Sophian, C., & Wood, A. (1997). Proportional reasoning in young children: The parts and the whole of it. Journal of Educational Psychology, 89, 309-317.

Evidence concerning intuitive foundations for fraction learning was obtained in a study of early developments in proportional reasoning. Children 5 to 7 years of age (kindergarten to second graders) were given problems constructed so as to differentiate between reasoning based on the relations of a part to the whole, versus reasoning based on relations between one part and another. The participants were able to use part-whole relations to compare proportions by 7 years of age. In addition, a developmental shift toward increasing reliance on part-whole reasoning was observed in children's responses to conflict problems which pitted part-whole and part-part matches against each other.

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