Abstract:

Based on teaching and solving social problems and fulfilling the requirements of the discipline called Mathematics II. , we found that a more in-depth and practice-oriented knowledge of geometry is necessary for our students. We analysed the solution process of problems (optimisation and finding maximum and minimum values) and identified students’ deficiencies. Companies generally use to calculate maximal profit and minimum loss, or minimum costs. In modern mathematics, such optimisation problem is solved first through simpex and second through geometry.

Research problem:
Development of spatial imagination from primary through tertiary education is more and more important. Geometry is utilised to solve professional problems in diverse professional communities, from economy to tourism. In our research, we investigate abilities and knowledge of high school students, how they can solve assignments in plane or space and identify their knowledge gaps. Generally, there is a problem with analytic geometry. Students are not table to imagine common aggregates of half planes (intersection of two circles), and inner or outer space of regular objects. Switching dimensions from planar thinking to spatial perception, where it is necessary to mentally visualise cube intersections or 3D intersections is found difficult.

Methodology:
We searched the validity of results in correlation with approaches. We explained various shapes and objects in spatial geometry by anaglyph technique to improve spatial imagination. We created three groups of students who differed in their approach of solving problems. First, students worked on their own, second, students worked under teacher supervision, and third, students were motivated by the demonstrations of various possibilities of problem solution. Besides the 3D course-books and tools they could solve their assignments by the Solid Edge software.

Results:
High school students constructed stationary and moving parts, interesting 3D objects or allocated objects. The most creative work was designing chessboard and chessmen.
Based on various types of methodologies (ways of explanation), we registered different results. We identified failings and successful 3D works.

Conclusion:
We assume that implementation of geometrical assignments and appropriate motivation can help to better understand substantive of 2D and 3D problems and enhance complex problem-solving tasks that involve fantasy. Knowledge of geometrical rules supports successful solution of assignments well beyond economy and tourism.

Keywords:

Math, geometry knowledge, spatial imagination, solving economy problems.