Search Results (6)

This study is focused on the analysis of the level of geometric thinking of 15-year-old Slovak pupils in relation to the difficulty of geometric problems, their gender, and their assessment in mathematics. The main aim of this study was to determine the level of geometric thinking of 15-year-old Slovak pupils, to examine the relationship between their mathematics assessment and the level of geometric thinking, and to find out gender differences in relation to the different levels of geometric thinking. The van Hiele test was adapted and applied to a representative sample of 15-year-old Slovak pupils to determine the level of geometric thinking. We used reliability/item analysis. The reliability of the knowledge test (after adaptation) was assessed using Cronbach’s alpha (0.64). The validity of the test was demonstrated by the correlation of the Usiskin test results with pupils’ mathematics grades (Goodman–Kruskal’s gamma, p < 0.05). Statistical analysis showed that 15-year-old Slovak pupils achieve different levels of geometric thinking depending on the difficulty of the tasks. Pupil achievement declined significantly as task difficulty increased. Pupils had the greatest difficulty with tasks classified as the fifth (rigorous) and partly the fourth (deductive) van Hiele level, which require a deep understanding of geometric systems and the ability to prove logically. The lower-level tasks (visualization, analysis, and abstraction) were able to differentiate students according to different levels of geometric thinking. The results showed a significant positive relationship (Goodman–Kruskal’s gamma, p < 0.05) between the pupils’ overall mathematics scores (expressed as a grade) and their level of geometric thinking as detected by the van Hiele test. The analysis of gender differences (Duncan’s test, p < 0.05) showed that in the less challenging tasks, corresponding to the first three van Hiele levels (visualization, analysis, abstraction), girls performed statistically significantly better than boys. In the more challenging tasks, classified as the fourth (deductive) and fifth (rigorous) levels of geometric thinking, there were no statistically significant differences between boys and girls. In the more challenging tasks, the performances of both genders were comparable. The presented study identifies significant deficits in the development of higher levels of geometric thinking among 15-year-old Slovak pupils. These findings strongly imply the necessity for the transformation of the curriculum, textbooks, and didactic approaches with the aim of systematically developing deductive and rigorous reasoning, while it is essential to account for the demonstrated gender differences in performance. Full article

Ensuring mathematics education for all learners, including students with blindness learning in mainstream classrooms, is crucial. This exploratory research aims to clarify the characteristics of geometric learning among students with blindness and to identify the factors contributing to the challenges faced by this population. The Van Hiele theory of geometric thought served as a reference framework. Qualitative data were gathered through group interviews with specialists in the field of education for students with blindness and analyzed using inductive analysis. Participants affirmed that students with blindness progress through Van Hiele levels of geometric thought in a manner similar to sighted students, suggesting that much of the learning can take place alongside sighted peers in mainstream classrooms. However, they also highlighted the unique challenges these students face in reaching level 0, a level where students recognize shapes without a formal understanding of their properties or attributes. Among the reasons for these challenges were that for these particular students, subskills, such as bimanual exploration, hand coordination, and cognitive integration, are required to reach level 0. The study also identified the necessity for specialists in visual impairment education to guide students using appropriate tasks and learning materials that reflect the characteristics of haptic perception. Since level 0 serves as a gateway to both basic and advanced geometry, the findings underscore the importance of providing differentiated support that targets these subskills early in students’ schooling. To ensure meaningful geometry instruction, mainstream teachers are encouraged to collaborate with specialists in visual impairment education, who can guide the selection of appropriate learning tools and support the development of the subskills. Full article

Helping learners to develop a solid grasp of geometric concepts poses a challenge for teachers. Therefore, it is important that teachers have a sound understanding of the geometry they teach. The aim of this qualitative study was to explore pre-service teachers’ (PST’s) understanding of the concept of similarity in Euclidean geometry and to use van Hiele’s theory to explain misconceptions evidenced by the PSTs. Data in this study were collected from 34 first-year PSTs studying for a Bachelor of Education degree in high school mathematics. The authors analysed the written responses to a 13-item worksheet and also conducted interviews with seven of the participants. The analysis of the data was guided by van Hiele’s theory which was used to identify misconceptions amongst PST’s who had not yet developed the appropriate reasoning skills linked to particular van Hiele levels of geometric thought. It was found that these students used reasoning that is characteristic of the elementary levels to make judgments. Many PST’s faced challenges with similarity notation and the process of proving the similarity between two figures. This study recommends that PST’s should be given more opportunities to connect visual and analytic representations of similarity. Full article

In mathematics teaching, great efforts are made, and diverse teaching strategies are employed in order to facilitate students’ learning process. Informal environments have proven to be conducive and motivating spaces for science learning. In particular, science museums can be used as a complement and collaborate in order to leverage each of their strengths to motivate mathematics learning. Educational models give a global explanation to the learning process. Taking into account all these aspects and considering van Hiele’s model as didactic reference, we propose the design of a general workshop that has among its objectives the learning of mathematics. To do this, we start from the three main elements and processes set forth in van Hiele’s model: insight, reasoning levels and learning phases. The insight or student’s competence are formulated through Hoffer’s abilities, and for the development of the activities of the learning phases, the STEAM (science, technology, engineering, art and maths) strategy. Once the general proposal has been made, we use it to design a scientific workshop for learning mathematics about cryptography. Our greatest challenge was in generating activities adapted to the established requirements. It would be interesting, for future works, to design research to evaluate the effectiveness of the proposal presented. Moreover, it would be interesting to develop a proposal for assessing student learning. Full article

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. Full article

In mathematics education, technology offers many opportunities to enrich curricular contents. Plane symmetries is a topic often skipped by primary teachers. However, it is important and may be worked in attractive ways in dynamic geometry software environments. In any regular classroom there are students with different levels of mathematical attainment, some needing easy tasks while others, particularly mathematically-gifted students, need challenging problems. We present a teaching unit for plane symmetries, adequate for upper primary school grades, implemented in a fully interactive electronic book, with most activities solved in GeoGebra apps. The book allows student to choose which itinerary to follow and attention is paid to different levels of students’ mathematical attainment. The research objective of the paper is to make a networked analysis of the structure and contents of the teaching unit based on the Van Hiele levels of mathematical reasoning and the levels of cognitive demand in mathematical problem solving. The analysis shows the interest of networking both theories, the suitability of the teaching unit, as the Van Hiele levels and the cognitive demand of the activities increases, and its usefulness to fit the needs of each student, from low attainers to mathematically-gifted students. Full article