Tasks 8 and 9 involved the same operations as Tasks 6 and 7 but with larger sets. The major difference in results was greater spontaneous use of the blocks available when the numbers were larger.
The difficulty experienced by children in effecting the exchange of a base-ten long for the correct number of units was probably attributable to a difference in viewing the requirements of the problem. Some considered the need to retain the same number property and hence focused on a "fair" exchange. Others focused on the need to be able to furnish six units and traded to be able to accomplish that. Only 24 children saw the correct exchange of a long for ten units, either immediately or as the result of the trial and error. How children think about the regrouping involved in our numeration system at ages 6 through 8 needs careful examination. Some evidence that many children in second grade consider equality an operator rather than a relation has been obtained(Behr, Erlwanger, & Nichols, 1974). How does this c onfusion about equality affect their notions of the equivalence of a group of ten and a set of ten ungrouped units? Do they decompose ten into ones because a ten is equivalent to ten ones or because they need so many ones to be able to do a particular subtraction?