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		<id>http://de.evo-art.org/index.php?action=history&amp;feed=atom&amp;title=Artefacts_to_Enhance_Geometrical_Thinking</id>
		<title>Artefacts to Enhance Geometrical Thinking - Versionsgeschichte</title>
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		<updated>2026-05-03T01:55:05Z</updated>
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		<id>http://de.evo-art.org/index.php?title=Artefacts_to_Enhance_Geometrical_Thinking&amp;diff=33142&amp;oldid=prev</id>
		<title>Gubachelier: /* Bibtex */</title>
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				<updated>2016-12-27T11:19:40Z</updated>
		
		<summary type="html">&lt;p&gt;‎&lt;span dir=&quot;auto&quot;&gt;&lt;span class=&quot;autocomment&quot;&gt;Bibtex&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
&lt;table class=&quot;diff diff-contentalign-left&quot; data-mw=&quot;interface&quot;&gt;
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				&lt;td colspan=&#039;2&#039; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;← Nächstältere Version&lt;/td&gt;
				&lt;td colspan=&#039;2&#039; style=&quot;background-color: white; color:black; text-align: center;&quot;&gt;Version vom 27. Dezember 2016, 11:19 Uhr&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l23&quot; &gt;Zeile 23:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Zeile 23:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; publisher&amp;#160;  = {Tessellations Publishing},&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; publisher&amp;#160;  = {Tessellations Publishing},&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; address&amp;#160; &amp;#160;  = {Phoenix, Arizona},&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; address&amp;#160; &amp;#160;  = {Phoenix, Arizona},&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; url&amp;#160; &amp;#160; &amp;#160; &amp;#160;  = {http://de.evo-art.org/index.php?title=Artefacts_to_Enhance_Geometrical_Thinking},&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;+&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; url&amp;#160; &amp;#160; &amp;#160; &amp;#160;  = {http://de.evo-art.org/index.php?title=Artefacts_to_Enhance_Geometrical_Thinking },&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; note&amp;#160; &amp;#160; &amp;#160; &amp;#160; = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-173.html}}&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160;&amp;#160; note&amp;#160; &amp;#160; &amp;#160; &amp;#160; = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-173.html}}&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160; }&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#160; }&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;−&lt;/td&gt;&lt;td style=&quot;color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot;&gt;&amp;#160;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Used References ==&lt;/div&gt;&lt;/td&gt;&lt;td class=&#039;diff-marker&#039;&gt;&amp;#160;&lt;/td&gt;&lt;td style=&quot;background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;== Used References ==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Gubachelier</name></author>	</entry>

	<entry>
		<id>http://de.evo-art.org/index.php?title=Artefacts_to_Enhance_Geometrical_Thinking&amp;diff=33088&amp;oldid=prev</id>
		<title>Gubachelier: Die Seite wurde neu angelegt: „  == Reference == Zekeriya Karadag: Artefacts to Enhance Geometrical Thinking. In: Bridges 2016, Pages 173–178.   == DOI ==  == Abstract == This pape…“</title>
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				<updated>2016-12-26T22:14:13Z</updated>
		
