Elementary mathematics instruction strives for both meaningful understanding and the mastery of algorithms. One variable relating to the mastery of algorithms is a proficiency in facts. Thornton (1978) evaluated strategies for fact memorization with second and fourth graders. Her addition sequence included teaching doubles (e.g., 4 + 4, 5 + 5), doubles plus 1, sharing numbers to make a double (e.g., 6 + 8, 9 + 7), addition of 9 (i.e., 1 less than adding 10), and the remaining facts. Extending Thornton's work, two studies explored the following question: Are strategies effective for teaching easier facts (most having addends of 1, 2, and 3)? The studies investigated a strategy for teaching easy facts to younger students who had not yet been taught addition facts. The strategy was based on the counting relationship between successive facts, indicated by the circled numerals that appear in the counting order.
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Carnine et al. (1981) studied this question.