.
This seems to create a supportive environment for all students,
not just the respondent. To encourage discussion, I will let a
few students answer before making any comments or asking further
To encourage students to take the group work seriously and, therefore,
benefit from it, group work should influence the course grade.
It is recommended that group work should influence at least 20%
of the grade with no single assignment accounting for more than
60% . It is also important that there be some peer evaluation
component, which seems to encourage personal responsibility and
Susan Feichtner and Elaine Davis  have studies student reaction
to group work and have found that the following group activities
appear to be ideal:
no more than one class presentation
less than three reports
between one and three group exams
They also found that students also appreciated having class time
allocated to group activities.
During the fall of 1992, 1993, and 1994, I taught a theory of
computation course using three different methods. The Fall 1992
course was pure lecture, with the students completing 10 homework
assignments, three term exams and a cumulative final exam. There
was no group work. The Fall 1993 course included active and group
learning in the form of classroom group problem solving, and group
homework and exams. The number of homework assignments was increased
to 20. The Fall 1994 course was the same as Fall 1993, except
that the classroom problem solving was replaced by questioning
from me. I would categorize these three course offerings as having
no active learning (Fall 1992), high active learning (Fall 1993)
and medium active learning (Fall 1994). (For more details on this
study, see .)
Since I do not return final exams, I was able to use the exact
same final exam all three years. After a regrade of the exams
and a statistical analysis of student grade point average (GPA)
and exam performance, I found a statistically significant improvement
of exam scores when active learning was used. Further, the analysis
showed that this was not due to a difference in the abilities
of the students, since the course with the highest exam average
had, by a slight amount, the lowest average of GPAs. Active learning
had improved student performance by about 50%.
5. Further Examples
The examples of student centered learning presented below represent
the full inclusion of active and group learning concepts and minimize
lecture time. These classes take preparation that is different
from that for a pure lecture. In the fall, 1995 semester, I will
be teaching three courses using active learning. A computer graphics
course could use adaptations of these forms.
My "Theory of Computation" and "Analysis of Algorithms"
courses, will begin with the students (in groups) developing a
list of questions that they had from the reading. They will then
need to rank this in the order they want me to answer them. The
questions must be more specific than "explain X." This
process is allocated no more than 20 minutes. I will then answer
as many questions as possible in the next 20 minutes (or less).
For the remaining 35 minutes of the class, the students will work
on a problem set, with answers turned in at the end of class.
The last course, "UNIX and C," meets once a week for
fourteen weeks. In this course, each class will begin with a short
(10 minute) group session for the students to clear up any questions.
The next 10 minutes will be a true/false and multiple choice quiz
on the reading material. Students will next take the quiz as a
group while I grade the individual quizzes (about 10 minutes).
The quizzes will be returned and students will then work in their
groups on a programming exercise. The resulting program will be
due the following week. There will be no midterm exams; however,
all students will need to successfully complete a mastery exam
at the end of the course, to show competence in the course material.
(It should be noted that exam scanning equipment exists, that
allows this structure to be used in large classes.) A colleague
of mine, Frank Dinan, has successfully used a structure similar
to this for his organic chemistry course .
Adopting active learning techniques can be risky for faculty,
but the risk can be minimized. As your comfort level with active
learning increases, riskier strategies can be tried. Though the
loss of control can be scary at first, I have found myself invigorated
and look forward to the challenge of active learning.
The reality of today's higher education in the United States is
that students do not seem to be as interested in learning as they
once were. By employing active learning strategies, students not
only learn content, but process as well. This makes them better
students in later courses, and better professionals after finishing
I would like to thank the participants of the Third Eurographics
Workshop on Graphics and Visualization Education (Maastricht,
August 28-29, 1995) for their comments on an earlier version of
 Charles C. Bonwell and James A. Eison. Active Learning: Creating
Excitement in the Classroom. ASHE ERIC Higher Education Report
No. 1, Washington, D.C.: The George Washington University,
School of Education & Human Development, 1991.
 Frank J. Dinan and Valerie A. Frydrychowski, "A Team
Learning Method for Organic Chemistry," Journal of Chemical
Education, Vol. 72, pp. 429-431, May, 1995.
 Susan Brown Feichtner and Elaine Actis Davis. "Why Some
Groups Fail: a survey of students' experiences with learning groups."
Organizational Behavioral Teaching Review, Vol. 9, pp.
 Jeffrey J. McConnell, "Active Learning and Group Work
in a Theory of Computation Course," submitted to the 27th
SIGSCE Symposium on Computer Science Education.
 G. Scott Owen, "HyperGraph - A Hypermedia System for
Computer Graphics Education." In Interactive Learning
Through Visualization, S. Cunningham, and R. J. Hubbold (eds),
Springer-Verlag, Berlin, 1992.
 M.B. Rowe, "Using Wait Time to Stimulate Inquiry."
In Questions, Questioning Techniques and Effective Teaching,
W.W. Wilen (ed), National Education Association, Washington, DC.,
 Dino Schweitzer, "Designing Interactive Visualization
Tools for the Graphics Classroom." In the Proceedings
of the Twenty-third SIGCSE Technical Symposium on Computer Science
Education, Kansas City, Missouri, March 5-6, 1992, pp. 299-303.
 John Stuart, and R. J. Rutherford, "Medical Student Concentration During Lectures." The Lancet, Vol. 2, pp. 514-516, September 1978.