vinylmath, 2021. 4. 6.

In this session, participants are introduced to the launch-explore-share format of our subsequent sessions and to GeoGebra through interactions with pre-made applets. After a quick demonstration comparing “dynamic” and “static” objects, participants build their own dynamic sketches and look for patterns and relationships, generating conjectures as a prelude to formal proof.

• 1. Dynamic Squares
• 2. Dynamic or not?
• 3. Midpoint Quadrilaterals
• 4. Midpoint Quadrilateral Exploration

In this launch-explore-share session, we use GeoGebra to create quadrilaterals from other quadrilaterals and explore conjectures that result from observing how these mathematical objects behave. Following an initial launch that explores a dynamic sketch, participants will create their own dynamic GeoGebra sketches in groups and determine ways to use GeoGebra to test their conjectures.

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In this launch-explore-share session, we introduce participants to GeoGebra tools available for displaying and summarizing data sets. Following a brief launch in which participants orient themselves to the context of a data set, participants will explore and share multiple ways to display and draw conclusions from the original and subsequent data sets. The session concludes with an exploration of available GeoGebra tools for Exploratory Data Analysis.

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In this launch-explore-share session, we introduce participants to the Measure-Trace-Algebratize (MTA) framework as a means for motivating student work with mathematical models. The session begins with a quick launch with a pre-made GeoGebra sketch. As participants drag the vertices of a square, they notice an ordered pair traced in a second Graphics view. They use CAS tools and simple algebra to derive a model that fits the plotted points. During an extended explore phase, participants work in pairs to find fit models for sketches of their own design.

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In this launch-explore-share session, we explore a number of interesting probability scenarios generated within GeoGebra (e.g., plotting random points along a circle or in a square), then use knowledge of school geometry and algebra to derive theoretical probabilities for various events. During an extended explore phase, participants to uncover a number of surprising connections between algebra, geometry, and probability, reporting findings and questions for further exploration on the GeoGebra Groups blog.

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In this session, we share ways that GeoGebra simulations can be utilized to build students’ inferential reasoning (e.g., re-randomization, resampling, etc.). The second half of this session will be an opportunity for participants to share what they have determined to be best practices for finding, modifying, and sharing GeoGebra sketches.

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