1 Geometry and Spatial Reasoning 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

2 Why Geometry? Practical experiences involve problem solving situations that require knowledge in geometric concepts Making frames Building furniture Grass seed, fertilizer required Wallpaper and paint

3 Teaching Strategy Incorporate geometry into everything you do not just mathematics instruction Help develop spatial reasoning and understanding

4 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

5 Van Hiele Levels of Geometric Thinking Level 0 Visualization Description: Children recognize shapes by their global, holistic appearance 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

6 Van Hiele Levels 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

7 Van Hiele Levels 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

8 Van Hiele Levels Level 2 Informal deduction Description: Children deduce properties of figures and express interrelationships both within and between figures Example, all squares are rectangles but not all rectangles are squares

9 Van Hiele Levels Level 3 Formal deduction Description: 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.

10 Comments on the Levels of Thought 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

11 Van Hiele Levels Level 4 Rigor Description: Children rigorously compare different axiomatic systems (college level) Example: Children at this level can think in terms of abstract mathematical systems