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

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

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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)

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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

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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.

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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 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

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(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

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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

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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)

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Role of teacher – as a bridge TEACHER Formal school knowledge Childs informal knowledge Pizzas shape basketball triangle sphere

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Levels of Geometric Thinking by Perre 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

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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 rectangles properties

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

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

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

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

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

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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

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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

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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

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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

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

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