doktorska disertacija
Špela Cerar (Author), Jože Rugelj (Mentor)

Abstract

Rekurzija je v računalništvu ena izmed temeljnih metod za reševanje kompleksnih problemov. Končna rešitev problema je odvisna od rešitev manjših podproblemov, na katere razdelimo prvotni problem, pri čemer za reševanje delnih problemov uporabimo enak postopek kot za reševanje osnovnega problema. Delitev na manjše podprobleme se ponavlja toliko časa, dokler dobljeni podproblem ni trivialno rešljiv. Z rekurzijo se učenci prvič srečajo pri učenju programiranja, kjer programski jeziki omogočajo definicijo rekurzivnih funkcij, ki kličejo same sebe in praviloma pri vsakem nadaljnjem klicu zmanjšujejo svoje definicijsko območje, dokler le-to ni minimalno in je funkcija trivialno rešljiva. Raziskave kažejo, da imajo učenci težave z razumevanjem rekurzije, saj takega načina reševanja problemov v praksi pred tem ne srečajo. Za razumevanje tega koncepta si morajo učenci zgraditi ustrezen miselni model. Skozi zgodovino poučevanja računalništva so se številni avtorji ukvarjali prav z iskanjem najboljših rešitev za poučevanje rekurzije. Za poučevanje rekurzije so v preteklosti uporabili raznolike pristope: predstavitev rekurzije na osnovi njene implementacije, preko razumevanja matematične indukcije, s sledenjem izvedbi rekurzije, z uporabo vizualnih pripomočkov in fraktalov, z analizo predlog programske kode, s pomočjo rekurzivnih primerov iz realnega življenja in kot predstavitev načina za reševanje problemov. Ker rekurzija velja za težko razumljivo učno vsebino, so raziskovalci želeli najti tipične napake v razumevanju rekurzije, na podlagi česar so določili in kategorizirali različne miselne modele rekurzije, ki jih pridobijo učeči se. Miselni modeli rekurzije in tipične napake so predstavljeni v teoretičnem delu disertacije. V empiričnem delu je predstavljena raziskava, v kateri smo analizirali miselne modele rekurzije, ki si jih učenci zgradijo, zaznali neustrezne med njimi ter z uporabo primernega didaktičnega pristopa in zagotavljanjem potrebnih predznanj podprli gradnjo ustreznejših miselnih modelov. Izvedli smo akcijsko raziskavo z učenci zadnjega triletja osnovne šole. Na začetku akcijske raziskave smo preverili interes in motiviranost učencev za učenje programiranja. Z različnimi učnimi aktivnostmi so učenci najprej spoznali ali utrdili in dopolnili potrebno predznanje za razumevanje rekurzije, ki jim je sledilo preverjanje znanja konceptov spremenljivka, iteracija in podprogram. V nadaljevanju so učenci spoznavali rekurzijo. Miselne modele, ki so jih zgradili med spoznavanjem rekurzije, smo preverjali z opazovanjem učencev pri reševanju nalog iz rekurzije med učnimi urami in analizo rešitev nalog na pisnih preverjanjih znanja rekurzije. Na podlagi izsledkov smo načrtovali nadaljnje akcijske korake, s katerimi smo želeli podpreti preoblikovanje neustreznih miselnih modelov rekurzije, ki so si jih zgradili učenci, v ustrezen miselni model. Izsledki raziskave so pokazali, kakšne napake v razumevanju rekurzije smo zaznali pri učencih in katere miselne modele rekurzije so si zgradili učenci. Ugotovili smo, da imajo učenci manj težav pri sledenju izvajanja rekurzivnih podprogramov kot z generiranjem programske kode za rešitev podanega problema. Miselne modele, ki smo jih zaznali pri učencih pri sledenju izvedbe rekurzivnih podprogramov, smo kategorizirali po obstoječem modelu. Več težav smo imeli pri kategorizaciji generativnih miselnih modelov, zato smo na podlagi več obstoječih kategorizacij miselnih modelov sestavili svojo kategorizacijo miselnih modelov rekurzije in jo uporabili na našem vzorcu rešitev. Z novim modelom za kategorizacijo generativnih miselnih modelov rekurzije smo v ustrezne kategorije uvrstili večje število rešitev kot pri obstoječih kategorizacijah.

