F. Learning the application of the combinations to higher decades may for the less gifted pupils involve as much time and labor as learning all the original addition tables. And even for the most gifted child the formation of the connection '8 and 7 = 15' probably never quite insures the presence of the connections '38 and 7 = 45' and '18 + 7 = 25.'
G. Learning to write the figure signifying units rather than the total sum of a column. In particular, learning to write 0 in the cases where the sum of the column is 10, 20, etc. Learning to 'carry' also involves in itself at least two distinct processes, by whatever way it is taught.
We find evidence of such specialization of functions in the results with such tests as Woody's. For example, 2 + 5 + 1 = .... surely involves abilities in part different from
2
4
3
—
because only 77 percent of children in grade 3 do the former correctly, whereas 95 percent of children in that grade do the latter correctly. In grade 2 the difference is even more marked. In the case of subtraction
4
4
—
involves abilities different from those involved in
9
3
—,
being much less often solved correctly in grades 2 and 4.
6
0
—