Sophian, C. (2004).  A prospective developmental perspective on early mathematics instruction.  In Clements, D. H., Sarama, J., &.DiBiase, A.-M. (Eds.)  Engaging young children in mathematics: Findings of the 2000 national conference on standards for preschool and kindergarten mathematics education. Hillsdale, NJ: Lawrence Erlbaum Associates.

A prospective developmental perspective is concerned with the impact of early mathematics instruction on aspects of mathematics learning that become important later in development.  The modes of instruction that produce the greatest immediate learning may not always be the ones that are best for the long term.  Accordingly, instructional standards should be directed toward maximizing the long-term as well as the short-term effectiveness of early mathematics instruction.  I will focus on the arena of fraction learning to develop this idea. I will suggest that much of the difficulty in fraction learning stems from conceptual issues that are not unique to fractions, but that have their origins in the way very young children think about counting and whole-number quantities.
 
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