Spatial reasoning of mathematics education students: an analysis of differences in solving hyperbola problems based on level of geometry ability
Authors:   Universitas Negeri Surabaya, Rangkuti Rizki Kurniawan , Khabibah Siti ,   Universitas Negeri Surabaya, Ekawati Rooselyna ,   Universitas Negeri Surabaya
Published: January 2025

Introduction. The facts show that students at the school level still have low spatial reasoning abilities at the
school level, but the spatial reasoning abilities of students at the university level are not yet known. The results
of students' spatial reasoning abilities are not yet known, so it is necessary to carry out detailed research so
that it can be understood more widely. The purpose of this research is to analyze how hyperbolic problem
solving differs based on the level of student ability, so that students with high, medium and low ability can be
described more specifically at each step of problem solving.
Study participants and methods. The subjects in this research were undergraduate students in the mathematics
education study program at the Institut Pendidikan Tapanuli Selatan, Indonesia, who were determined using
purposive sampling on the condition that they had taken analytical geometry courses. The research subjects
selected were 3 students, each of whom had high ability with a score of 95, medium ability with a score of
85 and low ability with a score of 73 who were tested with a geometric ability test. The results of solving
hyperbolic problems refer to indicators of spatial reasoning. Hyperbola problem solving data is analyzed based
on the level of geometric ability with stages of data reduction, data presentation, and drawing conclusions. This
research method is a qualitative descriptive research method with a single case design.
Results. First, subjects with high geometric abilities based on analysis of spatial reasoning indicators, namely
spatial visualization, mental rotation, and spatial orientation, have good problem-solving skills with an average
achievement of 92.4.In spatial reasoning on hyperbolic objects, starting from the steps to understand the
problem and planning a solution based on the problem, as well as carrying out the solution and evaluating the
solution, there is no difficulty in solving the hyperbolic problem. Second, subjects with moderate geometric
abilities based on analysis of spatial visualization abilities, mental rotation, and spatial orientation have good
learning achievements, which are also shown based on spatial reasoning indicators. It is known that the average
problem-solving ability for moderate geometry is 84.83. Third, subjects with low geometric ability based on
analysis of spatial visualization ability, mental rotation, and spatial orientation showed poor performance, with
the average achievement of problem solving with low geometric ability being 73.2.
Conclusion. This research describes how the ability to solve hyperbola problems differs based on the level of
geometric ability. The results of this research provide a basic description that can be used to show differences
in hyperbola problem solving abilities from the four steps based on high, medium and low geometric abilities.