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Using geometric vocabulary with meaning

Using geometric vocabulary with meaning. Math Alliance November 16, 2010 Beth Schefelker, Judy Winn, & Melissa Hedges. Learning Intention and Success Criteria. We are learning to…

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Using geometric vocabulary with meaning

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  1. Using geometric vocabulary with meaning Math Alliance November 16, 2010 Beth Schefelker, Judy Winn, & Melissa Hedges

  2. Learning Intention and Success Criteria • We are learning to… • Scaffold learning experiences that support students’ understanding of geometric ideas while concurrently developing the specialized vocabulary of geometry. • We will be successful when… • we can identify GKT (Geometry Knowledge needed for Teaching) and instructional moves necessary to push student understanding.

  3. What’s in the bag? Round #2 • Person 1 selects a shape from the bag and describes without removing it from the bag. • Person 2 and Person 3 draw the shape based on the description. Person 2 or 3 may ask a total of 3 clarifying questions. • Person 4 records descriptive language questions.

  4. Round #3 What’s in the bag? • Goal: “Find/Name that shape” in 3 clues or less. (No questions are permitted.) • Describer silently selects a shape and crafts 3 clues that will help participants identify that shape. • Describer: Give one clue at time. • Finder: Finds the shape. • Recorder: Keep track of descriptive language in the clues.

  5. What’s in the bag? • Debrief • Look back on the notes taken by the recorder. What characteristics “made up” a good description or helpful clues? • In general, discuss what you chose to tell about the shapes in your clues. What did you tend to leave out? • Consider the level of complexity of language used by your group. (van Hiele level.)

  6. Case #3 Describing Geometric Blockspp.15-19 • What were the teacher’s mathematical goals of the lesson? • What were some instructional moves Rosemarie made to scaffold children’s thinking to reach those goals? • What did the teacher learn about her students’ geometric thinking? • What GKT does Rosemarie need to plan for subsequent learning experiences?

  7. Strategic Instruction Characteristics of the van Hiele levels • The levels are sequential. • The levels are not age dependent. • Students required to wrestle with objects of thought that have not been constructed at the earlier level may be forced into rote learning and achieve only temporary and superficial success. • Geometric experience is the greatest single factor influencing advancement through the levels.

  8. Strategic Instruction In what ways might the “What’s in the bag?” be used to transition students from… • Pre-level 0 to Level 0 • Level 0 to Level 1

  9. PreLevel 0 to Level 0Level 0 to Level 1 • Teachers should involve students in lots of naming, describing, sorting, and classifying of shapes. • Students need numerous opportunities to identify and express similarities and differences between shapes. • As children surface properties such as symmetry, numbers of sides and corners, etc. appropriate geometric terms are introduced by the teacher. • As sorting tasks continue teachers should challenge students to use features (sides, angles, etc.) to classify shapes. • Students should be provided numerous, and focused, opportunities to draw, build, make, put together, and take apart shapes in both 2-D and 3-D.

  10. Level 0 to Level 1– Geometry Knowledge for Teaching Accurate use of Level 0 and Level 1 vocabulary and Level 1 and Level 2 understanding of geometric properties on behalf of the teacher is critical!

  11. Strategic Instruction • In what ways might the “What’s in the bag?” be used to transition students from Level 1 to Level 2?

  12. Level 1 to Level 2 • Focus more on properties of shapes rather than on simple identification of shapes. As new geometric concepts are learned, the number of properties that figures have can be expanded. (Example: sort quadrilaterals first with “2 pairs of opposite sides are parallel” then with “2 pairs of opposite sides are congruent.” What do we notice?) • Apply ideas to all classes of figures (e.g., all rectangles, all prisms) rather than individual models. Example: Find ways to sort all possible triangles into groups. From these groups define types of triangles.

  13. Level 1 to Level 2 -- GKT Teachers must be comfortable guiding students through classifying shapes, identifying and defining properties, and using geometric vocabulary with meaning.

  14. Resource Binder Big Idea #1 Description, Classification, and Analysis of Polygons We will all use the Triangle Task Project for this first Big Idea. Page 5 of the syllabus: • As a learner of mathematics • How is what you are learning supporting your teaching? • As a teacher of mathematics • Identifying student levels of understanding. • What have we learned from the assessments? • Research/Trace how the Big Idea is presented in the textbook program you use. (This is the instructional implications portion of your Triangle Task.)‏

  15. Homework • Work on Part C of the Resource Binder project. Complete the analysis of the lessons portion. (Remember, you have already completed Parts A and B. You turned them in tonight.) • For November 30, come ready to share your analysis of the lessons. We will share your analysis of the differentiation suggestions on December 7.

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