Reviewing the Van Hiele model and the application of metacognition on geometric thinking

Metacognition, or the ability to think about thinking, is essential in the development of geometric thinking. However, studies on the Van Hiele model and the application of metacognition on geometric thinking are still under-researched. This study aimed to provide a review of the Van Hiele model and the application of metacognition on geometric thinking. A total of 844 articles were retrieved through internet search engines from 1995 to 2020 and manually selected and reviewed systematically. The keywords used related to the Van Hiele model, metacognition, and geometric thinking. The findings that emerged from the review were categorized into two main themes which were the effectiveness of the Van Hiele model towards geometric thinking and the effectiveness of the application of metacognition on geometric thinking. Most articles revealed the positive indication of the geometric thinking development through the Van Hiele model intervention. It also seems that the potential of the application of metacognition in the Van Hiele model can strengthen geometric thinking development. Researchers and educators may find this knowledge useful in conducting empirical studies and developing learning instructions based on the application of metacognition in the development of geometric thinking

Video tutorial screencast and sketchup make (VTS-SUM) for low achievers in learning 3d geometry

Students’ weaknesses in learning 3-Dimensional (3D) geometry are mostly associated with their low level of geometric thinking. Although a 3D software has been proposed as a manipulative learning tool, they had difficulties using it. Therefore, a suitable learning strategy should be designed to overcome the problems. The purpose of the study was to assess a learning strategy, known as Video Tutorial Screencast SketchUp Make (VTS-SUM), which integrates screencast techniques with a 3D software. VTS-SUM is a know-how video that assists students to visualize steps in drawing the orthogonal projections for 3D objects. A total of 180 students from a secondary school were involved in the study, conducted using a quantitative approach, where, a van Hiele Geometric Thinking (vHGT) test was employed to find out the level of students’ geometric thinking. The findings obtained showed that the majority of the students were at the Lowest Level (Level L1). As for usability test, a total of thirty students were selected from among those below this level. They were given some time to watch the video and perform hands-on activities using the software. A seven-point Likert scale questionnaire, comprising four constructs, namely, usefulness, ease of use, ease of learning and satisfaction, was used to measure the students’ perceptions of the usability test. The results obtained indicated that the students had positive perceptions towards the usage of VTS-SUM in their learning, thus accentuating its good potentials to enhance learning in mathematics

An investigation of the use of mobile technologies in the teaching and learning of congruence in mathematics.

Doctoral Degree. University of KwaZulu-Natal, Durban.The study explored the feasibility of using mobile technology in teaching and learning the congruence of triangles, with a particular focus on conceptual understanding. A mixed-method case study methodology was used, in which 25 grade 9 learners who were purposefully selected from a school in Durban took part. Two questionnaires and semi-structured interviews were administered. The validity and reliability of both questionnaires were assessed and confirmed. The triangulation of the results from the first questionnaire, the second questionnaire, and the semi-structured interviews revealed that learners were willing to use mobile technology in learning mathematics. The results also showed that it was practical to use curriculum-tailored GeoGebra applets on mobile devices to learn the congruence of triangles. The study could directly benefit the grade 9 educators and learners in South Africa. Educators can use the applets and the worksheet designed in this study when teaching the congruence of triangles. The study responds to the call made in the Action plan to 2024, to align technology integration to the improvement of learning outcomes. To the board of knowledge of social sciences, the research contributes a modified FRAME or model that emerged in this study, which I named the FRAME_applet model; that emphasizes the use of curriculum tailored applets on mobile devices in teaching and learning, to enhance conceptual understanding. This study is relevant in the current context of the COVID-19 pandemic, where the time for face-to-face learning and teaching has been reduced. Learners can self-learn new content through the use of curriculum-tailored GeoGebra applets

Evaluating Grade ten learners’ change in understanding of similar triangles following a classroom intervention

Geometry, in particular Euclidean geometry, has been highlighted as a subject in mathematics that presents a variety of challenges to many secondary school learners. Many students struggle to gain appropriate knowledge of geometrical ideas as well as to display solid reasoning and problem-solving abilities. Mathematics educators, parents, and the government, represented by the Department of Basic Education (DBE), have all expressed worry over students' poor performance in Euclidean Geometry. The purpose of this study was to evaluate Grade 10 learners’ changes in the understanding of similar triangles following a classroom intervention. This study explored the following main research question: How can a classroom intervention be designed to improve Grade 10 learners’ understanding of similar triangles? The study followed the social constructivism paradigm since learners should learn under a cooperative learning method to construct conceptual knowledge. The van Hieles’ model assisted the researcher to determine and identify Grade 10 learners’ geometric level. Furthermore, participatory action research was employed because the researcher was part of the study, responsible for the teaching design. The study adopted a mixed method design. A qualitative approach used the following instruments to collect data: an intervention, observation, and semi-structured interview. Eight (8) participants contributed to the qualitative data and were chosen via purposeful sampling to determine their understanding. These data were subjected to analysis. The quantitative approach used baseline test and the post-test as data collection instruments. The population consisted of (43) FET band learners who chose mathematics as an area of study at a Secondary School. The baseline test was used to determine the learners’ present knowledge of geometry considering the van Hieles' levels (VHL). After the designed intervention, the post-test, in comparison with the baseline test, was used to determine the effectiveness of the intervention and the change in understanding of the learners’ concepts of similarity within the topic, geometry. Statistical and descriptive data analysis was deployed to describe the effect of the change. The study shows that the designed intervention was effective, and the results indicate that half of the learners in this group improved in their understanding of similar triangles.Mathematics EducationM. Ed. (Mathematics