ALGEBRAIC STRUCTURES BY CREATING MIND MAPS WITH STUDENTS GIFTED IN MATHEMATICS

Abstract

Working with mathematically gifted students is the subject of many studies. In the literature, one can find various examples of the positive impact of the use of mind maps on learning by understanding and connecting concepts in appropriate schemes, but the impact of creating mind maps on the achievements of students gifted in mathematics has not been sufficiently researched. Having that in mind and that algebraic structures represent a teaching topic in which it is necessary for students to have adequate theoretical knowledge about these structures and relations between them, this method was implemented in order for students to connect the proper concepts in a scheme. For that purpose, (two) mathematics classes of systematization are conducted for the teaching topic on Algebraic structures in order for students to create two mind maps each (one for algebraic structures with one and with two binary operations and another for homomorphism). The effects of this approach to the systematization classes were examined by analyzing the students’ success achieved in two fifteen-minute tests (before and after the systematization classes) where they had to mark the correct statements (precisely formulated algebraic structures and homomorphisms). The results obtained by statistical analysis indicate that the students achieved statistically significantly better results in the test held after the systematization classes. In other words, the creation of mind maps by students gifted in mathematics had a positive effect on systematization of knowledge about Algebraic structures and on students’ achievement in mathematics (specifically Linear Algebra and Analytical Geometry). This result implies that teachers who work with students gifted in mathematics should seriously consider organizing mathematics classes where students will systematize and deepen their theoretical knowledge by creating mind maps.