The provision of problem-solving, analytical, systematic, critical, and creative skills is important to improve human resources that can be obtained from learning mathematics. Geometry is a field of ...mathematics that aims to develop logical thinking skills, develop spatial intuition, and interpret mathematical arguments. Several studies show that students' understanding of geometry material is still at a low level, so it is necessary to develop or improve the geometry learning process. The purpose of this study is to describe the increase in students' geometric thinking levels based on Van Hiele's theory with a constructivism approach. The method used in this research is descriptive qualitative with data analysis techniques using the Miles & Huberman model in the form of data reduction, data presentation, and drawing conclusions. The results showed that before the learning process using a constructivist approach, students' geometric thinking skills were at levels 1 to 3 or the analysis stage to a formal deduction with the average being at the informal deduction and pre-formal deduction stages. Meanwhile, after the learning process using a constructivist approach was carried out, geometric thinking skills increased at levels 2 to 4 or the informal deduction stage to the rigor with an average increase in the formal deduction stage.
Background: Students' low critical thinking skills negatively impact their mathematics learning outcomes. One contributing factor is the insufficient optimization of instructional media.Aim: This ...study aims to design instructional media, assess its feasibility and practicality, and evaluate the effectiveness of an augmented reality-based pocket book in enhancing the critical thinking skills of fifth-grade students at SDN 01 Bligorejo Doro Pekalongan.Method: The study adopts the Borg & Gall development model and employs a pre-experimental design with a one-group pretest-posttest approach. Data collection techniques include observation, interviews, questionnaires, tests, and documentation. Initial data analysis involves normality tests, while final data analysis uses mean difference tests and N-Gain tests.Results: The findings reveal an improvement in students' critical thinking skills, as indicated by the increase in average test scores from 51.5 to 76.6. The N-Gain analysis result of 0.5052, classified as moderate, provides evidence that the augmented reality-based pocket book is effective in enhancing students' critical thinking skills.Conclusion: The augmented reality-based pocket book proves to be an effective tool for improving students' critical thinking skills, as demonstrated by the significant increase in average test scores and N-Gain values.
Las primeras operaciones elementales eran tan importantes para cubrir también sus múltiples necesidades del hombre. Entonces la matemática representaba un instrumento para resolver dichos problemas. ...Actualmente la contribución en la enseñanza de la matemática, se vio reflejada en los aportes de dos profesores holandeses de matemática, Pierre Marie Van Hiele y Dina Van Hiele-Geldof, quienes sentaron las bases del modelo que lleva su nombre, trabajado en dos componentes. El primero es la descripción de los distintos tipos de razonamiento geométrico de los estudiantes, desde el intuitivo hasta lo formal y abstracto, y el segundo, presenta cinco fases como propuesta en la enseñanza de la geometría, mediante las cuales los estudiantes puedan llegar el nivel de razonamiento superior. Entonces su influencia de la aplicación del Modelo de Van Hiele y con ayuda del software GeoGebra, en el aprendizaje de estudiantes en áreas y perímetros de regiones poligonales resultó positiva y significativamente en el aprendizaje de dichos temas.
Background: Reversible thinking is a cognitive strategy that involves tracing the path from an end result back to the starting point. It is particularly useful in problem-solving.Aim: This study aims ...to describe the thought process of high school students in finding solutions to van hiele geometry problems using reversible thinking ability.Method: A case study approach was employed. The participants were two high school students, and the research tools included written tests and interviews. These instruments were used to delve into the students' written responses.Result: The findings revealed two key aspects: firstly, the students' van Hiele geometry thinking was predominantly at the deduction stage, evidenced by their ability to model geometric shapes based on their characteristics. Secondly, their reversible thinking in geometry was demonstrated through the simplification of fractional operations to obtain whole parts.Conclusion: The study highlights the efficacy of reversible thinking in solving geometric problems and provides insights into the cognitive processes of high school students. The ability to reverse engineer solutions from a known outcome back to the starting conditions is a valuable skill in mathematical problem-solving.
