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Panel A: Individual learning functions of the artificial data set (n 100). Panel B: Overall power-function fits for aggregated mean reaction times (RTs) and standard deviations of the artificial data set. M y 2262.4 7803.0 * t i ** (0.62). R 2 99.8%. SD y 1190.7 1585.7 * t i ** (0.62).
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The power law of practice is often considered a benchmark test for theories of cognitive skill acquisition. Recently, P. F. Delaney, L. M. Reder, J. J. Staszewski, and F. E. Ritter (1998), T. J. Palmeri (1999), and T. C. Rickard (1997, 1999) have challenged its validity by showing that empirical data can systematically deviate from power-function f...
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... Participants therefore had to infer that a change had occurred from the received binary outcomes (i.e., shock or no shock). To avoid false conclusions that can arise during averaging of temporal trajectories (Haider & Frensch, 2002), we used a data-driven approach to estimate the time point when the participant switched their beliefs after each reversal. Specifically, we extracted 5 trials before and 15 trials after each reversal (20 trials in total), calculated the cumulative sum of shock probability ratings and demeaned the time series (Page, 1954). ...
The angiotensin receptor blocker losartan has been linked to aspects of aversive learning such as fear acquisition and extinction, inhibition of aversive learning rates and reduced post-traumatic stress disorder (PTSD) symptoms. Here, we investigate the influence of losartan on aversive Pavlovian conditioning using a probabilistic learning paradigm. In a double-blind, randomised placebo-controlled design, we tested 45 healthy volunteers during a baseline session (session 1), after application of losartan or placebo (session 2) and during a follow-up session (session 3). On each session, participants engaged in a task where they had to predict the likelihood of an electrical stimulation on every trial while the true shock contingencies repeatedly switched between phases of high and low shock threat. Computational reinforcement learning models were used to investigate learning dynamics. Acute administration of losartan significantly reduced participants' adjustment during both low-to-high and high-to-low threat changes. This was driven by reduced aversive learning rates on the drug session compared to baseline. The 50mg drug dose did not induce reduction of blood pressure or change in reaction times, ruling out general reduction in attention and engagement. Decreased adjustment of aversive expectations to low-to-high, but not high-to-low, threat change was maintained on a follow up session 24hrs later, suggesting a possible role of losartan in prevention of formation of aversive associations on longer time scales.
... Some participants notice the covariation, but decide not to use it. Gaschler et al. (2019), see also Gaschler et al. (2015), Haider and Frensch (2002), and Lustig et al. (2021) have reported further behavioral evidence for that the usage of the covarying stimulus feature takes place based on a top-down decision to change the task strategy. Using four colors and four positions Gaschler et al. (2019) could vary the frequency with which particular color-position pairings occurred during practice. ...
Based on instructions people can form task representations that shield relevant from seemingly irrelevant information. It has been documented that instructions can tie people to a particular way of performing a task despite that in principle a more efficient way could be learned and used. Since task shielding can lead to persistence of inefficient variants of task performance, it is relevant to test whether individuals with attention deficit/hyperactivity disorder (ADHD) – characterized by less task shielding – are more likely and quicker to escape a suboptimal instructed variant of performing a task. The paradigm used in this online study builds on the observation that in many environments different covarying features could be used to determine the appropriate response. For instance, as they approach a traffic light, drivers and pedestrians monitor the color (instructed stimulus feature) and/or the position of the signal (covarying stimulus feature, more efficient in case of reduced color sight). Similarly, we instructed participants to respond to the color of a stimulus without mentioning that color covaried with the position of the stimulus. In order to assess whether with practice participants would use the non-instructed feature position to an increasing extent, we compared reaction times and error rates for standard trials to trials in which color was either ambiguous or did not match the usual covariation. Results showed that the covariation learning task can be administered online to adult participants with and without ADHD. Performance differences suggested that with practice ADHD participants (n = 43 out of a total N = 245) might increase attention to non-instructed stimulus features. Yet, they used the non-instructed covarying stimulus feature to a similar extent as other participants. Together the results suggest that participants with ADHD do not lag behind in abandoning instructed task processing in favor of a learned alternative strategy.
