Research Perspectives of Initial Geometry Education

The paper discusses the perspectives of teaching geometry based on the study The International Commission on Mathematical Instruction ICMI. Bearing in mind the current needs in geometry teaching, we considered that the topics of space and spatial reasoning should be part of it as key issues, as well as teaching approaches, RME, learning through (re)discovering mathematical ideas, the role of textbooks in the initial mathematics education, and so on. Therefore, this research paper offers a general insight into our need to deal with these topics, and invites researchers from the broader mathematical community, who we herewith familiarize with the results of our research in the sphere of initial geometry teaching in Serbia

Realistic mathematics In teaching and learning elementary geometry

Основни циљ почетне наставе математике је да ученике математички описменимо, а заступници смо гледишта да су циљеви, поред наведеног, и стварање стања упитаности, тежња ка стварању истраживачког духа ученика, као и осећаја за успостављање веза формалне математике са једне стране са појавама из реалног окружења са друге. Ово нас је довело до реалног окружења као једног од могућих наставних приступа који успоставља такве везе. Рад се састоји од четири основна поглавља са више подпоглавља. Бавили смо се теоријским и експерименталним испитивањем и проучавањем ефеката наставног приступа реално окружење у почетној настави геометрије базираног на теорији реалистичног математичког образовања подржан пропратним иновативним моделом уџбеника. Издвојили смо три циља рада. Први се односио на проучавање теоријских основа (геометријских и дидактичко-методичких) употребом методе теоријске анализе. Указали смо на неке међународне и домаће пројекте које у својим концепцијама математичког образовања за основно полазиште користе реално окружење. Други циљ односио се на представљање резултата експерименталног дела нашег истраживања којим смо испитали на који начин реално окружење у геометријским садржајима IV разреда почетне наставе математике утиче на постигнућа ученика (по нивоима знања) и резоновање, као и ученичку мотивацију за учење. Овде смо употребили експерименталну методу. И, коначно, трећи циљ односио се на представљање иновативног модела уџбеника као практичне имплементације који подржава конструктивистички приступ настави у реалном окружењу, а указали смо и на кључне резултате и њихове методичке импликације на почетну наставу математике добијене на основу експерименталног истраживања. Наше истраживање било је усмерено на откривање пута шта води ученике до појмова са значењем од, са једне стране, визуелних представа до, са друге стране, вербалних уопштавaња и анализа, наглашавајући повезаност визуелног и вербалног процеса као значајне у ученичком раду и изграђивању математичких појмова у математичкој свести ученика. На тој основи следили смо идеје изграђивања и елаборирања постојеће интуиције о простору, развијајући безусловно и геометријску интуицију. Додајући овоме и конструктивистички поглед, у истраживању смо се бавили развојем геометријских појмова и геометријског мишљења у реалистичном окружењу у коме се учи...The main aim of teaching elementary mathematics is to make students mathematically literate. This is why we advocate the view that aims, apart from the stated ones, are, as well, creating the states of curiosity, tendency towards crating researching minds of students and the sense for creating connections between formal Mathematics on one side and appearances from real environment on the other side. This has led us to realistic mathematics as one of the possible teaching approaches towards creating such a connection. There are four basic chapters and many sub-chapters. We have done both theoretical and experimental research and studying effects of the teaching approach to realistic mathematics in teaching elementary geometry based on the theory of realistic mathematical education supported by the additional innovative model of the course book. We have selected three aims of the paper. The first refers to studying theoretical bases (geometrical and didactic-methodological) by using the method of theoretical analysis. We have pointed at some international and domestic projects, which in their concepts of mathematical education, use realistic mathematics for their starting point. The second aim refers to presenting results of the experimental part of our research which is aimed at the examining ways in which realistic mathematics in geometry contents of the fourth grade of teaching elementary Mathematics influences the students‟ achievements (according to the levels of knowledge) and reasoning, as well as students‟ motivation for learning. We have used the experiential method here. Finally, the third aim refers to referring the innovative model of the textbook as practical implementation, which supports constructivist approach in teaching realistic mathematics, and we pointed at key results and their methodological implications on teaching elementary Mathematics gained according to experiential research. Our research is directed to revealing to the way, which leads the students to terms with meaning, from, on one side, visual concepts to, on the other hand verbal generalizations and analyses, stressing the connection between visual and verbal process as an important issue in mathematical mind of students. On this basis, we followed the ideas of building up and elaborating the existing intuition about space, developing, unconditionally geometrical intuition. Adding constructivist approach, in the research we have dealt with development of geometrical terms and geometrical thinking in realistic mathematics in which students learn. We have studies development of students‟ knowledge in realistic mathematics, as well as how teachers use this from learning and how this process occurs..

