Chapter 7
Analysis of the Instructional Design of
An Interactive Multimedia Based Learning Environment for Teaching
Cryptography
Modern learning theory and existing paradigms of multimedia based learning
environments have contributed to the design of the interactive multimedia based learning
environment as an effective and stimulating learning tool. Therefore, I will first lay the
groundwork by discussing the three most prominent learning theories: behaviorism,
cognitivism and constructivism (section 7.1). I will then investigate their value for the
tutorial design and explain why no single discussed learning theory is sufficient for the
instructional design. However, I will explain why Dewey’s pragmatic approach lays the
proper foundation for the design of the learning environment (section 7.2). Finally,
accounting for specific learning conditions such as learning group, learning objectives
and learner motivation, I will describe the design of the learning environment (in section
7.3).
7.1 Learning Theories
Learning is essentially making and maintaining connections. Biologically through neural
networks. Mentally through concepts, ideas and meanings. Experientially through
interaction between the mind and the environment. For thousands of years, learning
theories have attempted to reflect such complex processes. The evolution of learning
theories has brought us to a more complete understanding of learning. Many theories
have been created; only few (i.e. behaviorism, cognitivism and constructivism) have been
widely recognized and used in educational settings.
Learning theories are trendy in nature: they have provided adequate models for human
learning at a given time and are usually replaced by more modern theories that enhance
previous explanations. This cycle will very likely continue until we know which exact
biological and cognitive processes are involved in human learning. Each learning theory
seems to get us a step closer to this goal. I am mentioning this to caution that no learning
theory fully reflects the complexity of the act of learning, however, each learning theory
brings light to important aspects involved in learning.
As one of the first modern learning theories, Behaviorism became popular during the
1950's when B.F. Skinner proposed his content centered, behavioral, preprogrammed
method of educating American children. I will describe the behaviorist view of learning
in section 7.1.1. While the behaviorist view concentrated on investigating the observable
behavior of humans and animals resulting from exposure to different stimuli such as
reinforcement, punishment and conditioning, the Cognitivist School acknowledged that
each learner possesses a brain and mental processes formed the primary object of study.
Thus, the Cognitivist school explored the human brain and mental processes as factors
that were irrelevant in Behaviorist models. I will describe the Cognitivist School in
section 7.1.2. Constructivism is the youngest learning theory. In constructivism, the
objective character of behaviorism and cognitivism is replaced by the subjectivity of the
1
learner. The emphasis is placed on the individual that constructs knowledge or mental
models through experiences in complex and authentic situations. Learning is viewed as
the process of adjusting our mental models to accommodate new experiences. I will
describe the constructivist view in section 7.1.3.
7.1.1 Behaviorism
Central to the theory of behaviorism is the study of behaviors that can be observed and
measured (Good & Brophy, 1990). The mind is perceived as a "black box" that acts in a
deterministic manner: response B will occur given stimulus A. Thus, to provoke a desired
behavior, the correct stimulus has to be given. Thorndike’s law of exercise resulted from
the observation that the more a stimulus response bond is practiced the stronger it will
become. He also found that this bond strengthens even more when positive rewards are
involved and weakens when negative responses are involved.
Behaviorist learning is viewed as a conditioned reflex that is acquired through interaction
with the outer world. Teaching simply involves practicing the desired stimulus response
relationships. The teacher knows what exactly the student has to learn and his efforts
focus on how to teach. In his regard, behaviorism provides an authoritarian learning
model: obedient student execution without reflection or critical thinking.
Key behaviorist researchers: I. Pavlov, E. Thorndike, J. B.Watson and B.F. Skinner.
Reflection: Behaviorism is concerned with regulation of learner’s behavior and not with
cognitive processes inherent to humans. In that, behaviorism does not fully reflect human
learning. Applying research on animal behavior (such as Pavlov’s dog experiments) to
human behavior has to be limited.
Behaviorist teaching methods seem to work best in creating desired behaviors and
physical skills. The learner shall be able to respond instinctively to provided stimuli. For
example, World War II pilots were conditioned to react to silhouettes of enemy planes.
Such responses were supposed to occur automatically.
A major limitation of behaviorist learning models is the inability to act in novel and
unexpected situations that the learner is not trained for.
7.1.2 Cognitivism
Cognitivism followed behaviorism in an attempt to find explanations to the limitations of
behaviorism. For example, children do not necessarily behave in a way that was
reinforced; they may alter their behavior contrary to the reinforcements or rewards.
Cognitivism recognizes that humans can process information mentally and don’t act
necessarily in a predictable trained manner. Cognitivism emphasizes the inner cognitive
processes occurring between stimulus and response. Although different classifications of
cognitivism exist all agree that human thinking involves some information processing
abilities. This explains why computers appear to be appropriate models when examining
human thinking processes such as learning, memorizing or recalling.
2
Cognitivist learning does not focus on provoking the correct answer that follows a given
stimulus. Rather, students shall learn rules, formulas and terminologies that form
cognitive capacities and create inert knowledge. Learners possess transformation and
adaptation capacities. Typically, complex problems are subdivided and posed as
simplified stand-alone problems to the learner. Students develop problem-solving skills
that help solve such predefined problems in their own way.