... To test these hypotheses, we analyzed the results obtained during three transfer sessions carried out after 12 training sessions in an alphabet-arithmetic task. Following Haider and Frensch (2002), according to whom an effect of surprise could contaminate the results of a single transfer session, three transfer sessions were implemented instead of one as in classical transfer studies (e.g., Logan & Klapp, 1991). The results of the training phase have already been reported in and will not be discussed further in the present paper. ...
The alphabet-arithmetic paradigm, in which adults are asked to add a numeral addend to a letter augend (e.g., D + 3 = G), was conceived to mimic the way children learn addition. Studies using this paradigm often conclude that procedural learning leads to the memorization of associations between operands and answers. However, as recently suggested, memorization might only be used by a minority of participants and only for problems with the largest addend. In the present paper, we aim at investigating these individual differences through transfer effects from trained problems to new ones. Participants were trained over 12 learning sessions, followed by 3 transfer sessions. A group of participants, that we called the nonbreakers, showed a linear function associating solution times and addends throughout the experiment. In this group, transfer was observed during the first transfer session, suggesting that a procedural strategy, transferable to new items, was still used at the end of training. In another group of participants, that we called the breakers, we observed a decrease in solution times for problems with the largest addend. In this group, transfer was only observed after two transfer sessions, suggesting that procedural strategies were not used as often in this group than in the other group. This was especially true for problems with the largest addend because transfer effects were stronger when they were excluded. Therefore, during learning and for breakers, the answers to problems with larger addends are retrieved first and, as for non-breakers, the answers to problems with very small operands remain computed.
... Specifically, we investigated adults' learning to efficiently perform an alphabet arithmetic task (G ϩ 5 ϭ ?), a task that has been used in a wide variety of theoretical contexts in cognitive science (Haider & Frensch, 1996, 1999, 2002Klapp et al., 1991;Logan, 1988;Pyke & LeFevre, 2011;Rabinowitz & Goldberg, 1995;Rickard, 1997;Wagenmakers & Brown, 2007) and may be directly relevant to cognitive models of genuine arithmetic (Pyke & LeFevre, 2011;Zbrodoff & Logan, 2005). Alphabet arithmetic problems are solved initially using a counting algorithm to increment letter by letter the specified number of steps to reach the correct letter answer (e.g., G ϩ 5 ϭ G H 1 I 2 J 3 K 4 L 5 ). ...
... The 30 Block ϫ Addend cell means for percent retrieval in the right panel of Figure 5 correlated .98 with the RT means in the left panel of Figure 5, which presents the mean RT for the 10 blocks in which strategy reports were obtained. Did strategy switches (e.g., from counting to retrieval) for a given problem indicate a new stable strategy for that item (e.g., Bajic & Rickard, 2009, p. 114;Haider & Frensch, 2002), or was strategy transition relatively volatile across blocks for a given problem (e.g., Siegler & Araya, 2005;Siegler & Shipley, 1995)? Across the nine opportunities to measure a strategy switch for each problem the mean number of switches for ϩ1 problems was 2.1, for ϩ2 it was 3.2, and for ϩ3 problems it was 2.8 switches. ...
... Thereafter, the switch rate declined across blocks as retrieval became the dominant strategy by the end of the second session. The strategy stability analysis demonstrated that the transition from counting to retrieval for individual problems did not generally occur abruptly and finally (e.g., Haider & Frensch, 2002), but instead entailed a gradual shift over trial blocks (see Siegler & Araya, 2005). ...