Potential of Natural and Recycled Concrete Aggregate Mixtures for Use in Pavement Structures

This study investigates the feasibility of using recycled concrete aggregate (RCA) as a partial substitution of natural aggregate in pavement engineering. Despite RCA’s good properties, such as polishing value and freeze-thaw resistance, its use is limited by low resistance to fragmentation and high-water absorption. This paper parent the experimental results of mineralogical-petrographic and physical-mechanical properties of RCA, natural stone (dolerite) and their combination (RCA content—15%, 30%, 45%, and 60%). The tested granular mixtures showed good resistance to fragmentation and wear (LA 22–27%, MDE 14–15%), as well as satisfactory Polished Stone Value of 55–57, which means they can be used in different layers of pavement structures. According to the obtained testing results, the application of RCA is possible in different flexible and rigid pavement layers and for various traffic loads.Special Issue: "Minerals and Other Phases in Constructional Geomaterials

Young pupils’ intuitive understanding and strategies of area measurement

Learning area measurement in mathematics instruction implies certain phases that entail rhetorical and symbolical generalizations in terms of mathematical formulas (Smith III & Barrett, 2017; Zacharos, 2006; Zeljić & Ivančević, 2019). It is through mathematical formulas that geometry is represented in Serbian mathematics curricula and this fact is the starting point of our research. When pupils have to solve mathematical tasks, they use various strategies that differ in terms of the correctness of their solution, the time needed for completing the task, and task requirements and scope (Siegler, 1991). To measure the area of a rectangular and overcome the problems arising from pupils’ misunderstanding of the area formula, it is recommended to take a closer look at the structure of the rectangular array by covering the area of the rectangular with a mathematical manipulative in the form of a unit of measurement that pupils are intuitively familiar with from the onset (Đokić, 2014, 2017; Van de Walle, Karp & Bay-Williams, 2013). The concept of covering would enable pupils to conceptualize the relationship between the unit’s dimensions and the dimensions of the rectangular. After this phase, through length measurement and multiplication, pupils can solve the area measurement task using mathematical formulas with understanding.Book of proceedings: 28th International Scientific Conference “Educational Research and School Practice”, December 9th , 2022 Belgrade

Mortgage market in the Republic of Serbia: present situation and prospects

This paper discusses the development of mortgage loans market in the Republic of Serbia through development of the instruments for provision of legal security of investments - both to creditors and to debtors. It explains the process of establishment of Real Estate Cadastre as a prerequisite for registration of real estate mortgages. Creation of the Central Mortgage Register is an additional service that provides transparency of the procedures and mortgage market development. The entire procedure has been illustrated by the statistical data on the increase of the number of registered mortgages, starting from 1998 through the end of 2011. The impact of the global economic crisis on the moderate decrease of the number of new mortgages in the Republic of Serbia is quite evident

