scholarly journals Geometric explorations with dynamic geometry applications based on van Hiele levels

2005 ◽  
Author(s):  
Sinan OLKUN
Keyword(s):  
Dynamic Geometry ◽  
Van Hiele ◽  
Van Hiele Levels

scholarly journals Networked Analysis of a Teaching Unit for Primary School Symmetries in the Form of an E-Book

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 832
Author(s):  
Angel Gutiérrez ◽  
Adela Jaime ◽  
Pablo Gutiérrez
Keyword(s):  
Primary School ◽  
Mathematical Reasoning ◽  
Dynamic Geometry ◽  
Gifted Students ◽  
Cognitive Demand ◽  
Mathematically Gifted ◽  
Van Hiele ◽  
Van Hiele Levels ◽  
Teaching Unit ◽  
Different Levels

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.

scholarly journals Mathematical Abstraction of Year 9 Students Using Realistic Mathematics Education Based on the Van Hiele Levels of Geometry

2019 ◽  
Vol 6 (1) ◽  
pp. 1-12
Author(s):  
Heris Hendriana ◽  
Nelly Fitriani
Keyword(s):  
High School Students ◽  
Mathematics Education ◽  
Traditional Learning ◽  
Realistic Mathematics Education ◽  
Reflective Abstraction ◽  
Van Hiele ◽  
Level Of Abstraction ◽  
Realistic Mathematics ◽  
Van Hiele Levels ◽  
Mathematical Abstraction

Previous research regarding abstraction has not discussed abstraction qualitatively based on van Hiele levels. Thus, it is necessary to study abstraction analysis based on van Hiele levels through Realistic Mathematics Education (RME) approach. The purpose of this research was to analyze mathematical abstraction based on van Hiele levels of geometry (VHLG) through RME and traditional learning approach reviewed from the levels of prior knowledge. This research employed a descriptive qualitative method involving Year 9 junior high school students as the subjects. The instruments were a mathematical abstraction test, van Hiele geometry test, and interview guidelines. The results of the high- and medium-ability students in the classroom using RME approach showed that VHLG was at the Deduction level and the abstraction ability was dominated by Empirical and Reflective Abstraction, whereas the low-ability students are at the level of Abstraction, they had imperfect Empirical and Reflective Abstraction. As for the high-ability students in the traditional learning classroom, the VHLG was at the level of Abstraction; their Reflective Abstraction was at the Representation level. While concerning the low- and medium-ability students, the VHLG was at the Analysis level; they mastered the Reflective Abstraction at the level of Recognition. This study indicates that the RME approach can trigger the development of mathematical abstraction, and accelerate the van Hiele levels of geometry progress.

Characterizing the van Hiele Levels of Development in Geometry

1986 ◽  
Vol 17 (1) ◽  
pp. 31 ◽  
Author(s):  
William F. Burger ◽  
J. Michael Shaughnessy
Keyword(s):  
Van Hiele ◽  
Van Hiele Levels

Geometry in the Junior High School

1985 ◽  
Vol 78 (6) ◽  
pp. 411-418
Author(s):  
Fernand J. Prevost
Keyword(s):  
High School ◽  
Junior High School ◽  
Junior High ◽  
Research Interest ◽  
Van Hiele ◽  
Van Hiele Levels ◽  
Van Hiele Model

The van Hiele model of the learning of geometry currently enjoys both popular and research interest. Hoffer (1981) provides an overview of the model and identifies problems that are appropriate for students at each of the five van Hiele levels, the first three of which will be considered in this paper.

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