Key cognitivism researcher:
J. Piaget, E. Tolman, D. Ausubel, J. Bruner, L. Vygotsky.
Reflection: Cognitivism eliminates some of the limitations of behaviorist learning
models. Learning also involves human cognitive capacities resulting in a variety of
problem solving abilities. Learners apply their set of acquired rules to tackle even novel
problems. The teacher-student is not authoritarian anymore, teachers act as advisors.
They observe the learning process and possibly assist in solving the posed problem.
While the limitations of behaviorism can be seen in its narrow focus on physical
behavior, the limitations of cognitivism are rooted in its overemphasis of mental
information processing. Situations that involve instinctive (physical) behavior cannot be
explained. Additionally, authentic problems that are complex in nature and embedded in
their contextual settings cannot be solved using cognitivist strategies. These are typically
acquired in given isolated predigested settings and not in ill-defined complex settings that
require a different type of strategies.
7.1.3 Constructivism
As a philosophy of learning, constructivism can be traced at least to the eighteenth
century and the work of the Neapolitan philosopher Giambattista Vico, who stated that
humans can only clearly understand what they have themselves constructed. The
fundamental difference to other learning theories is that constructivism denies the ability
to objectively describe reality. Although reality may be objective in nature, we perceive it
subjectively with our senses. Neurobiological evidence shows that we not only project
reality but also interpret it at the same time (Anderson 1988).
Therefore, constructivists believe that "learners construct their own reality or at least
interpret it based upon their perceptions of experiences, so an individual's knowledge is a
function of one's prior experiences, mental structures, and beliefs that are used to
interpret objects and events… What someone knows is grounded in perception of the
physical and social experiences which are comprehended by the mind." (Jonasson, 1991).
Under the constructivist view, learning is seen as an active process in which humans
construct knowledge in complex authentic situations. The fundamental basis of learning
is discovery or reconstruction of knowledge. Learners will go through stages in which
they develop, accept and, later on, reject their ideas. In the classroom, the teacher takes
on the role as facilitator. He provides a classroom environment that allows learners to
discover relationships and to develop ideas through activities that are of interest to them.
3
Problems shall be situated in realistic settings and connect to learner’s previous
experiences and knowledge.
The Assumptions of Constructivism (Merrill 1991)
 Knowledge is constructed from experience
 Learning is a personal interpretation of the world
 Learning is an active process in which meaning is developed on the basis of
experience
 Conceptual growth comes from the negotiation of meaning, the sharing of
multiple perspectives and the changing of our internal representations through
collaborative learning
 Learning should be situated in realistic settings; testing should be integrated with
the task and not a separate activity
Key Constructivism researchers: L. Vygotsky, J. Bruner, J. Dewey, J. Piaget, S. Papert,
E. von Glaserfeld.
Reflection: The creation of knowledge is an individual process that can not be
transmitted through a teacher. In that way, constructivism differs fundamentally from
behaviorism and cognitivism. The focus is on learning as opposed to teaching; classes are
student-centered and not teacher-centered. The teacher’s role shifts to that of a facilitator
Since he may not know more than the learner, a solid amount of self confidence is
needed. He considers how students learn, considers their beliefs and attitudes, thinks of
learning as a process and supports cooperative learning.
7.1.4 Analysis of these Learning Theories
The following overview of these three most popular learning theories shall outline their
key foci. Schuhman summarized the three prominent theories as follows:
Behaviorism: Based on observable changes in behavior. Behaviorism focuses on a
new behavioral pattern being repeated until it becomes automatic. The mind is
perceived as a black box, stimulus A produces response B.
Cognitivism: Based on the thought process behind the behavior. Changes in
behavior are observed, and used as indicators as to what is happening inside the
learner's mind.
Constructivism: Based on the premise that we all construct our own perspective of
the world, through individual experiences and schema. Constructivism focuses on
preparing the learner to problem solve in ambiguous situations.
Figure 1: Behaviorism, Cognitivism and Constructivism – An Overview (Schuhman,
1996)
4
When considering the key concepts of the three learning theories together with their
particular strengths and weaknesses, none of them appears to be appropriate for all
educational settings. Depending on specific learning conditions such as the learner, the
learning situation and the learning objectives, specific learning theories appear to be more
suiting than others. Schwier (1995) states that: We must allow circumstances surrounding
the learning situation to help us decide which approach to learning is most appropriate.
It is necessary to realize that some learning problems require highly prescriptive
solutions, whereas others are more suited to learner control of the environment.
Any of the three learning theories may provide a meaningful and an appropriate model
for an underlying learning situation. As long as their strengths and limitations are realized
and their uses are newly assessed given the particular learning situation, their flexible
combination can be very beneficial. If we want to our students to become self-driven
autonomous learners that feel comfortable solving ill-defined problems in complex
situations, constructivism should be our preferred learning model. Then, behaviorist and
cognitivist models gain their significance by enabling the learner to reach that stage. It
would be too farfetched to ask a learner to engage in the self-exploration of an unknown
yet complex topic. Learning theories shall be related to educational content and expertise
of the learner.
