Elisabet Tubau

Modes of Executive Control in Sequence Learning: From Stimulus-Based to Plan-Based Control

The authors argue that human sequential learning is often but not always characterized by a shift from stimulus- to plan-based action control. To diagnose this shift, they manipulated the frequency of 1st-order transitions in a repeated manual left-right sequence, assuming that performance is sensitive to frequency-induced biases under stimulus- but not plan-based control. Indeed, frequency biases tended to disappear with practice, but only for explicit learners. This tendency was facilitated by visual-verbal target stimuli, response-contingent sounds, and intentional instructions and hampered by auditory (but not visual) noise. Findings are interpreted within an event-coding model of action control, which holds that plans for sequences of discrete actions are coded phonetically, integrating order and relative timing. The model distinguishes between plan acquisition, linked to explicit knowledge, and plan execution, linked to the action control mode.

Overcoming illusory inferences in a probabilistic counterintuitive problem: the role of explicit representations.

In the context of conditional probabilities, a good example of the marked discrepancy between intuition and formal reasoning is the Monty Hall dilemma (MHD). We used the MHD to study the effects of practicing the game, making explicit the underlying structure, or enhancing the representation of the different possibilities, on reaching and stating the correct answer. The results of the experiments showed that accumulated experience with the MHD increased the proportion of switching responses but did not change erroneous intuitions (Experiment 1). However, when the dilemma was presented in the form of an adversary game that made the underlying structure more explicit, more participants formed complete mental representations that enabled them to reason correctly (Experiment 2). This result was observed even without any practice with the game if the participants were encouraged to represent possibilities (Experiment 3). Therefore, in this context, correct reasoning seems to depend more on the ability to consider different possibilities than on extensive practice with the game.

Individual differences in arithmetic skill reflected in event-related brain potentials.

We used event-related brain potentials (ERP) to study the problem-size effect in individuals with high and low arithmetic skill. Participants were presented with a classic equality verification task, and problem size was manipulated by using small (e.g., 3+4), medium (e.g., 7+8) and large problems (e.g., 16+29). ERP analyses were time-locked to the onset of the second operand in order to address brain potentials during the production phase. High-skill individuals showed a positive slow wave when solving large problems and no differences in the ERP pattern when solving small and medium problems. In contrast, low-skill individuals showed a positive slow wave when solving medium and large problems. Given that differences between high and low skill individuals have been related to differences in calculation strategies, these results provide further support to the utility of using ERP as a signature of arithmetic strategy.

Comprehension and computation in Bayesian problem solving

Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian inferences relative to normalized formats (e.g., probabilities, percentages), both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on “transparent” Bayesian problems varies widely, and generally remains rather unimpressive. We suggest there has been an over-focus on this representational facilitator (i.e., transparent problem structures) at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct vs. incorrect reasoners depart, and how individual differences might influence this time point.

Individual differences in sequence learning and auditory pattern sensitivity as revealed with evoked potentials

Research on motor sequence acquisition has shown significant differences between learners. Learners who develop explicit knowledge respond faster than non‐explicit ones and they show larger amplitude in event‐related brain potentials to sequence deviants. There is evidence that memory span correlates with the amount of sequence learned, but the specific mechanisms subserving such differences are still unknown. Recently, it has been observed that performance of explicit learners, but not of non‐explicit ones, improves when presented with auditory action effects. Accordingly, differences between learners might be related to differences in auditory rhythm perception. To test this hypothesis, the mismatch negativity (MMN)‐evoked potential elicited to stimuli violating stimulus alternation (i.e. low pitch, high pitch) was recorded in explicit and non‐explicit sequence learners. Results confirmed our prediction: explicit learners showed larger amplitude of the MMN to the violation of the auditory rhythm, suggesting new theoretical implications to account for individual differences in sequential action control.

Reasoning and choice in the Monty Hall Dilemma (MHD): implications for improving Bayesian reasoning

The Monty Hall Dilemma (MHD) is a two-step decision problem involving counterintuitive conditional probabilities. The first choice is made among three equally probable options, whereas the second choice takes place after the elimination of one of the non-selected options which does not hide the prize. Differing from most Bayesian problems, statistical information in the MHD has to be inferred, either by learning outcome probabilities or by reasoning from the presented sequence of events. This often leads to suboptimal decisions and erroneous probability judgments. Specifically, decision makers commonly develop a wrong intuition that final probabilities are equally distributed, together with a preference for their first choice. Several studies have shown that repeated practice enhances sensitivity to the different reward probabilities, but does not facilitate correct Bayesian reasoning. However, modest improvements in probability judgments have been observed after guided explanations. To explain these dissociations, the present review focuses on two types of causes producing the observed biases: Emotional-based choice biases and cognitive limitations in understanding probabilistic information. Among the latter, we identify a crucial cause for the universal difficulty in overcoming the equiprobability illusion: Incomplete representation of prior and conditional probabilities. We conclude that repeated practice and/or high incentives can be effective for overcoming choice biases, but promoting an adequate partitioning of possibilities seems to be necessary for overcoming cognitive illusions and improving Bayesian reasoning.

