The performance of second year primary children on missing addend sentences

This study examined the accuracy, solution strategy use, and level of response use of second year children when solving missing addend problems at four levels of difficulty and in two placeholder positions. The relationship between these aspects of Missing Addend performance and performance on a measure of Class Inclusion ability, was then examined. Subjects of the study were 40 year two students from an urban community in British Columbia, Canada. A Missing Addend Test and a Class Inclusion Test were administered individually to all subjects. The level of difficulty of the Missing Addend Test items (as defined by the magnitude of the constants) affected accuracy. Process errors were more common than conceptual errors as the difficulty of the item increased. The level of difficulty of the item also affected the child's level of response. Children tended to use more externalized processes and concrete aids as the difficulty increased. The level of difficulty did not, however, appear to affect strategy choice to the same degree. Placeholder position was found to have little or no effect on children's accuracy, strategy choice, or level of response use. Children interpreted the missing addend as a situation requiring an incrementing, or additive process in 68% of the cases. In 9% of the cases they used decrementing or subtractive processes. Children used recall of basic fact combinations to solve 9% of the items. Conceptual misinterpretations of the number sentence, as indicated by the use of an incorrect sentence transformation, occurred in 8% of the examples. Children omitted items or used unidentifiable processes in 6% of the examples. Of the 248 items where an additive or subtractive process was used, by far the preferred process was a counting procedure. Two counting procedures were particularly popular: Counting-All and Counting-On. Other identified strategies were Semi-Guesses, Substitution procedures, and procedures involving Associative reasoning. Concrete materials were used in 45% of the examples, and usually in association with Semi-Guess, Substitution, and Counting-All strategies. Internalized reasoning procedures were used in 37% of the examples, and usually in association with the Recall and Associative strategies. Fingers were used as aids for 17% of the examples, and were used almost exclusively with the Counting-On strategy. It was concluded that the use of fingers provided a valuable transition between external and internalized solution procedures. It was also concluded that the ability to count-on was key to the development of more sophisticated solution processes. Class Inclusion performance was found to be positively related (p<.05) to Missing Addend performance. Class Inclusion performance was significantly related to the use of two solution strategies. The use of Recall was positively related (p<.01) and the use of an Incorrect Transformation was negatively related (p<.01). Class Inclusion performance was not related to the use of any of the identified levels of response.

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