HELPING ELEMENTARY TEACHERS DEVELOP VISUAL AND SPATIAL SKILLS FOR TEACHING GEOMETRY ICME 11 TSG 12 Stewart Craven, York University, Toronto, Canada ICME 11 TSG 12 Stewart Craven, York University, Toronto, Canada

Helping Elementary Teachers Develop Visual and Spatial Skills for Teaching Geometry Walter J. Whiteley Margaret Sinclair Stewart CravenLily Moshe Anna DutfieldMelissa Seco

Helping Elementary Teachers Develop Visual and Spatial Skills for Teaching Geometry Sequence of Tasks (over 3 days) 1.Tangram Activity (visual memory) 2.Buildings (cubes, drawings - 2D/3D) 3.Reflection Symmetries (folding, 3D planes) 4.Rotation Symmetries (rotating acetates and rods) 5.Reflections and Rotations (relationships) 6.Tessellations (infinite planes) 7.Dilation Activity with GSP (pre-constructed sketches) 8.Filling Activity (pyramid, water, tilt -> surface shape) Sequence of Tasks (over 3 days) 1.Tangram Activity (visual memory) 2.Buildings (cubes, drawings - 2D/3D) 3.Reflection Symmetries (folding, 3D planes) 4.Rotation Symmetries (rotating acetates and rods) 5.Reflections and Rotations (relationships) 6.Tessellations (infinite planes) 7.Dilation Activity with GSP (pre-constructed sketches) 8.Filling Activity (pyramid, water, tilt -> surface shape)

Helping Elementary Teachers Develop Visual and Spatial Skills for Teaching Geometry Overview of Findings difficulties in three key areas: inquiry, making connections and communication. In general, participants lacked systematic inquiry strategies, and their ability to conjecture was limited by prior knowledge participants grew in their understanding of spatial (both 2D and 3D) relationships through opportunities to explore unfamiliar concepts with physical objects some participants experienced AHA! moments Overview of Findings difficulties in three key areas: inquiry, making connections and communication. In general, participants lacked systematic inquiry strategies, and their ability to conjecture was limited by prior knowledge participants grew in their understanding of spatial (both 2D and 3D) relationships through opportunities to explore unfamiliar concepts with physical objects some participants experienced AHA! moments

Helping Elementary Teachers Develop Visual and Spatial Skills for Teaching Geometry Recommendations To benefit from visual/spatial experiences, teachers must possess a repertoire of investigative strategies. In particular they require approaches to: inquiry, making connections, and communicating that are appropriate for visual/spatial contexts. Recommendations To benefit from visual/spatial experiences, teachers must possess a repertoire of investigative strategies. In particular they require approaches to: inquiry, making connections, and communicating that are appropriate for visual/spatial contexts.

Helping Elementary Teachers Develop Visual and Spatial Skills for Teaching Geometry Inquiry The following strategies build the required familiarity with the objects and also with investigation processes, and prepare teachers to recognize whether/when a child is doing something sensible in an exploration: 1. Physical inquiry strategies 2. Organizational strategies Glaser notes that while novices often fail to see the big picture experts are able to employ decomposing and chunking to organize information. 3. Experimentation strategies The experimenter needs to be: a) open to variation, and b) able to pose questions. Inquiry The following strategies build the required familiarity with the objects and also with investigation processes, and prepare teachers to recognize whether/when a child is doing something sensible in an exploration: 1. Physical inquiry strategies 2. Organizational strategies Glaser notes that while novices often fail to see the big picture experts are able to employ decomposing and chunking to organize information. 3. Experimentation strategies The experimenter needs to be: a) open to variation, and b) able to pose questions.

Helping Elementary Teachers Develop Visual and Spatial Skills for Teaching Geometry Making Connections Spatial investigations provide interesting possibilities for making connections. Our research touched on: using multiple representations, moving between dimensions, considering the finite and the infinite, and thinking about the particular and the general. Making Connections Spatial investigations provide interesting possibilities for making connections. Our research touched on: using multiple representations, moving between dimensions, considering the finite and the infinite, and thinking about the particular and the general.

Helping Elementary Teachers Develop Visual and Spatial Skills for Teaching Geometry Communicating Investigations are enriched by collaboration - working together to manipulate objects, planning approaches, and communicating via gesture, sketching and language. Communicating Investigations are enriched by collaboration - working together to manipulate objects, planning approaches, and communicating via gesture, sketching and language.