I recently experimented with my classroom teaching experiment
using the Socratic method with a graduate class at NUS. This
experiment was inspired by the article, ‘The Socratic
Method: Teaching by Asking Instead of by Telling’, written
by Rick Garlikov. I was fortunate to obtain this article as
part of the reading materials distributed at a seminar organised
by the Centre for Development of Teaching and Learning, and
was immediately fascinated by the teaching experiment conducted
by Garlikov, in which he succeeded in teaching a regular third
grade class in elementary school the subject of binary arithmetic
only by asking them questions.
I knew that Socrates was a great Philosopher who had a unique
way of teaching his disciples by asking them questions instead
of preaching. But I had never imagined that such a method
could be applied to other fields besides philosophy. If Garlikov
could use the Socratic method to teach the difficult concept
of binary numbers to elementary school kids, couldn’t
we also apply it to our engineering education?
The advantages of the Socratic method are obvious. It is
one of the most efficient ways to get students involved because
they have to figure out the answers by themselves most of
the time. In the purest form of the Socratic method, questions
(and only questions) are used to arouse curiosity as well
as to guide the students logically to figure out a complex
subject through their own thinking. When preparing the questions
for my class, I found out that it was extremely difficult
to adopt this pure form because of the complexity of the concepts
and the time constraint. Therefore I decided to modify the
Socratic method: when the students became stuck at some point,
I would give them a hint or simply tell them the answer. When
such kind of ‘telling’ happens, hopefully by that
time, the students would have been sufficient aroused by the
questions to absorb an explanation with great interest.
This experiment was carried out during the first class on
the topic of control systems design for the guided weapons,
part of the MDTS (Master of Defense Technology and Systems
Programme) Module 5705. There were thirty students in the
class who were from the military. Two students were from the
USA, and one from Israel. Two weeks before the class started,
I emailed them to request their background information, in
particular, how much they knew about systems and control.
It turned out that they had diverse educational backgrounds
such as electrical engineering, mechanical engineering, civil
engineering, physics and even political sciences; unfortunately,
most of them knew very little about control systems. I realised
that I had a harder job than expected. Most of the questions
were prepared before the class; but depending on what answers
were given, some questions would have to be thought up spontaneously.
After a brief introduction of myself, I told them that my
teaching style might be different from others. A lot of questions
would be raised during the course and they were expected to
figure them out by themselves or with my guidance. They could
just call out the answer if they thought they knew it and
did not have to raise their hands or wait for me to call up
their names. But I would call upon their names if there were
no volunteers. Since they were all from the military, I was
afraid that they would keep silent initially. Quite surprisingly,
many of them participated in the process right from the beginning
and I never had to resort to calling upon names. As a matter
of fact, they were much more responsive to my questions than
the NUS undergraduates in my tutorial class. The fact that
they were more mature and three of them were international
students may have helped a lot in this perspective.
The following is the transcript of the beginning part of
my lecture conducted on 23 August 2002:
XC: Have you ever heard anything about autopilot before?
Where is it?
Student(s): Yeah, on the airplane!
XC: What’s the usefulness of the autopilot for the
plane?
(One student called out; the others laughed.)
Student(s): The autopilot can fly the plane when the pilot
wants to sleep.
XC: Yeah. The autopilot can do some simple manoeuvring of
the plane. But why do we need autopilot for a missile? Is
it because the operator wants to have a rest too?
(The students were puzzled; nobody answered. Since I
didn’t expect them to answer this question directly,
I carried on.)
XC: The task of a missile is to hit a certain target. In
many cases, the missile may not fly in the right direction
toward the target. For example, I want to hit the right corner
on the bottom of the white board with the pencil in my hand.
(I aimed at the corner with my pencil and then threw
at it. But the pencil missed the target.)
XC: Why can’t the pencil hit the target?
(One student called out; the others laughed.)
Student(s): Because it is out of control.
XC: Exactly. Once the pencil is out of my hand, it is out
of control, and there is no way to correct its motion. To
prevent this from happening for the missile, we need to build
a control system to make sure that the missile is on the right
track. Such a control system is also called an autopilot.
With the help of the autopilot, the missile can correct its
motion after it is launched and hit the target with high precision.
However, the missile must be able to see the target in the
first place, right? Then what are the eyes of the missile?
Student(s): The radar… the guidance system…
(I was quite pleased by the students’ right answers
since the part of the guidance system was just covered by
my colleague before my session.)
XC: That’s very good. The guidance system will tell
the missile whether it is on the right track as well as how
much correction it has to make, and the autopilot will follow
the order and perform the right manoeuvres. The main focus
of my lectures will be the fundamental principles for building
an autopilot and some common design techniques. Flying a plane
is kind of similar to driving a car. How many of you have
driving experience?
(Some students raised their hands.)
XC: How do you steer your car in the right lane?
