With the help of problem solving education students acquire new knowledge and experience. They have to face a new problem and challenge with each new task. The more realistic the task is the students will be able to solve much better real life problems. To acquire new knowledge not only successfully, but also the most efficiently we have to be familiar with the essence of problem solving methodology and its different steps, furthermore we have to use various teaching aids to model real life problems for the students.
The studying and teaching process of IT subjects does not resemble that of the traditional theoretical subjects, since data memorising is not that important here. It rather focuses on practical and problem solving knowledge. Thus students can easily gain experience, explore the problems; carry out research work and experiments. Problem solving and task completion are the focal points.
Consequently in IT education problem solving as a special teaching method proves extremely useful.
To be able to compare the equipment of problem solving methodology with other methods of different subjects first we have to study the concept and special equipment of problem solving.
Let us begin with the definition of problem solving. György Pólya, an internationally acknowledged expert of the topic defines it the following: “we are consciously looking for such an adequate task that is capable of reaching a clearly defined but directly not accessible goal.” Then he continues: “When we are consciously thinking we mainly think about problems to solve. When not daydreaming our thoughts focus on a special goal.(...) The most specific human activity is problem solving, focusing on the goal, and searching for aids to reach the defined aim." (Pólya, 2010)
According to Pólya the process of problem solving itself can be understood, learned and developed. His other famous book A gondolkodás iskolája analyses problem solving from
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the heuristic approach and examines the steps of the process. Such as any other task solving – problem solving can be divided into four parts: 1. Understanding the task 2. Making a plan 3.
Carrying out the task 4. Solution analysis. (Pólya, 2000)
Another prominent representative of our method Ferenc Lénárd thinks that Pólya talks in general and reduces all problem solving to the adequate usage of thinking process, without including the emotional element in the process of problem solving. In his summary book about the topic A problémamegoldó gondolkodás Lénárd not only completes the definition of Pólya with naming and explaining the thinking processes, but also expands it with the emotional element and human characteristics.
“Thinking process is a complex procedure which can be analysed only through the person and the task or problem that they have to solve.” (Lénárd, 1984a) Lénárd separates task solving and problem solving. He analyses the compounds of problem solving, thinking process (such as analysis, synthesis, deduction, comparison, theoretical data comparison, understanding relationships, completion, generalisation, specification, arrangement, analogy) (Lénárd, 1984b) and the emotional compounds (astonishment, preference, anger, doubt, giving up work, etc.). (Lénárd, 1984c)
It is evident that whichever approach we use to analyse problem solving it is always a complex process where we have to encourage experimenting, researching and skill building.
At the end there has to be set up a solution system to reconstruct problem solving.
When we return to IT subjects education we can immediately recognize a few specific features of the above mentioned problem solving methodology. Let us examine them closely!
The teaching aids of IT subjects are rather different from other theoretical or technical subjects. It is evident that this subject uses the computer - as an aid – not only for demonstration, as the knowledge the students have to acquire is about the IT world. Other ICT aids (problem solving simulators, education support applications, multimedia teaching material) are frequently used as well.
Using the above aids students can acquire thorough experience.
The creation of some IT course books also reflects the problem solving approach. According to the categorization of Nagy Sándor such books are called workbooks. He describes the differences compared to other books the following: “ (…) these books are not just letters all
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over – the pages have enough space, there is less text, they have much more illustrations or figures, exercises and space to fill. It is obvious that the workbook does not want to transfer ready-made information, but besides the short essential information it contains different exercises from which teachers and students can select what they need. Such books ensure longer-lasting knowledge then those that require only the memorization of the information."
(Nagy, 1997)
One of the important segments of IT education is teaching IT network in technical secondary schools and higher education institutes. Now I would like to demonstrate the methodology and practical usage of problem solving education concentrating on a small field. This means IP address creation and planning in enterprise environment. This segment is just one of the several network fields. Thus the following methodology with all the details can serve as an example for other network or IT fields.
IP addresses are the unique identifiers of real or virtual IT devices and of computers communicating via networking. When planning them students carry out the most complex tasks during their networking studies which include the knowledge of different skills (mathematics and other IT elements). In IT networking this knowledge is taken as granted though traditional school programs or even the program of Cisco Networking Academy, which is specialized in this field cannot finish with the students the topic work or cannot make them understand it completely.
