The Construction of Fraction Schemes Using the Generalized Number Sequence
In this chapter, we trace the construction of the fraction schemes of two of the children in our teaching experiment, Nathan and Arthur, who apparently had already constructed a generalized number sequence before we began working with them. We interacted with these two children as we did with the other children in the sense that our history of the children along with their current mathematical activity served in creating possibilities and hypotheses that we continually explored in teaching episodes. In our interactions, we found that their construction of the operations that produce the generalized number sequence opened possibilities for their constructive activity that we did not experience with the other children. We did not decide a priori to use higher-order tasks in our interactions with these two children than we used with the other children. Rather, their ways of operating served as the basis for our constructions of tasks that we used. Nathan participated in the teaching experiment during his third, fourth, and fifth grades, whereas Arthur participated only during his fourth and fifth grades.
KeywordsFigurative Material Recursive Partitioning Fraction Scheme Unit Fraction Split Operation
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