Here are four problems. Four children solved one problem each, as given below. Identify the strategies the children have used while solving them.

a) 8 + 6 = 8 + 2 + 4 = 14

b) 4 + 9 = 5, 6, 7, 8, 9, 10, 11, 12, 13

c) 3 + 12 = 12, 13, 14, 15.

d) 7 + 5 = 1 + 1 + ... + 1 (seven times) + 1 + ...+1 (5 times) = 12

Thus, we can say that standard algorithms discourage children from thinking and constructing their own understanding of mathematics. They also reduce mathematics to a mere mechanical activity of observation and manipulation of symbols. This is reinforced by most teachers who give children marks only for the mechanical steps they follow in applying an algorithm.