Ertmer and Newby (1993) as described in Mergel (1998) match learning theories with the
content to be learned as follows:
A behavioral approach can effectively facilitate mastery of the content of a profession
(knowing what). Behavioral tasks requiring a low degree of processing (e.g., basic paired
associations, discriminations, rote memorization) seem to be facilitated by strategies most
frequently associated with a behavioral outlook (e.g., stimulus-response, contiguity of
feedback/reinforcement).
Cognitive strategies are useful in teaching problem-solving strategies where defined
facts and rules are applied in unfamiliar situations (knowing how). Cognitive tasks
requiring an increased level of processing (e.g., classifications, rule or
procedural
executions)
are
primarily
associated
with
strategies
having a stronger cognitive emphasis (e.g., schematic organization, analogical
reasoning, algorithmic problem solving).
Constructivist
strategies
are
especially
suited
to
dealing
with
ill-defined
problems
through
reflection-in-action.
Constructive
tasks demanding high levels of processing (e.g., heuristic problem solving,
personal selection and monitoring of cognitive strategies) are frequently easiest learned
with
strategies
advanced
by
the
constructivist
perspective
(e.g.,
situated
learning,
cognitive
apprenticeships,
social
negotiation.)
Ertmer and Newby feel that the strategies promoted by different learning theories overlap
(the same strategy for a different reason) and that learning theory strategies are
5
concentrated along different points of a continuum depending on the learner’s task
knowledge and the level of cognitive processing required.
Ertmer and Newby's suggestion that theoretical strategies can complement the learner's
level of task knowledge, allows the designer to make the best use of the strategies
provided by the different learning theories. With this approach the designer is able to
draw from a large number of strategies to meet a variety of learning situations.
7.2 A Pragmatic Approach
In designing instructional content, we shall not limit ourselves methodologically but
rather be in a position that permits us to select the most suiting existing educational
principles given the particular learning situation. Thus, we shall act pragmatically in a
way that John Dewey proposed more than a century ago. John Dewey (1859-1952) was
an American philosopher and educator who rejected authoritarian teaching methods. He
was the founder of the “Experimental Laboratory School” and influential in the further
development of constructivist learning models. He regarded education in a democracy as
a tool to enable the citizen to integrate their culture and talents usefully. To accomplish
those objectives, both curricula and pedagogical methods needed radical reform.
Although not put forward by him, “learning by doing” within a dynamic social context
describes Dewey's educational philosophy, called Pragmatism. Dewey's view of
democracy as a primary ethical value permeated his educational theories.
As one of the principal figures in the “Progressive Education Movement” from the 1880s
to 1904, Dewey set the tone for educational philosophy as well as concrete school
reforms. His reactions to the prevailing theories and practices in education and his
corrections made to these philosophies were vital for the development of educational
6
thinking in the late nineteenth and early twentieth centuries. Dewey (1897) points out the
major shortcoming of US schools in attempting to prepare the learner for later life:
“I believe that much of present education fails because it neglects this fundamental
principle of the school as a form of community life. It conceives the school as a place
where certain information is to be given, where certain lessons are to be learned, or
where certain habits are to be formed. The value of these is conceived as lying largely in
the remote future the child must do these things for the sake of something else he is to do;
they are mere preparation. As a result they do not become a part of life experience of the
child and so are not truly educative.”
Educational pragmatism does not add a new learning theory to the existing ones. It also
does not value existing learning theories as good or bad, it rather classifies them as useful
or not. As pragmatism (“Pragma”: greek for “Action” or “Practice”.) is guided by
practical experience and observation rather than theory it asks “Does it work?" as
opposed to "Is it right?"
Educational pragmatism is rooted in the social context the learner finds himself: “True
education comes through the stimulation of the child’s power by the demands of the
social situations in which he finds himself.” (Dewey 1897). Therefore, learning objectives
vary with the particular learner and are thus not absolute. Dewey emphasizes the
relational character of objectives, means and consequences in education in his works. In
particular, this means, that different children may learn different things in the same
educational setting depending on their individual capacities, interests and habits. Dewey
(1897) believes that “Education must be conceived as a continuing reconstruction of
experience and that the process and the goal of education are one and the same.” The
best preparation for life is obtained by providing an environment which places the learner
in authentic situations and lets him act on them. “To prepare him for the future life means
to give him command of himself; it means so to train him that he will have the full and
ready use of all his capacities; that his eye and ear and hand may be tools ready to
command, that his judgment may be capable of grasping the conditions under which it
has to work, and the executive forces be trained to act economically and efficiently”.
(Dewey 1879) Examinations are of use if they test his fitness for social life and detect
areas in which he shall be supported.
Pragmatism provides a template for educational settings by placing the learner in the
center of all educational activities. Based upon the learner’s capabilities and his social
situation, the teacher provides appropriate learning experiences. Such experiences are
educational once reflected upon and its diversity help him prepare for life. To provide
these experiences, no single learning theory shall solely be used from a pragmatic point
of view. Rather, didactic decisions are solely based on the specific learning situation as
defined by the learner, the social setting and subject matter. Constructivist, cognitive and
behaviorist principles may be used in combination based upon their utility for particular
educational experiences.
