The Program

Numerycles

The Program

Numerycles is an innovative, interdisciplinary, four-phase educational program. 

The abstraction-based content package and the technology used in its deployment seek to trigger new creativity (musical, artistic and literary) and to instill self-esteem and confidence in the Apprentices as they become Instructors of new groups. The program is usually started with a three-hour, on-site workshop for both students and their teachers and is continued on line.




The four phases of the program are: Discovery, Creativity, Technology and Leadership.









This first phase consists of three sections:

1. Inventory
Discovery of the INVENTORY of Necklaces. A Necklace is a cyclical sequence determined by the digit sum of the Fibonacci series, but Apprentices follow a path in which every step is discovered from scratch, hypothesizing, experimenting and arriving at conclusions based on irrefutable evidence which is hidden at first sight. There are only five Necklaces as defined in this phase I. A Numerycle is defined here as any portion of a Necklace.

2. Matrix

A matrix of "intelligent" squares is obtained by plotting two-digit numbers on a 9 x 9 Matrix. 

Description of the "logic" of the pattern is a first step into abstraction-based creativity which will be further developed in Phase II of the program.

Following the general philosophy of "discovery" of the phase I, Apprentices are never told what the best way of describing the pattern is, and free analogies are encouraged to describe the coreography of colors they observe.

3. Game


Serial numbers on bills (dollar, euro or any currency) are transformed into Numerycles through translations and sums. An equal mix of luck and strategy makes this game innovative and unique. Don't count on your most capable student winning... luck has a say in the outcome, and perseverance is a valuable asset!



Phase II. Creativity

Musical: Melodies emerge from the numerycle sequences. Apprentices decide on rythm, duration of notes and digit-to-note translation.

Artistic: Substitute shapes for musical notes... is that a butterfly, a bow tie or a sideways hourglass?

Literary:  What stories come to the Apprentice's mind when shapes and melodies are interpreted as words? 







Phase III. Technology


How do we use a spreadsheet to generate longer, more complex Numerycles? What happens outside of our number system? This phase is focused on both the use of a spreadsheet (at a fairly advanced level which 11-year-old apprentices handle very well) and the justification for its use.




Phase IV. Leadership


The Apprentices become Instructors and amaze peers, teachers and parents with their degree of self confidence and self esteem, and with the ability to communicate their new knowledge.


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