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AutomaticityWhy Automaticity in Math Facts?An essential component of automaticity with math facts is that the answer must come by means of direct retrieval, rather than following a procedure. This is tantamount to the common observation that students who "count on their fingers" have not mastered the facts. Why is "counting on your fingers" inadequate? Why isn't procedural knowledge or counting a satisfactory end point? The notion is that the mental effort involved in figuring our facts tends to disrupt thinking about the problems in which the facts are being used. Some of the argument of this information-processing dilemma was developed by analogy to reading, where difficulty with the process of simply decoding the words has the effect of disrupting comprehension of the message. Gersten and Chard illuminated the analogy between reading and math rather explicitly: "Researchers explored the devastating effects of the lack of automaticity in several ways. Essentially they argued that the human mind has a limited capacity to process information, and if too much energy goes into figuring out what 9 plus 8 equals, little is left over to understand the concepts underlying multi-digit subtraction, long division, or complex multiplication (1999, p.21)."...Practice is required to develop automaticity with math facts. "The importance of drill on components [such as math facts] is that the drilled material may become sufficiently over-learned to free up cognitive resources and attention. These cognitive resources may then be allocated to other aspects of performance, such as more complex operations like carrying and borrowing, and to self-monitoring and control (Goldman & Pellegrino, 1986. 134)." |
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