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This study examines the position of the unknown set and children's representation and solution processes for verbal addition and subtraction problems. Forty-seven first-grade children were given three joining problems and three separating problems in an individual interview. Each joining and separating problem had a different quantity as the unknown. Small blocks were available for children to use to model the problems. Results indicated that the position of the unknown had a profound effect on children's modeling behavior, which in turn affected the choice of the solution process and the relative difficulty of the problem.
James Hiebert (Mon,) studied this question.