The below quotes, from the book “The Number Sense” by neuroscientist Stanislas Dehaene, suggest that it is possible to improve various aspects of mental calculation by simply learning shorter names for numbers.
memory span in China soars to about nine digits, while it averages only seven in English. Why this discrepancy? Are speakers of Chinese more intelligent? Probably not, but their number words happen to be shorter. When we try to remember a list of digits, we generally store it using a verbal memory loop.
This memory can hold data only for about two seconds, forcing us to rehearse the words in order to refresh them. Our memory span is thus determined by how many number words we can repeat in less than two seconds. Those of us who recite faster have a better memory. Chinese number words are remarkably brief. Most of them can be uttered in less than one-quarter of a second (for instance, 4 is “sì” and 7 “qī”). Their English equivalents—“four,” “seven”—are longer: pronouncing them takes about one-third of a second. The memory gap between English and Chinese apparently is entirely due to this difference in length.
there is a reproducible correlation between the time required to pronounce numbers in a given language and the memory span of its speakers. In this domain, the prize for efficacy goes to the Cantonese dialect of Chinese, whose brevity grants residents of Hong Kong a rocketing memory span of about 10 digits.
Number names also play a critical role in counting and calculating, and here again bad marks can be attributed to languages with the longest number names. For instance, it takes a Welsh pupil one second and a half more than an English pupil, on average, to compute 134 + 88. For equal age and education, this difference seems solely due to the time taken to pronounce the problem and the intermediate results: Welsh numerals happen to be considerably longer than the English. English is certainly not the optimum, though, because several experiments have shown that Japanese and Chinese children calculate much faster than their American peers.
In a fascinating experiment, Kevin Miller and his colleagues asked matched groups
of American and Chinese children to recite the counting sequence. Startlingly, the
linguistic difference caused American children to lag as much as one year behind their Chinese peers. When they were four, Chinese children already counted up to 40 on average. At the same age, American children painfully counted up to 15. It took them one year to catch up and reach 40 or 50. They were not just globally slower than the Chinese; up to the number 12, both groups stood on an equal footing. But when they reached the special numbers “13” and “14,” American children suddenly stumbled, while the Chinese, helped by the unfailing regularity of the language, moved right along with much less trouble
The influence of numeration systems carries through into subsequent school years. The organization of spoken Chinese numerals directly parallels the structure of written Arabic numerals. Hence, Chinese children experience much less difficulty than their American counterparts in learning the principles of place-value notation in base ten. When asked to form number 25 using some unit cubes and some bars of 10, Chinese schoolboys readily select two bars of 10 and five units, suggesting that they understand base ten. At a matched age, American children behave differently. Most of them laboriously count twenty-five units, thus failing to take advantage of the shortcut provided by the groups of 10. Worse yet, if one provides them with a bar comprising twenty units, they use it more frequently than two bars of ten. Thus they seem to attend to the surface form of the word “twenty-five,” while the Chinese already master their deeper base-10 structure. Base 10 is a transparent concept in Asian languages, but is a real headache for Western children.
These experimental findings impose a strong conclusion: Western numeration systems are inferior to Asian languages in many respects—they are harder to keep in short-term memory, slow down calculation, and make the acquisition of counting and of base ten more difficult.
At the beginning of the twentieth century, the Welsh willingly relinquished their old numeration system, which was more complex even than present-day French, and selected instead a simplified notation quite similar to Chinese. Unfortunately,
Welsh changed only to fall prey to another error: The new Welsh number words, while grammatically regular and thus easy to learn, are so long that memory suffers! Psychological experiments would probably dictate the adoption of a well-tested numeration system such as Mandarin Chinese, but national interests make this a rather distant and unlikely prospect.
Taking a step back, this also suggests that there are a number of low-hanging fruits in this area. It’s likely that a systematic analysis of cognitive processes followed by training, perhaps on specialized software, would improve cognitive abilities.
The below quotes, from the book “The Number Sense” by neuroscientist Stanislas Dehaene, suggest that it is possible to improve various aspects of mental calculation by simply learning shorter names for numbers.
Taking a step back, this also suggests that there are a number of low-hanging fruits in this area. It’s likely that a systematic analysis of cognitive processes followed by training, perhaps on specialized software, would improve cognitive abilities.