Modeling developmental transitions on the balance scale task

Periods of relatively stable, rule‐like behavior alternated with short transition periods characterize cognitive development on reasoning tasks like the balance scale task. Each transition gives rise to an improvement in behavior, until a phase is reached in which performance is flawless or improvement is not worthwhile given the necessary extra effort. Several computational models have been developed to capture the developmental phenomena associated with the balance scale task. These models, which originate from different computational traditions, explain the main phenomena of development. Recently, empirical phenomena have been reported that these models cannot easily accommodate. We propose a computational model that is implemented in ACT‐R and that is based on the evaluation of success of applied knowledge, combined with a mechanism to construct newknowledge by searching for differences between the left‐ and right‐hand sides of presented balance scale problems. This model accounts for the main empirical phenomena as well as for the recently reported empirical phenomena such as learning without feedback.     

Rule transition on the balance scale task: a case study in belief change

For various domains in proportional reasoning cognitive development is characterized as a progression through a series of increasingly complex rules. A multiplicative relationship between two task features, such as weight and distance information of blocks placed at both sides of the fulcrum of a balance scale, appears difficult to discover. During development, children change their beliefs about the balance scale several times: from a focus on the weight dimension (Rule I) to occasionally considering the distance dimension (Rule II), guessing (Rule III), and applying multiplication (Rule IV; Siegler, 1981). Because of the detailed empirical findings the balance scale task has become a benchmark task for computational models of proportional reasoning. In this article, we present a large empirical study (N = 420) of which the findings provide a challenge for computational models. The effect of feedback and the effect of individually adapted training items on rule transition were tested for children using Rule I or Rule II. Presenting adapted training items initiates belief revision for Rule I but not for Rule II. The experience of making mistakes (by providing feedback) induces a change for both Rule I and Rule II. However, a delayed posttest shows that these changes are preserved after 2 weeks only for children using Rule I. We conclude that the transition from Rule I to Rule II differs from the transition from Rule II to a more complex rule. Concerning these empirical findings, we will review performance of computational models and the implications for a future belief revision model.

It is one Thing, to show a Man that he is in an Error, and another, to put him in possession of Truth. John Locke

     

The development of children's rule use on the balance scale task

Cognitive development can be characterized by a sequence of increasingly complex rules or strategies for solving problems. Our work focuses on the development of children's proportional reasoning, assessed by the balance scale task using Siegler's (1976, 1981) rule assessment methodology. We studied whether children use rules, whether children of different ages use qualitatively different rules, and whether rules are used consistently. Nonverbal balance scale problems were administered to 805 participants between 5 and 19 years of age. Latent class analyses indicate that children use rules, that children of different ages use different rules, and that both consistent and inconsistent use of rules occurs. A model for the development of reasoning about the balance scale task is proposed. The model is a restricted form of the overlapping waves model (Siegler, 1996) and predicts both discontinuous and gradual transitions between rules.     

A connectionist model of a continuous developmental transition in the balance scale task

A connectionist model of the balance scale task is presented which exhibits developmental transitions between ‘Rule I’ and ‘Rule II’ behavior [Siegler, R. S. (1976). Three aspects of cognitive development. Cognitive Psychology,8, 481–520.] as well as the ‘catastrophe flags’ seen in data from Jansen and van der Maas [Jansen, B. R. J., & van der Maas, H. L. J. (2001). Evidence for the phase transition from Rule I to Rule II on the balance scale task. Developmental Review, 21, 450–494]. The model extends a connectionist model of this task [McClelland, J. L. (1989). Parallel distributed processing: Implications for cognition and development. In R. G. M. Morris (Ed.), Parallel distributed processing: Implications for psychology and neurobiology (pp. 8–45). Oxford: Clarendon Press] by introducing intrinsic variability into processing and by allowing the network to adapt during testing in response to its own outputs. The simulations direct attention to several aspects of the experimental data indicating that children generally show gradual change in sensitivity to the distance dimension on the balance scale. While a few children show larger changes than are characteristic of the model, its ability to account for nearly all of the data using continuous processes is consistent with the view that the transition from Rule I to Rule II behavior is typically continuous rather than discrete in nature.     

