The Development of Network Retrieval in Addition.

Simple mental addition was examined in grade school children (grades 1 and 5) and college students. Reaction time performance varied with task (verbal production vs. verification), problem size, and age. Priming manipulations also permitted a developmental evaluation of the Ashcraft network-retrieval model of mental arithmetic. Note. Experiment 1 formed the basis of an M.A. thesis by Bennett A. Fierman, Department of Psychology, Cleveland State University, August, 1980. We wish to thank the principal and teachers of Boulevard School, Cleveland Heights, Ohio, for their cooperation in this project. U S DEPARTMENT OF HEALTH. EDUCATION t WELFARE NATIONAL INSTITUTE OF EDUCATION THIS DOCUMENT HAS BEEN REPRO. oucEo EXACTLY AS RECEIVED FROM THE PERSON OR ORGANIZATION ORIGIN. AT1NG IT POINTS OF VIEW OR OPINIONS STATED DO NOT NECESSARILY REPRE SENT OFFICIAL NATIONAL INSTITUTE OF EDUCATION POSITION OR POLICY "PERMISSION TO REPRODUCE THIS MATERIAL HAS BEEN GRANTED BY gar k Ashrsd-fTO THE EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC)." The Development of Network Retrieval in Addition For the past several years, we have been conducting research on the structures and processes involved in simple mental arithmetic. Our paper at last year's Psychonomics convention, entitled "Network Representations of Mental Arithmetic", summarized much of this research, and as the title implies, suggested that mental arithmetic can be fruitfully investigated as an instance of retrieval from organized, long-term memory. To quote from our conclusion, "Taken as a whole, these results suggest that mental arithmetic is a memory retrieval phenomenon, one which takes time, one which develops with the experiences of elementary school, and one which can be understood in general as retrieval from organized network representations." (Ashcraft, Stazyk, & Fierman, Note 1). Today's presentation focuses on the development of this memory retrieval .phenomenon in children, and does so in the context of ordinary simple addition. We are interested in addition here for a variety of reasons: It is the first formal mathematics topic encountered in most school curricula; it is the most heavily investigated operation in psychological studies, and it has given rise to the major models of arithmetic performance. In general, the research we are presenting today indicates that two models are necessary to describe the development of addition performance, a simple counting model for children in the early stag-7, of mastery, then the network retrieval model from about the fourth or filth grade on. We also will present evidence which indicates that a standard true/false verification task yields relatively more analytic results than the seemingly more natural task of verbal production. The most basic result in studies of mental arithmetic is called the problem size effectthere is a regular increase in reaction time(RT) as the numerical size of the problem increases. In fact, we know of no study which fails to demonstrate this effect in one fashion or another. The form