Speedy and accurate Addition (Part I)

Let us return to the difficulties experienced by children in doing multiplication. There I had suggested a method called “Hindu System” for children who have difficulty in managing “carrying”. This system of multiplication is also called “Lattice multiplication”. This system not only solves the difficulty in learning to carry but also solves the difficulty in placing partial products incorrectly and errors with zeros in multiplier or multiplicand. This form, which was introduced in the 15th century for purposes of recording products, is of interest to children because of its novelty and historical significance.

However, whether the child gets the final answer correct depends on his/her ability to carry out the required additions accurately. Let us then see how we can make our children add accurately.

I would like here to give you a brief reference to the findings of research on methods in addition. Knowledge of these findings may remove some obstacles in understanding how to carry out additions for some children.

There are two methods to carry out addition. In the first method we can add upwards, and in the second we can add downwards. Which of these is suitable for children? The Scottish Council for Research in Education found very small differences between children taught to add upwards and those taught to add downwards¹. American research has shown that upward addition leads to slightly greater efficiency². They therefore suggested that the child should be first taught upward addition and then should be encouraged to use downward addition as a check.

We should always keep in mind that backwardness is in part due to the practice of allowing children to begin a new process or step before they have thoroughly mastered the preceding ones. It is unsound to introduce a child to the difficulties of ‘carrying’ in addition before s/he has attained a high degree of efficiency in the basic addition facts involving numbers less than 10. These facts are given here for ready reference.

Although for experienced children 9 + 7 is the same as 7 + 9 it is not so with beginners. It is found that a child who knows 9 + 7 = 16 may not necessarily give the correct answer to 7 + 9. Hence, all these additions need supervised practice by the child.

Once the mastery of basic addition is achieved the child could be given practice in higher decade addition. Sometimes it is observed that a child knows 2 + 7 but does not add correctly 52 + 7 or gives the correct answer to 6 + 9 but errs in 36 + 9. Here we start wondering how far there is transfer from simple combinations to the higher decade combinations. In other words, if children know all the basic combinations under 10, are they likely to succeed with the same combinations in numbers over 10?

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