A new mathematical model

Aug 3, 2007 08:14 GMT  ·  By

"Oh, my God, I swear he has just said 'daddy'. He is definitely so smart!"

Toddlers can impress you with learning 10 new words daily, but it appears to be quite simple for them, who must handle this vocabulary milestone to eventually reach the adult vocabulary.

When being 18 months old, human offspring experience a "vocabulary explosion" involving a sudden learning of new words, leaving their parents astonished by the speed of the process. Scientists have previously imagined complex mechanisms controlling this voracious rhythm of word-learning.

"The field of developmental psychology and language development has always assumed that something happens at that point to account for this word spurt: kids discover things have names, they switch to using more efficient mechanisms and they use their first words to help discover new ones. Many such mechanisms have been proposed. But these mechanisms aren't necessary," said author Bob McMurray of the University of Iowa, who developed a mathematical model for describing the vocabulary explosion.

"While children may engage those types of specialized mechanisms to help them learn new words, computational simulations suggest that simpler mechanisms-such as word repetition and learning multiple words at once-can explain the vocabulary explosion." said McMurray.

"Children are going to get that word spurt guaranteed, mathematically, as long as a couple of conditions hold. They have to be learning more than one word at a time, and they must be learning a greater number of difficult or moderate words than easy words. Using computer simulations and mathematical analysis, I found that if these two conditions are true, you always get a vocabulary explosion." he added.

The researcher compared the word-learning process with filling up jars, in a situation in which jar size expands with the difficulty of the word. Previously, it had been suggested that when a child learned a word, it was easier for him/her to learn more words, like shrinking the jar size. But the new model shows that even if jar size is increased, the word spurt still takes place.

The secret is in a relative number of small jars to big jars (easy words to difficult words): difficult words must dominate in number the easy words for a vocabulary explosion to take place.

"Clearly, the specialized mechanisms aren't necessary. Our general abilities can take us a lot farther than we thought," said McMurray.