Geometric Thinking, the Paradise of Abstraction

2019 ◽  
pp. 1-44
Author(s):  
Mateusz Hohol
Keyword(s):  
Geometric Thinking

Effects of Computer and Noncomputer Environments on Students' Conceptualizations of Geometric Motions

1994 ◽  
Vol 11 (2) ◽  
pp. 121-140 ◽  
Author(s):  
Kay Johnson-Gentile ◽  
Douglas H. Clements ◽  
Michael T. Battista
Keyword(s):  
Control Group ◽  
Treatment Groups ◽  
Geometric Thinking ◽  
Paper And Pencil ◽  
Computer Environments

This study investigated the effects of computer and noncomputer environments on learning of geometric motions. Two treatment groups, one of which used specially designed Logo computer environments, and one of which used manipulatives and paper and pencil, received eight lessons on geometric motions. Interviews revealed that both treatment groups, especially the Logo group, performed at a higher level of geometric thinking than did a control group. Both treatment groups outperformed the control group on immediate and delayed posttests; though the two treatment groups did not significantly differ on the immediate posttest, the Logo group outperformed the nonLogo group on the delayed posttest. Thus, there was support for the effectiveness of the curriculum and for the notion that the Logo-based version enhanced the construction of higher-level conceptualizations of motion geometry.

Logo and Geometric Thinking

1997 ◽  
Vol 14 (1-2) ◽  
pp. 95-110 ◽  
Author(s):  
Leping Liu ◽  
Rhoda Cummings
Keyword(s):  
Geometric Thinking

scholarly journals CONTRIBUTIONS OF FIGURES NUMBERS IN THE DEVELOPMENT OF GEOMETRIC THOUGHT

2019 ◽  
Vol 7 (1) ◽  
pp. 16-30
Author(s):  
Maria José Costa dos Santos ◽  
Arnaldo Lopes Bezerra
Keyword(s):  
Mathematics Teaching ◽  
Teaching And Learning ◽  
Basic Education ◽  
Mathematical Thinking ◽  
Algebraic Thinking ◽  
Ethical Awareness ◽  
Pedagogical Tools ◽  
Geometric Thinking ◽  
Virtual Libraries ◽  
Abstract Content

This study was constituted with the purpose of promoting reflections on Mathematics of basic education, from a transdisciplinary view of teaching and learning processes. To do so, we aim to analyze the contributions of figures in the development of geometric thinking. We characterize this research in empirical-exploratory, because for Lakatos and Marconi (2017), this type of research distinguishes itself as a scientific process of investigation that allows the researcher to formulate questions, with three purposes: to raise hypotheses, to increase the familiarization of the researcher in order to research, modify or clarify concepts, based on a qualitative and quantitative approach, according to the depth of the discussion about the object in question. For this, we look for information in other researches, databases of universities and virtual libraries, periodicals.  We hope that the results contribute to the critical and ethical awareness from views of the importance of the development of mathematical thinking, but specifically of geometric thinking, aiming at non-rupture with arithmetic thinking, in order to interweave with algebraic thinking . We consider this research relevant because mathematics teaching is based on abstract content that often makes no sense to the student, and here we show a part of mathematics that is formal but can be fun when well crafted in the classroom. Finally, we present pedagogical tools of innovation, aimed at contributing to the emancipation of the knowledge of this science, without ruptures. Keywords: Geometric thinking. Figurative numbers. Mathematics Teaching.

scholarly journals Evaluating Mathematic- Textbooks of Intermediate Stage in KSA according  to Van Hiele’s Geometric Thinking Model

2019 ◽  
Vol 3 (6) ◽  
Author(s):  
Mohammed Najjar Al Otaibi
Keyword(s):  
Intermediate Stage ◽  
Third Grade ◽  
Hierarchical Level ◽  
Second Grade ◽  
Middle Stage ◽  
The Third ◽  
Geometric Thinking ◽  
Secondary Stage ◽  
Grade Average ◽  
Descriptive Method

This study aimed to find out the relevance of mathematics books in the intermediate stage of Van Hill levels of geometric thinking, in order to achieve this goal, the researcher utilized the analytical descriptive method, using the analysis card as a tool to conduct this study and prepared a list of skills in which Van Hill's levels of geometric thinking (conceptual, analytical, quasi- Inductive, Inductive, abstract). A number of results were found, most notably: the incompatibility of the engineering subjects in the second- grade books as well as the third- grade average with the hierarchy of Van Hill levels of geometric thinking. Failure to observe mathematics books in the middle stage, to include engineering activities at the induction level, to equip students to deal with secondary engineering topics. The researcher recommended a number of recommendations, the most important of which are: To reconsider the hierarchy of the levels of engineering thinking in the engineering activities included in the mathematics books in the intermediate stage. The work on enriching mathematics books in the second grade is average of engineering activities of semi- inductive level, to match the hierarchy of the levels of engineering thinking of the intermediate stage. The work of enriching mathematics books in the third grade is an average of engineering activities of semi- inductive and indicative level to match the hierarchical level of the engineering thinking of the middle stage, which is the basis for higher levels of engineering thinking in the secondary stage. The inclusion of additional topics in engineering and measurement in mathematics books for the third- grade, to contribute to the development of levels of engineering thinking for students.  

Geometry, philosophical issues in

2018 ◽  
Author(s):  
T.A. Ryckman
Keyword(s):  
The Other ◽  
Exact Science ◽  
Theory Of Relativity ◽  
Visual Aids ◽  
Sense Experience ◽  
Geometric Figures ◽  
Geometric Thinking ◽  
Land Surveying ◽  
Vital Component ◽  
Physical Quantities

The least abstract form of mathematics, geometry has, from the earliest Hellenic times, been accorded a curious position straddling empirical and exact science. Its standing as an empirical and approximate science stems from the practical pursuits of land surveying and measuring, from the prominence of visual aids (figures and constructions) in geometric proofs and, in the twentieth century, from Einstein’s General Theory of Relativity, which holds that the geometry of spacetime is dependent upon physical quantities. On the other hand, very early on, the symmetry and perfect regularity of certain geometric figures were taken as representative of a higher knowledge than that afforded by sense experience. And its concern with figures and constructions, rather than with number and calculation, rendered geometry amenable to axiomatic formulation and syllogistic deduction, establishing a paradigm of demonstrative knowledge which endured for two millennia. While the progress of mathematics has surmounted traditional distinctions between geometry and the mathematics of number, leaving only a heuristic role for geometric intuition, geometric thinking remains a vital component of mathematical cognition.

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