Sadržaji kombinatorike u nastavi matematike

master's thesis

• Author: Petra Ćurjurić
• Mentor: Sanja Varošanec (mentor)
• Committee member: Sanja Varošanec (predsjednik povjerenstva)
• Committee member: Dijana Ilišević (član povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Nikola Sandrić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2024-11-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Traženje uzoraka jedan je od glavnih instinkata koje čovječanstvo posjeduje. Matematika je često opisana kao znanost o uzorcima, a može se reći da se time ponajviše bavi kombinatorika, u odnosu na ostale matematičke grane. Ona je prirodno usađena u sadržaje matematike još od osnovne škole, a njena je domena prebrojavanje konačnih skupova. Još u nižim razredima osnovne škole učenici mogu rješavati zadatke slične ovome: "Ema ima 2 haljine i 3 jakne. Na koliko načina može iskombinirati po jednu haljinu i jaknu koje će obući za odlazak u kazalište?" Pri prvom susretu učenika s ovom vrstom zadataka nastavnik treba učenike uspješno dovesti do rješenja, a potom ih pustiti da samostalno rješavaju zadatke. Stoga nastavnik treba dobro poznavati teoriju koja se krije u pozadini ovakvih zadataka, ali treba imati i vještinu osmišljavanja novih zadataka čije se rješenje temelji na primjeni nekog od kombinatornih principa. Ovaj je diplomski osmišljen kao pomoćni priručnik nastavniku kako bi što prirodnije u nastavu uveo kombinatorne pojmove te kod učenika potaknuo motivaciju i interes za tim sadržajima. Prvi analizirani nastavni sadržaj jesu temeljni principi prebrojavanja: princip umnoška, princip zbroja, princip razlike i princip kvocijenta. Za svaki od navedenih principa dani su primjeri uvodnih zadataka za nastavu s detaljnim raspisom rješenja. Osim toga, definirani su pojmovi varijacije, permutacije i kombinacije sa i bez ponavljanja te binomna formula. Osim definicija, navedene su nastavne aktivnosti, to jest zadatci koji zorno predočuju navedene pojmove. Navedeni su i ishodi učenja koji se ostvaruju usvajanjem nastavnih sadržaja iz područja kombinatorike te primjer rasporeda nastavnih sati.

Abstract (english)

The topic of this thesis are contents of combinatorics in mathematics classes and a methodical approach to these contents. The search for patterns is one of the main instincts that humanity possesses. Mathematics is often described as the science of patterns, and it can be said that it is mainly concerned with combinatorics, compared to other branches of mathematics. Combinatorics is naturally embedded in the contents of mathematics since elementary school, and its domain is the counting of finite sets. Even in the lower grades of elementary school, students can solve tasks similar to this: "Ema has 2 dresses and 3 jackets. In how many ways can she combine one dress and one jacket that she will wear to go to the theater?" When encountering the students to this type of tasks for the first time, the teacher should successfully lead them to the solution, and then let them find it themselves. Therefore, the teacher should have a good knowledge of the theory that is hidden in the background of such tasks, but should also have the skill of devising new tasks, the solution of which is based on the application of one of the combinatorial principles. This thesis was designed as an auxiliary manual for the teacher in order to introduce combinatorial concepts in the lesson as naturally as possible and to stimulate students' motivation and interest in these contents. The first analyzed teaching content is the basic principles of counting: the principle of multiplication, the principle of sum, the principle of difference and the principle of quotient. For each of the mentioned principles, examples of introductory tasks for teaching are given with a detailed call for solutions. In addition, the concepts of variation, permutation and combination with and without repetition and the binomial formula are defined. In addition to the definitions, teaching activities are listed, that is, tasks that clearly present the mentioned concepts. The learning outcomes that are realized by adopting teaching content from the field of combinatorics and an example of the schedule of teaching hours are also listed.

• Keywords: uzorak; kombinatorika; učenik; nastavnik; nastava matematike
• Keywords (english): combinatorics; patterns; student; teacher; teaching mathematics
• Language: croatian
• URN:NBN: urn:nbn:hr:217:678238
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar edukacije matematike (sveučilišni magistar edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-11-12 15:58:06