{"id":1973,"date":"2026-04-15T17:14:12","date_gmt":"2026-04-15T17:14:12","guid":{"rendered":"https:\/\/research.ced.ncsu.edu\/ptmt\/?page_id=1973"},"modified":"2026-09-02T16:04:30","modified_gmt":"2026-09-02T16:04:30","slug":"lead-dg-module-3-exploring-quadrilaterals-the-technology-based-geometric-thinking-framework","status":"publish","type":"page","link":"https:\/\/research.ced.ncsu.edu\/ptmt\/leading-productive-discussions-with-web-based-dynamic-geometry-tools-lead-dg\/lead-dg-module-3-exploring-quadrilaterals-the-technology-based-geometric-thinking-framework\/","title":{"rendered":"LEAD DG Module 3 – Exploring Quadrilaterals & The Technology-Based Geometric Thinking Framework"},"content":{"rendered":"\n

Leading Productive Discussions with Web-Based Dynamic Geometry Tools (LEAD DG)<\/a> > Module 3<\/p>\n\n\n\n

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LEAD DG Module 3 – Exploring Quadrilaterals & The Technology-Based Geometric Thinking Framework<\/h1><\/div>\n<\/div>\n\n\n\n

In this module, teachers investigate quadrilateral relationships while learning to recognize and interpret students’ geometric thinking in dynamic geometry environments. Through quadrilateral tasks, video cases, and the Technology-Based Geometric Thinking Framework, teachers learn to use students’ technology interactions as evidence of their mathematical reasoning.<\/p>\n<\/div>\n<\/div>\n\n\n\n

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Module Elements<\/strong><\/h2>\n<\/div>\n\n\n\n
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3.1 The Technology-Based Geometric Thinking Framework<\/strong>

Teachers explore a Which One Doesn’t Belong? task in a dynamic geometry environment before analyzing videos of students engaged in the same activity. This section introduces the Technology-Based Geometric Thinking Framework and helps teachers identify evidence of exploration, investigating invariances, developing definitions, and generating explanations through students’ actions and language.
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3.2 Defining & Classifying Quadrilaterals<\/strong>

Teachers use Desmos Polygraph and GeoGebra investigations to define, classify, and organize quadrilaterals based on their defining properties and hierarchical relationships. This section emphasizes distinguishing definitions from properties while exploring how precise mathematical language supports students’ geometric reasoning.<\/td>
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3.3 Exploring the Midpiont Quad & Examining Students’ Geometric Thinking with DGEs<\/strong>

Teachers investigate the Midpoint Quadrilateral task in GeoGebra before analyzing videos of students solving the same task. Using the Technology-Based Geometric Thinking Framework, this section focuses on interpreting students’ reasoning by examining both their mathematical language and their interactions with the dynamic geometry environment.
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Class Slides<\/strong>
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Leading Productive Discussions with Web-Based Dynamic Geometry Tools (LEAD DG) > Module 3 In this module, teachers investigate quadrilateral relationships while learning to recognize and interpret students’ geometric thinking in dynamic geometry environments. Through quadrilateral tasks, video cases, and the Technology-Based Geometric Thinking Framework, teachers learn to use students’ technology interactions as evidence of their […]<\/p>\n","protected":false},"author":88,"featured_media":1930,"parent":953,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"test-blank-page","meta":{"_acf_changed":false,"ncst_custom_author":"","ncst_show_custom_author":false,"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-1973","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/1973","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/users\/88"}],"replies":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/comments?post=1973"}],"version-history":[{"count":9,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/1973\/revisions"}],"predecessor-version":[{"id":2101,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/1973\/revisions\/2101"}],"up":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/953"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/media\/1930"}],"wp:attachment":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/media?parent=1973"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}