HOW TO TEACH THE FUNDAMENTALS OF INFORMATION SCIENCE, CODING, DECODING AND NUMBER SYSTEMS?
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1 6th INTERNATIONAL MULTIDISCIPLINARY CONFERENCE HOW TO TEACH THE FUNDAMENTALS OF INFORMATION SCIENCE, CODING, DECODING AND NUMBER SYSTEMS? Cecília Sitkuné Göömbei College of Nyíegyháza Hungay Abstact: The Intoduction of Infomatics subject deals with the udiments of infomatics within the education system of the College of Nyíegyháza whee infomatics teaches and pogamme mathematics ae tained as well. The poblem that made us examining the subject is that thee has been high ate of failed exams in this subject since yeas. In the fist semeste of 2004/2005 the 83% of the examinees failed at the fist exam and afte the 2 nd, 3 d o 4 th exam still the 47% of the students wee unsuccessful. The aim of this pape is to a) intoduce the content, the equiements and the concete exam equiements of the Intoduction of Infomatics subject, b) the mathematical backgound of the execises and c) the solutions of one basic execise of the test. Based on 646 test papes we ty to detemine the most common mistakes and based on the expeience we make suggestions. Keywods: infomatics, education, numeical systems.. INTRODUCTION Within the taining system of the College of Nyíegyháza fo infomatics teaches and pogamme mathematics the Intoduction of Infomatics subject that is about udiments of infomatics is an obligatoy subject in the fist semeste. Thee is lectue in evey week, the numbe of the cedit points is 2 and at the end of the semeste the examinees have to take teminal examination. The poblem that that made me examining the subject is that thee has been high ate of failed exams in this subject since yeas. The exam esults of the fist semeste of the yea 2004/2005, as it follows: At the fist exam thee wee 349 students with the following esults: excellent: 2 people good: 0 people satisfactoy: 3 people pass: 3 people unsatisfactoy: 293 people; aveage:,27 The following diagam shows the maks of the fist exam in pecentage:
2 The maks of the fist exam 83% %3% 4% 9% excellent good satisfactoy pass unsatisfactoy Figue. The esults of the fist exam At the end of the examination season (afte epeated exam) not moe than 47% of the students concened passed the examination. The total esults can be seen below: Total 53% 3% 0% % 23% excellent good satisfactoy pass unsatisfactoy Figue 2. Total esults 2. THE CONTENT OF THE SUBJECT, THE METHOD OF EXAMINING 2.. The main aim of the subject is to make the students familia with the theoetical base and technical tems of infomatics. To ecapitulate: I. The compute and the algoithm: The notion of the compute, the Neumann-pinciples, inne build-up of the compute, the peipheal devices; The notion of algoithm, descipto devices, complexity. II. Infomation and data epesentation: Measuing the infomation, entopy, decimal value numbe epesentation, numeical systems, fixed point epesentation, floating point epesentation, decimal epesentations, logic data, chaacte, sting epesentation, logic opeations and thei tuth tables, logic opeations of fixed point numbes. III. Data stuctues and thei epesentations: Linea data stuctues: aays, linked lists, odeing, special linea data stuctues: stack, evaluation of postfix expession, tansfom infix expession to postfix, pogession.
3 Non-linea data stuctue: ecod data stuctue, gaph data stuctue 2.2. The teminal examination is in witten fom. The test (0 execises) has to be solved within 30 minutes and calculato cannot be used. The examinees get the test in pinting, they can count on the test, the esults should be copied in a box beside the execises. Duing the coection these esults ae taken into consideation. The maximum points fo the execises ae 0, 0,5 o point. The maks depend on the points and ae counted the following way: 9,5-0 excellent (5) 8,5-9 good (4) 7,5-8 satisfactoy (3) 6,5-7 pass (2) To be able to solve the execises of the test the following knowledge is equied:. Convet fom decimal system 6. Logic opeations 2. Convet to decimal system 7. Convet fom floating point fom 3. Convesion infix expession to 8. Convet to floating point fom postfix 9. Convet between numeical systems 4. Convesion to binay complement 0. Convesion fom binay complement 5. Counting infomation content It can be seen fom the test that the most stessful expect two execises it occus in evey execise topic is the numeical system topic. If we take into consideation the efficient solutions we can daw the conclusion that expect the execise 0. less then 50% of the students can solve the execises (the aveage is unde 40%!). The following diagam shows the efficiency by execises: Efficiency by execises efficiency 00% 80% 60% 40% 20% 0% o 0,5 point point numbe of the execise Figue 3. Efficiency by execises 3. MATHEMATICAL BACKGROUND OF THE EXERCISES [] 3.. The notion of the decimal value numeical system The based decimal value numeical system is defined by the following theoem: i 2 2 (... a 2 a a 0. a a 2 ) = ai = + a + a + a + a + a + () i= 2 0 2
