Herbert Simon, Sciences of the Artificial

Simon includes in this book (MIT Press, 1969) some early remarks on the importance of representation in problem solving and design. He uses as a motivating example the game of "number scrabble", in which players alternately take digits from the collection {1,2,3,4,5,6,7,8,9}, seeking to secure three digits whose sum is 15. Simon notes that this game is isomorphic to tic-tac-toe: if the digits are arranged thus,
4 9 2
3 5 7
8 1 6
the triples whose sum is 9 are exactly the rows, columns, and diagonals that constitute wins in tic-tac-toe. Thus a change of representation for the game allows players of number scrabble to engage their preexisting knowledge of how to play tic-tac-toe. Though Simon doesn't make the connection explicit, the context of this discussion suggests that he might also have been thinking that the re-represented game engages spatial reasoning abilities that the original game does not.

Simon calls for further work on representations: "This view can be extended to all of problem solving: solving a problem simply means representing it so as to make the solution transparent. If the problem solving could actually be organized in these terms, the issue of representation would indeed become central. But even if it cannot-- if this is too exaggerated a view-- a deeper understanding of how representations are created and how they contribute to the solution of problems will become an essential component in the future theory of design. ... We have only a sketchy and incomplete knowledge of the different ways in which problems can be represented and much less knowledge of the significance of the differences. ... But even though our classification is incomplete, and perhaps superficial, we can begin to build a theory of the properties of these representations. (pp. 77-79)