Резюме. The present study aims at characterizing the solutions of tasks in Informatics from National competitions and Olympiads for Group D students relevant to 6th school grade. The study covers a 10-year-period (2004-2013). An application proposes a classification of these tasks based on their main characteristics. An evaluation of the relative difficulty of the tasks is also included.
Over the recent years competitions in Informatics have rapidly increased, both in our country and abroad. Bulgaria could be proud with very good results achieved in Informatics competitions, both national and international. Since 2001, regularly each year Bulgaria organizes six national competitions in Informatics following exactly the same rules and regulations as those of the International Olympiad in Informatics: 3 tournaments per year (in autumn, winter and spring) and 3 rounds of the National Olympiad. Since 2002, the competitions in Informatics have been targeting participants of different age groups: group A (11 – 12th school grade), Group B (9 – 10th school grade), group C (7 – 8th school grade) and group D (4 – 6th school grade).
In the autumn of 2004 the group E has been introduced which includes 4 – 5th school grade and this has led to a new distribution of the age groups: A, B, C and D, covering 12th, 10-11th, 8-9th and 6-7th school grades, respectively. In the autumn of 2007, with the establishment of the Balkan Olympiad in Informatics (JBOI) for students up to 15.5 years age we have applied a modified age system in which Group D has covered only 6th school grade and the distribution of the other groups are as follows: group A (11 – 12 grade), group B (9 – 10 grade), group C (7 – 8 grade), Group D (6th grade) and group E (4 – 5 grade).
The most important goal of the competitions is to enhance students’ knowledge, skills and abilities. Competitions encourage self-education. They are a powerful regulator, because students get the opportunity to assess their own level of expertise. Thus, the participants have the possibility to make necessary adjustments in their further training and self-preparation. To solve tasks of different competitions successfully, one needs in-depth knowledge not only in the field of algorithms and programming, but also in the domain of Mathematics.
Preparation of students for national competitions involves various extracurricular activities. The main objectives of the extracurricular training in Informatics are:
Expanding opportunities for students to demonstrate their practical skills and preparing them to participate in national and international competitions in Informatics.
Developing students’ algorithmic methods of thinking. Expanding their knowledge in programming. Analyzing and understanding the solutions of different tasks included in Informatics Olympiads.
Learning standard algorithmic methods and acquiring skills to apply them to other types of tasks.
Developing creative thinking, teaching a creative approach to task solving.
Thought - provoking methods aiming at improving the effectiveness of the algorithms and their rapid functioning.
Enjoying moral and emotional satisfaction with their achievements.
Developing self-discipline, perseverance, sportsmanship and striving for selfeducation (Старибратов & Танева, 2009).
In this paper we follow Emil Kelevedjiev’s and Zornitca Djenkova’s fundamental ideas (Келевджиев & Дженкова, 2008) and (Келевджиев & Дженкова, 2012) for problem systematization and classification. After accumulating a sufficient number of tasks from national competitions, it is possible to conduct different kinds of research, for example classifications based on task basic characteristics.
Consider the coefficient k = (y – x)/(x + y), where x denotes the number of the contestants with more than 60 points (out of 100) for task performance and y denotes the number of the contestants with less than 30. The maximum value is k = 1 (for x = 0), meaning that there is no contestant with more than 60 points, which shows that the task is difficult. The minimum value is k = – 1 (at y = 0), i.e. no contestants’ result is under 30 points, which indicates in turn that the task is easy. The coefficient k gives information about the extent to which the authors of the tasks have made the paper selection according to the particular competition and the age of the students. (Келевджиев & Дженкова, 2008)
Below the main characteristics of the tasks are summarized in the following three points:
1. Elements of the programming language related to the types of the processed data in the program: numbers, symbols, strings, one-dimensional and two-dimensional arrays, arrays of strings. The following diagram (Fig. 1) shows the proportion (in percentages) of the processed data in the tasks of group D (2004-2012):
Fig. 1. Processed data for task solving
Fig. 2. Relative difficulty of the tasks
It is obvious from the above chart that most of the tasks involving numbers are relatively less difficult. This is completely natural because students use to know this type of data when they are still in Group E (4-5th grade). The tasks with an array of strings as processed data are the smallest in number and pose most difficulties to students.
2. Programming language elements related to the syntactic structures used in the program: conditional operator – if, loop (for, while, do... while), nested loops, use of functions. The following diagram (Fig. 3) shows the proportion (in percentages) of the syntactic constructions in the tasks of Group D (2004-2012):
Fig.3. Syntactic structures in task decisions
The relative difficulty of the tasks is established according to the syntactic structures used in the solutions of the tasks of Group D, presented in Figure 4. It is shown in the diagram that students meet relatively more difficulties in doing tasks on loop syntax with functions and nested loops with functions.
3. A theory of data structures and algorithms used in the solutions of the tasks: divisibility, long numbers, classification, number systems, recursion, text processing, geometry – rectangles with sides parallel to the coordinate axes, etc.
Classification of the tasks given in National competitions in Informatics Group D (2004 – 2012)
Legend: NAT – National Autumn Tournament in Informatics; WCI – Winter Competition in Informatics; NOI2 – National Olympiad in Informatics (regional round); NSTI – National Spring Tournament in Informatics; NOI3 – National Olympiad in Informatics; DIGIT – separation and Processing digits of numbers; RSPCA – rectangle with sides parallel to the coordinate axes; OPT – find the optimal (maximal/minimal) element; UNIT – conversion of measure units; SUM – finding the sum of a final number of numbers.
Fig. 4. Relative difficulty of the tasks with syntax structure
Conclusions. There are no difficult tasks in general but tasks, with which students are familiar and have practiced them in school. The others are completely new. Tasks of medium difficulty are those that combine knowledge and different algorithms. The Diagrams (Fig.5 and Fig. 6) show that tasks such as (co-efficient ‘k’ is negative) during the last two school years.
Fig.5. Relative difficulty of the competition tasks for the school year 201
Fig.6. Relative difficulty of the tasks in competitions for the school year 2012/2013
We used all these data for further analysis and classification of the problems which might be useful for the teachers concerned with extracurricular activities as well as selfeducating students. The current report will also help the preparation of future competition topics. It is necessary for us to improve the processing of the studied algorithms to achieve better results. To be confident in our success in competitions we need to apply the acquired theory and to put it into considerably more practice.
NOTES
1. http://infoman.musala.com/
2. http://www.math.bas.bg/infos
REFERENCES
Келеведжиев, Е. & Дженкова, З. (2012). Състезателните задачи по информатика за 9. – 10. клас. Математика и математическо образование, 41, 359 – 365.
Келеведжиев Е. & Дженкова, З. (2008). Състезателните задачи по информатика за 4. – 7. клас. Математика и математическо образование, 37, 367 – 378.
Старибратов, Ив. & Танева, Б. (2009). Различният начин за мотивиране на учениците за развитие на информатиката в средното образование. Сборник доклади на Национална конференция „Образованието в информационното общество“. Пловдив.
