Experts and designated users evaluations on visual tools screencast SketchUp Make (ViToS-SUM)

The problem and the aim of the study. Students at secondary school are facing problems in learning Mathematics for topic Geometry. The purpose of this study is to examine the validity of a learning strategy for 3-dimensional Geometry, using Visual Tools Screencast SketchUp Make, called ViToS-SUM. Research methods. ViToS-SUM consists of four components: level of van Hiele geometrical thinking, visual spatial skills, visual tools and video tutorial screencast SketchUp Make. A topic in form 3 mathematics, Plans and Elevations was chosen for this study. The whole process of design and development of ViToS-SUM adopted the five cyclic stages of ADDIE instructional design model. This article addresses the details of the final two stages specifically, implementation and evaluation prior to pilot test. Twelve students from a secondary school and three experts involved in this study. Quantitative approaches were used to collect data as well as to analyse the experts’ and students’ views on the appropriateness of ViToS-SUM. Results. The experts agreed that both visual spatial skills (mean = 5.00) and level of van Hiele geometrical thinking (mean = 4.61) should be embedded in ViToS-SUM. Moreover, the experts also agreed that the content of ViToS-SUM is suitable (mean = 4.51) with the mathematics content for topic Plans and Elevations. The pre and post test showed that there were significant differences in mean scores of visual spatial skills, before and after learning via ViToS-SUM (t=12.21; p<0.05). Furthermore, the pre and posttest also revealed that there is a significant difference in students’ level of van Hiele geometrical thinking before and after intervention (Z =-3.18; p < 0.05). Thus, ViToS-SUM had supported most of students in constructing concepts of Geometry. Meanwhile, the findings revealed that all experts agreed that ViToS-SUM served as pedagogical learning strategy for Geometry. Conclusion. This learning strategy should be integrated in the mathematics curricular for secondary schools to increase students’ performance in Geometry. Training is needed for teachers in order to deliver the concepts of Geometry effectively using this mode of teaching. More computer facilities should be equipped to schools in order to encourage teachers and students to utilize technology in teaching and learning.

Effect of the VAN Hiele Instructional Model on Students’ Achievement in Geometry

The purpose of this study was to determine the effect of the Van Hiele instructional model on students’ achievement in Circle Geometry at Daffiama Senior High School in the Daffiama-Bussie-Issa District of the Upper West Region in Ghana. The purposive and simple random sampling techniques were employed to select a sample of 75 participants for the study. The sample involved two groups: the experimental group and the control group. While teaching based on the Van Hiele model was carried out in the experimental group, teaching with the traditional method was carried out in the control group. The study employed a quasi-experimental research design. The instruments used for data collection were tests, interviews, and classroom observation. Findings from the data analysis suggested that participants were at the prerecognition level before the intervention, improved from the prerecognition level to level 2 after the intervention as the model facilitated learning. It was recommended that teachers determine the geometric thinking levels of students before instruction; the Van Hiele learning and instructional model is adopted in curriculum design and applied in the teaching of geometry and other areas of mathematics.

Analisis Berpikir Siswa Level Van Hiele dalam Memecahkan Masalah Segiempat Berdasarkan Langkah Polya

This study aims to describe student’s level thinking of understanding geometry according to van Hiele’s theory (informal deduction, deduction, and rigor) in solving of a quadrilateral problems based on Polya’s steps. The subjects of the study were 3 students Olympiad of SMPN 2 Jember, each of them have the level in informal deduction, deduction, and rigor. These students were given tests of geometry problem test at beginning and then proceeded to interview. The descriptive qualitative research was used in this study. The results showed that the subjects are able to fulfill all of the indicators according to their level in the step of understanding the problem and make arrangements. In part of carry out the plan, a student with informal deduction level is not able to solve the three indicators and a student with deduction levels is not able to solve one of the indicators, whereas the rigor’s student is not to able accomplish two indicators according to the levels. In step of looking back, a student with informal deduction level and a student with deduction level are not capable to solve the whole of indicators, however the rigor’s student is not able to accomplish two indicators according to the levels.

Proses Berpikir Siswa Kelas VIII SMPN 1 Rambipuji dalam Menyelesaikan Soal Segiempat Berdasarkan Teori Van Hiele

The study came into the background by the many students who had difficulty learning geometry in particular. The purpose of the study to describe the process of eighth graders' thinking in resolving a fourth matter. The type of research used is a qualitative approach. The data-gathering method used is tests and interviews. The subject of this study is two visualization level students, two analytic levels, and one informal deduction student. The result is that students of the visualize level are often quelled to settle the matter at a level of four, but when given a student's explanation can adjust, resulting in an equilibrium. Students' level analysis has been quizzing when seeking a consensus solution, but after accommodations are underway, students can understand the problem by equilibrium. The students of the informal deduction level have not been quizzed to complete the fourth matter, so the information gained is assimilated and equilibrium.

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

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.

Prospective teachers constructing dynamic geometry activities for gifted pupils: Connections between the frameworks of Krutetskii and van Hiele

The Swedish educational system has, so far, accorded little attention to the development of gifted pupils. Moreover, up to date, no Swedish studies have investigated teacher education from the perspective of mathematically gifted pupils. Our study is based on an instructional intervention, aimed to introduce the notion of giftedness in mathematics and to prepare prospective teachers (PTs) for the needs of the gifted. The data consists of 10 dynamic geometry software activities, constructed by 24 PTs. We investigated the constructed activities for their qualitative aspects, according to two frameworks: Krutetskii’s framework for mathematical giftedness and van Hiele’s model of geometrical thinking. The results indicate that nine of the 10 activities have the potential to address pivotal abilities of mathematically gifted pupils. In another aspect, the analysis suggests that Krutetskii’s holistic description of mathematical giftedness does not strictly correspond with the discrete levels of geometrical thinking proposed by van Hiele.