Numbers and combinatorics
Data Sheet
CLASSES: 6, 7 and 8.
Skills:
The pupil:
- analyses and interprets data representations to obtain measures of variability and make decisions;
- compares different procedures and produces formalisations that allow them to move from a specific problem to a class of problems.
METHODS:
The pathway introduces elements of combinatorics through various tools, including anagrams. Students are invited to think calmly and look for a way to order the objects so as to count them better. Combinatorics problems set in concrete contexts help develop enumeration processes, as well as conjectures and generalisations. Students have no difficulty finding strategies when the context is meaningful (English, 2005). Although the main aim of the activities is not to reach combinatorics formulas, older students may manage to generalise what they have found. Recognising structural analogies in concrete situations lays the foundations for a gradual process of abstraction.
This pathway was designed by Luigi Bernardi and Giorgia Damiano.
Data Sheet
CLASSES: 6, 7 and 8.
Skills:
The pupil:
- analyses and interprets data representations to obtain measures of variability and make decisions;
- compares different procedures and produces formalisations that allow them to move from a specific problem to a class of problems.
METHODS:
The pathway introduces elements of combinatorics through various tools, including anagrams. Students are invited to think calmly and look for a way to order the objects so as to count them better. Combinatorics problems set in concrete contexts help develop enumeration processes, as well as conjectures and generalisations. Students have no difficulty finding strategies when the context is meaningful (English, 2005). Although the main aim of the activities is not to reach combinatorics formulas, older students may manage to generalise what they have found. Recognising structural analogies in concrete situations lays the foundations for a gradual process of abstraction.
This pathway was designed by Luigi Bernardi and Giorgia Damiano.
Ramon Llull
Ramon Llull was a Spanish writer, theologian and logician. He travelled across much of Europe, partly to spread his ideas and his doctrine. In his work Ars Magna he sets out a method of reasoning and of classifying knowledge: concepts are represented by geometric or algebraic symbols so that they can be combined in every possible way. We like to think that this idea, later taken up in Leibniz's better-known Ars Combinatoria, indirectly anticipates modern combinatorics.
“Lull's art serves to speak without judgement of what one in fact does not know” Descartes
