Language & Mathematics 2

Lack of logic in Number Names

By the time we become adults, we have heard number name sequences thousands of times and have become very familiar with them. We become so familiar that we do not notice the lack of logic in the number name sequences in many languages. This certainly affects children who are learning these number names for the first time.

English Number Names

While learning number names in English, students always get stuck while learning number names after Ten up to Nineteen, especially Eleven and Twelve. However, numbers beyond Twenty follow a logic which is very apparent. Why is that?

Numbers from twenty upwards, follow the logic of the decimal system. Twenty to Ninety are the names of bundles, from 2 up to 9 bundles. They are combined with names for sticks which are one to nine. To an extent, numbers Thirteen to Nineteen also seem to have a logic of calling “ten” as “teen”. This logic is completely absent in Eleven and Twelve.

It is possibly because these number names have been used to denote these quantities, before the decimal system was formalised. Hence these have stubbornly remained a part of daily language of quantities even though they do not follow the strict logic of the numeral form of numbers.

Number Names in Indian Languages

Situation is some Indian languages is worse. Numbers say Thirty One, Thirty Two etc will follow a logical pattern but suddenly 39 would be called "One Less Than Forty". The reason for this anomaly is not very clear.

In contrast, number names in Sanskrit, Tamil follow the pattern Ten One, Ten Two etc. This is an area of impact of culture on number names needs more research!

However even Tamil has an anomaly when it comes to numbers where 9 is involved.

9 - One Padhu - meaning one less than ten

90 - Thon Nooru - ten less than hundred

900 - Thol aayiram - hundred less than thousand.

Another issue in both English & Indian languages is that the number names are long which may make learning & remembering them more difficult. In contrast number names in Chinese are very short.

Impact on Learning Math

Research seems to indicate that because of this lack of logic & length, students take a considerably more time to fully internalise the “sound” form of the word with its “numeral” form and hence its “magnitude”. Malcolm Gladwell in his book “Outliers” has spent an entire chapter discussion why Chinese students may be doing better in Math compared to their US counterparts, basically because the Chinese number words are more logical and shorter.

One easy solution in English medium schools would be to call numbers from 11 to 19 as Onty One, Onty Two … up to Only Nine in the Primary School, or simply One one, One Two… to One Nine, and switch over to standard terminology in Middle School once students have good understanding of numbers. Of course, the greatest opposition to this move would be from parents!

Names of Large Numbers

Sometimes, the separate place values are not “spoken”. In 346 which is 3 Hundred Forty Five, each place value is distinct. But 56432 is called 56 Thousand ….. The Ten Thousand place is not very clear as compared to the Hundred. This creates problems in doing long division, particularly in problems where the quotient ends up with 0 in the thousandths place.