Cognitive Skill Learning

Younger and older adults solved novel arithmetic problems and reported the strategies used for obtaining solutions. Age deficits were demonstrated in the latencies for computing and retrieving solutions and in the shift from computation to retrieval. Rates of improvement within age groups were parallel for computations and retrievals, suggesting a single, age-attenuated mechanism that affects practice-related speedup. The age-related delay in strategy shift suggests either reluctance to use retrieval or an associative memory deficit. Experiment 1 showed that skill acquisition was unaffected by the presence and frequency of postresponse strategy probes for both age groups. Experiment 2 showed that pretraining item-learning operations facilitated subsequent item learning and that pretraining either item-learning operations or the algorithm did not alter the age trends. Article: The learning of cognitive skills is fundamental to effective functioning at any age. Compared with younger adults, older adults acquire new skills more slowly and usually do not reach the same asymptotic level of skilled performance as younger adults (e.g., Charness & Campbell, 1988; Dunlosky & Salthouse, 1996; Harrington & Haaland, 1992; Hashtroudi, Chrosniak, & Schwartz, 1991; Hoyer, Cerella, & Onyper, 2003; Jenkins & Hoyer, 2000; Rogers, Hertzog, & Fisk, 2000; Salthouse, 1994; Salthouse & Somberg, 1982; Siegler & Lemaire, 1997; Strayer & Kramer, 1994; Touron & Hertzog, 2004a, 2004b; Touron, Hoyer, & Cerella, 2001). That there is an age-related deficit in skill learning has been known for a long time (Bryan & Harter, 1897; Miles, 1933; Thorndike, Bregman, Tilton, & Woodyard, 1928). In the study by Thorndike et al., for example, pronounced age differences were observed in training right-handed younger and older adults to write left-handed. Studies have advanced several kinds of explanations for age-related deficits in skill learning, including relatively inefficient learning strategies and response biases on the part of older adults (e.g., Rogers & Gilbert, 1997; Rogers et al., 2000; Strayer & Kramer, 1994; Touron & Hertzog, 2004a, 2004b), age-related deficits in the associative aspects of learning and retrieval for repeated problems (e.g., Hoyer et al., 2003; Jenkins & Hoyer, 2000; Touron et al., 2001), and the pervasive influence of age-related slowing on some or all of the component processes involved (e.g., Brigman & Cherry, 2002; Dunlosky & Salthouse, 1996; Fisk & Warr, 1998; Salthouse, 1994; Verhaeghen & Marcoen, 1994). Empirical work to date has not convincingly demonstrated that just one of these factors is largely responsible for age-related skill-learning deficits. Indeed, current theories of skill acquisition point to both strategy factors, such as qualitative differences and practicerelated shifts in how solutions are obtained and practice-related improvements in processing efficiency (e.g., Anderson, 1993; Gupta & Cohen, 2002; Haider & Frensch, 2002; Logan, 1988; Rickard, 1997). It is quite possible that strategy inefficiencies, process-general slowing, and associative deficits all contribute to the extent to which older adults show deficits in skill-acquisition tasks. We offer a precise depiction of age differences in the component processes of skill acquisition, allowing for a clearer consideration of prospective causal mechanisms. Aging and Strategies in Skill Acquisition Skilled performance in natural settings is typically memory based, relying on the individual's adoption and adaptive use of recurring instances that comprise the skill domain (e.g., Bosman & Charness, 1996; Ericsson & Charness, 1994; Hoyer & Ingolfsdottir, 2003). Only for relatively novel problems is it necessary to apply the computations or rules that govern the skill domain to the problem at hand. Studies of the acquisition of cognitive skills in the laboratory have uncovered the same dynamics (e.g., Logan, 1988; Rickard, 1997; Schunn, Reder, Nhouyvanisvong, Richards, & Stroffolino, 1997). Early in training, computationally based responding is slow but applies successfully to the entire problem domain; late in training, memory-based responding is fast but is limited to the training set. A shift in the way solutions are obtained, from computationally based responses to memory-based responses, occurs with repetitions (e.g., see Haider & Frensch, 2002; Logan, 19880, 19920; Rickard, 1997, 2004). We apply the term strategy to refer to the method used for obtaining solutions in skill-learning tasks in which different methods are possible. It is usually, if not always, the case that different strategies can be used in acquiring and executing cognitive skills, and there is now a substantial amount of evidence to indicate that the strategies used by older adults in a variety of learning situations are less optimal than those used by younger adults (e.g., Dunlosky & Hertzog, 2001; Hulicka & Grossman, 