PathFinder is a new eMathTeacher for actively learning Dijkstra's algorithm. In Sanchez-Torrubia et al. (2007) the concept of eMathTeacher was defined and the minimum as well as some additional requirements were described. The tool presented here is an enhanced paradigm of this new concept on Computer Aided Instruction (CAI) resources: an application designed following the eMathTeacher philosophy for active eLearning. The highlighting new feature provided by this application is an animated algorithm visualization panel showing, on the code, the current step the student is executing and/or where there is a user's mistake within the algorithm running. PathFinder also includes another two interesting new features: an active framework area for the algorithm data and the capability of saving/retrieving the created graph

López-Martínez, Miguel A.

Sanchez Torrubia, Maria Gloria

Torres Blanc, Carmen

Servicio de Coordinación de Bibliotecas de la Universidad Politécnica de Madrid

Fifth Program Visualization Workshop 85
PathFinder: A Visualization eMathTeacher for Actively
Learning Dijkstra’s algorithm
M. Gloria Sa´nchez-Torrubia, Carmen Torres-Blanc, Miguel A. Lo´pez-Mart´ınez
Applied Mathematics Department, Universidad Polite´cnica de Madrid
gsanchez@fi.upm.es
Abstract
PathFinder is a new eMathTeacher for actively learning Dijkstra’s algorithm. In
Sa´nchez-Torrubia et al. (2007) the concept of eMathTeacher was defined and the minimum
as well as some additional requirements were described. The tool presented here is an en-
hanced paradigm of this new concept on Computer Aided Instruction (CAI) resources:
an application designed following the eMathTeacher philosophy for active eLearning. The
highlighting new feature provided by this application is an animated algorithm visualiza-
tion panel showing, on the code, the current step the student is executing and/or where
there is a user’s mistake within the algorithm running. PathFinder also includes another
two interesting new features: an active framework area for the algorithm data and the
capability of saving/retrieving the created graph.
1 Introduction and Preliminaries
Graphical and dynamic web based tools are more appealing for students than traditional
learning materials. It has been confirmed that learners spend much more study time when
visualization is involved; however, there has been some skepticism about the real value of visu-
alizations as a pedagogical tool. Many educators think that visual tools enhance their lectures
and significantly increase student’s comprehension, but such tools are of little effectiveness
when students are not actively engaged in the learning process (Naps et al., 2003). Further-
more, when students are not required to wonder about the concepts, to provide answers and
to predict what is happening next, they might adopt a passive attitude that is not beneficial
at all, and may even be harmful for their training. The analysis presented by Hundhausen
et al. (2002) asserts that ”how students use AV technology, rather than what students see,
appears to have the greatest impact on educational effectiveness” and their study ”suggests
that the most successful educational uses of AV technology are those in which the technol-
ogy is used as a vehicle for actively engaging students in the process of learning algorithms”.
They concluded that, those who are actively engaged with the visualization have consistently
outperformed the other ones who passively viewed them. Thus, in order to avoid a passive at-
titude, during the execution, the program should interact continuously with the users, forcing
them to predict the following step.
In Clear et al. (2001), the authors state that a ”consciously designed approach informed
by a constructivist view holds the most potential for effective online learning designs”; and
that ”learners must construct their understanding through an active process building on
past experiences and knowledge and that knowledge cannot be simply accepted from others”.
According to this opinion, we believe that active learning is the only effective way of acquiring
knowledge and that students cannot only look how the processes evolves, but they must get
involved in the process itself.
The challenge of discovering new ways to motivate students in active learning encouraged
us to develop a new kind of web based tools. Our main goal has been to get students in-
volved, as actively as possible, in their learning process. With this objective in mind, we
have been developing several interactive Java applets, that allow visualized execution of algo-
rithms (Sa´nchez-Torrubia et al. (2008a), Sa´nchez-Torrubia and Gutie´rrez-Revenga (2006) &
Sa´nchez-Torrubia et al. (2008b)). Those applets have been designed under the eMathTeacher
philosophy and are being used as complementary material for blended learning (bLearning)
(Sa´nchez-Torrubia et al., 2008a) both for teachers on classroom lectures and students when
86 Fifth Program Visualization Workshop
learning by themselves. This way, the power and effectiveness of face to face teaching are
boosted with the flexibility and technical capabilities of eLearning, turning out the students