Keywords

didaktika računalništva;poučevanje programiranja;rekurzija;miselni modeli rekurzije;motivacija;osnovnošolci;

Data

Language: Slovenian
Year of publishing:
Typology: 2.08 - Doctoral Dissertation
Organization: UL PEF - Faculty of Education
Publisher: [Š. Cerar]
UDC: 004.42:373.3(043.2)
COBISS: 225008131 Link will open in a new window
Views: 45
Downloads: 19
Average score: 0 (0 votes)
Metadata: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Other data

Secondary language: English
Secondary title: Understanding recursion in computer programming among students in the third cycle of the primary school
Secondary abstract: Recursion is a fundamental method for solving complex problems in computer science. The final solution to a problem depends on the solution of smaller subproblems into which the original problem is divided, using the same subroutine for solving the subproblems as for the basic problem. The division into smaller problems is repeated until the resulting problem is trivially solvable. The concept of recursion is first encountered by students when learning to program, where programming languages permit the definition of recursive functions that call themselves. These functions typically reduce the definitional range of each successive call until it is minimal, thereby rendering the function trivially solvable. Research indicates that students have difficulty understanding recursion because they have not previously encountered this type of problem-solving in practice. In order to comprehend this concept, students must construct an appropriate mental model. Throughout the history of computer science education, numerous authors have endeavoured to identify the most effective methodologies for the teaching of recursion. In the past, a variety of approaches have been employed to facilitate the learning of recursion, including the presentation of recursion based on its implementation, the utilisation of mathematical induction to elucidate the concept, the tracing of the execution of recursion, the utilisation of visual aids and fractals, the analysis of programming code templates, the incorporation of real-life recursive examples, and the demonstration of recursion as a means of solving problems. Given the difficulty of understanding recursion, the researchers sought to identify the most common misconceptions associated with this concept. Based on this analysis, they were able to categorize the various mental models of recursion that learners tend to develop. These findings are presented in the theoretical section of the thesis. The empirical part presents a study in which we analysed the mental models of recursion that learners construct, identified those that are inappropriate, and supported the construction of more appropriate mental models by using an appropriate didactic approach and providing the necessary background knowledge. We conducted action research with pupils in the last three years of primary school. At the beginning of the action research, we assessed the students' interest and motivation to learn programming. The students were first introduced to recursion through a series of learning activities, which aimed to provide them with the necessary background knowledge to understand the concept. This was followed by a review of the concepts of variables, iteration and subroutines. Once the students had acquired a basic understanding of recursion, they were presented with a series of practical exercises designed to reinforce their knowledge. The mental models that the students constructed during this learning process were then evaluated through a combination of observation, written tests and analysis of the students' solutions to recursion problems. Based on the findings, we devised further action steps to facilitate the transformation of the inadequate mental models of recursion constructed by the students into an appropriate mental model. The results of the survey demonstrated the misconceptions of recursion that were identified in the students and the mental models of recursion that the students had constructed. It was found that students experienced less difficulty in following the execution of recursive subroutines than in generating program code to solve a given problem. The mental models that were detected in students when tracing the execution of recursive subroutines were categorised according to the existing model. The categorisation of generative mental models proved more challenging, necessitating the construction of a bespoke categorisation of recursion mental models based on several existing categorisations. This was then applied to the sample of solutions. The new model for categorising generative mental models of recursion resulted in a larger number of solutions being placed in the relevant categories than in the existing categorisations.
Secondary keywords: computer science didactics;teaching computer programming;recursion;mental models of recursion;motivation;primary school students;Didaktika;Osnovnošolsko učenje in poučevanje;Računalništvo;Univerzitetna in visokošolska dela;
Type (COBISS): Doctoral dissertation
Study programme: 0
Embargo end date (OpenAIRE): 1970-01-01
Thesis comment: Univ. v Ljubljani, Pedagoška fak.
Pages: 1 spletni vir (1 datoteka PDF (XX, 165, XXII str.))
ID: 25814606