1967; Rogers & Gilbert, 1997; Rogers et al., 2000; Touron & Hertzog, 2004a, 2004b). The findings of the studies by Rogers et al. (2000) and Rogers and Gilbert (1997) suggested that age-related differences in skill acquisition are exacerbated by the use of nonoptimal strategies by older adults. For example, Rogers et al. (2000) compared the performance of young and older adults in a task in which participants judge whether a centrally presented target noun pair is matched in a key presenting the full set of consistent noun pairings at the top of the screen. As noun pairs are repeated, responses may be made either by scanning the key or by retrieving the solution from memory. At the end of training, each participant's strategy performance was classified as being primarily based on either scanning or retrieval by means of individual response time (RT) distributions. Rogers et al. (2000) showed that the age groups were not different in terms of absolute performance and ability-performance relations when age group comparisons were made within strategy classifications. In an earlier study using the same noun-pair task and classification system, Rogers and Gilbert (1997) reported that age-related differences in performance (i.e., RT improvements) were attributable to strategy differences in that older adults were less likely to use retrieval as the method for making responses. Rogers and Gilbert also found that use of the more efficient strategy, retrieval, could be increased in older adults by making the benefits of retrieval more conspicuous. The advantage of using retrieval instead of scanning was made salient by presenting noun pairs without the look-up key on some trials. Touron and Hertzog (2004a, 2004b) have reported that there is a greater reluctance on the part of older adults to shift from a scanning strategy to retrieval of noun pairs during the course of skill learning, even when they have sufficient knowledge of the noun-pair associations to do so. In the experiments reported here, we used relatively difficult pseudoarithmetic computation instead of a scanning versus retrieval task because of the built-in incentive to retrieve instead of to perform a calculation. In this task, the demands of computation could provide an even stronger incentive for the old than for the young. In skill-learning tasks that contain repeated problems, improvements in performance with practice can be tied to at least three types of processing operations: (a) computing efficiency in terms of speed and accuracy; (b) retrieval speed and accuracy; and (c) a repetitions-based shift from computing to retrieving. Computing is required when individuals apply a rule or algorithm to obtain solutions to novel or rare problems. An agerelated deficit in the efficiency of computing could contribute to impaired performance. With repeated presentations of the same problem, solutions can be retrieved from memory in lieu of computation. For example, adults presumably possess a knowledge base of numerical facts that enables them to retrieve solutions from memory (e.g., 12 + 12 = 24) instead of having to carry out a counting algorithm. The shift to retrieval and the speed and accuracy of retrieval could also be sources of age-related deficits in skill learning. One method for directly examining practice-related changes in the components and strategies used in skill learning involves the use of postresponse reports by participants of the strategies used for obtaining solutions (Compton & Logan, 1991; Delaney, Reder, Staszewski, & Ritter, 1998; Rickard, 1997, 2004; Schunn et al., 1997). In one of the first studies using this method, Compton and Logan (1991) had participants make verification responses to repeated alphabet arithmetic equations of the form H + 3 = K; in this case, the answer is true because K is three steps away from H in the alphabet. After one sixth of the trials, participants were instructed to report whether the answer to the problem just presented was obtained by counting or by remembering the answer without counting (as problems were repeated). Compton and Logan provided evidence to suggest that there was a transition from counting to memory-based processing. To assess the validity of the probe procedure, an RT estimation procedure was used to show that the retrieval responses were represented in the same proportions on probed and nonprobed trials. In Rickard (1997), participants were taught to solve pseudoarithmetic problems that contained a novel synthetic operator, #. Participants reported whether they used the taught algorithm to obtain the answer, retrieved the answer directly from memory, or used some other strategy that did not correspond to either computation or retrieval. Strategy probes were administered after the participants' responses on one third of the trials, and responses to the probes allowed for the extraction of separate curves for computes, retrieves, and the shift