Patterns and Design
Age: 9 & up
Prerequisites: The child should have considerable experience with design work using fraction circles and sectors together with polygons, including use of the third row of buttcons in the designer's pallette. The child should also be familiar with basic LOGO commands, including FORWARD, BACK, RIGHT, LEFT, PEN UP, PEN DOWN, and PEN SIZE.
Screen objects: A LOGO geometry microworld with a turtle in the middle. A SWEEPER attachment (described below) has been added to the microworld.
Presentation: (Individual or small group)
Variations: In subsequent presentations, show size of sweeper can be changed. Show how size of sweeper and degrees of sweep can be put into programs as variables to create designs.
Extensions: Work with tesselations, islamic patterns, African textile designs.
Points of Interest: Discovery of relationships between sectors, external angles, and turtle turns.
Control of Error: Student's aesthetic judgement.
Direct Aims: Opportunity to apply understanding sectors, external angles, and turtle turns, experiment through design to discover relationships.
Indirect Aims: Relating LOGO geometry to Euclidean geometry.
Software Affordance: The figures can be perfectly formed to allow children to discover true relationships between them. Figures of many sizes can be drawn (e.g., a number of concentric pentagons can be drawn inside a circle with five sectors).
Tension between adoption and continuing research
Throughout her career, Montessori was constantly revising her materials and devising new ones as her research progressed.