Re-thinking stages of cognitive development: an appraisal of connectionist models of the balance scale task

The present paper re-appraises connectionist attempts to explain how human cognitive development appears to progress through a series of sequential stages. Models of performance on the Piagetian balance scale task are the focus of attention. Limitations of these models are discussed and replications and extensions to the work are provided via the Cascade-Correlation algorithm. An application of multi-group latent class analysis for examining performance of the networks is described and these results reveal fundamental functional characteristics of the networks. Evidence is provided that strongly suggests that the networks are unable to acquire a mastery of torque and, although they do recover certain rules of operation that humans do, they also show a propensity to acquire rules never previously seen.     

Towards better computational models of the balance scale task: a reply to Shultz and Takane

In contrast to Shultz and Takane [Shultz, T.R., & Takane, Y. (2007). Rule following and rule use in the balance-scale task. Cognition, in press, doi:10.1016/j.cognition.2006.12.004.] we do not accept that the traditional Rule Assessment Method (RAM) of scoring responses on the balance scale task has advantages over latent class analysis (LCA): RAM is similar to a very restricted form of LCA. The apparent shortcomings of LCA are also less severe than they suggest. Via new simulations we show that LCA detects small classes reliably. We also counter their concerns regarding the torque difference effect and we underline the problems connectionist models have with correctly responding to balance items. Despite these differences in opinion we agree with Shultz and Takane on the possible avenues for future research.     

Complexity effects on the children's gambling task

The children's gambling task (CGT [Kerr, A., & Zelazo, P. D. (2004). Development of “Hot” executive function: The children's gambling task. Brain and Cognition, 55, 148–157]) involves integrating information about losses and gains to maximize winnings when selecting cards from two decks. Both cognitive complexity and control (CCC) theory and relational complexity (RC) theory attribute younger children's difficulty to task complexity. In CCC theory, identification of the advantageous deck requires formulation of a higher-order rule so that gains and losses can be considered in contradistinction. According to RC theory, it entails processing the ternary relation linking three variables (deck, magnitude of gain, magnitude of loss). We designed two less complex binary-relational versions in which either loss or gain varied across decks, with the other held constant. The three closely matched versions were administered to 3–5-year-olds. Consistent with complexity explanations, children in all age groups selected cards from the advantageous deck in the binary-relational versions, but only 5-year-olds did so on the ternary-relational CGT.     

Young children's performance on the balance scale: the influence of relational complexity

Three experiments investigated the effect of complexity on children's understanding of a beam balance. In nonconflict problems, weights or distances varied, while the other was held constant. In conflict items, both weight and distance varied, and items were of three kinds: weight dominant, distance dominant, or balance (in which neither was dominant). In Experiment 1, 2-year-old children succeeded on nonconflict-weight and nonconflict-distance problems. This result was replicated in Experiment 2, but performance on conflict items did not exceed chance. In Experiment 3, 3- and 4-year-olds succeeded on all except conflict balance problems, while 5- and 6-year-olds succeeded on all problem types. The results were interpreted in terms of relational complexity theory. Children aged 2 to 4 years succeeded on problems that entailed binary relations, but 5- and 6-year-olds also succeeded on problems that entailed ternary relations. Ternary relations tasks from other domains--transitivity and class inclusion--accounted for 93% of the age-related variance in balance scale scores.     

Modelling response selection in task switching: Testing the contingent encoding assumption

The contingent encoding assumption is the idea that response selection in task-switching situations does not begin until the cue and the target have both been encoded. The authors tested the assumption by manipulating response congruency, stimulus order, and stimulus onset asynchrony (SOA) in two experiments. They found evidence of response selection prior to cue encoding for congruent targets with target–cue order at a long SOA, indicating that the contingent encoding assumption is invalid. The authors describe how contingent encoding can be removed from an existing task-switching model by introducing baseline evidence—task-neutral evidence that serves as a baseline for response selection prior to stimulus encoding. Simulations revealed that the modified model could reproduce the full pattern of response time data and generate responses prior to cue encoding. The authors conclude by discussing directions for further model development.     

A joint modeling framework of responses and response times to assess learning outcomes

Abstract

A general modeling framework of response accuracy and response times is proposed to track skill acquisition and provide additional diagnostic information on the change of latent speed in a learning environment. This framework consists of two types of models: a dynamic response model that captures the response accuracy and the change of discrete latent attribute profile upon factors such as practice, intervention effects, and other latent and observable covariates, and a dynamic response time model that describes the change of the continuous response latency due to change of latent attribute profile. These two types of models are connected through a parameter, describing the change rate of the latent speed through the learning process, and a covariate defined as a function of the latent attribute profile. A Bayesian estimation procedure is developed to calibrate the model parameters and measure the latent variables. The estimation algorithm is evaluated through several simulation studies under various conditions. The proposed models are applied to a real data set collected through a spatial rotation diagnostic assessment paired with learning tools.     