Knowing What to Respond in the Future Does Not Cancel the Influence of Past Events

Everyday tasks seldom involve isolate actions but sequences of them. We can see whether previous actions influence the current one by exploring the response time to controlled sequences of stimuli. Specifically, depending on the response-stimulus temporal interval (RSI), different mechanisms have been proposed to explain sequential effects in two-choice serial response tasks. Whereas an automatic facilitation mechanism is thought to produce a benefit for response repetitions at short RSIs, subjective expectancies are considered to replace the automatic facilitation at longer RSIs, producing a cost-benefit pattern: repetitions are faster after other repetitions but they are slower after alternations. However, there is not direct evidence showing the impact of subjective expectancies on sequential effects. By using a fixed sequence, the results of the reported experiment showed that the repetition effect was enhanced in participants who acquired complete knowledge of the order. Nevertheless, a similar cost-benefit pattern was observed in all participants and in all learning blocks. Therefore, results of the experiment suggest that sequential effects, including the cost-benefit pattern, are the consequence of automatic mechanisms which operate independently of (and simultaneously with) explicit knowledge of the sequence or other subjective expectancies.

From reading numbers to seeing ratios: a benefit of icons for risk comprehension

Promoting a better understanding of statistical data is becoming increasingly important for improving risk comprehension and decision-making. In this regard, previous studies on Bayesian problem solving have shown that iconic representations help infer frequencies in sets and subsets. Nevertheless, the mechanisms by which icons enhance performance remain unclear. Here, we tested the hypothesis that the benefit offered by icon arrays lies in a better alignment between presented and requested relationships, which should facilitate the comprehension of the requested ratio beyond the represented quantities. To this end, we analyzed individual risk estimates based on data presented either in standard verbal presentations (percentages and natural frequency formats) or as icon arrays. Compared to the other formats, icons led to estimates that were more accurate, and importantly, promoted the use of equivalent expressions for the requested probability. Furthermore, whereas the accuracy of the estimates based on verbal formats depended on their alignment with the text, all the estimates based on icons were equally accurate. Therefore, these results support the proposal that icons enhance the comprehension of the ratio and its mapping onto the requested probability and point to relational misalignment as potential interference for text-based Bayesian reasoning. The present findings also argue against an intrinsic difficulty with understanding single-event probabilities.

Structural mapping in statistical word problems: A relational reasoning approach to Bayesian inference.

Presenting natural frequencies facilitates Bayesian inferences relative to using percentages. Nevertheless, many people, including highly educated and skilled reasoners, still fail to provide Bayesian responses to these computationally simple problems. We show that the complexity of relational reasoning (e.g., the structural mapping between the presented and requested relations) can help explain the remaining difficulties. With a non-Bayesian inference that required identical arithmetic but afforded a more direct structural mapping, performance was universally high. Furthermore, reducing the relational demands of the task through questions that directed reasoners to use the presented statistics, as compared with questions that prompted the representation of a second, similar sample, also significantly improved reasoning. Distinct error patterns were also observed between these presented- and similar-sample scenarios, which suggested differences in relational-reasoning strategies. On the other hand, while higher numeracy was associated with better Bayesian reasoning, higher-numerate reasoners were not immune to the relational complexity of the task. Together, these findings validate the relational-reasoning view of Bayesian problem solving and highlight the importance of considering not only the presented task structure, but also the complexity of the structural alignment between the presented and requested relations.

Post-error response inhibition in high math-anxious individuals: Evidence from a multi-digit addition task☆

The aim of the study was to investigate how high math-anxious (HMA) individuals react to errors in an arithmetic task. Twenty HMA and 19 low math-anxious (LMA) individuals were presented with a multi-digit addition verification task and were given response feedback. Post-error adjustment measures (response time and accuracy) were analyzed in order to study differences between groups when faced with errors in an arithmetical task. Results showed that both HMA and LMA individuals were slower to respond following an error than following a correct answer. However, post-error accuracy effects emerged only for the HMA group, showing that they were also less accurate after having committed an error than after giving the right answer. Importantly, these differences were observed only when individuals needed to repeat the same response given in the previous trial. These results suggest that, for HMA individuals, errors caused reactive inhibition of the erroneous response, facilitating performance if the next problem required the alternative response but hampering it if the response was the same. This stronger reaction to errors could be a factor contributing to the difficulties that HMA individuals experience in learning math and doing math tasks.