This research pursued a fine-grained analysis of the acquisition of a procedural skill. In two experiments (n = 29 and n = 27), adults practiced 12 alphabet arithmetic problems (e.g., C + 3 = C D E F) in two sessions with 20 practice blocks in each. If learning reflected speed up of a counting algorithm, response time (RT) speed up should be proportional to the number of counting steps (+ 1, + 2, or + 3). Instead, we found about 50% of RT gains occurred in the first six blocks of practice during which speed up was parallel for + 1, + 2, and + 3 problems. In both experiments, RT initially was a linear function of addend size, reflecting a letter counting strategy. Mean RT for + 3 problems was eventually equal to + 2 problems, which suggests that speed up reflected a gradual shift to associative fact retrieval. Trial by trial strategy self-reports in Experiment 2 revealed that the proportion of trials reported as memory retrieval as opposed to counting predicted 96% of the variance in RT as a function of addend size and practice block. As such, the results provided no evidence for speed up of a counting algorithm and indicated that skill acquisition for this task entailed speed up of task-general processes independent of addend size and rapid transition from counting to fact retrieval. (PsycINFO Database Record (c) 2019 APA, all rights reserved).
... Specifically, after seeing all repeated trajectories, some participants indicated that they had reverted back to algorithmic strategies on all trials once novel trajectories were introduced, even though they continued to see well-practiced repeated trajectories as well. This result differs from findings from mathematical and visual search tasks, in which retrieval shifts tend to be itemspecific rather than collective (Rickard, 2004;Touron, 2006;Wilkins & Rawson, 2010; but see Haider & Frensch, 2002). Additionally, whereas our previous results were inconsistent with a general algorithmic speedup for repeated trials, it is possible that item-specific algorithmic speedup, not retrieval, was responsible for the improvements on repeated trajectories. ...
How do people improve their ability to intercept moving targets? Prior research and theories of skill acquisition suggest that individuals engage in item-specific retrieval shifts (Anglim & Wynton, 2015; Logan, 1988; Palmeri, 1997; Rickard, 1997, 2004; Touron, 2006; Wilkins & Rawson, 2010). However, this prior research examined performance on nonspatial, nondynamic tasks. In three experiments, we pitted four hypotheses against each other, to test skill acquisition for intercepting repeated trajectories in a spatial and dynamic task: the item-specific algorithmic speedup hypothesis, the item-specific retrieval shift hypothesis, the collective retrieval shift hypothesis, and the combined hypothesis (item-specific algorithmic speedup followed by a collective retrieval shift). We found evidence for the combined hypothesis. Specifically, under easy conditions, we found small improvements on repeated trajectories that were attributable to item-specific algorithmic speedup. By contrast, under difficult conditions, we found strong evidence that the performance benefits for repeated trajectories were driven primarily by a collective shift from algorithmic to direct-retrieval strategies. This evidence for collective retrieval shift is in direct contrast to theories suggesting item-specific retrieval shifts. Theoretical and practical implications are discussed.
... Importantly, the incremental ''learning curve" pattern in the population-level crash data can be generated from discontinuous changes (i.e., phase changes) in crash risk at the individual-level (Mirman, Curry, & Mirman, 2019). Researchers in the fields of cognitive and developmental sciences have previously demonstrated that within-and between-subject aggregation can smooth out critically important developmental discontinuities, thereby providing a very misleading picture about underlying change processes (Gray & Lindstedt, 2017;Haider & Frensch, 2002;Seigler, 2006;Thelen & Ulrich, 1991). Therefore, it is important to broaden explanatory models of learning to drive to include the sorts of psycho-behavioral change processes that can sensibly account for the changes in the population-level rates after licensure, and to consider other dimensions and processes of change in addition to those associated with individual differences in learning rates (i.e., slopes). ...
... In addition, detecting phase transitions may also require new or different measures or analytic strategies. Discontinuous patterns of change are common in ontogeny, but they can be obscured: (1) when measurements are taken too infrequently (i.e., with wide sampling intervals), (2) by averaging within individuals (e.g., averaging across time; averaging across trials) (Seigler, 2006;Siegler & Shipley, 1995;Siegler, 1987), and (3) by averaging across individuals (Haider & Frensch, 2002;Murre & Chessa, 2011). Finally, researchers must pivot from thinking about variability as ''noise" towards viewing variability as evidence of important change processes associated with a complex system self-organizing to meet changing task demands. ...