from algorithm computation to retrieval. Hoyer et al. (2003) further validated the strategy probe methodology by demonstrating that reported computations for an alphabet-arithmetic task increased with addend size, whereas reported retrieval responses did not vary by addend. Aging, Memory, and Associative Deficits in Skill Acquisition As mentioned, the prevailing theories of cognitive skill acquisition call attention to improvements associated with task strategies and improvements in the accuracy and speed of carrying out the requisite learning processes (e.g., Anderson, 1993; Gupta & Cohen, 2002; Logan, 1988; Rickard, 1997). It is well known that there are large age-related deficits in the efficiency of many types of learning, including associative learning (e.g., Salthouse, 1994; Salthouse, Kausler, & Saults, 1988; for a comprehensive review, see Kausler, 1994). Further, there are numerous reports of age-related differences in skill-learning tasks, which might be partially attributable to agerelated deficits in associative learning (e.g., Hoyer et al., 2003; Jenkins & Hoyer, 2000; Rogers & Gilbert, 1997; Rogers et al., 2000; Touron & Hertzog, 2004a, 2004b; Touron et al., 2001). Jenkins and Hoyer (2000) showed that the number of repetitions needed to reach automaticity in an enumeration task with repeated configurations was greater for older adults than for younger adults. The findings suggested an age-related deficit in associating particular configurations with particular digits and in shifting from a counting strategy to retrieving instances. In the study by Touron et al. (2001), younger adults and older adults were given training with one set of alphabet arithmetic problems and then were given training on a second set of different problems that involved using the same algorithm or memory retrieval. Analyses of the parameters of power function fits by age and problem set revealed age deficits in asymptotes and learning rates for both problem sets. These age deficits were found in the acquisition of both problem sets; in addition, the age difference in the learning rates was larger for Problem Set 2 than for Problem Set 1, suggesting that older adults derived less benefit from practice with rule use or from practice in building associations between problems and their solutions in Set 1 training. Without strategy probes, it was not possible to evaluate separately the effects of practice on item retrieval and computational speedup for younger and older adults or to distinguish the contributions of retrieval and computational speedup in Set 1 to skill learning performance in Set 2. Comparative Assessment of the Components of Skill Acquisition We report the results of two experiments in which we examined the effects of practice on strategy shifts and on the speed and accuracy of computing and retrieving solutions to repeated problems. By comparing the components of skill acquisition, we can inform a fundamental debate in the study of cognitive aging: whether age-related cognitive declines are based on a general mechanism that is insidious to many functions or whether declines for different tasks (or task components) are process specific. A considerable amount of evidence indicates that processing speed accounts for a substantial part of the age variance in performance across a wide range of cognitive measures (e.g., for a comprehensive review, see Salthouse, 1996). To our knowledge, no studies have comprehensively evaluated age differences and practice-related improvements for multiple processing components during skill acquisition. In the two experiments that comprise the current study, on-line strategy probes were used to identify computes and retrieves on individual trials. We examined the effects of age on speedup for responses categorized as computes and retrieves by fitting the data to a power function. RT data in skill-learning studies usually exemplify the ―power law of practice‖ (Newell & Rosenbloom, 1981), and the fits of data sorted by strategy to a power function are particularly impressive (Delaney et al., 1998; Rickard, 1997, 2004). In its simplest twoparameter form, the power law states that latencies (RT) will decline with blocks of training (N) on a power function, RT = aN -b , where the coefficient a determines the starting value at N = 1 and the exponent b determines the rate of decline. Given data from two age groups ( RT1 and RT2 conforming to the power law, the extent to which there is a difference in skill learning is reflected in the difference between b1 and b2. The test for an Age Group × N interaction can be described exactly as a test for the constancy of RT2 − RT1 over N. The constancy of RT2 − RT1 reflects the equality of b1 and b2. Thus, a simple, straightforward approach is to apply a log transform to both RT values and N. In logarithmic units, RT will be a linear function of N. As shown by Newell and Rosenbloom in their original study (1981), if RT = aN -b , then ln(RT) = -bln(N) + ln(a). The slope of the function is equal to the power function exponent, and the intercept is equal to the log of the starting value. Log-transformed values can then be submitted to an analysis of variance (ANOVA)-based trend analysis on N. The strength of the linear component exposed by the analysis serves as an index to the validity of the power function model. Given that the log-log data are largely linear, a significant interaction between condition and the linear component of N can be legitimately interpreted as a difference in slopes between groups or conditions or, equivalently, as a difference in the power function exponent (and conversely for a nonsignificant interaction). In every case, the Group × Linear N interaction term, if statistically reliable, correctly signals a difference in learning rate. Further, in log-log plots, the linearity of the trends (and hence the appropriateness of the power function model) is apparent on visual inspection, as is the relation between two trends (parallel, divergent, or convergent lines). The use of strategy probes allows for analysis of the proportion of retrieval responses P (or its complement [1 P], the proportion of computational responses). P can be plotted block by block and has been found to rise from 0 to 1 on a negatively accelerated function of N (e.g., Rickard, 1997). The P × N trace reflects the progression of the strategy shift across blocks of training. Consistent with Rickard's (1997) neural network simulation of the shift from computation to retrieval, some of the classic work on paired-associate learning points to a negative exponential item-acquisition function (e.g., Atkinson, Bower, & Crothers, 1965). We suggest that the strategy shift rate reflects both the efficiency with which stimulus-response connections are encoded and represented in episodic memory as well as any response bias against using retrieval as a strategy. In light of well-known agerelated deficits in associative learning and binding (e.g., Naveh-Benjamin, 2000), as well as a possible disinclination to use retrieval as a strategy (see Touron & Hertzog, 2004a, 2004b), it is likely that the probability of retrieval across blocks of training is an age-sensitive component in skill learning. The effects of training on P in two groups (P1 and P2) are assessed by examining the Group × N interaction term. This test will be direct if the P1 × N and P2 × N traces are linearized. If the growth in P is negative exponential, P = 1 − e -c(N − 1) , a straightforward transformation is applicable, and that is to first form the complement of P, Q = 1 P, and then to do a log transform of the Q values. (N values are not transformed; this is described as a semilog rather than as a log-log transform.) In semilog units, Q will be a linear function of N, whose slope is equal to the exponential rate parameter. Mathematically, if P = 1 exp(-c(N 1)), then Q = exp(c(N -1)) and ln(Q) = -c(N -1). If a trend analysis is performed on the semilog values, we are justified in interpreting an interaction between condition and the linear component of N, as a difference in the learning rate. Also, from semilog plots, the linearity of the trends (and hence the appropriateness of the negative exponential model) is apparent on inspection, as is the relation between two trends (collinear or divergent lines). To summarize our treatment of the data in the current experiments, three steps were involved. First, strategy probes were used to decompose performance into three components of skill—computation times, retrieval times, and proportions of retrievals—all as a function of block. Second, the indicated transformations were applied to the component data, a log-log transform in the case of the latencies and a semilog transform in the case of the proportions. Linear trends in the resulting traces captured the learning rate for each component. Third, rate differences between conditions or age groups were assessed visually in terms of parallel, divergent, or convergent trends and confirmed statistically by means of ANOVA-based trend analysis. Experiment 1 One of the aims of this experiment is to provide a relatively precise description of practice-related speedup in computed and retrieved responses and the shift from computation to retrieval in younger and older adults. To our knowledge, age effects in these particular components of skill learning have been assessed in only three studies: one that examines age and item difficulty effects in an alphabet arithmetic task (Hoyer et al., 2003) and two that examine age and strategy choice effects in the noun-pair task (Touron & Hertzog, 2004a, 2004b). Although these previous studies primarily examined strategy information to compare rates of strategy shift across groups, the current research offers a detailed depiction of improvements within each of the component processes as well as a more precise