Lecture 3 - 3D Objects Flashcards
What is van heile theory
5 hierarchical levels of children’s thinking
5 phases of leaning - teachers role
How do children learn geometry?
Progression relates to cognitive development theories eg.
Sensori-motor- respond to stimuli with touch and sound
ikonic - mental images of shapes
concrete symbolic - drawings of shapes and base their reasoning of them
ENRP
- Not apparent
- Holistic recognition of shapes
- Classification of shapes, attending to visual features
- Identification of classes of shapes by some properties
- Definition of shapes using early properties
Level 1?
Recognition
Shape viewed holistically without specific attributes
Students recognise shapes based on real world objects
Students must recognise a range of shapes and object and describe them at their own language level
Activities for level 1?
Attribute blocks
Dime solids
Polyhedron construction sets
Real world objects - boxes, dice and balls
Level 2?
Analysis
Children become aware of the properties (attributes of corners, edges, verifies and sides)
Level 3?
Informal deduction
Classifying shapes
Relationships between attributes and shapes begin to emerge
Students should be able to justify why using natural language
Level 4?
Formal deduction
(High school level)
Formulas and definitions
Level 5?
Rigor
Mathematicians
What are the van heile phases of learning?
Inquiry
Directed orientation
Explication
Free organisation
Integration
3 catagories of solids
Those with a flat surface are polyhedrons - prisms and pyramids
Those with curved surface (spheres and egg shapes)
Those with flat and curved surfaces (cylinders and cones)
Learning about solids involves:
Exploration
Mix of play and teacher directed activities
Naming, describing, classifying, drawing and modelling objects
Polyhedral/polyhedrons
Type of solid figure
Two square based pyramids joined together at the base
Types of polyhedra?
Some are prisms
Cube
Rectangular, triangular and hexagonal
Some are pyramids
Triangular and square based
Platonic solids?
Sub class of polyhedrons
Regularity of form and perfect symmetry
It is a regular, convex polyhedron. Same number of congruent faces meet at each vertex.
