1. GEOMETRY AND SPATIAL SENSE IN THE EARLY CHILDHOOD CURRICULUM
By Copley, J.V.(2000)

2. GEOMETRY
Shapes, sizes, positions, directions and movements
CHILDREN SPATIAL SENSE
Their awareness of themselves in relation to people and objects around them

3. Some Spatial Concepts:
On and In (1)
On and In (2)
Inside and Outside Up
Down
Behind and In Front (1)
Behind and In Front (2)
Beside
Under
Over
Over and Under (1)

4. In 1850s Friedrich Froebel (The Father of kindergarten)
Designed curriculum that use special materials (“gifts”) to explore and grasp basic forms and relationship
“gifts”
Colored balls
Cubes, spheres, cylinder
Geometric blocks

5. In later years, less attention given to the study of geometry and spatial sense especially in childhood classroom
Teachers only introduced shapes definition but not manipulation of shapes and spatial exploration especially to the real world.

6. NCTM Standards: Key aspects of G and SS for early childhood
Analyze characteristics and properties of 2D and 3D objects
Semicircle = one curved side, one straight side, two corners and flat face
Cube = 2 square bases, 6 faces, 8 vertices, 12 edges
Cuboid = 2 rectangular bases, 6 faces, 8 vertices 12 edges
(b) Specify locations and describes relationship using coordinate
geometry or other rep. system
(c)Apply transformations by recognizing and applying slides, flips
and turns

7. (d) Using visualization to create mental images of geometric shapes by using spatial memory, can recognize structure in environment and specify location
Example
Shoebox ~ cuboid

8. By having the above abilities children will be
able to understand many areas in Math
Examples
Count sides and faces of cube - number relationship
Identify patterns in space (ex: relationship between # of faces, vertices, edges of 3D objects)– patterns , functions and rudiments in algebra
Compare shapes , direction and positions in space- develop new concepts and vocabulary
Grouping items (ex: sizes, shapes) – skills in data collection

9. Spatial sense come into play in Arts, Science ,Social studies, Music
Arts~ create 2D and 3D objects (spatial relationship and geometric forms are critical elements)
Social studies ~make and read maps (need spatial thinking skills)
Young children enjoy manipulating shapes in
space, their spatial capabilities often exceed
numerical skills(NCTM2000)

10. Role of teacher – as a bridge
Formal school knowledge
Child’s informal knowledge
TEACHER
Pizza’s shape
basketball
triangle
sphere

11. Levels of Geometric Thinking by Perre Van Hiele
Recognize geometric figures by their holistic physical appearance, do not think of attributes and properties of shapes
“Circle ~ because looks like a clock”

12. Level 1
Children can isolate characteristics or
attributes of the forms,
“ a square has four equal sides”
Level 2
Children establish relationships between
attributes of the forms
“a square is a rectangle because it has all of rectangle’s properties”

13. (thinking activity) LOOK, MAKE and FIX by Mr Quintanilla
Students : 7 tangram pieces

14. Mr Q :
(i)Medium triangle and a square
(ii) “LOOK”
(iii) Cover
(iv) “MAKE”
(iv) Remove cover
Mostly correct
(v) ‘FIX”

15. Fernando : A turtle with no legs
Gina : One part at a time, start with mountain, add other stuff, lastly weird piece

16. Conclusion from LMF Spatial sense takes a long time to develop
Interesting sidelight: ss activities not easy (Mr. Q)
Teachers : “ some have, some don’t”
Mr Q : importance of effort rather than luck or intelligence

17. Main purpose in assessing children's understanding is to tailor learning experiences to their needs.
Through this activity, teacher notes growth in Fernando’s confidence and in Gina’s use of startegies

18. Children at play-With G and SS
Young children love exploring G and spatial aspects around them
Teacher: ask q, suggest other activities, show various transformations, provide materials..to develop childs understanding on G and SS
Mirrors : their images and reflections - ss
Blocks creation-opportunities to make discoveries abt 2D & 3D shapes-g

19. Promoting development of key skills and concepts
Many teachers ignore gemetry and spatial sense.
NCTM 2000 emphasizes g & ss as an important area in preschool

20. Specific Expectation for young children on shape
Before school, begin to form shapes concepts
Age 6,7 , concepts fairly stable
Age between 3 and 6 -ideal to learn shapes
To develop shape concepts, need to handle, manipulate, draw shapes in many ways
Solid cutouts of shapes are more conducive than printed forms-trace around cutouts
Computer programs

21. Square sitting on its vertex
Triangle
i) recognize shape as a whole-3 sides
(ii) they do not recognize types of rectangles
Good triangle
Square sitting on its vertex
Bad triangle

22. Children must be shown variety of triangles examples and no triangles so that they are ready to learn critical attributes of geometric shapes