In this paper, we share major lessons we have learned in our curriculum analysis explorations and provide suggestions for future mathematics curriculum research. Specifically, we will discuss the ...successes and challenges of using comparative methods and developing analytical frameworks. Using an old Chinese saying, follow the vine to get the melon (顺藤摸瓜), our journey starts with getting a holistic picture of standards and moves to identifying a specific topic in the textbooks. We first conducted a study to compare the geometry standards of the Common Core State Standards for Mathematics (CCSSM) and the Chinese Compulsory Education Mathematics Curriculum Standards (CMCS); then we analyzed the presentation of a specific topic, triangle congruence, in multiple geometry textbooks. For each comparative study we conducted, developing the analytical framework that can be used to guide future investigations constituted a critical step in the research methodology. We have learned lessons from adapting the well-known van Hiele model, which was created for the development of geometric reasoning, into a lens for a detailed curriculum analysis. We have also learned lessons from elaborating on the key constructs from the “Mathematics Curriculum as Story” framework for coding and analysis. These lessons as well as our future directions serve as the primary focus of this paper.
A look into students’ misconceptions help explain the very low geometric thinking and may assist teachers in correcting errors to aid students in reaching a higher van Hiele geometric thinking level. ...In this study, students’ geometric thinking was described using the van Hiele levels and misconceptions on triangles. Participants (N=30) were Grade 9 students in the Philippines. More than half of the participants were in the van Hiele’s visualization level. Most students had imprecise use of terminologies. A few had misconceptions on class inclusion, especially when considering isosceles right triangles and obtuse triangles. Very few students correctly recognized the famous Pythagorean Theorem. Implications for more effective geometry teaching are considered.
Teaching geometry at the elementary level is challenging. This study examines the impact of van Hiele theory-based instructional activities embedded into an elementary mathematics methods course on ...preservice teachers’ geometry knowledge for teaching. Pre- and post-assessment data from 111 elementary preservice teachers revealed that van Hiele theory-based instruction can be effective in improving three strands of participants’ geometry knowledge for teaching: geometry content knowledge, knowledge of students’ van Hiele levels, and knowledge of geometry instructional activities. As a result, this paper offers implications for teacher educators and policy makers to better prepare elementary preservice teachers with geometry knowledge for teaching.
•The van Hiele theory-based instruction had a positive impact on preservice teachers’ geometry knowledge for teaching.•Preservice teachers’ knowledge of geometry content, students’ geometric thinking, and geometry activities were significantly improved.•Connections between preservice teachers’ three types of geometry knowledge for teaching were strengthened.•The integration of mathematics content, students’ mathematics thinking development, and instructional activities supported preservice teachers’ learning.
Thinking is a cognitive way of generating ideas for problem-solving decision-making strategies. This study aims to analyze and describe intuitive thinking processes in solving students' mathematical ...assignments about geometry based on Van Hiele's theory. The method used is descriptive qualitative. The research subjects were students of class VIIIA. The research location is one of the Madrasah Tsanawiyah in Pasuruan Regency. Credibility uses source data collection techniques using the VHGT test to determine the level of the subject, geometry problem tests, document studies, and interviews. The main instruments are researchers and supporters of geometry tests and interviews. The results of this study indicate that students who think intuitively through catalytic inference are obtained spontaneously and suddenly in completing the math tasks they face without using prior knowledge, and intuitively appear globally and use shortcuts. Whereas students who think intuitively with common sense are obtained directly and directly using the steps to complete mathematical tasks neatly and neatly, intuitively, the sequence of completing tasks appears by their experience and knowledge. Based on Van Hiele's level, students who think intuitively with catalytic inference are included in level 0 (visualization), and students who think intuitively with common sense are included in level 1 (analysis). Students who think intuitively with common sense can directly and immediately use the steps to complete math tasks neatly and neatly, intuitively appearing in the sequence of completing tasks according to their experience and knowledge. Based on Van Hiele's level, students who think intuitively with catalytic inference are included in level 0 (visualization), and students who think intuitively with common sense are included in level 1 (analysis). Students who think intuitively with common sense can directly and immediately use the steps to complete math tasks neatly and neatly, intuitively appearing in the sequence of completing tasks according to their experience and knowledge. Based on the Van Hiele level, students who think intuitively with catalytic inference are included in level 0 (visualization).
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