*Geometry and Spatial ReasoningDevelop adequate spatial skillsChildren respond to three dimensional world of shapesDiscovery as they play, build and explore toysSpatial reasoning creates mental images of ones surroundings and objects in them(NCTM 2000)Spatial skills are important for everyday life

*Why Geometry?Practical experiences involve problem solving situations that require knowledge in geometric conceptsMaking framesBuilding furnitureGrass seed, fertilizer requiredWallpaper and paint

*Teaching StrategyIncorporate geometry into everything you do not just mathematics instructionHelp develop spatial reasoning and understanding

*Van Hiele LevelsTwo Dutch educators studied childrens acquisition of geometric concepts and the development of geometric thoughtThe Van Hieles concluded that children pass through five levels of reasoning in geometry

*Van Hiele Levels of Geometric ThinkingLevel 0 VisualizationDescription: Children recognize shapes by their global, holistic appearance

For example, a child might think of shapes in terms of what they resembleA triangle may be described as a mountainAt this level children can sort shapes into groups that look alike to them in some way

*Van Hiele LevelsLevel 1 AnalysisDescription: 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

*Van Hiele LevelsAt level 1 analysis children think in terms of propertiesThey understand that all shapes in a group such as parallelograms have the same propertiesFour sidesOpposite sides parallelOpposite sides are congruentOpposite angles are congruent

*Van Hiele LevelsLevel 2 Informal deductionDescription: Children deduce properties of figures and express interrelationships both within and between figures

Example, all squares are rectangles but not all rectangles are squares

*Van Hiele LevelsLevel 3 Formal deductionDescription: Children create formal deductive proofs (high school level)

Example: Children at this level think about relationships between properties of shapes and understand relationships between axioms, definitions, theorems, corollaries and postulates.

*Comments on the Levels of ThoughtNot age dependent but related to experiences that children have hadThe levels of sequentialTo move from one level to the next, children need to have many experiencesLanguage must match the childs level of understandingIt is difficult for two people at different levels to communicate effectively

*Van Hiele LevelsLevel 4 RigorDescription: Children rigorously compare different axiomatic systems (college level)

Example: Children at this level can think in terms of abstract mathematical systems