Geometric Thinking of Future Teachers for Primary Education—An Exploratory Study in Slovakia

Abstract

Various studies show that the level of knowledge achieved by pupils is influenced by the level of knowledge of their teachers. In this article, we focus on geometric thinking and the solutions for geometric tasks through a study of future teachers of primary education. The research sample consisted of 59 master’s students from the Teacher Training for Primary Education (TTPE) program. To determine the level of geometric thinking of TTPE students, the van Hiele geometric test was used. Two geometric multi-item tasks were proposed and the students’ solutions to these tasks were quantitatively and qualitatively evaluated. The main goal was to analyze students’ misconceptions while solving tasks and to compare and reveal the connections between their solutions and their achieved level of geometric thinking. A statistical implicative analysis was used for a deeper analysis, namely the statistical software C.H.I.C. The research findings show that more than 40% of TTPE students in the research sample did not reach the required level of geometric thinking. The achieved level of the geometric thinking of students is also influenced by the type of high school education. We observed problems with understanding the concept of the triangle and square in TTPE students. The connections between the solutions of two geometric tasks and the achieved level of geometric thinking were also revealed.

The Trend of Geometric Thinking Studies: A Systematic Review

“…The quality of the students depends on how well the teachers-to-be understand and use geometric thinking in learning [26]. According to [12,27,28], the teacher's ability to comprehend geometric thinking and implement it in learning is one of the most significant elements in students' geometric performance. Therefore, researchers can concentrate their investigations on educators' level of geometrical thinking.…”

“…According to previous studies, Indonesian pupils' geometric thinking levels still need to improve [8][9][10][11]. Thus, it is vital to pay attention to the fundamentals of geometry, especially geometric thinking, in the early years of education and to ensure that they are taught well [12]. The teacher must have sufficient knowledge and pedagogical abilities to develop students' geometric thinking [13].…”

“…Geometry has long been a difficult and incomprehensible topic for modern students [14,15]. Therefore, teachers are always experimenting with new learning strategies to understand and overcome students' misconceptions in this area [12,16]. The topic of geometric thinking was initially studied in the 1950s by Pierre van Hiele and Dina van Hiele-Geldof [5].…”

“…As a result, in 1957, they developed the van Hiele model of geometric thinking. The van Hiele model is currently the most widely used starting point for developing geometry curricula [12]. The thinking levels in geometry have five levels-Visualization, Analysis, Informal Deduction, Formal Deduction, and Rigoraccording to the van Hiele model of geometric thinking.…”

“…The thinking levels in geometry have five levels-Visualization, Analysis, Informal Deduction, Formal Deduction, and Rigoraccording to the van Hiele model of geometric thinking. They are numbered from 1 to 5, as expounded by [17], although the descriptors of the levels and their labels have varied in different works [1,3,12,17]. Level 1 (Visualization): At this level, students detect geometric shapes using their complex visual awareness, with shape orientation being the most critical factor.…”