HELPING ELEMENTARY TEACHERS DEVELOP VISUAL AND SPATIAL

SKILLS FOR TEACHING GEOMETRY

HELPING ELEMENTARY TEACHERS DEVELOP VISUAL AND SPATIAL

SKILLS FOR TEACHING GEOMETRY

ICME 11 TSG 12Stewart Craven, York

University, Toronto, Canada

ICME 11 TSG 12Stewart Craven, York

University, Toronto, Canada

Helping Elementary Teachers Develop Visual and Spatial Skills for Teaching

Geometry

Helping Elementary Teachers Develop Visual and Spatial Skills for Teaching

Geometry

Walter J. Whiteley

Margaret Sinclair

Stewart Craven Lily Moshe

Anna Dutfield Melissa Seco

Helping Elementary Teachers Develop Visual and Spatial Skills for Teaching

Geometry

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

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

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

Helping Elementary Teachers Develop Visual and Spatial Skills for Teaching

Geometry

InquiryThe 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 strategies2. 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.

InquiryThe 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 strategies2. 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

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

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.