Dynamical systems (DS) theoretical and methodological approaches have furthered our understanding of human development and behavior across many different domains, but have not yet been applied to driver behavior. Using a DS lens, a new theory of driver behavior is proposed, the phase transition framework (PTF), and then applied to understanding how novice drivers develop. The PTF can facilitate new lines of research by providing an individual-level explanatory account that yields the widely observed and poorly understood aggregate declines in novice drivers' crash rates in the early months of licensure. For the purpose of the PTF, learning to drive is defined as changes in the psychological system integral to the acquisition, refinement, automation, and maintenance of competencies necessary for safe driving. In the PTF, the greatest reductions in population-level collision rates observed in the early months of the post-licensure period are hypothesized to be due to qualitative cognitive reorganizations (e.g., adoption of strategies that reduce risk) that cause abrupt shifts in crash risk trajectories into lower risk strata followed by refinement of strategy use and deployment through real-world experience. Critically, the PTF differs from other theories of driver behavior in that it holds that drivers' behavioral development is self-organizing and emergent.
... Following controversial debates in cognitive psychology, there has been consensus that individual learning curves (i.e., for one item in one person) may follow diverse trends such as initial lags, sudden onsets of a target behavior (which would be formally equivalent to a step function), and episodes of rather continuous increases in performance (Gallistel, Balsam, & Fairhurst, 2004). Discontinuities average out when aggregating time courses across persons or across to-be-memorized items, resulting in a smooth rising curve with a negative acceleration (Haider & Frensch, 2002). While Blech and Gaschler (2017a) focused on students' understanding of this difference between individual and aggregate time courses, a drawing task applied in this former study was further developed in the current work to assess different facets of students' knowledge about learning and forgetting curves more in depth. ...
Learning and forgetting curves are not only integral issues for courses in introductory psychology, they are also of high practical relevance to students when it comes to the formation of realistic goals and expectations on learning outcomes. A paper-and-pencil-study investigated how well students of psychology (N = 82) have internalized the concepts of learning and forgetting curves. We developed a vignette-based assessment technique: drawing a hypothetical learning or forgetting curve in an empty coordinate system with time on the x-axis and performance on the y-axis, the starting point and endpoint being fixed. In spite of the free production format answers were quantified in a way that would allow for automated feedback in online teaching tools. For instance, learning which decelerates over time implies a curve above the diagonal while decelerated forgetting implies a curve below the diagonal. Deviating from this optimal solution, about 60% of the drawn learning and forgetting curves were classified as being close to the diagonal axis. Analyses on the individual level also documented poor consistency of knowledge. Students drawing a deceleration in learning were not more likely to also draw a deceleration in forgetting. Implications for future learning aids, for example, online feedback systems are discussed.
... Improved performance on higher-order problem-solving tasks can result from explicit instruction about optimal strategies or through spontaneous strategy discovery, and occur abruptly in a phase shift, as opposed to gradually over time [33][34][35][36][37]. Consistent with prior research on this topic (see Williams, 2007) our study did not provide strong evidence that practice quantity is protective [23]. ...
Purpose:
Although motor vehicle crashes are the leading cause of death for adolescents, there is a scarcity of research addressing adolescents' lack of pre-licensure practical driving experience, which is theorized to increase their post-licensure crash risk.
Methods:
Utilizing police-reported crashes and survey data from a randomized and quasi-randomized trial (n = 458 adolescents, 16 or 17 years of age at enrollment), the impact of a parent-directed supervised practice driving intervention and a comprehensive on-road driving assessment (ODA) with feedback was evaluated on adolescent drivers' motor vehicle crashes involvement.
