The current state is the current position held in the problem-solving process. It can be thought of as the "before-stage". For example, the current state could be the clues to a crossword problem. There is no definitive answer yet to the puzzle but they serve as clues to get to the final desired state.

Purpose in Group Problem-Solving: Current State

The desired state is the position hoped to be reached via problem-solving. It can be thought of as the "end-result". For example, the answer to a crossword puzzle could be the desired state.Whereas the current state would be the clues to the crossword puzzle, the desired state is the final answer using clues provided by the current state.

Purpose in Group Problem-Solving: Desired State

The goal of dividing work in problem-solving among a group is to collectively make efforts to transition from current state to the desired state. 

University of Michigan - Ann Arbor

Vine, A. D., &; Davis, J. H. (1968). Group Problem Solving, Task Divisibility, and Prior Social Organization. Proceedings of the Annual Convention of the American Psychological Association, 3, 411–412. https://doi.org/http://assets.press.princeton.edu/chapters/s9339.pdf 

Vine, A. D. & Davis, J. H. (1968)

Constructs in group problem solving define group dynamics and potential outcomes. They ostensibly determine the functions of a group.

Constructs in Group Problem Solving

Purpose for Group Tasking and Problem-Solving

Certain dynamics may impact the outcomes of reaching or not reaching an objective in group-problem solving. This can be in reference to group cohesion and the capability of  group to work together to solve a problem.

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