Students’ development of geometrical concepts through a dynamic learning environment

2004-07-11
Geometry is one of the important areas of mathematics over the world. Geometry provides experiences that help students develop understanding of shapes and their properties. It enables students to solve relevant problems and to apply geometric properties to real-world situations. National Council of Supervisors of Mathematics endorsed that geometry was one of the ten proposed basis skill areas (NCSM, 1976) and is indeed a basic skill that should be taught to students of all ability levels (Sherard, 1981). Technology is promoted and effective tool to teach and learn geometry. When technology is used appropriately, it can provide a rich environment in which students' geometric understanding and intuition can be developed (NCTM, 1989). Calculators and computers with appropriate software transform the mathematics classroom into a laboratory much like the environment in many science classes, where students use technology to investigate, conjecture, and verify their findings (NTCM, 1989). One of the important vehicles of technological chance in geometry classroom is the use of Geometers' Sketchpad (GSP) (Jackiw, 1991). This software allows mathematics to be taught visually to the class as a whole, to small groups, or to individuals by creating dynamic and productive three way interaction between teacher, student, and computer (Hativa, 1984). GSP enables a student to " drag " part of configurations around and other parts of sketch automatically adjust. It enables students and teachers to investigate and construct unlimited geometric shapes. The shapes are first created and then they are explored, manipulated and transformed to ideal concept. Students cannot be creative enough in a traditional class (Schoenfeld, 1989). GSP puts geometry exploration tools directly in the hands of students, enabling them to test whether their geometric constructions work in general or whether they have discovered a special case of the original construction. This software also has the capability to link synthetic constructions to analytic equations, and coordinate representations. Furthermore, challenging and time consuming mathematical problems could be easier through dynamic software (Lappan and Winter, 1984). As a result, GSP is used for exploration and guided or open-ended discovery—enabling students to test their conjectures and be more engaged in their learning. When the literature was searched, on the use of Geometer's Sketchpad, the studies investigated the geometric learning of secondary school students during instruction, on the basis of the Van Hiele model, with GSP as a tool (Battista, 2002; Choi-Koh, 1999).
ICME 10, (4 - 11 Temmuz 2004)

Suggestions

Cognitive analysis of students’ learning of trigonometry in dynamic geometry environment : a teaching experiment
Şahin, Zülal; Erbaş, Ayhan Kürşat; Department of Secondary Science and Mathematics Education (2015)
Trigonometry is a part of mathematics in which algebra and geometry converge. Dealing with trigonometric functions at secondary level is known as a difficult task because it requires to work with right triangles, the unit circle, and graphs of trigonometric functions simultaneously. For most students, this means excessive amount of formulas unless they can establish connections among different representational systems. There is a consensus in the literature that appropriate use of technology can be effectiv...
Fostering spatial abilities of middle school students through augmented reality: Spatial strategies
Ozcakir, Bilal; Çakıroğlu, Erdinç (2021-09-01)
In school mathematics, representations of solid figures and three-dimensional geometric objects generally rely on two-dimensional projective representation modes on students' textbooks. In learning environments, these representation modes create a kind of cognitive filter, which prevents students with low spatial ability to comprehend and envision three-dimensional objects. Studies showed that spatial ability could be improved by means of suitable concrete models and computer created models in learning sett...
Nonlocal symmetries and integrable ordinary differential equations: xuml+3xx center dot+x(3)=0 and its generalizations
Karasu, Emine Ayşe (AIP Publishing, 2009-07-01)
The equation xuml+3xx center dot+x(3)=0 is well known in many areas of mathematics and physics. It possesses the algebra sl(3,R) of Lie point symmetries, hence is equivalent to the equation for a free particle, and both left and right Painleveacute series. We investigate two higher-dimensional analogs in terms of their symmetry and singularity structures. We find a drastic reduction in symmetry and a loss of some of the singularity properties. From the nonlocal symmetries we are able to determine the comple...
A MATHEMATICAL PERSPECTIVE TO ECOLOGY AND ENVIRONMENTAL PROBLEMS
TURANLI, NECLA; Turanli, Ayse Merve (2012-01-01)
The footprints of mathematics can be seen in every part of environment. The examples of fractal geometry, fibonacci series and golden ratio can be seen in nature directly. Mathematics and environment relationship does not only depend on the physical similarities; mathematics is also a really important tool for understanding the nature. In this research the role of mathematics and mathematical modeling on ecology and environmental problems will be explained. Mathematics plays a key role in environmental and ...
Investigation of fifth and sixth grade students’ use of strategies and approaches in problem solving
Alkan, Cafer Sinan; Akyüz, Didem (null; 2019-04-28)
Purpose For many people mathematics is one of the subjects that they have difficulty with. Yet, mathematics underlines many subjects in the real world. Thus, there have been many studies that investigate the ways of supporting students' understanding of mathematical learning such as using different models, real-life contexts, and problem-solving process. Today, many school programs focus on students’ problem-solving skills. Many countries renewed instructional programs in the way of encouraging problem-solv...
Citation Formats
B. Ubuz, “Students’ development of geometrical concepts through a dynamic learning environment,” Copenhagen, Denmark, 2004, vol. 1, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/74948.