Student(s): I watch the road and turn the wheel.
XC: Very good. You have to constantly monitor the road condition
and decide whether you should turn the wheel or not. Such
kind of process consists of three steps: measurement, comparison,
and correction. In control theory, we call it FEEDBACK. It
is the fundamental principle for all the selfregulating systems,
natural or manmade. Therefore, you should not drive when
you are drunk because you would not be an efficient feedback
controller!
(Everybody laughed.)
XC: To be a good teacher, I also have to be a feedback system
instead of spoonfeeding. So if you have any questions or
comments, you may interrupt my lecture at any time, talk to
me after the class or email me. Don’t be afraid to make
mistakes in the class. If you make mistakes here and get corrected,
then you will not repeat the mistake in your final exam.
(They all nodded.)
XC: O.K. Since most of you have very little background in
systems and control, we’d better start from the scratch.
I believe that ‘system’ is one of the most commonly
used words in science and technology. But what is a ‘system’?
(The students hesitated a little bit, and finally one
guy attempted an answer.)
Student(s): A set of elements.
XC: You are almost right. Intuitively, we can consider a
‘system’ to be a set of interacting components
subject to various inputs and producing various outputs. In
fact, a ‘system’ is such a general concept that
there is no universally accepted definition. It is like the
concept of a ‘set’ in mathematics, everyone knows
what a ‘set’ is, but we cannot define a ‘set’!
Similarly, we cannot define a system! But we are all familiar
with many different types of systems. For example, the mechanical
systems. Can you list some of them?
Student(s): Clocks… pistons…
(I wrote the students’ answers down on a transparency
film that was projected via an overhead projector.)
XC: Electrical systems?
Student(s): Radios… TVs…
XC: Electricalmechanicalchemical systems?
Student(s): Cars… harddisk drives…
XC: Industrial systems?
Student(s): Microsoft company…
XC: Medical systems?
Student(s): Hospitals…
XC: Educational systems?
Student(s): NUS…
XC: Biological systems?
Student(s): Animals… human beings…
XC: Information processing systems?
Student(s): Computers…
XC: This brief list is sufficient to emphasise the fact
that one of the most profound concepts in current culture
is that of a ‘system’. Now if I ask you to classify
all the systems into two broad categories, what would you
say?
(After some thought, one guy called out.)
Student(s): Animate and lifeless…
XC: Another way?
Student(s): Natural and manmade…
XC: Can you classify them in terms of mathematical properties?
(The students all hesitated, and someone murmured.)
Student(s): Continuous time and discrete time…
(This was a right answer, but not what I aimed at.)
XC: Another try?
(After about one minute of contemplation, one guy finally
called out.)
Student(s): Linear and nonlinear…
XC: You got that right! Excellent! But what’s the
fundamental difference between linear and nonlinear systems?
Now imagine that I give you two black boxes to choose. One
is linear and another one is nonlinear. There are one million
dollars inside the linear box, while a tiger in the nonlinear
one. You can take away one of the boxes, and you are allowed
to use any types of inputs to probe the black boxes. But you
cannot open either one. What’s your winning strategy?
Student(s): Pump in a constant input and the output of the
linear one should be a constant.
XC: But the output of the nonlinear one could be constant
too. Another try?
Student(s): Pump in a sinusoid and the output of the linear
one should be a sinusoid.
(I was quite pleased to hear this answer, which showed
that the student knew something about frequency response of
the linear system. But it was not what I looked for.)
XC: But the output of the nonlinear one could also be a
sinusoid. Another try?
(This time it seemed that they really got stuck, and
I decided to bail them out.)
XC: Do you want any hints?
(One student called out; the others laughed.)
Student(s): Yeah, give us a hint…
XC: How about the superposition principle? Have you ever
heard of that?
(One student called out the answer immediately.)
Student(s): I’ve got it! I pump in two different inputs
and record the outputs. And then pump in a third one that
is the summation of the previous two. The output of the linear
system should be also the summation of the previous two outputs.
XC: Well done!
(I then drew the following diagram to explain the superposition
property of a linear system.)
XC: Superposition property is the most fundamental property
of a linear system. Just because of this, linear systems are
much easier to analyse than nonlinear ones. Now come the
good news and the bad news regarding the real world systems.
Which one do you want to hear first?
Student(s): The good news…
XC: O.K. The good news is that many nonlinear systems can
be well approximated by linear systems. The bad news is that
linear approximation is good only locally, in other words,
only in a neighbourhood around certain operating points. Most
real world systems are nonlinear systems, which is indeed
a very fortunate thing. That’s why the world is full
of wonders.
Of course, the systems will rarely be black boxes as in
the previous milliondollar question. In fact, many systems
can be described by mathematical equations, like the springmassdamper
system. The equations can be derived by Newton’s second
law. We will do the same thing with missiles later.