		<summary type="html">&lt;p&gt;Die Seite wurde neu angelegt: „  == Reference == Zekeriya Karadag: &lt;a href=&quot;/index.php?title=Artefacts_to_Enhance_Geometrical_Thinking&quot; title=&quot;Artefacts to Enhance Geometrical Thinking&quot;&gt;Artefacts to Enhance Geometrical Thinking&lt;/a&gt;. In: &lt;a href=&quot;/index.php?title=Bridges_2016&quot; title=&quot;Bridges 2016&quot;&gt;Bridges 2016&lt;/a&gt;, Pages 173–178.   == DOI ==  == Abstract == This pape…“&lt;/p&gt;
&lt;p&gt;&lt;b&gt;Neue Seite&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&lt;br /&gt;
&lt;br /&gt;
== Reference ==&lt;br /&gt;
Zekeriya Karadag: [[Artefacts to Enhance Geometrical Thinking]]. In: [[Bridges 2016]], Pages 173–178. &lt;br /&gt;
&lt;br /&gt;
== DOI ==&lt;br /&gt;
&lt;br /&gt;
== Abstract ==&lt;br /&gt;
This paper briefly reports on research exploring how pre-service teachers may improve their geometrical thinking while pursuing a realistic mathematics education activity. The participants were encouraged to photograph artefacts that include basic geometrical objects as the first step of the activity. They then created dynamic GeoGebra worksheets inspired by those pictures. Their work and online communication during the activity were explored to understand to what extent they could improve their geometrical thinking. Data suggest that the activity led them think more visually, dynamically and adventurously, and that the project has the potential to foster their creativity.&lt;br /&gt;
&lt;br /&gt;
== Extended Abstract ==&lt;br /&gt;
&lt;br /&gt;
== Bibtex == &lt;br /&gt;
 @inproceedings{bridges2016:173,&lt;br /&gt;
  author      = {Zekeriya Karadag},&lt;br /&gt;
  title       = {Artefacts to Enhance Geometrical Thinking},&lt;br /&gt;
  pages       = {173--178},&lt;br /&gt;
  booktitle   = {Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture},&lt;br /&gt;
  year        = {2016},&lt;br /&gt;
  editor      = {Eve Torrence, Bruce Torrence, Carlo S\&amp;#039;equin, Douglas McKenna, Krist\&amp;#039;of Fenyvesi and Reza Sarhangi},&lt;br /&gt;
  isbn        = {978-1-938664-19-9},&lt;br /&gt;
  issn        = {1099-6702},&lt;br /&gt;
  publisher   = {Tessellations Publishing},&lt;br /&gt;
  address     = {Phoenix, Arizona},&lt;br /&gt;
  url         = {http://de.evo-art.org/index.php?title=Artefacts_to_Enhance_Geometrical_Thinking},&lt;br /&gt;
  note        = {Available online at \url{http://archive.bridgesmathart.org/2016/bridges2016-173.html}}&lt;br /&gt;
 }&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Used References ==&lt;br /&gt;
[1] M. Arik &amp;amp; M. Sancak, Pentapleks: Kaplamalar, Turkey: Tubitak Populer Bilim Kitaplari, 2006.&lt;br /&gt;
&lt;br /&gt;
[2] N. Boakes, Integrating Origami Art with Mathematics in a College General Studies Course, the Proceedings of Bridge 2015: Mathematics, Music, Art, Architecture, Culture, pp. 239-246. 2015.&lt;br /&gt;
&lt;br /&gt;
[3] H. Freudenthal, Revisiting Mathematics Education, China Lectures, Dordrecht: Kluwer Academic Publishers, 1991.&lt;br /&gt;
&lt;br /&gt;
[4] B. Grunbaum &amp;amp; G. C. Shephard, Tilings and Patterns, New York: W.H. Freeman and Company, 1986.&lt;br /&gt;
&lt;br /&gt;
[5] H. Kilickan, Turk bezeme sanati [The art of Turkish patterns], Inkilap kitabevi, 2004.&lt;br /&gt;
&lt;br /&gt;
[6] M. J. Koehler &amp;amp; P. Mishra, What is technological pedagogical content knowledge? Contemporary Issues in Technology and Teacher Education, 9(1), 60-70, 2009.&lt;br /&gt;
&lt;br /&gt;
[7] M. Majewski, Szkice O Geometrii I Sztuce: miedzy Wschodem i Zachodem.Wydawnictwo Aksjomat, 2012.&lt;br /&gt;
&lt;br /&gt;
[8] The Freudenthal Institute for Science and Mathematics Education (FIsme), http://www.fisme.science.uu.nl/fisme/en/&lt;br /&gt;
&lt;br /&gt;
[9] A. Treffers, Three Dimensions: A Model of Goal and Theory Description in Mathematics Instruction, Dordrecht: Reidel Publishing Company, 1987.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
== Links ==&lt;br /&gt;
=== Full Text === &lt;br /&gt;
http://archive.bridgesmathart.org/2016/bridges2016-173.pdf&lt;br /&gt;
&lt;br /&gt;
[[intern file]]&lt;br /&gt;
&lt;br /&gt;
=== Sonstige Links ===&lt;br /&gt;
http://archive.bridgesmathart.org/2016/bridges2016-173.html&lt;/div&gt;</summary>
		<author><name>Gubachelier</name></author>	</entry>

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