Bridging the gap between theory and model: a reflection on the balance scale task

At first glance, the two lead articles in this issue share little except the balance scale task, yet we view them as complementary rather than unrelated or contradictory. Our Reflection focuses on the individual strengths of the two lead articles and, to a greater extent, the potential power of their combined perspectives. Our general approach is to allow psychological theory to suggest a model of performance that can both evaluate specific theoretical claims and reveal important features of the data that had been previously obscured using conventional statistical analyses. Our guiding principle is that model, theory, and data all should be connected.     

A meta-analysis of the n-back task while driving and its effects on cognitive workload

This study investigates the effect of the n-back task on cognitive workload while driving. Results of 20 studies with over 800 participants in total show a moderate to high mean effect size. That means the n-back task varies cognitive load while driving in a substantial matter. Further analysis reveals several moderator variables: experiments conducted in a driving simulator showed larger effect sizes than on-road studies. This effect decreases with increasing driving simulator fidelity. Furthermore, the specific driving task assignment moderates the effect: lane change task scenarios result in higher effects than other situations. Regarding the different measurement methods of cognitive workload, subjective questionnaires seem to have very high sensitivity. In contrast, n-back performance measures, detection response task measures, and physiological measurements result in moderate effect sizes, and driving performance measures show reduced sensitivity. Regarding different implementations of the n-back task itself, surprisingly, no moderators are found. Overall, the findings highlight the suitability of the n-back task as a method of inducing cognitive load in transportation research. The moderator analysis gives an overview of different methodological designs and how these designs will affect effect sizes.     

Attention,spatial integration,and the tail of response time distributions in Stroop task performance

A few studies have examined selective attention in Stroop task performance through ex-Gaussian analyses of response time (RT) distributions. It has remained unclear whether the tail of the RT distribution in vocal responding reflects spatial integration of relevant and irrelevant attributes, as suggested by Spieler, Balota, and Faust (2000 Spieler, D. H., Balota, D. A. and Faust, M. E. 2000. Levels of selective attention revealed through analyses of reaction time distributions. Journal of Experimental Psychology: Human Perception and Performance, 26: 506–526. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Here, two colour–word Stroop experiments with vocal responding are reported in which the spatial relation between colour and word was manipulated. Participants named colours (e.g., green; say “green”) while trying to ignore distractors that were incongruent or congruent words (e.g., red or green), or neutral series of Xs. The vocal RT was measured. Colour words in colour, white words superimposed onto colour rectangles (Experiment 1), and colour rectangles combined with auditory words (Experiment 2) yielded Stroop effects in both the leading edge and the tail of the RT distributions. These results indicate that spatial integration is not necessary for effects in the tail to occur in vocal responding. It is argued that the findings are compatible with an association of the tail effects with task conflict.     

Effects of context on the rate of conjunctive responses in the probabilistic truth table task

The probabilistic truth table task involves assessing the probability of "If A then C" conditional sentences. Previous studies have shown that a majority of participants assess this probability as the conditional probability P(C│A) while a substantial minority responds with the probability of the conjunction A and C. In an experiment involving 96 participants, we investigated the impact on the rate of conjunctive responses of the context in which the task is framed. We show that a context intended to lead participants to consider all the possible cases (i.e. the throw of a die known to allow six possibilities) elicited more conjunctive responses than a context assumed not to have this effect (an unfamiliar deck of cards). These results suggest that the step of inferring the probability can distort our assessment of participants' interpretation of conditional sentences. This might compromise the validity of the probabilistic task in studying conditional reasoning.     

The effects of funny and serious task content and expectations of fun versus importance on children's cognitive performance

This study investigated how children's performance on a cognitive task was influenced by funny and serious task content, and by fun or important instructions. Eighty‐four children in Grades 1 and 5 performed two versions of a paired‐associates word‐learning task, which paired nonsense words with novel definitions and illustrations. All children completed a version in which the definitions and illustrations were funny, and a version in which they were not, with either fun or important instructions. Results revealed significantly better performance on the funny than on the serious version, but only when the funny version was presented first. There were no significant effects of task instructions. The findings confirm that making children's cognitive tasks funnier can enhance task performance. Although there were no effects of expectations as created by task instructions, the enhancing effect of funny content was influenced by children's expectations as created by their prior experience with the task.     

