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…  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.

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.

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.

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.)

Case #3 Describing Geometric Blocks pp 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?

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.

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

PreLevel 0 to Level 0 Level 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.

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!

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

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.

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.

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.)‏

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.