GEOMETRY AND SPATIAL GEOMETRY AND SPATIAL SENSE IN THE EARLY SENSE IN THE EARLY

CHILDHOOD CURRICULUMCHILDHOOD CURRICULUM

GEOMETRY AND SPATIAL GEOMETRY AND SPATIAL SENSE IN THE EARLY SENSE IN THE EARLY

CHILDHOOD CURRICULUMCHILDHOOD CURRICULUM

By Copley, J.V.(2000)By Copley, J.V.(2000)

GEOMETRY• Shapes, sizes, positions, directions

and movements

CHILDREN SPATIAL SENSE• Their awareness of themselves in

relation to people and objects around them

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)

• ... . ...

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

• 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.

NCTM Standards: Key aspects of G and SS for early childhood(a) Analyze characteristics and properties of 2D and 3D

objects

Semicircle = one curved side, one straight side, two corners and 1 flat face

Cube = 2 square bases, 6 faces, 8 vertices, 12 edgesCuboid = 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

(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

By having the above abilities children will beable 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

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)

Role of teacher – as a bridge

TEACHERFormal school

knowledgeChild’s informal knowledge

• Pizza’s shape

• basketball

• triangle

• sphere

Levels of Geometric Thinking byPerre Van Hiele

Levels of Geometric Thinking byPerre Van Hiele

• Level 0 Recognize geometric figures by their holistic physical appearance, do not think of attributes and properties of shapes

“Circle ~ because looks like a clock”

• Level 1Children can isolate characteristics or attributes of the forms, “ a square has four equal sides” • Level 2Children establish relationships betweenattributes of the forms

“a square is a rectangle because it has all of rectangle’s properties”

(thinking activity) LOOK, MAKE and FIX by Mr Quintanilla

• Students : 7 tangram pieces

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

• Fernando : A turtle with no legs• Gina : One part at a time, start with

mountain, add other stuff, lastly weird piece

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

• 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

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

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

Specific Expectation for young children on

shape• 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

Triangle• i) recognize shape as a whole-3

sides• (ii) they do not recognize types of

rectangles

Good triangle

Bad triangle

Square sitting on its

vertex

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