Higher Order Thinking in Young Children’s Engagements with a Fraction Machine

Abstract

A group of six second grade children (average age 7 years 5 months) and their class teacher, were sitting around a table. On the table were arrangements of small wooden objects - mostly representations of animals There were two rabbits, four bears, six roosters, eight trees, 10 peacocks, and 12 worms. Starting with the two rabbits, the teacher had introduced each larger set in turn, asking a child to divide the set of objects in half, and to write symbols for the number of objects in each subset. The children offered their own interpretations for each partition, but through discussion and assistance most children, in the end, had written the sequence of fractions $\frac{1}{2},\frac{2}{4},\frac{3}{6},\frac{4}{8},\frac{5}{{10}},\frac{6}{{12}}$ The teacher then said: “You have told me that each is a half of their combined total. How can these all be halves when we have got different numbers in each group?” In this instant those children were brought face to face with the possibility of developing a deeper interpretation of the fraction one half: that of a meta-relation.