In particular, this holds true for the design of multimedia based learning environments.
Consequently, the selected media are a result of the desired learning situation to be
7
created. Kerres (2002) states that “The situation determines the value of the used media,
not the media themselves…Media for themselves are of no value, they obtain their value
through their usage by humans in their specific contexts at specific times.
Teaching methods and media shall be employed in a “pragmatic” manner to produce the
desired educational experiences. In particular, the learner shall be involved in activities
that
 allow him to relate previous experiences to new ones.
 are authentic and of interest to him.
 provoke curiosity and the need to act.
 allow him to experience the consequences of his actions.
 require him to research and provoke original thoughts.
 don’t overwhelm the learner. He can manage the task or solve the problem.
 contribute to democratic and human structures in education.
 promote development of individual capacities.
I will now proceed to the design of the interactive multimedia based learning
environment for teaching cryptography. In order to properly use Dewey’s pragmatic
approach, I will analyze the particular learning conditions in the following section.
7.3 Design of the Multimedia Based Learning Environment
For a proper analysis of the particular learning conditions, I will use Kerres’ Guide for a
media-didactic Conception (1999). This guide allows systematic analysis of the particular
learning conditions as well as the reasons and functions of the used media.
7.3.1 Project
Teaching Cryptography in an American High School using An Interactive Multimedia
Learning Environment.
7.3.1.1 Brief Description of Project
Cryptography is the art and science of encoding and decoding information. High School
students at Antilles School in the U.S. Virgin Islands learn Cryptographic Methods and
Applications through the use of an interactive Cryptography Tutorial.
7.3.1.2 Persons and Institutions involved
Dr. Michael Hortmann, University of Bremen, Germany
Salvatore Angilletta, University of Bremen, Germany.
7.3.1.3 Educational Setting
Antilles School is a college-preparatory K-12 school with an enrolment of 503 students
of wide ethnic background. The spoken language is American English. The school has 3
computer labs with 20 workstations each. The course takes place in the School’s library
that runs Windows2000 on each of their 400MHz Celeron / 64MB RAM workstations.
8
7.3.1.4 Characterization of Learning Group
Students that are part of this study are enrolled in the elective Advanced Placement Math
classes. This learning group consists of 26 students whose ages range from 17 to 18
years. The students participating in this study are enrolled in Advanced Placement (AP)
math classes in the school year 2002-2003. Advanced Placement math classes are
elective courses that only students with a particular interest in Mathematics enroll. The
study took place during the last two weeks of the school year after the students had
completed their nation wide AP tests.
15 students are in 11th grade and are 17 years old, the other 11 students are 12th graders
and are 18 years old. 13 students are male, 13 are female. Based upon a survey conducted
before the study, the students using the tutorial had very little to no prior knowledge of
cryptography. All students have experience in using the Internet, primarily to check
email, to visit educational and recreational sites and to use Instant Messenger. The
majority of students have limited experience in self-explorations and cooperative
learning. Most students have been classmates for many years and have known each other
very well. Moreover, all students appeared open-minded and ready to engage in the
studies of cryptography.
Learner Motivation: None of the students has systematically studied cryptography
before. I therefore consider them novices in the field of cryptography. Because students
are exposed to critical privacy issues in today’s Internet usage such as secure online
payments, email privacy or using PIN’s for automatic teller machines, they - generally
speaking - quickly develop an interest for cryptography. Others are familiar with historic
cryptographic events (i.e. Enigma machine during WW2) or may have used
cryptographic or stenographic methods in a playful manner. As students of elective
Advanced Placement Math classes, they usually have a strong mathematical interest and
a solid background equal to 12 years of High School Mathematics.
7.3.1.5 Learning Content and Learning Goals
The security concerning online purchases (i.e. a book order at Amazon.com), sending an
encrypted Email or performing an ATM money withdrawal depends upon encryption
method that is utilized. As these technological conveniences become increasingly
important in our modern society, the question ultimately arises: How much security do
the utilized encryption methods offer? In order to effectively evaluate the integrity of an
encryption method, it is essential to understand the underlying mathematics of the
encryption method (“Cipher”). Thus, the focus of modern cryptography and, in particular,
of this tutorial is testing the security of existing encryption methods and exploring their
underlying mathematical methods.
The following topics are studied within the tutorial:
- Terminology used in Cryptography
- Distinction between 1 and 2 Key Cryptography
- Transposition Ciphers
- Substitution Ciphers
9
- Applications of Cryptography
- Caesar Cipher
- The One Time Pad
- Multiplication Cipher
- Linear Cipher
- Polyalphabetic Ciphers
- RSA Ciphers
- Cryptography Tools and Mathematical Tools on:
- Modular Arithmetic
- Euclidean Algorithm
- Extended Euclidean Algorithm
- Euler’s Phi Function
- Euler’s Theorem
- Letter Frequencies Counter
- Crypto Calculator
- Cipher Challenge
The tutorial was designed to motivate and require the learner to study encryption methods
and their underlying mathematical concepts. The listed ciphers and the chosen sequential
order were purposely selected to achieve this goal. Starting with the simplest cipher and
ending with the most complex cipher, the study of each cipher teaches a new
mathematical concept required to understand the following ciphers and ultimately the
most complex and prominent cipher, the RSA cipher.