In a complex multisite network the IP address of computers and other devices is usually not set by an external service provider, so it is important to plan the IP addresses individually for each company, which would also mean the best utilization of it for the companies.
During the planning process it is required to use one’s knowledge on skill-level and proficiency level. However there are many tasks or steps that are less important “in the classroom”, but they become relevant in professional life, so it is not that important to know those knowledge panels for accomplishing the tasks successfully. These panels are categorized as proficiency skills. I would like to go through the knowledge panels required for IP address planning. (S) labels the required skill for completing the task sufficiently. (P) stands for those knowledge panels that include the understanding of deeper correlation and proficiency.
Different operations used in planning:
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Knowledge of basic concepts: host, network, subnet, default gateway, mask, network address, broadcast address (S)
Knowledge of different network address ranges (public/private; classes - A, B and C) (S)
If the network is part of a more complex network one has to know the addressing of the network (P)
To define the most optimal address range in case of a complex network (the goal is to enable a would-be network address aggregation) (P)
To define the number of the required host IP addresses in the designed network (S)
To define the size of the most optical network within the designed network with its subnet masks (S)
To design the default gateway by a standard system. E.g. should it be the first or the last address of the network? (P)
To carry out the above steps systematically, concerning all the required sites, and the requirements of not only the LAN, but also the WAN networks’ IP addresses. (S)
It is advised to include the option of future expansion when designing the address ranges. (P)
To plan the optimised addressing ad system that can be reached while using the routing protocol (in case of OSPF e.g. designing different areas, or CIDR settings) (P)
Panels labelled with (S) mean the skill with which an elementary level planning task can be accomplished, however compared to an optimal stage there could be great differences (e.g.
various usage of addressing within the same network or defining unnecessarily big subnets).
About steps marked with (P) the students can learn more during the courses, they can even test the steps, nevertheless there is no time to get engaged deeper in the correlations. By the steps labelled with proficiency it becomes easier to repair a network, to integrate it into a complex system or to make it work optimally.
The skills - that the students should have acquired during the school years – enable them to design network address ranges without any problems. Moreover gaining further proficiency
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(turning it into real routine) makes it easier to solve professional challenges. The usage of various teaching aids plays an important role in understanding of this material. These aids can help beginners a lot while planning particular steps or making calculations. It can make easier not only the calculations or transparency of the materials for the students, but also it can support the anchoring and internalization of the new knowledge to their network concept system (according to the constructivist pedagogical approach)
This table extract (see Figure 1) is an example of one of the above mentioned aids. It makes different calculations easier for students (the possible amount of subnets and hosts in class C).
Figure 1: Calculation aid, hosts and subnets in class C
The various glossaries may also be useful, or explanatory mind maps (see Figure 2) revealing the relationships between the various concepts. These can greatly facilitate the student's learning process in the course of the summary. It could also be a great help to review a new kind of problem or to draw new solutions.
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Figure 2: Mind map of IP addressing
In addition to study-aids it is required to establish those task types that play an effective role in monitoring the competences and skills of the chosen topic (and further development as well). Simple task types - such as the use of multiple-choice tests - can effectively be used for monitoring.
Example 1.
If 172.16.112.1/20 address and mask is set on Ethernet interface of a router, then how much is the maximum number of hosts that can connect to the router's Ethernet network?
a) 2046 b) 1024 c) 4096 d) 8190 e) 4094
f) None of them Solution: e
Beside simple tasks more complex, deeper understanding and improved visual assuming task types are required in order to the students meet real problems. Such tasks may involve developing a complex network addresses, which can be further expanded with the actual implementation of task topology and configuration of the devices - routing, access rules. (For example, through the use of the described hereinafter Packet Tracer software application).
159 Example 2.
IP range 192.168.100.0/24 is given. Plan the following IP addressing of multi-site network, the best possible way! The figure numbers shown next to each LAN IP address represent all needs of IP addresses of the given network (including current needs of each device as well as subsequent change requests). Indicate all the established network address space giving the first and last addresses, and describe the required subnet mask of both forms (e.g.
255.255.255.0 or /24). The aim is to get a working network by IP addresses, where individual hosts can communicate with each other (see Figure 3 and Figure 4).
Figure 3: IP addressing complex task
Figure 4: Solution of IP addressing complex task
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This worksheet is a good example of problem solving tasks used in teaching methodology.