into the protagonists of their own learning progression.
In the next sections, we review the definition of eMathTeacher as well as its main require-
ments. This kind of application introduces a new concept in computer aided education as
they can act as genuine virtual trainers extending the teacher’s hand through the Web.
1.1 eMathTeacher Definition
An eLearning tool is eMathTeacher compliant (Sa´nchez-Torrubia et al., 2007) if it works as
a virtual maths trainer. In other words: if it is an on-line self-assessment tool that help users
to actively learn math concepts or algorithms by themselves, correcting their mistakes and
providing them with clues to find the right solution.
They can also be applied as bLearning complementary material for being used both by
teachers on classroom lectures and by students when learning maths by themselves. However,
the most important feature of these tools is the feasibility of being used for practicing with
maths methods or algorithms while the system guides the user towards the right answer.
1.2 Minimum requirements for an eMathTeacher
These, as described in (Sa´nchez-Torrubia et al., 2007), are the minimum conditions we estab-
lish a tool must fulfil to be considered an eMathTeacher :
• Step by step inquiring: for every process step, the student should provide the solution
while the application waits in a stand by mode, expecting the user’s input.
• Step by step evaluation: just after the user’s entry, the eMathTeacher evaluates it,
providing a tip for finding the proper answer if it is wrong or executing it if ok.
• Visualization of every step change that happens.
• Easy to use.
• Flexible and reliable: allowing the user to introduce and modify the example and to
repeat the process if desired.
• Clear presentation within a nice and friendly graphic environment, helping insight.
• Platform independency and continuous availability (anytime, anywhere).
1.3 Additional requirements for an eMathTeacher
The requirements listed above are mandatory for an application to be considered an eMath-
Teacher. In addition, there are some other desirable conditions, containing those described
in (Sa´nchez-Torrubia et al., 2008b), that these tools should meet. The main features to be
included are:
• Algorithm visualization panel.
• Framework panel showing the current state of the algorithm data structures. It should
also allow the user to update those structures.
• Samples library and/or saving/retrieving capabilities. This requirement should include
saving, for later analysis, both the basic structure the user is working with, and also the
user’s interaction history.
• Language menu.
Fifth Program Visualization Workshop 87
• Integration of different tools as a complete suite, able to cover the whole topic.
• Automatic execution process (optional), especially designed for very complex exercises.
• Capability to find and show alternative solutions once the problem has been solved.
• A theoretical introductory part.
• No installation or maintenance tasks required and light downloading weight.
Other authors (see e.g. Jarc et al. (2000), Ro¨ßling and Naps (2002) & Naps et al. (2003))
have already highlighted most of the above listed features as being required for a learning tool
to be effective. Last year, we performed a literature search & study (Sa´nchez-Torrubia et al.,
2007), which allowed us to identify a number of systems designed under Java Technology and
oriented to help students on learning different Computer Science topics (e.g. IDSV, JHAVE´,
TRAKLA2, JFLAP or AulaWeb Self-Assessment Module). Though those tools seem similar
in terms of functionality, there is actually a feature that makes eMathTeachers (i.e. eLearning
tools that are eMathTeacher compliant) different: they only execute the current step in case
the input is ok and return a customized error message, providing a tip for finding the proper
answer, otherwise. This unique characteristic provides eMathTeachers with full interactive
learning capabilities, and distinguishes them from other systems so far.
2 PathFinder: an eMathTeacher for Dijkstra’s algorithm
Dijkstra’s algorithm (Dijkstra, 1959), commonly known as shortest path algorithm, solves the
problem of identifying the shortest path in a weighted graph from an initial vertex to the
other vertices. The central idea behind the algorithm is that each subpath of the minimal
path is also a minimum cost path.
Keeping the features described in the preliminaries, we have designed and implemented an
application, available at http://www.dma.fi.upm.es/java/matematicadiscreta/dijkstra,
(see Figure 1) for active learning of Dijkstra’s algorithm, including both with and without fi-
nal node possibilities. Our PathFinder has been designed under the eMathTeacher philosophy
(section 1.1) and meets all the minimum requirements listed in section 1.2 as well as nearly
all the additional ones (section 1.3).
Figure 1: PathFinder: an eMathTeacher for Dijkstra’s algorithm
2.1 Detailed description
The application runs in a Java Web Start window. The window is split into four areas: graph,
algorithm, messages and framework areas (see Figure 1), where graph and framework panels
are the main working areas. The first one is a panel where the graph is displayed and allows