For example, one of the first ciphers to study is the Caesar Cipher that motivates learning
the basics of modular arithmetic. Modular arithmetic itself is again the underlying
mathematical concept of successive ciphers such as the RSA Cipher. These mathematical
concepts are – in addition to the studied encryption methods - thoroughly explained in the
“Crypto Tools” section of the tutorial.
Through the detailed study of the mathematical background of cryptography, the learner
realizes that cryptography is an application of the mathematical discipline Number
Theory – a theory that may be considered the last “pure” mathematical discipline as it
had virtually no real-life applications until Cryptographers (which are mainly
Mathematicians) started using Number Theory theorems to devise secure ciphers. Central
concepts of number theory are i.e. Euler’s Theorem and the Euclidean Algorithm with its
Extension.
Learning Goals
The learning goals reflect the above-mentioned issues of modern cryptography. Central
here are the mechanism and the security issues revolving around the studied encryption
methods as well as their mathematical foundation. The learning goals are described on
each tutorial page and can be categorized into two classes: procedural and
communicative. Students shall not only develop the skills necessary to understand and
devise elementary Ciphers, they should also be able to communicate and intelligently
discuss cryptography-related issues such as the security of a studied or devised cipher.
10
The exercises provided on each page of the tutorial are designed to achieve the following
learning goals:
The students shall
 develop an understanding of the primary uses and applications of cryptography.
 be able to distinguish between one- and two-key cryptography.
 be able to distinguish between transposition and substitution ciphers.
 be able to develop transposition and substitution ciphers.
 know how to cryptoanalyze transposition as well as the learned mono- and
polyalphabetic ciphers.
 know how to use a letter frequency counter.
 develop an understanding of the mathematical basis of the RSA cipher and its
underlying security.
 be proficient in modular arithmetic.
 conceptually understand the Euclidean algorithm and its extension.
 be able to communicate and intelligently discuss the learned cryptographic
concepts.
7.3.2 Didactic Media
Cryptography is taught using “The Interactive Cryptography Tutorial” which provides a
multimedia based learning environment designed by the author for this purpose. The
tutorial is hosted on the school’s Internet server and thus is available to students from any
campus computer as well as from home.
7.3.2.1 Reasons for using this Medium
There is a vast body of research that suggests that Interactive Multimedia based Learning
Environments can be very beneficial and effective. Firstly, the interactive nature of the
tutorial provides an authentic coding environment. Students can actively participate in
encoding and decoding processes. Secondly, in addition to discovering and verifying
encryption mechanisms, students are given the opportunity to create their own encryption
methods as well as breaking existing ones. Moreover, the Interactive Multimedia based
Learning Environment provides a platform for self directed investigations. A vast number
of links to cryptography related Internet websites are provided that permit students to
explore aspects of interest in cryptography on their own. Altogether, the tutorial provides
a student centered learning environment that can be used to develop a thorough
understanding and appreciation of cryptography and its use.
7.3.2.2 Costs and Benefits of Project
The time required to explain the usage and navigation through the tutorial is minimal. It
does not pose any more difficult tasks than “surfing” the Internet. According to Kerres
(2000), such skills are common place and may be considered as elementary culture
techniques.
11
Benefits:
 closest way to simulate encoding and decoding in school settings.
 learning and reinforcing computer and Internet related skills
 important real life application of mathematics
 the hyperlinked learning environment provides immediate access to relevant
Internet based cryptography information.
Costs:
 Creation of learning environment is very time consuming; it also requires
advanced web design skills.
 More than rudimentary understanding of mathematics encountered.
7.3.2.3 Function of Didactic Medium
Introducing cryptography in form of a tutorial seemed most appropriate as it serves the
following four important functions:
Firstly, cryptography is the art and science of encoding and decoding information such as
words or texts. This process shall be made accessible to the learner in a realistic setting.
The interactive components of the tutorial provide the means for students to immediately
test, falsify and confirm own ideas immediately. In addition to discovering existing
ciphers interactively, students are given the opportunity to create their own encryption
methods as well as break existing ones.
Initial studies of cryptography shall consist of a high degree of interaction in order to
develop a profound understanding of underlying cryptographic mechanisms. Ideally, by
performing these cryptographic investigations, general encryption, decryption and cryptoanalytic methods are explored by each learner.
Secondly, students have the option to do self-directed cryptography related studies on the
Internet through the use of the tutorial. Each page contains hyperlinks that link to
cryptography-related information on the Internet. In particular, the first section of the
Tutorial (“Cryptography”) provides hyperlinks to a variety of historic, social and
mathematical aspects of cryptography. Here, each learner has the opportunity to further
explore uses, history or latest developments of cryptography that are of particular interest
to him. I deem this section of the tutorial to be highly instrumental in allowing the learner
to pursue that particular aspect of cryptography that is of most importance to him.
