Mathematical Intuition and Intuition in the Teaching of Mathematics

Autor u radu ističe da svaka znanstvena i filozofska spoznaja počinje intuicijom, kao sposobnošću ljudskoga uma da neposredno naslućuje, otkriva i spoznaje skrivene istine materijalne i duhovne stvarnosti i da je, u sprezi s maštom, stalni pratilac logike i filozofije spoznaje. Postanak i razvoj matematičkih pojmova i teorija pokazuje da matematička intuicija na prirodan i pravovremeni način otvara strogo logičke putove matematiče istine, koja se, na tim putovima, podvrgava logičkoj analizi. Matematika se, na svim svojim razinama, mora predstaviti kao sredstvo, ali i kao model egzaktnog, racionalnog i apstraktnog rasuđivanja, veoma značajnog za didaktičko–metodičko i gnoseološko stajalište, za svako teorijsko i praktično djelovanje. Nastava matematike u opisivanju matematičkih pojmova i iskaza, kao i njihovoj praktičnoj primjeni, prilazi intuitivno, otkrivajući njihove empirijsko–intuitivne korijene, uvažavajući njihovu genezu i evoluciju, kako bi njihova spoznaja bila što dublja i usvajanje što učinkovitije.The author of this paper highlights that each and every scientific and philosophical insight starts with intuition, as the ability of the human mind to indirectly intuit, discover and cognise the hidden truths of our material and spiritual reality and as – together with imagination – the permanent companion of both the logic and philosophy of cognition. The emergence and development of mathematical concepts and theories show that mathematical intuition, in a natural and timely fashion, opens the strictly logical paths of the mathematical truth, which is on these paths subjected to logical analysis. On all its levels mathematics must present itself as both the means and model of exact, rational and abstract judgement, which is tremendously important for the didactical-methodical and gnoseological perspective, for each and every theoretical and practical action. The teaching of mathematics approaches the description of mathematical concepts and statements, as well as their practical application, intuitively, unveiling their empirical-intuitive roots, appreciating their genesis and evolution, in order for their comprehension to be as deep and their acquisition as efficient as possible