Abacus Skill In Chinese Children: Imagery In Mental Calculation.

This research is an investigation of the phenomenon of abacus-based mental addition among 11-year-old Chinese children. The children, all trained in abacus calculation, report doing mental calculation by visualizing a mental image of the abacus, and by moving beads on this mental abacus as they would on a real abacus. Studying this phenomenon enables one to investigate the nature and function of mental imagery, and the mechanisms involved in acquiring images. This study had two specific purposes: first, to gather basic information about the abacus and children's skill in both abacus and mental abacus calculation; second, to gather evidence that might clarify the nature of the mental representation involved in mental abacus calculation. Three groups of four children each were studied, representing expert, intermediate, and novice abacus operators. Response times and errors were recorded for both abacus and mental addition of a large and varied set of problems. Four American adults also performed mental calculations on the same set of problems. The Chinese children also performed a task requiring them, both mentally and using the abacus, to answer questions about intermediate states in abacus addition problems. The abacus experts were found to be amazingly fast at both abacus and mental calculation, and faster when using mental solution than when using the physical abacus. Response times for both abacus and mental addition were a linear function of the total number of digits in the problem, calculated as number of digits (per addend) times number of addends. With total digits held constant, number of digits per addend was positively related to Chinese mental calculation time, but not abacus or American mental calculation times. Several pieces of evidence converged in showing the mental abacus to be an analog representation, isomorphic with the structure and function of the physical abacus. Evidence supporting this conclusion were the facts that subjects mentally were able to answer questions about intermediate states unique to abacus calculation, and errors in mental calculation showed that Chinese, but not Americans, made errors predicted from analysis of abacus operation.PhDDevelopmental psychologyPsychologyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/127633/2/8304606.pd