Јелена Р. Стојкановић, Гимназија ,,Јосиф Панчић”, Бајина Башта, Србија, имајл: sanjamaricic10@gmail.com
Сања М. Маричић, Универзитет у Крагујевцу, Педагошки факултет, Ужице, Србија
Иновације у настави, XXXVIII, 2025/4, стр. 78–94

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DOI: 10.5937/inovacije2504078S

Резиме: Циљ рада је да истражи да ли се помоћу визуелно задатих растућих низова може достићи апстрактни ниво мишљења, односно да ли ученици могу да одреде чланове низа на удаљеним позицијама и да ли и колико њих може самостално достићи ниво генерализације. Рад је усмерен на то да утврди да ли ученици, ослањајући се на визуелизацију, могу да уоче правило раста низа, одреде чланове на удаљеним позицијама и формулишу општи члан низа. Истраживање је спроведено на узорку од 252 ученика и обухватило је три задатка, у којима се од ученика захтевало да наставе визуелни образац, нумерички представе односе и симболички изразе генерализацију. Добијени резултати показују да већина ученика успешно уочава правило и одређује удаљене чланове низа, али мало њих успева да симболички запише општи члан, што указује на недовољно развијено разумевање појма променљиве. Визуелна природа задатака подстиче функционално размишљање и омогућава ученицима да остваре напредак ка апстрактном нивоу резоновања. Налази указују на вредност визуелно задатих растућих низова као подршке развоју алгебарског мишљења и сугеришу потребу за њиховом већом заступљеношћу у настави математике у млађим разредима основне школе.

Кључне речи: растући низ, визуелизација, функционална зависност, генерализација

Summary: The aim of the paper is to investigate whether, with the help of the visually given growing patterns, an abstract level of thinking can be reached, namely, whether students can determine the members of the sequence at distant positions and whether and how many of them can independently reach the level of generalization. The paper aims to define whether students, relying on visualization, can observe the rule of the growing pattern, determine terms at distant positions, and formulate the general term of the sequence. The research was done on the sample of 252 students and included three tasks requiring students to continue a visual pattern, represent relationships numerically, and express generalization symbolically. The obtained results show that the majority of the students observe the rule and determine the distant members of the sequence successfully, but a small number of them manages to write down the general member symbolically, indicating insufficiently developed understanding of the concept of a variable. The visual nature of the given tasks encourages functional thinking and allows students to make progress towards an abstract level of reasoning. The findings point to the value of visually assigned growing patterns as a support for the development of algebraic thinking and suggest the need for their greater representation in the teaching of mathematics in the lower grades of primary school.

Keywords: growing patterns, visualization, functional dependence, generalization

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