Cryptography is a highly interdisciplinary conglomerate of history, mathematics and
social sciences among which students shall be able to gain access and interest to
cryptography through their avenue of choice.
Moreover, performing self-directed cryptography related research on the Internet may be
quite time consuming and not turn out to be successful as the Internet is itself an
unorganized world. The tutorial provides order in the disorderly world of the Internet.
12
Students are usually only one mouse-click away from finding the desired outside
information so that time efficient learning and research can take place.
Thirdly, cryptography is intimately related to computer science. In practice, many aspects
such as developing and testing ciphers as well as the art of breaking ciphers, called
crypto-analysis, require the use of computers. Two examples are:
Breaking the mono-alphabetic ciphers which involves counting the number of letters in a
text. Performing an RSA Cipher requires the computation of two large prime numbers.
Naturally, just as any cryptographer uses powerful computer tools, learners can use the
power of computers as well. A lot of precious time would be lost if such time consuming
tasks would be performed by hand.
Fourthly, using interactive web pages to explore the mechanisms of Ciphers broadens the
students’ abilities in making use of such digital media. Generally speaking, collegebound students are well-seasoned Internet surfers involving searching and navigating
through the Internet, communicating interpersonally via Email and using Instant
Messenger software. However, typically, such students have less experience in using
interactive applications for the purpose of further exploring or discovering mathematical
mechanisms. Commonly, the Internet is not used for inquiry-based tasks of a researcher.
Such skills are formed and reinforced through the use of the tutorial.
7.3.3 Didactic Structure
When creating the tutorial, my main focus was to create a stimulating learning
environment that allows the learner to easily, independently and joyfully study historic
and modern encryption systems. In order to accomplish this goal, the most important
question to answer is how to design the learning environment to produce the best learning
results? Therefore, a crucial question has to be answered: Which learning theory serves
the stated goals best? In the above discussion, I argue that no single learning theory
possesses universal functionality. Instead – using a pragmatic approach - based upon the
described learning group, the learning objectives and the learner motivation, suiting learn
theoretic principles as laid out in section 7.1.4 shall be used.
As described before, in order to support self-driven autonomous learning that enables
learners to solve ill-defined problems in complex authentic situations, constructivism
provides my preferred learning model. Clearly, constructivist principles shall not be
employed with novices of cryptography. Beginners will be frustrated when attempting to
solve complex problems without a proper foundation. In general, behaviorist and
cognitivist methods are more appropriate for beginners and intermediate learners to form
a solid foundation.
Cognitivist methods are used with the introduction of all historic ciphers in the sections
titled “Challenge”, “Substitution Ciphers”, “Transposition Ciphers”, “The Goldbug” and
“The Adventure of the Dancing Men”. As their unknown underlying mechanisms are not
too complex, students are given the opportunity to discover these ciphers by themselves
using the interactive encryption tools. Students can take their time to figure the
13
underlying mechanisms in a playful manner. No teacher pressure is involved, no risk of
public embarrassment in case of failure, no grade pressure involved. A safe learning
environment allows for placing the entire focus on the mechanisms of the cipher. This
discovery based learning can be performed in cooperation with another learner or
individually. Learners may also request hints from the teacher or other students.
Explanations can be checked for correctness using the interactive encryption tools.
As learners proceed from one substation cipher to the next via the head menu, new
cryptographic information is compared to the existing learner’s cryptographic knowledge
structure. Substitution ciphers are combined, extended or altered to create new
substitution ciphers. For example, the Linear Cipher is a combination of the Caesar
Cipher and the Multiplication Cipher. Here, cognitivist principles are used as existing
rules are modified and applied to form new rules.
Behaviorist methods are employed when ciphers were not successfully discovered by the
learner. In that case, the following sections titled “How It Works” ask the learner to
encode and decode in the explained manner. Answers can be verified using the
encryption tools or the CTRL-A option. Immediate positive reinforcement shall
strengthen the established stimulus response relationship and encourage the learner to
continue with a positive attitude. Following the behaviorist ”law of exercise” with
immediate feedback, the learner is asked to encode and decode a few times messages.
According to Thorndike, the stimulus response bond becomes stronger with repetition
and positive feedback.
Both cognitivist and behaviorist methods are employed on the pages that lay the
mathematical foundation of the encryption systems (these are the pages titled “Modular
Arithmetic” through “Euler’s Theorem” that are part of the head menu column titled
“Crypto Tools”). Here, students can – in a limited manner – discover mathematical
principles such as modular arithmetic (referred to as “clock arithmetic”). However,
mostly explanations are provided that students are to follow. Following the explanations,
students are asked to perform mathematical computation based on the given rules. It
would be practically impossible to discover advanced mathematical theorems such as the
Euler’s Theorem or the Euclidean Algorithm. These mathematical discoveries were made
by mathematicians with a vast mathematical background and are impossibly rediscovered
by students with a beginning knowledge in this field. This general instructional dilemma
occurs in many areas of mathematics where students are simply introduced to underlying
theorems and have to digest them. Usually, behaviorist strategies follow this initial
exposure with a list of computational exercises to practice the newly introduced.