Results:
Compared with the control condition, a nonsignificant 20% relative reduction in risk was observed for the parent-directed intervention: adjusted hazard ratio = .80 (95% confidence interval [CI] .44, 1.43); the unadjusted absolute risk reduction was 1.1% (95% CI -4.4, 7.1). Exposure to the ODA resulted in an 53% relative reduction of risk: adjusted hazard ratio = .47 (95% CI .24, .91); the unadjusted absolute risk reduction was 5.4% (95% CI -.3, 10.7).
Conclusions:
Comprehensive ODA might be protective for adolescents; however, additional research is needed.
... One such advantage is that in a hierarchical model, variability from participants and items is modeled simultaneously, resulting in in both participant-level and group-level parameter estimates. As such, the hierarchi-cal model allows the researcher to avoid aggregating single estimates across individuals, which can be problematic (Haider & Frensch, 2002;Heathcote, Brown, & Mewhort, 2000;Pratte, Rouder, & Morey, 2010). Another advantage is both philosophical and pragmatic. ...
A popular method for indexing numerical representations is to compute an individual estimate of a response time effect, such as the SNARC effect or the numerical distance effect. Classically, this is done by estimating individual linear regression slopes and then either pooling the slopes to obtain a group-level slope estimate, or using the individual slopes as predictors of other phenomena. In this paper, I develop a hierarchical Bayesian model for simultaneously estimating group-level and individual-level slope parameters. I show examples of using this modeling framework to assess two common effects in numerical cognition: the SNARC effect and the numerical distance effect. Finally, I demonstrate that the Bayesian approach can result in better measurement fidelity than the classical approach, especially with small samples.
... We accept the basic framework established by Fitts and Posner (1967) and elaborated by Newell and Rosenbloom (1981) and Anderson (1982Anderson ( , 1987. We are especially friendly toward the amendments to this view offered by revisionist power law researchers such as Rickard (1997Rickard ( , 1999, Delaney, Reder, Staszewski, and Ritter (1998), Haider and Frensch (2002), and Donner and Hardy (2015). ...
... 3. Practice: The behavioral marker of the early trials of practice on the new method is the leap, which takes performance with the new method beyond that of the old. However, with extended practice the new method produces fewer gains per trial and, as would be expected by traditional (Anderson, 1982(Anderson, , 1987Fitts & Posner, 1967;Newell & Rosenbloom, 1981) or revisionist (e.g., Donner & Hardy, 2015;Haider & Frensch, 2002) accounts of skill acquisition, increments in practice produce smaller and smaller increases in skilled performance-which eventually reaches a new, albeit higher, plateau. ...
... We see plateaus, dips, and leaps as behavioral markers of (a) the discovery of new task goals, (b) the working out of new methods, and (c) the leap of rapid progress gained from the initial use of a better method. This view is largely compatible with the three-tier framework of Fitts and Posner (1967) in both traditional (e.g., Anderson, 1987;Newell & Rosenbloom, 1981) and revisionist (e.g., Delaney et al., 1998;Donner & Hardy, 2015;Haider & Frensch, 2002;Rickard, 1997Rickard, , 1999 accounts. However, none of these works have a story about the invention or discovery of new goals and methods. ...
The framework of plateaus, dips, and leaps shines light on periods when individuals may be inventing new methods of skilled performance. We begin with a review of the role performance plateaus have played in (a) experimental psychology, (b) human–computer interaction, and (c) cognitive science. We then reanalyze two classic studies of individual performance to show plateaus and dips which resulted in performance leaps. For a third study, we show how the statistical methods of Changepoint Analysis plus a few simple heuristics may direct our focus to periods of performance change for individuals. For the researcher, dips become the marker of exploration where performance suffers as new methods are invented and tested. Leaps mark the implementation of a successful new method and an incremental jump above the path plotted by smooth and steady log–log performance increments. The methods developed during these dips and leaps are the key to surpassing one's teachers and acquiring extreme expertise.