4 The numbe is the base figue of the numeical system, the signs a i ae the numeals of the numbe, the ai numbe maked by the a i is called the fomal value of the numbe, the i powe is the decimal value of the numbe ( i = 0, ±, ± 2,...), and. is the point of efeence Switch fom one numeical system to anothe one 3.3. theoem Let 2 be a natual numbe. In this case an abitay v 0 eal numbe can be noted in the based decimal value numeical system v = ( a n a n... a 2 aa 0. a a 2...) (2) fom, whee 0 a i natual numbe fo all i = n, n-, and a 0, if n. v intege pat: n factional pat: [] v ( a n a n... a 2 aa 0.0) =, (3) Let based numeical system. {} v ( 0. a a 2...) =. (4) v 0 is a given numbe in the R based numeical system. Define the numeals of v in the Fist define the numeals of v intege pat: based on the theoem.3. [ v ] can be witten fom, in anothe way a n n n + an + + a + a0 (5) (...(( an + an ) + an 2 ) + + a) + a0 (6) Pefom the esiduum division with ; the esiduum based on thei inceasing decimal value give the fomal values of the numeals in the based numeical system: [] v = v + a0 v = v2 + a v2 = v3 + a2 (7) vn = vn + an vn = 0 + an Now define the numeals of the factional pat of v : based on the theoem.3. { can be witten in fom. Thus 2 a + a + (8) 2 {} v = a + a 2 +, (9) whee the intege pat of {} is, the factional pat is a +. Multiply by the v a 2 factional pat of the poducts of multiplication. These poducts ae always fom the peceding v}
5 steps. The intege pat of the poducts give by deceasing intege pat the fomal values of the numeals in the {} v based numeical system. Since we did the opeations in the oigin (R based) numeical system the fomal values of numeals as the esults of the steps taken ae also in this numeical system. Afte this we wite the numeals which mak the fomal values of the numeals in the based numeical system, in the places of the fomal values: so we get the fom of v in the based numeical system. 4. THE COMMON MISTAKES IN THE EXERCISE. The concete execise: Convet the given numbe fom decimal system to numeical system of based thiteen in a way that the factional should be 3-digit coect! The numbe is: ~The students note the execise wongly, they do not count with the numbes in the execise. ~Counting mistakes - The most of the counting mistakes occu in the dividing. The students detemine wongly the numeals in the quotient o the esiduum, but mostly both. They cannot do division with 2-digit diviso confidently. - In the multiplications the typical counting mistakes that pimay school students also often make ae fequent, fo example: 9 x 9 = 8; 6 x 3 = 2. They have poblem in multiplying with 2-digit numbe, they multiply the multiplicand with only one decimal value. Vey fequently they define wongly the place of the point of efeence (decimal point). ~ Defectiveness in the udiments of mathematics In some test thee ae mistakes that indicate the defectiveness in the udiments of mathematics. ~ Defectiveness of making algoithm 5. MISTAKES IN COUNTING THE INTEGER PART Most of the students (7) use algoithm to count the intege pat. Occuing mistakes: 5.. The student applies the algoithm popely, counts coectly, but the esult o the pat of the esult is wong The student chooses good algoithm, applies it well, counts coectly but does less division than equied The student chooses good algoithm, but unable to execute it coectly. He o she confounds the place of the quotient o the esiduum in the same execise seveal times.
6 5.4. He o she ties to use the algoithm in the execise 2. based on the decimal values of the decimal numeical system o the numeical system of based thiteen The student does not use the algoithm acquied. He o she divides the intege pat by 3 and chooses the quotient and esiduum as esults. 6. MISTAKES IN COUNTING THE FRACTION PART 6.. The student chooses good algoithm, uses the algoithm well, counts well, intepets the esult badly He o she puts the faction point at the wong place in the poduct He o she counts with the intege pat in the multiplications He o she uses the same algoithm (divisions) fo counting the factional pat and the intege pat The student wites down the following elation: = 0.abc = a 3 + b c He o she multiplies by 3 o 3 by tuns The multiplication is good, but the taking down is wong The student counts the factional pat with the algoithm used in the execise THE REASONS OF FAILURES 7.. Thei pevious mathematical knowledge is impefect The students poblem-solving and algoithm using ability is in low level Thee is a big diffeence between the abstaction level of the new and the pevious knowledge One lectue a week is not enough to pactise the empiical execises beside the theoy Pobably the leaning methods of the students ae not convenient The students do the algoithms mechanically and unable to intepet the esults They ae not familia enough with the algoithm o the way the algoithm is witten down is embaassing because it is diffeent fom the common fom of the division o the multiplication. 8. REFERENCES [2] Knuth: At of Compute Pogamming, Volume Műszaki Könyvkiadó Budapest. [] D. Váteész Magda: Matematikai pogamozás (főiskolai jegyzet)
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