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Reasoning Mathematical Ability Retrieving arithmetic facts from longterm memory Memory span Mental calculation ability Psychometric Cognitive …….. 12 Numerical Facility A battery of Paperandpencil Test: ? numerical facility, ? perceptual speed (., speed of encoding, or reading symbols such as numbers ? spatial ability Computeradministered arithmetic test: ? number encoding (reading numbers off the puter screen ? retrieving arithmetic facts from longterm memory, ? carrying (or trading) Time required for each ponent process is recorded 13 Relationship between Numerical Facility and Cognitive Abilities ? The faster arithmetic facts could be retrieved from longterm memory and the faster the carry (or trade) operation could be executed, the better the performance on the paperand pencil numerical facility tests. ? Speed of executing these arithmetical processes was not directly related to performance on the perceptual speed and spatial tests. 14 Implications ? Basic arithmetic skills underlying individual differences (agreed with psychometricians) ? numerical facility is arithmetical in nature. 15 Other Studies (Geary amp。 Brown, 1991, …) strategychoice: ability to use the right strategy