This qualitative case study, grounded within the interpretive paradigm, analyzed the errors and misconceptions made by 11th-grade learners when tackling the tangent-chord theorem task in Euclidean geometry. Studying Euclidean geometry helps learners develop critical thinking skills, such as constructing arguments and applying logical reasoning.…

This study addresses high school students' conceptions of mathematical definitions of congruent and similar triangles. The findings indicate that many of the participants differentiated between definitions and theorems and did not always accept the congruent and similar triangles theorems as formal definitions of congruency and similarity. Based…

This study was conducted to reveal potential sources of students' difficulty and misconceptions about geometrical concepts with the help of eye tracking. In this study, the students' geometrical misconceptions were explored by answering the questions on the geometry test prepared based on the literature and test-taking processes and represented…

We present action research of a problem posed as part of a multi-participant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16-17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the…

Grade 8 students were given a task that had pairs of shapes that had been transformed (i.e., preimages and images). Students were to identify which of the three rigid transformations--reflections, rotations, or translations--were used to map the preimage to the image. Students were also asked to give a justification for their choice of…

The aim of the present study is to determine the elementary pre-service mathematics teachers' understanding on solids. For this purpose, pre-service teachers' definitions and drawings of these objects were examined. Qualitative research method was used. A written questionnaire consisting of sixteen open-ended and multiple-choice questions was…

Research suggests that teachers struggle to find effective ways to introduce proof. In 1940, in an article in this journal, Roland Smith argued that being aware of student misconceptions in geometry is the first step in preparing to address the fundamental challenges of learning to prove. Through careful study, he identified and analyzed…

Continuing our critique of the classical derivation of the formula for the area of a disk, we focus on the limiting processes in geometry. Evidence suggests that intuitive approaches in arguing about infinity, when geometric configurations are involved, are inadequate, and could easily lead to erroneous conclusions. We expose weaknesses and…

The paper focuses on students' understanding of the concepts of axial and central symmetries in a plane. Attention is paid to whether students of various ages identify a non-model of an axially symmetrical figure, know that a line segment has two axes of symmetry and a circle has an infinite number of symmetry axes, and are able to construct an…

The 21st-century mathematics classrooms should equip learners with well-grounded knowledge and thinking skills pertaining to geometry. However, Euclidean geometry remains one of the challenging, if not the most difficult topic for many learners. As a result, the purpose of this article is to interpret Grade 12 learners' learning difficulties in…

The aim of this study is to obtain information about students' definitions, mistakes, misconceptions, and van Hiele geometry thinking levels by using the definitions of 4th grade students for geometric shapes of rectangle, square, isosceles triangle, equilateral triangle, and scalene triangle. The study was carried out with 156 primary school 4th…

Many students share a certain amount of discomfort when encountering proofs in geometry class for the first time. The logic and reasoning process behind proof writing, however, is a vital foundation for mathematical understanding that should not be overlooked. A clearly developed argument helps students organize their thoughts and make…

This study aims to introduce a method that is based on the relationship between numbers and geometry, which can be used to show the exact location of rational numbers on the number line, compare rational numbers, make calculations, and examine rational numbers conceptually through parallel lines. It is believed that this method will to contribute…

The concept of angles is important for future geometric knowledge (Arslan et al., 2016; Moore, 2013; Yigit, 2014). However, although Piaget (1948) suggests angles lead to the discovery of lines, angles are typically taught later in schools, after points, lines, and planes (Charles, 2011). Therefore, the way in which angles are taught can affect…

In this paper, we demonstrate how atypical visual representations of a triangle, square or a parallelogram may hinder students' understanding of a median and altitude. We analyze responses and reasoning given by 16 preservice middle school teachers in a Geometry Connection class. Particularly, the data were garnered from three specific questions…