Journal of Experimental Psychology: General 1991, VoL 120. No. 1,20-33 Copyright l99lbytheAmerican Psychological Association. Inc. 0096-3445/91/43.00 Lifetime Maintenance of High School Mathematics Content Harry P. Bahrick and Lynda K. Hall Ohio Wesleyan University An analysis of life span memory identifies those variables that affect losses in recall and recognition of the content of high school algebra and geometry courses. Even in the absence of further rehearsal activities, individuals who take college-level mathematics courses at or above the level of calculus have minimal losses of high school algebra for half a century. Individuals who performed equally well in the high school course but took no college mathematics courses reduce performance to near chance levels during the same period. In contrast, the best predictors of test performance (e.g., Scholastic Aptitude Test scores and grades) have trivial effects on the rate of performance decline. Pedagogical implications for life span maintenance of knowledge are derived and discussed. This research explores life span retention of content ac- quired in high school mathematics courses by 1,726 individ- uals. The investigation also illustrates the use of multiple regression techniques to examine individual-difference vari- ables in life span memory. Background The present study is the fourth in a series concerned with maintenance of knowledge throughout the life span. The previous investigations (Bahrick, 1983a, 1984; Bahrick, Bah- rick, & Wittlinger, 1975) identified basic issues for research concerned with maintenance of knowledge that are summa- rized here because they provide background and focus for the current investigation. Most knowledge remains accessible only if it is periodically rehearsed or used. Some aspects of knowledge appear to be so well learned, however, that access is maintained for decades or for the entire life span without further rehearsals. Thus, the rules of simple arithmetic, the meanings of common words in one's native language, and so on, may never be forgotten even in the absence of further rehearsals. Such permanent storage is difficult to document because most overlearned knowledge continues to be in frequent use. However, our. prior findings document life span retention in the absence of This investigation was supported by National Science Foundation Grant BNS-8417788. We thank Neal Johnson for allowing us to use space in his laboratory; Frederick Paul and Gretchen Rigol for making copies of the New York State Regents Examination available; Fritz Drasgow, Robert MacCallum, Tom Nelson, Carolyn Patterson, Gerald Rising, Earl Tharp, and Larry Wells for their expert advice; the participating schools and church and service organizations for helping with subject recruitment; the 1,946 participants for taking our tests; and the following students for their help in the collection and analysis of data: Shirley Bodi, Tammy Daily, Jill Daly, John Dunlosky, Diane Gatton, Irene Jenkins, Lisa Vandegrift, and Cara Wellman. Correspondence concerning this article should be addressed to Harry P. Bahrick, Ohio Wesleyan University, Delaware, Ohio 43015. rehearsals for the recognition of names and faces of high school classmates learned incidentally (Bahrick, Bahrick, & Wittlinger, 1975) and for a portion of the more formal knowl- edge acquired in foreign language classes (Bahrick, 1984). The content in these investigations was acquired over several years. In contrast, similar material acquired over shorter time pe- riods exhibits the continuous loss functions traditionally re- ported for episodic content (Bahrick, 1983b; Squire, 1989). Our goal in the present research was to explore the conditions of acquisition and the types of content of high school math- ematics courses that facilitate enduring knowledge. Cross-sectional investigations using multiple regression analysis have made it possible to study life span retention of naturalistically acquired semantic memory content. In such investigations, retention of content is tested for a large number of individuals who vary in the time elapsed since the content was acquired. Information regarding the length of the reten- tion interval, the degree of original knowledge, and the amount and type of rehearsals during the retention interval are obtained from various sources, including archival records and questionnaires administered to the participants. These data are used as predictor variables and the regression analysis yields equations that predict performance on the memory test. If the retention interval is used as one of the predictor variables, evaluating the regression equation for successive time intervals yields predicted retention functions. The mag- nitude of the multiple correlation indicates how adequately the function accounts for the observed memory data. We investigated life span retention of the content of high school algebra and plane geometry for the following reasons: (a) to obtain genera] retention functions for this content as normative information, (b) to determine the effect of a variety of individual-difference variables (pertaining to constitutional factors or to conditions of acquisition or rehearsal) on the rate of performance decline over a half century, and (c) to establish differential rates of loss for various aspects of content. Differ- ential loss rates associated with either individual-difference variables or content variables have pedagogical implications for the identification of relative strengths and weaknesses in curricula, and relevant findings may provide a basis for in- creasing the effectiveness of education. 20 This document is copyrighted by the American Psychological Association or one of its allied publishers. 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