Suconjunctval hemorrhages

Introduction:Subconjunctival hemorrhage or suffusion is bleeding that occurs between the conjunctiva and episclera. It has a distinctive look and often frightens patients. The causes can be varied. Objective: The research was undertaken in order to determine the characteristics of patients within whomsubconjunctival hemorrhage occur. Methods: Retrospective analysis of patients of the Eye Department of the Health Center in KosovskaMitrovica, during 6 months. Results were analyzed SPSS ver 22, i GraphPad INSTAT software package. Results: The change was observed in 63 patients. Male gender was significantly more frequent. The age of patients was diverse-between 5 and 86 years. The causes and conditions associated with subconjunctival hemorrhages are usually eye trauma, in young,and arterial hypertension in elderly patients. Conclusion: Subconjunctival hemorrhage is a relatively common diagnosis in ophthalmology. The change is benign and spontaneously disappears during one to two weeks. It is important to note that the subconjunctival hemorrhage occur in patients with certain risk factors

Copper Slag of Pyroxene Composition as a Partial Replacement of Natural Aggregate for Concrete Production

Copper slag, a by-product of the pyrometallurgical process used for obtaining copper from copper ore in Bor, Serbia, contains mainly silicon, iron, calcium, and aluminium oxides. Due to such properties, it is disposed of in landfills. Despite the favourable technical properties copper slag aggregates possess, such as low-water absorption (WA24 0.6%), low resistance to fragmentation (LA 10%), and low resistance to wear (MDE 4%), its use in the construction industry is still limited. The results of testing the technical properties of copper slag aggregates (CSAs) as a potential replacement for natural river aggregate (RA) are presented in this paper. The experiments included tests on three concrete mixtures with partial replacement of coarse natural aggregate with copper slag. The replacement of RA particle sizes of 8/16 mm and 16/31.5 mm with CSA in the amount of 20% + 50% and 50% + 50% resulted in an increase in the compressive strength of 12.4% and 10.5%, respectively. The increase of CSA content led to a decrease in water penetration resistance and salt-frost resistance of concrete, whereas the resistance to chloride ion penetration did not change significantly.This article belongs to the Special Issue Applied Petrography of Construction Material

Supplementary data for article: Djokic, L.; Spasic, J.; Jeremic, S.; Vasiljevic, B.; Prodanovic, O.; Prodanovic, R.; Nikodinovic-Runic, J. Immobilization of Escherichia Coli Cells Expressing 4-Oxalocrotonate Tautomerase for Improved Biotransformation of β-Nitrostyrene. Bioprocess and biosystems engineering 2015, 38 (12), 2389–2395. https://doi.org/10.1007/s00449-015-1474-8

Supplementary material for: [https://doi.org/10.1007/s00449-015-1474-8]Related to published version: [http://cherry.chem.bg.ac.rs/handle/123456789/1990

Supplementary data for article: Djokic, L.; Spasic, J.; Jeremic, S.; Vasiljevic, B.; Prodanovic, O.; Prodanovic, R.; Nikodinovic-Runic, J. Immobilization of Escherichia Coli Cells Expressing 4-Oxalocrotonate Tautomerase for Improved Biotransformation of β-Nitrostyrene. Bioprocess and biosystems engineering 2015, 38 (12), 2389–2395. https://doi.org/10.1007/s00449-015-1474-8

Supplementary material for: [https://doi.org/10.1007/s00449-015-1474-8]Related to published version: [http://cherry.chem.bg.ac.rs/handle/123456789/1990

Supplementary data for article: Đokić-Stojanović, D. R.; Todorović, Z. B.; Troter, D. Z.; Stamenković, O. S.; Veselinović, L. M.; Zdujić, M. V.; Manojlović, D. D.; Veljković, V. B. Triethanolamine as an Efficient Cosolvent for Biodiesel Production by Cao-Catalyzed Sunflower Oil Ethanolysis: An Optimization Study. Hemijska Industrija 2019, 73 (6), 351–362. https://doi.org/10.2298/HEMIND190822033D

Supplementary material for: [https://doi.org/10.2298/HEMIND190822033D]Related to published version: [http://cherry.chem.bg.ac.rs/handle/123456789/3797