Cognitivist strategies are used in the sections titled “Master It”, “Decode It” and “Break
It”. Here the ciphers are scrutinized, the underlying and previously established coding
mechanism is the basis for the decoding and the crypto-analytic process. Existing coding
rules are being manipulated. This is followed by behaviorist based decoding and cryptoanalytic exercises that can be verified using the interactive encryption tools and the
CTRL-A option.
14
Developing a thorough understanding of any cryptographic method requires investigating
the three main aspects of cryptography: encryption, decryption and crypto-analysis. In the
tutorial, the learner explores these 3 categories consecutively as shown in table1 below.
“Challenge” - permits students to discover the encryption and decryption method
of the investigated cipher from encrypted sample texts.
“How it works and Master” - develops and verifies students’ understanding of the
encoding method of the cipher.
“Decode It” - develops and verifies the students’ understanding of the decoding
method of the cipher.
“Break It” - develops and verifies the students’ proper understanding of how to
cryptoanalyze the cipher.
Table 1: The four tasks to investigate a cipher.
Constructivist strategies are effective once the learner has the ability to acquire advanced
knowledge of cryptographic methods. Then, the learner can freely start to investigate
aspects of cryptography that are of particular interest to him. He can use the provided link
for self-directed cryptographic studies such as the historic or the practical security aspects
of cryptography. The provided web links give the starting point to such investigations. A
simple, user-friendly navigation system facilitates the tutorial navigation.
Motivation is the driving force of self-directed studies. The tutorial tries to stimulate
intrinsic motivation as follows: Students are able to pursuit their preferred aspect of
cryptography. I.e. historic, real-life applications or mathematical aspects can be pursued
through the provided links to tutorial pages as well as to Internet pages. Real life
situations are portrayed in the tutorial that show how even the learner uses and relies on
cryptography. External motivation is provoked through the rewards that are given to
cryptography experts that solve the provided Cipher Challenge.
Other assumptions of constructivist learning are fulfilled as well:
 The learner can freely choose the aspect(s) to be investigated and has the freedom
of how to pursuit it.
 The selected topics are naturally embedded in their social setting and are not
prepared or simplified by the teacher.
 Learners are encouraged to work cooperatively. The provided exercises initiate
desired communication among students to exchange, create and clarify ideas
regarding the mechanisms of ciphers. Group efforts can be very productive and
rewarding i.e. when crypto-analyzing ciphers and when designing new ciphers.
Such hybrid learning environments in which communication and cooperation are
effective study elements have proven to be more attractive to the learner. Kerres
(2000) found that the acceptance of individualized learning systems as rather
limited whereas project-oriented exercises that support cooperative learning are
more attractive to the learner.
15

Learning is constructed through the free investigation of cryptographic rules.
Learners add new knowledge to prior knowledge.
Sequential Structure of Learning Environment
The Cryptography tutorial is divided into seven sections that can be navigated through
via the head menu located on top of each page. The first section (“Cryptography”)
introduces basic concepts, terminology and applications of cryptography on 9 web pages.
The next five sections (“Caesar Cipher”, “Multiplication Cipher”, “Linear Cipher”,
“Polyalphabetic Ciphers” and “RSA Cipher”) are dedicated to the introduction of the
mechanisms of such ciphers each using between 2 and 6 pages. The last section (“Crypto
Tools”) is a reference section that is used throughout the study of the tutorial. It serves
two purposes: it illuminates the underlying mathematical concepts of cryptography as
well as provides necessary cryptography tools such as a crypto calculator and a letter
frequency counter.
The tutorial ends with the “Cipher Challenge” which is the ultimate test of the
Cryptography Tutorial. It covers 8 of the most prominent ciphers which are investigated
in the tutorial. The ability to cryptoanalyze all 8 ciphers requires profound knowledge of
the learned ciphers. Students that already have a thorough knowledge of cryptography
may choose to begin the tutorial with the Cipher Challenge. The Cipher Challenge
contains hyperlinks that provide the learner with quick and easy access to all the
necessary information concerning the ciphers. Although the purpose of the cipher
challenge is ultimately to test the learner’s knowledge of the material, its successful
completion is very rewarding. In the cryptography class, students that master the Cipher
Challenge are encouraged to email the solution to me and are awarded an appropriate
prize.
The tutorial’s sequential design supports the natural learning process i.e. “from simple to
difficult”. Through gradually learning more complex ciphers, the learner may confidently
progress through the lessons. For example, to master the first basic ciphers the learner is
solely required to have mastered addition and to know the chronology of the letters in the
alphabet. With each cipher the learner learns a particular mathematical concept that is
required to master the subsequent ciphers. The final cipher to study, the RSA Cipher, is a
difficult cipher to comprehend and requires the knowledge of all mathematical concepts
studied previously.
