1234567 891011121314 15161718192021 22232425262728 29303132333435 36373839404142 43444546474849 Generalise for another number
12345678 910111213141516 1718192021222324 2526272829303132 3334353637383940 4142434445464748 4950515253545556 5758596061626364 Generalise for any number: variables and parameters
What new kinds of question can be asked and why?
New question-types On an 9-by-9 grid my tetramino covers 8 and 18. Guess my tetramino. What tetramino, on what grid, would cover the numbers 25 and 32? What tetramino, on what grid, could cover cells (m-1) and (m+7)?
Variations and their affordances Shape and orientation (comparable examples) Position on grid (generalisations on one grid) Size of number grid (generalisations with grid size as parameter) Object: grid-shape as ‘new’ compound object to be acted upon (abstraction as a new object-action) Nature of number grid (focus on variables to generalise a familiar relation) Unfamiliar number grid (focus on relations between variables)
Role of variation Awareness of variation as generating examples for inductive reasoning Using outcomes of inductive reasoning as new objects for new variations Twin roles of presenting variation and directing questions (cf. also the paper by Hart in Theme C)