Exploring Properties of Figures Using GSP

Exploring properties of figures using GSP Participant Handout

Puzzling Pentagons Using the ExploringProperties.gsp file, complete the chart below to identify the properties of and define the oddly named pentagons. Shape Properties Definition Glubber

Slubber

Blubber

Flubber

Plubber

Questions to consider: 1. Reflect on your thinking processes when generating your definitions. What properties did you consider important or not important? Did you create definitions that did not work? How did you know if a definition “worked” or not? 2. Compare your definitions with the definitions created by others. Consider similarities, differences, strengths, and weaknesses in the different definitions. 3. Describe the benefits and drawbacks of allowing students to interact with a constructed figure in a DGE to generate their own definitions versus a teacher providing a formal definition to students. 4. When students are generating their own definitions, describe how a teacher can bring these different ideas together so that the class is eventually working from a single definition.

Adapted from: Hollebrands, K. F., & Lee, H. S. (2012). Exploring quadrilaterals. In Preparing to teach mathematics with technology: An integrated approach to geometry (1-22). Dubuque: Kendall Hunt. Partitional vs. Hierarchical Definitions  Partitional definitions: considers concepts disjointly from one another; exclusive definition  Hierarchical definitions: defined as a subset of a more general concept; inclusive definition

Questions to consider: 1. Consider the following definitions of a trapezoid: Definition 1: A trapezoid is a quadrilateral with exactly one pair of parallel sides. Definition 2: A trapezoid is a quadrilateral with at least one pair of parallel sides. How would you categorize each definition, partitional or hierarchical? Why? 2. Why might students prefer partitional definitions to hierarchical definitions? 3. When students are generating their own definitions, describe how a teacher can bring these different ideas together so the class is eventually working from a single definition. 4. Look at your properties for the unknown pentagons. Determine which properties are “inherited” from other properties. Use this information to create a hierarchical classification of these pentagons. 5. Describe how you could apply this same approach you experienced to have students investigate properties of quadrilaterals and generate the accompanying sketch.

Adapted from: Hollebrands, K. F., & Lee, H. S. (2012). Exploring quadrilaterals. In Preparing to teach mathematics with technology: An integrated approach to geometry (1-22). Dubuque: Kendall Hunt.