Further Didactic Aspects of Learning Environment
Immediate Feedback: A learner shall be able to keep track of his learning progress. This
can be achieved through answering the posed questions and checking the answers using
the highlighting function of the key combination CTRL-A which displays the hidden
answers right next to the question.
The Cipher Challenge was created as stimulation for users that like to challenge
themselves by taking on the job of a cryptoanalyst. Here, the user is referred to the
16
relevant sections of the tutorial for assistance. Final solutions to the challenge may be
emailed to me resulting in immediate feedback.
Navigation System: I designed a menu driven tutorial. The head menu gives the user an
immediate overview of the full extent of the tutorial. Sequential tutorial navigation is
made simple: from left to right, top to bottom. Any page can be accessed at any time
allowing for quick look ups, references, reviews, etc. “Back”, “Next” and “Home” links
are provided on the top and “Back” and “Next” buttons at the bottom of every page
enabling quick access to neighboring pages and to the starting page.
The provided links to pertinent pages are usually provided in the right column of each
page. Different tutorial pages contain different links with some links used more than
once. I decided to leave the link column on each page unchanged. A central link page
which contains the links of all other tutorial’s web pages appears to be useful. It would
have eliminated the right columns on each page. However, I decided not to create this
page as a user is now two as opposed to one mouse click away from reading the desired
pertinent information. This does not seem to be a significant factor when accessing a few
outside websites only. However, significantly more time is needed when a great number
of outside web sites are visited. I also find that the right column is not very wide and does
not take away a significant amount of space from the remaining page. However, it does
provide the links where they seem most pertinent.
Page Length: It was my intention to keep the page length as small as possible. This goal
was realized on most pages of the learning environment. However, the pages that contain
a lot of text are pages that are usually used as reference pages or contain detailed
encryption explanations that the user may skip without a loss of the overall picture.
Additionally, pages that contain a lot of text often contain links to other pages or
interactive encryption tools that allow the user to verify the written information and by
doing so continues the interactive format and reduces any monotony.
7.3.4 Learning Organization
The two-week long cryptography course took place at the end of the school year 20022003. The 26 students took their nationwide Advanced Placement Math exams. Teacher
and students met for 50 minutes five times a week. In the first class, the students are
introduced to the structure of the tutorial and its usage. The teacher acts as a facilitator
who answers questions, assists in Internet research or any other needed area. The teacher
was accessible inside and outside the classroom and via email.
The tutorial is hosted on the school’s Internet server. During class periods, students
accessed the tutorial from their workstation in the school’s library. However, students
also accessed the tutorial from home. The Internet-accessible tutorial enabled students to
utilize the tutorial outside of their regular class period and, thus, is a preferable solution
to a tutorial that is exclusively accessible through the school’s network. The ability to
access the tutorial outside of class should not be underestimated as it enables the students
to review lessons at home or to engage in self-directed research.
17
Literature
Anderson, J.R. (1988). Kognitive Psychologie – Eine Einfuehrung. Heidelberg: Spektrum
der Wissenschaft.
Dewey, J. (1897). My Pedagogic Creed. School Journal vol. 54. Available online at:
http://www.pragmatism.org/genealogy/dewey/My_pedagogic_creed.htm
Ertmer, P. A., Newby, T. J. (1993). Behaviorism, cognitivism, constructivism:
Comparing critical features from an instructional design perspective. Performance
Improvement Quarterly, 6 (4), 50-70.
Good, T. L., Brophy, J. E. (1990). Educational psychology: A realistic approach. (4th
ed.).White Plains, NY: Longman
Kerres, M. (1999). Didaktische Konzeption multimedialer und telemedialer
Lernumgebungen. In: HMD – Praxis der Wirtschaftsinformatik. Available at:
http://www.educanet.ch/group/dm0121/kerresdk.pdf
Kerres, M. (2000). “Mediendidaktische Analyse digitaler Medien im Unterricht.” In
Computer und Unterricht: 10 (1). Available at: http://www.edumedia.uniduisburg.de/articles/CuU-kerres1-endf.pdf
Kerres, M.; de Witt, C. (2002). Quo Vadis Mediendidaktik? Zur theoretscien Fundierung
von
Mediendidaktik.
In:
MedienPaedagogik
2002.
Available
at:
http://www.edumedia.uni-duisburg.de/publications/kerres_dewitt1.pdf
Mergel B. (1998). Instructional Design and Learning Theory. Available at:
http://www.usask.ca/education/coursework/802papers/mergel/brenda.htm
Merrill, M. D. (1991). Constructivism and instructional design. Educational Technology,
May, 45-53.
Schuman, L. (1996). Perspectives on instruction. [On-line].
http://edweb.sdsu.edu/courses/edtec540/Perspectives/Perspectives.html
Available:
Schwier, R. A. (1995). Issues in emerging interactive technologies. In G.J. Anglin (Ed.),
Instructional technology: Past, present and future. (2nd ed., pp. 119-127)., Englewood,
CO: Libraries Unlimited, Inc.
Yang, Y. C. (2001). Learning Theories - Synthesis and Comparison. [On-line].
Available at: http://expert.cc.purdue.edu/~yangyc/index/theory.html
18