the user to create and edit nodes and weighted edges. The second one is the framework area.
A table, presenting the current state of the algorithm structures (fixed and unfixed nodes,
distances to the initial node and predecessors list), is displayed in this panel.
88 Fifth Program Visualization Workshop
The algorithm area displays the execution code, showing in blue the current step or in
red the point where the user’s mistake is located, while the message panel provides clues to
find the right solution or indicates the next step to be done. This panel also offers useful hints
when the graph is being edited.
The menu bar presents a graph saving/retrieving option, three execution options and a
language selector, currently implemented in Spanish and English.
2.2 Editing the graph
The graph nodes are drawn by left clicking the mouse, and the edges by right dragging
between two nodes. When an edge is being created, a text cell appears in the message panel
for entering the edge’s weight. The nodes can be moved or deleted at any time and the edges
can be erased or their weigh modified. The first created node is predefined as the initial node
(e.g. A in Figure 2) but the user has also the possibility of changing the initial node and/or
defining a final node (e.g. D in Figure 2).
Figure 2: The PathFinder showing an error on predecessors update
2.3 Executing the algorithm
Once the graph has been introduced and the algorithm mode has been selected, the application
checks whether it can be executed or not (as stated in Dijkstra (1959) ”we restrict ourselves
to the case where at least one path exists between any two nodes”, i.e. to connected graphs).
If the graph is not connected and thus the algorithm cannot be executed, an error message
indicating this fact is displayed, otherwise the algorithm starts.
The execution has three performance options: two modes of interactive running (step by
step and iteration verification) and an option of direct execution, able to directly provide the
final result (restricted to help on verifying results or to simplify the flow process in case of
very complex exercises).
In step by step verification option, for every algorithm iteration, the user must update
first the fixed and unfixed nodes, then check whether it is correct or not and finally update
distances and predecessors and check again the input correctness. Iteration verification
option is aimed at more advanced students as the user should perform a whole iteration before
checking the input correctness. For every verification (in both interactive running modes),
when any of the updates is not right, the message panel shows the event: an error message
pointing out the problem and providing hints for rectifying is displayed. Simultaneously, in
Fifth Program Visualization Workshop 89
the algorithm panel, the step where the mistake is located changes into red (see Figure 2). If
all the updates are right, the application changes the node and/or edge’s color and waits for
the next user’s entry.
2.4 Comparison with previous eMathTeachers and PathFinder analysis
While using the previous eMathTeachers as complementary material for bLearning, we have
realized the necessity of implementing an algorithm visualization panel inside the tool for
enhancing the student’s consciousness of each of the algorithm steps. Also, while encourag-
ing them to write down the algorithm structures, we found the necessity of including those
structures inside the tools. As a consequence, when designing PathFinder, we incorporated
several new features that, in our opinion, entail huge pedagogical enhancement:
• The algorithm visualization panel (see Algorithm area in Figure 1) provides a better
understanding of the algorithm execution code.
• The framework panel (see Framework area in Figure 1) allows users to practice every
algorithm step exactly as if they were implementing it by hand, but including the graphic
panel as well as the feasibility of being corrected and advised by the tool when a mistake
happens (this is the main feature of eMathTeacher philosophy: acting as a virtual maths
teacher).
• The retrieval option offers the instructor the possibility of preparing selected exercises
for the students, and gives the learner the advantage of saving the graph for later review.
In Hundhausen et al. (2002), the authors assert that ”AV technology has been successfully
used to actively engage students in such activities as what-if analysis of algorithmic behavior,
prediction exercises and programming exercises”. The eMathTeacher philosophy has been
mainly inspired by getting the students involved in the two first activities: what-if analysis
of algorithmic behavior (what means understanding the algorithm design in-depth) as well
as predicting the algorithm outcomes (that entails a good understanding of the algorithm
process). In our opinion, as a consequence of the above described improvements, PathFinder
will get the users even more engaged in the two first activities, obtaining as a result an active
learning of this algorithm and thus, hopefully, successful educational results.
3 Conclusions and next steps
