Natalija Budinski Primary and secondary school “Petro Kuzmjak” Serbia Dragica Milinkovic Faculty of Education, University of East Sarajevo, Bosnia and Herzegovina Learning mathematics trough real life situation with use of educational software

The availability of technology has a big impact on education, and that is the main reason that in our presentation we discuss the use of technologies in mathematical education. We base our research on elementary school students 9-11 old and present examples of technology appliance in primary school in Bosnia and Herzegovina and Serbia

Mathematics in elementary education Knowledge and skills that are gained during elementary mathematical education are: Counting; Cardinality; Operation and algebraic thinking; Numbers and operations; Fractions; Expressions and equations; Etc.

That implies understanding of: informal counting, meaning of number, patterns, four basic operations and their properties, algebraic methods and representations, associative, commutative, distributive properties, special properties of zero and one, equalities and inequalities, appropriate application of formulas, geometric figures, transformations, models, metric units…

Many research indicates that elementary mathematics plays an important role in later education. It was found that early mathematics skills were predictors of later academic achievement in both mathematics and reading more than attentional, socioemotional or reading skills (Duncan et al., 2007).

Elementary mathematical education as a starting point provides educators to build on students’ knowledge with an inquiry and model- based approach, developing determined and essential mathematical experiences in the classroom. The educators have to be aware that the ways that children in elementary school think in mathematical situation can different and unexpected.

Taking this into account, teaching of mathematics in elementary education need to take advantage of the cognitive competence of students. For example, exploring real world problems can be used for teaching simple, convenient and efficient ways that follow students’ capabilities. Modeling real-world problems can enable setting up and solving various problems. Mathematical modeling that is most appropriate students, implies certain procedures that can be applied to solve problems: the examination of verbal (textual, illustrative) display of real problems, the identification of numerical variables which are explicitly given as "unknown" and their graphical representation, the identification of algebraic relation expression in the visually, set up and solve algebraic equations, contextual interpretation of numerical and algebraic expressions in the real-world context.

Use of technology in elementary education Now Before

The availability of technology influenced on how mathematical contents could be presented to students even in the early or elementary level of learning mathematics trough exploring real- world situations. Thanks to the development of digital technology it is possible to model different problems, among them real-world in the obvious, dynamic and interesting way. We present benefits of learning mathematical concepts trough real life situations and share experiences from Serbia and Bosnia and Herzegovina.

Particularly, we analyze process of transition from real life to mathematical situation and vice versa trough classroom examples which gave more clear picture of mathematical importance to students and motivated them to explore benefits of mathematical theory. 

Use of existing software and prepared materials by geogebra community Geogebra can be used for exploring real- world problems such as determining distance on the map. It can be connected to the mathematical concept of geometrical figures and their properties

Interesting problem about cats’ movement trough maze can be use for introduction to the coding.

Software tailored to the students’ needs

Modeling geometrical problems in elementary education with technology Software for modeling geometrical problems in elementary education was designed to provide students development, trough feedback and evaluation. It was made at the University of East Sarajevo as a part of Dragica Milinkovic research about software usage in geometry lessons and modeling. Contents are divided into eight parts, with special emphasis on a differentiated approach to the modeling of real problems. It is consisted of definitions and the basic stages of mathematical modeling, solving real world problems related to geometry, theoretical explanation model, the practical application of the model in solving real problems and tasks with solutions . It also consists of eight tests, each of which contains four real problems with differentiated instruction and solutions. The program is designed so that the student can ask for help three times, get feedback for each level, and the choose the correct answer. It is appropriate for students at 10-11 years old.

Example There are four shelves in school library with 1334 books. There are three times less books on the first shelf than on the fourth, 120 more books on the second shelf than on the first, and 92 less books than on the third shelf. How many books are on the shelfs?

The solution is offered in few steps. Steps are guiding students to the equation which represents mathematical model. Manipulating with equation students receive the final solution of the real world problem.

Properties of the mathematical model can be explored with Geogebra. Students can observe the number of the books in library by changing values at first shelf. They can notice, for example, that the number of books on second and third shelf equals when the number of books on the first shelf is 60. Using proposed Geogebra model, students can propose world problem by them self, or they can check the results by calculating and practice subtraction.

Conclusion Even though technology is unavoidable in everyday life of young students, it application in the education process is not straight forward. It require careful preparation and research in order to provide students with knowledge and understanding of mathematical concepts and its application in real life.