Abstract:

Both combinatorics and geometry are very important components of mathematics education, so it seems to be useful to develop the combinatorial thinking by means of non-standard geometric problems. Combinatorial geometry studies geometric objects and their combinatorial structure. Specially, covering chessboard problems can be very attractive for students. For example, the well-known Gomory problem deals with the situation when we remove two arbitrary squares of different colors from the chessboard, and then we ask if it is possible to cover the remaining portion of the board with dominoes without disturbing the original piece.

In our paper, we will focus on geometric problems developing combinatorial thinking from the Mathematical Kangaroo competition, Junior category. We will show examples of such interesting problems with their solutions.

We will also show how to use Geogebra program during solution of some non-standard geometric problems (requiring combinatorial considerations), thus helping to develop digital literacy of pupils.

We will look, using Spearman's correlation coefficient, at the relationship between the number of examples requiring combinatorial considerations and the number of solvers with excellent results.

Keywords:

Non-standard geometric problems, mathematics education, combinatorial thinking.