generally, the game designer is focused on the experience of play rather than the rules of the game.
for a board game, the elegance of the gameboard is that it combines two operational functions: recording progress, and visually indicating progress.
design intent
take for example the game 3 to 15. this is a game exclusively of memory and math. if the design of this game is intended to be so, then it has good design intent. however, if it's meant to be a strategic placement game, then it has bad design intent. the purpose of design intent is to control the players' behaviors so that they cooperate with the game but don't feel limited by the boundaries.
elegance through clarity
take for example having the target audience of young children. as they have young attention, the design intent of the game must account for this. therefore, designing a gameboard records player movement and communicate it in an effective manner is paramount for the target audience's needs.
as a result, using design to abstract information or mathematics from the game can make it more fun.