Algebra in Geometry and Trigonometry

Kroz prvi dio rada odgovorili smo na pitanje "Zašto učimo algebru?", te budući da je prvi susret ključan za razvijanje pozitivnog stava o algebri, naveli smo načine uvođenja algebre u nastavu. Od samog početka učenja algebre, uz uvježbavanje manipuliranja algebarskim izrazima, važno je prikazivati razne primjere iz stvarnog života kako bi učenici shvatili kako im algebra pomaže pri rješavanju različitih problema.U drugom dijelu rada prikazali smo vezu algebre i geometrije. Učenici grafičke prikaze prihvaćaju s lakoćom jer pružaju bolji uvid u značenje različitih algebarskih izraza, a s druge strane učenici uočavaj kako je algebra moćan alat za rješavanje različitih geometrijskih problema. Prikazali smo kako algebru koristimo u jednakokračnom trokutu, te kako nam pomaže pri računanju kutova mnogokuta, opsega i površina različitih likova. Prikazali smo primjer kako problem iz stvarnog života rješavamo pomoću veze algebre i sličnosti trokuta, te nekoliko dokaza Pitagorinog teorema i njegovu primjenu u stvarnom životu. U trećem dijelu rada bavili smo se vezom algebre i trigonometrije. Budući da učenici često imaju negativan stav prema trigonometriji jer ju vide kao veliki broj formula koje nemaju smisao, važno je da od prvog susreta s trigonometrijom učenici shvate pojmove sinus, kosinus i tangens, a zatim svaku formulu izvedu pomoću poznatih činjenica kako bi uočili njihov smisao. Prikazali smo kako uvesti pojmove sinus, kosinus i tangens u nastavu, riješili smo nekoliko trigonometrijskih problema, upoznali se sa Sinusovim i Kosinusovim teoremima te izveli nekoliko trigonometrijskih identiteta. Prikazano je i nekoliko primjera iz stvarnog života kako bi učenici vidjeli primjenu trigonometrije, što razvija pozitivan stav i motivaciju za učenjem trigonometrije.Throughout the first part of the paper, we addressed the question "Why do we learn algebra", and listed ways of introducing algebra into teaching since the first encounter is pre-eminent for the development of a positive attitude towards algebra. From the very beginning of learning algebra, besides practicing manipulation with algebraic expressions, it is important to present a variety of real-life examples to help students understand how algebra helps them solving different problems. In the second part of the paper, we have demonstrated the interlink of algebra and geometry. Student accepts graphics display with ease because they provide a better insight into the meaning of different algebraic expressions. On the other hand, students realize that algebra is a powerful tool for solving all sorts of geometric problems. We have demonstrated how algebra is used in the isosceles triangle and how it helps us calculate the angles of a polygon, perimeter, and area of different shapes. We have also demonstrated how real-life problems are solved by using the interlink of algebra, similarity of the triangle, and Pythagorean theorem. The third part of the paper deals with algebra and trigonometry. Since students often have a negative attitude towards trigonometry, mainly because they perceive it as a large number of formulas with meaning, it is important that from the first encounter with trigonometry students understand the concepts of sinus, cosine, and tangent, and only then should the formulas be derived from known facts in order for students to be able to perceive their meaning. The paper shows how to introduce the concepts of sinus, cosine, and tangent to the teaching, and how to solve several trigonometric problems. The paper also shows how to get acquainted with the Sinus and Cosine theorems and to perform several trigonometric identities. In addition, there are some real-life examples of how should the students perceive the application of trigonometry, which develops a positive attitude and motivation towards learning trigonometry

Analysis of the existing condition and a suggestion for obesity prevention in early school-age children

Due to the importance of the role of this topic in the lives of children, but also adults, this paper tackles numerous studies that have explored the same issue. The research findings were analyzed with regards to the examined morphological characteristics (body height, body mass, body mass index, skin folds, body fat content) and activities of younger children in the city of Rijeka. The research was conducted in the Elementary School ‘Pehlin’ and the Elementary School ‘Kozala’ on a sample of 245 pupils enrolled in the lower four grades. It was found that younger school children in Rijeka have a moderate body mass, but the percentage of body fat in boys and girls suggests increased caution. A comparison between boys and girls in terms of the morphological characteristics resulted in no statistical differences. It has also been confirmed that children engaged in sports activities show better morphological characteristics, lower body mass as well as a lower body mass index, skin folds, and body fat than children who do not play sports. After the established condition, a preventive kinesiological program was proposed as well as advice that should be followed regarding the diet and the manner in which children spend their leisure time

Predictive value of spinal CSF volume in the preoperative assessment of patients with idiopathic normal-pressure hydrocephalus

IntroductionThe pathophysiology, diagnosis, and management of idiopathic normal pressure hydrocephalus (iNPH) remain unclear. Although some prognostic tests recommended in iNPH guidelines should have high sensitivity and high predictive value, there is often no positive clinical response to surgical treatment.Materials and methodsIn our study, 19 patients with clinical and neuroradiological signs of iNPH were selected for preoperative evaluation and possible further surgical treatment according to the guidelines. MR volumetry of the intracranial and spinal space was performed. Patients were exposed to prolonged external lumbar drainage in excess of 10 ml per hour during 3 days. Clinical response to lumbar drainage was assessed by a walk test and a mini-mental test.ResultsTwelve of 19 patients showed a positive clinical response and underwent a shunting procedure. Volumetric values of intracranial space content in responders and non-responders showed no statistically significant difference. Total CSF volume (sum of cranial and spinal CSF volumes) was higher than previously published. No correlation was found between spinal canal length, CSF pressure, and CSF spinal volume. The results show that there is a significantly higher CSF volume in the spinal space in the responder group (n = 12) (120.5 ± 14.9 ml) compared with the non-responder group (103.1 ± 27.4 ml; n = 7).DiscussionThis study demonstrates for the first time that CSF volume in the spinal space may have predictive value in the preoperative assessment of iNPH patients. The results suggest that patients with increased spinal CSF volume have decreased compliance. Additional prospective randomized clinical trials are needed to confirm our results