To understand task wording or the indirect sub-task formulated in the last sentence provide a challenging set of problems for students, which also try to map real life. In other words, students face more mistake opportunities in solving task but within a group session teacher can discuss issues with them in form of questions (in relation to the group's knowledge either before completing the task, or in the case of a more advanced group even subsequently). Such questions may occur: „Which network should you start with IP addresses? Should you name the addresses from the beginning or the end of the network address ranges? Can a /27 mask be enough for a network where 31 IP addresses are needed? If all the sites are done, have you finished the task?”
Based on the past few years of teaching experience the last example contains the most conspicuous failure possibility that is forgetting WAN IP addresses. Without WAN addresses the sites are not able to communicate to each other. The apparently incomplete formulation of the initial task could emphasizes error options because on the first figure in addition to WAN access IP addresses (that is usually two pieces at point-to-point connection) or blank fields are not given. Only the last sentence of the task expects functional communication (indirect subtask). It is such a knowledge element, which students should know because of previously acquired skills.
In addition to the specific tasks, a variety of ICT tools and applications can greatly facilitate the planning of IP addresses. A good example of a special simulation which was used in Cisco Networking Program is the Packet Tracer. Generally speaking it is true that the main request of simulation software is a more accurate editing of reality. According to Komenczi Bertalan, if the essential characteristics of the real processes are set and their interaction are defined in sufficient algorithms, they can be displayed as a model working in the computer.
(Komenczi, 2004)
These aspects are true to this application. The program is able to lead on students designing a complete operating system, all the way from planning topology to putting the devices in operation (with choosing the appropriate module and inserting the proper tools to the module). It is also able to set up utilities and what is more they demonstrate all important steps up to error-correcting. All this has to be developed with Cisco network devices, and PCs, servers, printers, phones can also be part of that. Therefore this application simulates any types of equipment which form an integral part of today’s modern network systems.
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Packet Tracer provides an excellent tool for students in the learning process but also provides a lot of benefit for teachers. The software task evaluation, namely the scoring subsystem automatically carries out an assessment of students solutions. The application provides many intelligent solutions which allow for great latitude for students, but also for the teachers in specifying the task or evaluating. For example the order of inputs is not relevant or different point values can be assigned to a single object (e.g. giving instructions) or to part of an object (switches or other parameters corresponding to other values). Scoring can be connected to conditions so that students can get points if they do not set all the instructions, but e.g. real connection does work between two computers. The variables can be selected at random (for example IP addresses) so as to guard against such abuses like coping tests or homework tasks.
Packet Tracer and the use of similar applications strengthen the acquirement of practical and theoretical curriculum, and they put theory into practice. Packet Tracer is an excellent tool to develop complex or simple academic tasks (see Figure 5, which tells an imaginary journey placed in the Mayan world with the help of network devices). Such an application plays an important role in the problem solving methodology as a tool for education. In addition to solving the tasks it provides an opportunity to explore the operation of real devices, to prepare unique circumstances, as well as experimentation and error-correction.
Figure 5: IT task placed in a fairytale environment
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According to Tóth Péter the problem raising objective is the most valuable objective because it creates the motivational base of education and promotes the development of thinking. Real-life problems capture the students and force them to solve the problem. However their existing knowledge for problem solving are not sufficient and need to be supplemented.
(Tóth, 2004)
IT Education opportunities provided by teaching tools correspond nicely to the problem solving approach to teaching methodology. In the consciousness of this one of the tasks of IT teachers can not only provide jobs for their students, but bring them to real problem situations.
Bibliography
Komenczi, B. (2004): Didaktika elektromagna? Az eLearning virtuális valóságai, Új Pedagógiai Szemle, november, 5.
Lénárd, F. (1984a): A problémamegoldó gondolkodás, Akadémiai, 44.
Lénárd, F. (1984b): A problémamegoldó gondolkodás, Akadémiai, pp. 222-227.
Lénárd, F. (1984c): A problémamegoldó gondolkodás, Akadémiai, 194.
Nagy, S. (1997): Az oktatás folyamata és módszerei, Volos, 138.
Pólya, Gy. (2000): A gondolkodás iskolája, Akkord
Pólya, Gy. (2010): A problémamegoldás iskolája, Typotex, pp. 129-130.
Tóth P. (2004): Gondolkodásfejlesztés az informatika oktatásában, Ligatura, 60.
Contact
Beleznay Péter Fast Lane Kft.
pbeleznay@flane.com
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