Korean children's understanding of multidigit addition and subtraction

This study examined Korean second and third graders' understanding of multidigit addition and subtraction and particularly their ability to explain the trading required when a column sum of the addends is 10 or more. 72 middle-class second- and third-grade children (aged 7-4 to 8-4 and 8-4 to 9-4, respectively, at the time of the midyear interview) attending 2 schools in Seoul, Korea, were asked to solve 2- and 3-digit problems given in vertical form and then were individually interviewed about their conceptual understanding of such problems. Even though the second graders had not yet received instruction in school on 3-digit problems, children in both grades were quite accurate solvers of the multidigit addition and subtraction problems and demonstrated knowledge of the place-value names "ten" and "hundred." Every child also correctly identified the trade between the ones and tens columns as a traded ten. Most of the third graders identified the 1 written in the hundreds column on the addition problems as a hundred, but half of the second graders identified it as a ten. Most of the third graders also gave correct descriptions of the trading (regrouping, borrowing) required by a 3-digit subtraction problem with 2 zeros in the top number. Children used 3 different conceptual structures in discussing the already-solved problems: a multiunit quantities structure, a regular one/ten trades structure, and a combination of these two. These results are compared to the literature on the performance and conceptual structures of children in the United States.

Characteristics of liquid crystal devices with improved response times

The response time and contrast are reported for a liquid crystal (LC) cell operated in the transmission mode. The cell yielded improved response times (e.g., of the order of 0.15 msec) that result from several features: (1) the LC material is a mixture of cholesteryl nonanoate, p-cyanophenyl p-butylbenzoate, and p-cyanophenyl p-heptylbenzoate in the weight ratio x:100:230, respectively; and (2) the cell is operated with the signal drive voltage superimposed on a low-frequency square-wave pedestal voltage. The influence of electrode surface treatment is discussed, and it is postulated that the rapid response time results from only the thin layer of LC material adjacent to the treated electrode surface.