Prospective memory and intraindividual variability in ongoing task response times in an adult lifespan sample: the role of cue focality

To contribute to the ongoing conceptual debate of what traditional mean-level ongoing task (OT) costs tell us about the attentional processes underlying prospective memory (PM), we investigated costs to intraindividual variability (IIV) in OT response times as a potentially sensitive indicator of attentional processes. Particularly, we tested whether IIV in OT responses may reflect controlled employment of attentional processes versus lapses of controlled attention, whether these processes differ across adulthood, and whether it is moderated by cue focality. We assessed 150 individuals (19–82 years) in a focal and a nonfocal PM condition. In addition, external measures of inhibition and working memory were assessed. In line with the predictions of the lapses-of-attention/inefficient-executive-control account, our data support the view that costs to IIV in OT trials of PM tasks reflect fluctuations in the efficiency of executive functioning, which was related to failures in prospective remembering, particularly in nonfocal PM tasks, potentially due to their increased executive demands. The additional value of considering costs to IIV over and beyond traditional mean-level OT costs in PM research is discussed.     

The discrepant effect of acute stress on cognitive inhibition and response inhibition

This study aimed to investigate how acute stress impinges on individual’s cognitive inhibition and response inhibition abilities. Electroencephalography was adopted when 35 healthy adult females performing the No Go Flanker task before and after the Trier Social Stress Test. Both inhibition processes evoked N2 and P3 components, but only the response inhibition evoked the late positive potential (LPP), indicating the response inhibition needed continuous cognitive effort to inhibit the prepotent response. The N2 and the P3 amplitudes were decreased, while the LPP amplitudes were increased under acute stress. These results suggested that acute stress caused the detrimental effect by occupying cognitive resources. Contrastingly, individuals actively regulated and made more efforts to counteract the detrimental effect of acute stress on response inhibition. Thus, acute stress impaired cognitive inhibition but did not affect response inhibition.     

Effects of stimulus-stimulus compatibility and stimulus-response compatibility on response inhibition

Previous studies demonstrated that interference control in stimulus–stimulus compatibility tasks slowed down stopping in the stop signal task (e.g., Kramer, A. F., Humphrey, D. G., Larish, J. F., Logan, G. D., & Strayer, D. L. (1994). Aging and inhibition: beyond a unitary view of inhibitory processing in attention. psychology and aging, 9, 491–512). In the present study, the impact of stimulus–stimulus compatibility and stimulus–response compatibility on response inhibition is further investigated. In Experiment 1, the stop signal task was combined with a traditional horizontal Simon task and with a vertical variant. For both dimensions, stopping responses was prolonged in incompatible trials, but only when the previous trial was compatible. In Experiment 2, the Simon task was combined with a spatial Stroop task in order to compare the effects of stimulus–stimulus and stimulus–response compatibility. The results demonstrated that both types of compatibility influenced stopping in a similar way. These findings are in favor of the hypothesis that response inhibition in the stop signal task and interference control in conflict tasks rely on similar mechanisms.     

Distorted estimates of implicit and explicit learning in applications of the process-dissociation procedure to the SRT task

We investigated potential biases affecting the validity of the process-dissociation (PD) procedure when applied to sequence learning. Participants were or were not exposed to a serial reaction time task (SRTT) with two types of pseudo-random materials. Afterwards, participants worked on a free or cued generation task under inclusion and exclusion instructions. Results showed that pre-experimental response tendencies, non-associative learning of location frequencies, and the usage of cue locations introduced bias to PD estimates. These biases may lead to erroneous conclusions regarding the presence of implicit and explicit knowledge. Potential remedies for these problems are discussed.     

The time course effect of moderate intensity exercise on response execution and response inhibition

This research aimed to investigate the time course effect of a moderate steady-state exercise session on response execution and response inhibition using a stop-task paradigm. Ten participants performed a stop-signal task whilst cycling at a carefully controlled workload intensity (40% of maximal aerobic power), immediately following exercise and 30 min after exercise cessation. Results showed that moderate exercise enhances a subjects’ ability to execute responses under time pressure (shorter Go reaction time, RT without a change in accuracy) but also enhances a subjects’ ability to withhold ongoing motor responses (shorter stop-signal RT). The present outcomes reveal that the beneficial effect of exercise is neither limited to motor response tasks, nor to cognitive tasks performed during exercise. Beneficial effects of exercise remain present on both response execution and response inhibition performance for up to 52 min after exercise cessation.