Transcript Geometry and Spatial Reasoning

Geometry and Spatial
Reasoning
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Develop adequate spatial skills
Children respond to three dimensional world of
shapes
Discovery as they play, build and explore toys
Spatial reasoning creates mental images of one’s
surroundings and objects in them(NCTM 2000)
Spatial skills are important for everyday life
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Why Geometry?
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Practical experiences involve problem
solving situations that require knowledge in
geometric concepts
 Making frames
 Building furniture
 Grass seed, fertilizer required
 Wallpaper and paint
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Teaching Strategy
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Incorporate geometry into everything you
do not just mathematics instruction
 Help develop spatial reasoning and
understanding
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Van Hiele Levels
Two Dutch educators studied children’s
acquisition of geometric concepts and the
development of geometric thought
 The Van Hieles concluded that children
pass through five levels of reasoning in
geometry
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Van Hiele Levels of Geometric
Thinking
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Level 0 Visualization
 Description: Children recognize shapes by their
global, holistic appearance
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For example, a child might think of shapes in
terms of what they resemble
 A triangle may be described as a mountain
 At this level children can sort shapes into groups
that look alike to them in some way
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Van Hiele Levels
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Level 1 Analysis
 Description: Children observe the
component parts of a figure (ex.
parallelogram has opposite sides that are
parallel) but are unable to explain the
relationships between properties within a
shape or among shapes
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Van Hiele Levels
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At level 1 analysis children think in terms of
properties
They understand that all shapes in a group such as
parallelograms have the same properties
Four sides
Opposite sides parallel
Opposite sides are congruent
Opposite angles are congruent
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Van Hiele Levels
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Level 2 Informal deduction
 Description: Children deduce properties of
figures and express interrelationships both
within and between figures
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Example, all squares are rectangles but not
all rectangles are squares
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Van Hiele Levels
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Level 3 Formal deduction
 Description: Children create formal deductive
proofs (high school level)
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Example: Children at this level think about
relationships between properties of shapes and
understand relationships between axioms,
definitions, theorems, corollaries and postulates.
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Comments on the Levels of
Thought
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Not age dependent but related to experiences that
children have had
The levels of sequential
To move from one level to the next, children need
to have many experiences
Language must match the child’s level of
understanding
It is difficult for two people at different levels to
communicate effectively
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Van Hiele Levels
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Level 4 Rigor
 Description: Children rigorously compare
different axiomatic systems (college level)
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Example: Children at this level can think in
terms of abstract mathematical systems
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