analytic approach for comparing strategy shifts. Because of the multistep nature of the selected computation, RTs were expected to be substantially shorter for retrieves than for computes. Consistent with Rickard (1997, 2004), it was predicted that RTs for both computes and retrieves would become shorter with repetitions. In terms of age effects, we expected that the strategy shift from computation to retrieval would require more repetitions for older adults than for younger adults. An agerelated reduction in the shift rate from computes to retrieves could be interpreted to reflect a true age-related deficit in the ability to learn and retrieve associations between problems and their solutions, or it could reflect a disinclination on the part of older adults to use retrieval as a strategy for obtaining solutions. Improvement rates for both computational and retrieval times were expected to be slower for older adults than for younger adults. Of most importance are the relations between age and the exponents of the trends for computes and retrieves. Findings showing that there are age differences in the log-linearized trends for both computes and retrieves, and that the trends are parallel for computes and retrieves within age groups, could be taken as strong evidence for a general learning mechanism that is age attenuated. Findings of different trends for computes and retrieves either within or between age groups suggest the need for a process-specific interpretation of computational learning and retrieval learning and the associated age effects. A second purpose of this experiment was to examine whether skill acquisition is reactive to the administration of probes and the frequency of probing. The examination of possible age differences in the extent to which probing affects processing efficiency and strategy use is essential to determining the value of postresponse strategy probes as a method for decomposing the strategies involved in skill learning. As mentioned, Rogers and Gilbert (1997) showed that interim tests served to increase older adults' use of retrieval as a strategy for obtaining solutions in a noun-pair learning task. Like the effects of interim tests or the effects of other task manipulations designed to boost retrieval use (e.g., presentation of trials without the look-up key), it is an open question whether the administration of postresponse strategy probes affects measures of response accuracy, speedup for computes and retrieves, or the probability of retrieves in either younger or older adults. Further, it must be established that the probe procedure used for identifying responses as computes and retrieves accurately reflects the speedup patterns observed during the course of acquisition. Rickard (2004) reported that strategy probes produced faster rates of item learning in younger adults. However, this outcome might have been confounded by the inclusion of an unrelated secondary task in the place of the strategy probe for the nonprobed group (judgment of spatial locations for geometric shapes). Switching from the primary pound-arithmetic task to an unrelated secondary task might have induced a task-switching effect, disrupting primary-task performance in the nonprobed group. We did not include a secondary task in our procedure, the more so because any interference or task-switching demand would likely be greater for older adults than for younger adults (e.g., Verhaeghen, Steitz, Sliwinski, & Cerella, 2003). Our experiment was designed to expose possible differences in skill acquisition with 33% probing, 100% probing, and no probes. We hoped to establish that skill acquisition assessed in the presence of strategy probes at either frequency was no different than that assessed without probes for either younger or older adults. In the current experiment, younger adults and older adults were taught to solve pseudoarithmetic equations that contained a novel operator (#) and were subsequently assessed on a skill-acquisition task consisting of repeated problems containing this operator. The task, referred to as pound arithmetic, was used previously by Rickard (1997) to examine the repetition-based shift from computation to retrieval in young adults. Problems having the form A # B = C, were presented on each trial. A, B, and C were two-digit numbers conforming to the operation [(B − A) + 1] + B = C. For different groups of participants, strategy probes either were administered on 33% of the correct trials or 100% of the correct trials or were not given. These frequencies were chosen to contrast outcomes from nonprobed responses and 100% probed responses to Rickard's (1997) reliance on probes for 33% of trials. For the 33% and 100% groups, the proportions of item retrievals were examined as a function of the number of repetitions, and response times for computes and retrieves were examined separately as a function of repetitions based on the strategy reports.