In this paper, PathFinder, a new tool for actively learning Dijkstra’s algorithm, has been
presented. Moreover, some new additional requirements for eMathTeacher tools have been
introduced. PathFinder is an enhanced paradigm of this new concept on CAI resources. The
highlighting new feature provided by this application is an animated algorithm visualization
panel. It shows, on the code, the current step the student is executing and also where there
is a user’s mistake within the algorithm running. Other important new attribute is the active
framework area for the algorithm data, designed for encouraging students to active learn
the algorithm process, as implemented by hand, while the application verifies the correctness
of each user’s input. Finally, the application runs in a Java Web Start window and this
technology allows it to read and write in the client’s hard disk, which gives us the feasibility
of saving and retrieving graphs. This way, the instructor can load an examples library and
the students can save the edited graphs for later revision or modification.
PathFinder has recently been finished, which means that it has not been used by any
students yet. Though there are not impact evaluations of it, based on our previous research,
we have high expectations regarding its potential effectiveness on helping learning activities.
As part of that research, the previous graph eMathTeachers impact has already been evaluated
by comparing the rates obtained on the graphs exercise in a Discrete Mathematics final exam.
90 Fifth Program Visualization Workshop
As detailed in Sa´nchez-Torrubia et al. (2007), the results showed a deeper understanding of
algorithms process in the study group, even considering that those tools offered neither the
algorithm visualization panel nor the framework panel.
In the near future, we aim to perform a tool effectiveness evaluation, following the models
proposed in (Reeves and Hedberg (2003) & Naps et al. (2003)), as well as measuring its impact
on the students’ learning. We are also preparing an users survey (covering both students and
teachers population) added to a collection of opinions, suggestions for improvement, etc.
Currently, we are designing and developing a whole suite which actually integrates different
types of graphs and graph algorithms fitted in it. The design includes all four panels described
in the PathFinder and will feature the above mentioned functions together with the possibility
of saving the user’s interaction history for later analysis and/or (automatic) assessment.
Acknowledges
This work has been partially supported by UPM (Spain) under Project No. IE07 1010-029.
References
Tony Clear, Arto Haataja, Jeanine Meyer, Jarkko Suhonen, and Stuart A. Varden. Dimensions
of distance learning for computing education. SIGCSE Bull., 33(2):101–110, 2001.
Edsger Dijkstra. A note on two problems in connexion with graphs. Numerische Mathematik,
1:269–271, 1959.
Christopher D. Hundhausen, Sarah A. Douglas, and John T. Stasko. A meta-study of algo-
rithm visualization effectiveness. J. Visual Languages & Computing, 13(3):259–290, 2002.
Duane J. Jarc, Michael B. Feldman, and Rachelle S. Heller. Assessing the benefits of inter-
active prediction using web-based algorithm animation courseware. SIGCSE Bull., 32(1):
377–381, 2000.
Thomas Naps, Guido Ro¨ßling, Vicki Almstrum, Wanda Dann, Rudolf Fleischer, Chris Hund-
hausen, Ari Korhonen, Lauri Malmi, Myles McNally, Susan Rodger, and J. A´ngel Vela´zquez-
Iturbide. Exploring the Role of Visualization and Engagement in Computer Science Edu-
cation. SIGCSE Bull., 35(2):131–152, 2003.
Thomas C. Reeves and John G. Hedberg. Interacive Learning Systems Evaluation. Educa-
tional Technology Publication. Englewood Cliffs, 2003.
Guido Ro¨ßling and Thomas L. Naps. A testbed for pedagogical requirements in algorithm
visualizations. SIGCSE Bull., 34(3):96–100, 2002.
M. Gloria Sa´nchez-Torrubia and S. Gutie´rrez-Revenga. Tutorial interactivo para la ensen˜anza
y el aprendizaje de los algoritmos de bu´squeda en anchura y en profundidad. In Proceedings
of the XII J. de Ensen˜anza Universitaria de la Informa´tica, pages 573–580, 2006.
M. Gloria Sa´nchez-Torrubia, Carmen Torres-Blanc, and Juan B. Castellanos. Defining eMath-
Teacher tools and comparing them with e&bLearning web based tools. In Proceedings of
the International Conference on Engineering and Mathematics (ENMA), 2007.
M. Gloria Sa´nchez-Torrubia, Carmen Torres-Blanc, and Vı´ctor Gime´nez-Mart´ınez. An eMath-
Teacher tool for active learning Fleury’s algorithm. International Journal Information
Technologies and Knowledge (IJ ITK), 2(5):437–442, 2008a.
M. Gloria Sa´nchez-Torrubia, Carmen Torres-Blanc, and Sanjay Krishnankutty. Mamdani’s
fuzzy inference eMathTeacher: a tutorial for active learning. WSEAS Transactions on
Computers, 7(5):363–374, 2008b.


PathFinder: A Visualization eMathTeacher for Actively Learning Dijstra's algorithm

Archivo Digital UPM

http://oa.upm.es/4238/1/INVE_MEM_2008_59184.pdf

PathFinder: A Visualization eMathTeacher for Actively Learning Dijstra's algorithm

Abstract

Similar works

Full text

Available Versions

Servicio de Coordinación de Bibliotecas de la Universidad Politécnica de Madrid

Archivo Digital UPM