{"id":1966,"date":"2026-04-15T16:58:25","date_gmt":"2026-04-15T16:58:25","guid":{"rendered":"https:\/\/research.ced.ncsu.edu\/ptmt\/?page_id=1966"},"modified":"2026-09-02T16:02:24","modified_gmt":"2026-09-02T16:02:24","slug":"lead-dg-module-2-exploring-triangles-developing-instructional-goals","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-2-exploring-triangles-developing-instructional-goals\/","title":{"rendered":"LEAD DG Module 2 – Exploring Triangles & Developing Instructional Goals"},"content":{"rendered":"\n

Leading Productive Discussions with Web-Based Dynamic Geometry Tools (LEAD DG)<\/a> > Module 2<\/p>\n\n\n\n

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LEAD DG Module 2 – Exploring Triangles & Developing Instructional Goals<\/h1><\/div>\n<\/div>\n\n\n\n

In this module, teachers investigate triangle concepts through dynamic geometry tasks while learning to write meaningful instructional goals, select cognitively demanding tasks, and anticipate student thinking. Through explorations in GeoGebra, Desmos, and Web Sketchpad, teachers examine how instructional decisions influence the mathematical reasoning students develop.<\/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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2.1 Exploring Triangles & Developing Instructional Goals<\/strong>

Teachers investigate the Triangle Inequality Theorem using GeoGebra and analyze videos of students working on the same task to identify the underlying mathematical goals. This section focuses on writing instructional goals that align geometric content, student reasoning, and the affordances of dynamic geometry environments.
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2.2 Triangle Classification & Construction<\/strong>

Teachers use GeoGebra, Web Sketchpad, and Desmos Geometry to classify and construct triangles whose defining properties remain true under dragging. This section explores how construction can deepen understanding of triangle classifications while reinforcing the relationship between defining properties and geometric invariance.<\/td>
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2.3 Cognitive Demand & Selecting Technology-Based Tasks<\/strong>

Teachers analyze and compare dynamic geometry tasks to evaluate their cognitive demand and how technology supports or limits students’ mathematical thinking. This section emphasizes selecting and refining technology-based tasks that align with instructional goals and promote meaningful geometric reasoning.
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2.4 Anticipating Student Thinking<\/strong>

Teachers learn to anticipate the strategies, misconceptions, and questions students may bring to dynamic geometry tasks before instruction begins. Using video cases and GeoGebra explorations, this section focuses on preparing for instruction by considering how both the mathematics and the technology shape students’ thinking.
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Class Slides<\/strong>
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Leading Productive Discussions with Web-Based Dynamic Geometry Tools (LEAD DG) > Module 2 In this module, teachers investigate triangle concepts through dynamic geometry tasks while learning to write meaningful instructional goals, select cognitively demanding tasks, and anticipate student thinking. Through explorations in GeoGebra, Desmos, and Web Sketchpad, teachers examine how instructional decisions influence the mathematical […]<\/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-1966","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/1966","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=1966"}],"version-history":[{"count":8,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/1966\/revisions"}],"predecessor-version":[{"id":2099,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/1966\/revisions\/2099"}],"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=1966"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}