Abstract:

In this paper we present the results of study where students of the 3rd Grade Junior High School are set to work and cooperate with each other in inter-connecting and associating concepts of Trigonometry with concepts from Algebra and Geometry. The students who took part experimented in studying the properties of the rectangle triangle which is formed by an acute angle (fixed in position and size) and with a changing length hypotenuse. They recalled the definition of the proportional amounts and got into the meaning and the features of the similarity of two triangles. They investigated the association between the sizes of the triangle along with the existence of their dependence from the fixed angle. The process led them to understand trigonometric numbers and their necessity of existence. The purpose of this assignment was to improve the students’ view of Mathematics and in the process of doing so, allowed them to realize that Mathematics is a subject worthy of exploration and not just a memorization of algebraic formulae. In this assignment, the students undertook activities that allowed them to observe, cooperate, speculate, verify and connect covariants and invariants associated with mathematical concepts. The methodology involved the use of a worksheet, which they used to observe and record the results through which they were able to search for the connection between the covariant sizes. They verified their observations with the help of Geogebra software, Then, they generalized, by formulating and recording the relations between trigonometric numbers and by imprinting the covariant of two sizes each time into the function y=ax on a Cartesian coordinate system. The Ontology of the Circle helps discover how the two meanings are related and this is demostrated in a supportive enviroment where this ontology is implemented. This assignment was evaluated on its results, its scalability, the tools used and the way was implemented.

Keywords:

Proportional Amounts, Function y=ax, Triangles Similarity, Trigonometric Numbers, Ontology of the Circle.