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Week 5: Geometric Reasoning (Van Hiele Model – Properties (Level 0 - Pre…
Week 5: Geometric Reasoning
What are spatial orientation and spatial visualisation and imagery?
SO – knowing where you are and how you get around e.g. looking at map in shopping centre trying to find a shop. Technology making this easier for people. Mapping skills – preparing students to deal with everyday situations.
SV&I – ability to imagine or visualise in your mind the positions of objects, their shapes, their spatial relations to one another and the movement they make to form new spatial relations. Spatial organization. Process of forming images, either mentally or with sketching/tech, to form images for MM discovery and understanding. Kind of reasoning based on the use of mental images e.g. parking your car, fitting things into your boot. Preparing kids for lifelong skills they will need.
Spatial thinking
Fundamental role in our lives
From assembling furniture to specilaised skills required for higher edu e.g. architecture, dentistry, medicine, art and design.
Connected to success in STEM – need to introduce in early learning to dev spatial skills e.g. building blocks, box construction, making stuff out of recyclable items.
Support the idea that the study of geometry needs to be an active, tactile experience.
The power of discussion and the need to build vocabulary e.g. parallel. Interacting and learning from each other
Classroom examples
Geometry – draw shapes using commands – uses angles
https://turtleacademy.com/playground
Van Hiele Model – Properties
Level 0 - Pre-recognition
attend to only some shape's characteristics
unable to identify many common shapes
Level 1 - Visualisation (primary)
look at figures based on overall appearance, but not their properties e.g. hexagon has six sides and can be irregular
reasoning dominated by perception - use visual shapes to link knowledge
Level 2 - Analysis (primary)
ideas on what makes a shape e.g. 6 sides being hexagons.
can describe shapes using language like sides, angles, degrees, right-angles, parallel
Level 3 - Informal deduction
foresee relations between properties and figures. More technical. Discuss rationality with reasoning.
Level 4 - Formal deduction
proofs of theorems can be constructed
Level 5 - Rigour
specialist, abstract, high lvl functioning
Sequential - sts must pass through all prior lvls to arrive at any specific lvl
Levels are not age-dependent in the way Piaget described development
Geometric experiences - greatest influence on advancement through levels.
Instruction and language at lvl higher - results in rote learning with little understanding - inhibit further lng
Teachers hold key for sts to transition - dependent on instruction delivery and students not being passive learners
Concrete materials
Physical manipulation
A 3D object unfolded into a net
Kids cutting a cube to fold out into a net