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Numbers and Numerosity

This project examines how signs for numbers emerged in Nicaraguan Sign Language, and how learning number language might help individuals develop an understanding of core number concepts. Computing exact quantities is an essential skill in modern society. In cultures around the world, adults constantly count objects, mentally adding and subtracting with little effort. Nevertheless, in typical development it takes years for children to become competent number users. Exactly what capacities are necessary to track and reproduce exact quantities? In children, a memorized count list (one, two, three…) appears to

play an essential role (Fuson, 1988; Le Corre & Carey, 2007; Wynn, 1990, 1992). But what if you never learned a count list? Is experience with cultural uses of number, such as money, or games with dice, sufficient to lay the foundations for numerical cognition?

      Previous work with speakers of languages that lack number words involved participants only from non-numerate cultures. Deaf Nicaraguan adults all live in a richly numerate culture, but vary with respect to whether number signs were available when they were children, allowing us to tease apart the contribution of these two factors.

The emergence of number signs

We have discovered that over the past several decades, a variety of number signs emerged in NSL, eventually converging on the conventionalized set in use today. Before 1990, there was high variability in the handshapes used. Number signs tended to be highly iconic, with a one-to-one mapping between the number of fingers extended and the value represented. (Under this system, the value six is represented by extending six fingers, the value ten by extending all ten fingers, and the value twenty by signing ten twice.)

      In the early 1990s, number signs underwent rapid standardization, and became one-handed. The new versions are quicker, smaller, and less iconic. Some parts of the original forms are evident in the new signs, but there is no longer a one-to-one match between fingers and values. (Under this system, six is produced with a rotation of the fist with the

thumb extended; ten, with a closing movement of the thumb and forefinger; and twenty, with a closing of the thumb against the first two fingers.)

      This history has produced a community with a range of counting systems and counting competence. Whether and how individuals count depends on their age. Today’s adolescents learned to count in childhood, using the new one-handed system. Younger adults learned the iconic, two-handed system in childhood, and learned the one-handed system later in life. Older adults, who had already come of age by the late 1970s, learned neither system as children. Some of these individuals eventually learned to count, and some never learned at all. However, all were immersed in the same numerate culture throughout their lives.

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Developing an understanding of number

So, how much did number language guide the development of number concepts? We found that adults who lack a recitable list of number words are unable to accurately quantify stimuli presented to them in a sequence. Evidently, living in a numerate culture is not enough to make an individual numerate. A memorized sequence of number symbols is required, though we found that even an unconventionalized or highly iconic system will do. Even those who learned number signs in adulthood can succeed at tracking quantities, although they are more error-prone than those who learned a counting sequence in childhood. With a lifetime of numerate culture as support, one can learn to count late in life.

We were surprised to discover that some adults without a recitable count list can assess the exact value of large sets, in certain situations. This finding has implications for aspects of number understanding that are thought to build on counting routines, such as the concepts of unique successors, stable ordering, and conservation of number (Le Corre & Carey, 2007). It would be worthwhile to explore whether noncounters are able to develop these other concepts, perhaps by alternative routes. The memorized, mentally recitable count sequence, that for most of us served as the gateway to an understanding of number, may not be the only way to get there.

Project Publications

Flaherty, M. and A. Senghas (2011). Numerosity and Number Signs in Deaf Nicaraguan Adults. Cognition, 121, 427-436.

Senghas, A., and S. Katseff (2008). Competing forces behind the form of Nicaraguan Sign Language number signs. Delivered at the SignTyp Conference, University of Connecticut, Storrs, CT, June 26-28, 2008.

Katseff, S., and A. Senghas (2004). Effects of acquisition on the Nicaraguan Sign Language number lexicon. Delivered at the Twenty-ninth Annual Boston University Conference on Language Development (BUCLD29), Boston, MA, November, 2004.