Once we write down the equations, the next step naturally
is to analyse or even solve the equations. As all of you know
something about calculus, can you solve following differential
equation?
(I wrote down the following homogenous first order differential
equation on the slide.)
(One student called out the right solution.)
Student(s):
XC: You are good. How about this one?
[I added an external input u(t) in
term in the previous equation (1).]
(It seemed that they could not recall the right formula
for this problem, just as I had expected.)
XC: Not an easy one, right? Then how about this one?
[I wrote down an algebraic equation where s replaced
the differential operator d/dt in equation (2).]
(The solution was trivial, and one student immediately
called out the answer.)
XC: All right. Equation (3) is very easy to solve because
it is a simple algebraic equation. Equation (2) is not so
easy because it is a differential equation with an external
force term. Now I am going to show you a trick that can turn
the problem of solving equation (2) into the problem of solving
(3), does that sound good?
Student(s): Good…
Following that, I explained the Laplace transform, which
is a powerful tool of solving differential equations. The
rest of the transcript is omitted here since it contains too
many technical details that may not be interesting for general
readers. Nevertheless, I hope this short transcript is sufficient
to prove that the Socratic method can be applied to engineering
education effectively.
The main advantages of the Socratic method are:
 it arouses students’ curiosity and stimulates their
thinking, rather than spoonfeeding them;
 it makes teaching more enjoyable for both the teacher
and the students as they interact with each other and learn
from each other; and
 it gives constant feedback and thus allows the teacher
to monitor of the students’ understanding as he/she
proceeds with the class.
By comparison, a teacher can lecture in much less time.
For instance, I could simply have stated in one sentence (which
is more timeefficient) that the fundamental difference between
the linear and nonlinear systems is the superposition property.
However, I believed that the students would be better stimulated
by thinking about the milliondollar puzzle. Hence, the Socratic
method is more efficient in helping students think, understand
and learn material.
Although the Socratic method seems a perfect approach for
teaching almost any subject, it is much harder to adopt than
the traditional way of telling. There are big challenges that
the practitioner has to face:
 It is first necessary to change one’s mindset
or teaching philosophy. The teacher must accept that excellent
teaching is not about just giving a nice presentation, but
rather about helping the students to really understand and
learn some thing. Otherwise, the teacher would never bother
adopt this method of teaching by asking questions.
 The next challenge is how to prepare the questions that
are interesting and logically leading. Not any question
will do. That is the whole point of the method. Undoubtedly,
asking the proper questions in the proper order is more
of an art than technique, and there is no recipe to follow
other than persistent practice.
I have to admit that the questions I designed were far from
ideal since I am just a beginner in this art. Nevertheless,
I believe the following guidelines, derived from my experience,
may prove useful to those who wish to practise the Socratic
method:
 Always stick to the principle of ‘teach
by asking instead of telling’. Whenever you
want to convey some idea, always try to do it by asking
questions, and consider ‘telling’ only as the
last straw. This guideline is hard to follow because ‘telling’
is always an easy way out.
 Play the role of the student, and ask
yourself: “What would I answer if I were asked this
question?” In other words, you have to imagine the
students’ responses, which will in turn help you structure
your next question. This is the best way I can think of
deciding the sequence of the questions. Preparing the questions
for the class becomes ‘writing a play’ to some
degree. Of course in the real classroom, the students will
surprise you in different ways: you may be pleased that
they are cleverer than you thought or you may have to come
up with new questions on the spot. Thus prior preparation
is vital, as it will help you to improvise when you need
to do so.
 Start with some thing that the student may be
familiar with. For instance, although I wanted
to ask the students about the purpose of having autopilot
for missiles from the very beginning, I realised that some
students might not be aware of such a feature on a missile,
while most of them should know about autopilot on planes.
Hence, I began with a general question of whether they knew
anything about autopilot or not.
 Ask specific questions; avoid broad, openended
questions. Otherwise, students will have nothing
in particular to focus on and few will come up with the
answer that you are looking for. For example, the question
about classifying systems into two broad categories turned
out to be not specific enough because there are so many
ways to classify systems. In contrast, the question about
classifying systems in terms of mathematical properties
was more specific and helped the students to could focus
and narrow their choices till they arrived at the expected
answer.
The task of preparing questions forces the teacher to think
about the logic of a topic and how it can be most easily assimilated,
as well as to play the roles of both lecturer and students.
Obviously, it is much more mindboggling and timeconsuming
than simply preparing the traditional lecture notes. However,
this investment of time and energy is worth the while. In
my case, the students appreciated my efforts; one of them
sent me a message saying: “I think I would say this
for the class that we are very fortunate to have you as our
lecturer.”
Reference
Garlikov, Rick. (11 June 2000). ‘The Socratic Method:
Teaching by Asking Instead of by Telling’. http://www.garlikov.com/Soc_Meth.html (Last accessed: 23 July 2003).
