Is Cognitive Flexibility Equivalent to Shifting? Investigating Cognitive Flexibility in Multiple Domains

The study addresses whether cognitive flexibility is a unitary, domain-general mechanism (often equated with executive set shifting) or a domain-specific property emerging within particular cognitive processes. The literature offers divergent conceptualizations (e.g., task/rule switching, divergent thinking flexibility, representational/perceptual flexibility, and broader psychological or cultural flexibility). The authors propose that flexibility may be an emergent property of the cognitive system, arising from interactions among mechanisms (e.g., shifting, inhibition, goal maintenance) and contextual factors, and test whether performance associations across domains support a common mechanism or indicate domain-specific flexibility.

The paper reviews four main traditions: (1) Executive functions research where cognitive flexibility is often proxied by set shifting (switching between rules/tasks), though definitions vary and self-report vs task performance often diverge; (2) Creativity research where flexibility is an aspect of divergent thinking (e.g., number of category shifts in the Alternative Uses Test), intertwined with fluency and originality; (3) Studies of representational, linguistic, mathematical, and perceptual flexibility (e.g., cross-classification in categorization, flexible word use, multiple solution strategies in math, and perceptual bistability in ambiguous figures) that treat flexibility as a property of specific processes; (4) Broader psychological perspectives (e.g., openness to experience, psychological flexibility in ACT, cultural flexibility). These traditions do not converge on a single definition. An integrative account suggests flexibility is a property of the cognitive system or subsystems, likely emergent from multiple mechanisms in interaction and context-dependent, implying that shifting alone will not suffice for flexibility to arise.

Design: Mixed design with within-task manipulations and cross-task correlations. Participants: 223 first-year undergraduates (94 USA, 129 Romania) were recruited; 2 excluded for noncompliance; final N=221 (Mage=19.52, SD=2.67; 47 male, 165 female, 2 other, 7 not reported). Ethics approvals obtained at both sites; participants received course credit. Technical/Linguistic: Tasks built in PsychoPy 2022.1.1 (v3.8.10) and run online via Pavlovia. US sample completed tasks in English; Romanian sample in Romanian. Instructions translated and piloted. RAT used country-normed items; AMAS translated and piloted for RO. Tasks and measures:

• Set Shifting (adapted Dots–Triangles task): Stimuli were red circles (congruent same-side response) and green triangles (incongruent contralateral response) appearing left/right of a vertical line. Three parts: single-task blocks (circles then triangles) each with 30-trial training and 54-trial test; mixed-task block with 48 training and 96 test trials. RTs (ms) trimmed (<120 ms or > mean+2.5 SD). Scores: switching cost; mixing cost (congruent, incongruent). Prior tasks show adequate construct validity; switching/mixing costs have moderate reliability.
• Language Flexibility (Remote Associates Test): 1 training + 15 test triads; respond with a word forming compounds with all three cues. Feedback after each response. Selected items spanned 25–75% difficulty in norms. Scores: accuracy (0–15), median RT (s). Internal consistency: Cronbach’s alpha US=0.72; RO=0.72.
• Perceptual Flexibility (Ambiguous Figures): 1 training (Duck/Rabbit) + 6 test images (two each from meaning content reversals, figure–ground reversals, perspective reversals). Each image: 10 s initial viewing to report first interpretation; up to 50 s to report second; if not found, both interpretations provided; then 60 s continuous reporting of perceptual switches (keyboard). Scores: sum of switches across images (0–6 images with two interpretations found initially), switch rate (median number of perceptual reversals during 60 s), and switch rate RT (median RTs in s). Individual switching rates vary across stimuli but show within-stimulus consistency.
• Math Flexibility Task: 18 equations total (2 training; 16 test: 8 flexibility, 8 control). Flexibility items allowed shortcuts via regrouping/structure; control items required sequential computation. Each equation presented up to 60 s; participants typed answers; feedback provided. Post-task, participants described strategies. Reliability for overall accuracy: alpha=0.61. Scores: overall accuracy (0–16), flexibility accuracy (0–8), control accuracy (0–8), accuracy difference (flexibility–control); median RTs for overall, flexibility, control; RT difference (control–flexibility).
• Math Anxiety (AMAS): 9 items, 1–5 Likert; averaged to total score. Reliability overall alpha=0.86 (US=0.91; RO=0.80). Procedure: After consent and demographics, participants completed the four tasks in random order, then AMAS. Entire session ~60 minutes, online on personal computers. Instructions emphasized responding quickly and accurately and avoiding external aids for math/language. Data processing and analyses:
• Outlier handling: Task-by-task exclusions for low accuracy or noncompletion (e.g., SH: 7 excluded for switching cost and 7 for mixing costs; RAT: 7 excluded; Math: 9 excluded; AF: 1 excluded; AMAS: 1 missing). No imputation; analyses used available cases per measure.
• MANOVA for country and gender effects on task variables.
• Partial Pearson correlations across task scores controlling for country; Benjamini–Hochberg correction applied to 136 tests (R p.adjust method='BH').
• Exploratory Factor Analysis (Maximum Likelihood extraction, Direct Oblimin rotation) on task variables to examine common factors; separate EFAs by country reported in supplements.
• Median RTs used for all tasks except shifting (means with trimming per literature).

• MANOVA: Significant main effect of country (Pillai’s Trace=.197, F(15,178)=2.92, p<.001, η²=.197); no significant gender effect (p=.058) and no Gender×Country interaction (p=.254). Country differences: RO > US on AF sum of switches (M 5.1 vs 4.7), Math overall accuracy (13.4 vs 12.8), and Math flexibility accuracy (7.0 vs 6.6); US > RO on RAT accuracy (8.7 vs 6.8) and had lower RAT RTs (11.7 s vs 15.0 s).
• Cross-task partial correlations (controlling for country; BH-corrected): • RAT accuracy with AF switch rate RT: r=.22, p=.011 (weak positive). • RAT accuracy with Math overall accuracy: r=.22, p=.011; and with Math control accuracy: r=.21, p=.011 (weak positives). • RAT RT with Math RTs: overall r=.27, p<.001; flexibility r=.24, p=.008; control r=.23, p=.008 (processing speed commonality). • Math flexibility accuracy with AF switch rate RT: r=.19, p=.029 (weak positive). • No other significant cross-task correlations; notably, shifting task variables did not correlate with other domains.
• Exploratory Factor Analysis (N=200): Four factors (eigenvalues >1) accounted for 56.3% total variance; model fit: χ²(24)=25.085, p=.40. • Factor 1: Strong loading from AF switch rate RT (.99). • Factor 2: Math RTs (flexibility ~.86; control .90) and a smaller loading from RAT RT (.31): a processing speed factor across math and language. • Factor 3: Shifting task measures (mixing cost congruent ~.75; mixing cost incongruent ~.69; switching cost ~.36). • Factor 4: Math accuracies (flexibility ~.76; control ~.61). • No factor captured all domains, indicating task/domain-specific clustering rather than a unitary flexibility factor.
• Math anxiety (AMAS): One significant relation with Math Task outcomes was observed (details in Supplementary File 3); not central to the primary research question. Overall, results show few and small associations across domains and no evidence for a single executive or shifting-based factor underlying flexibility; the primary shared component observed was processing speed across language and mathematics RTs.

Findings provide little support for a single, domain-general cognitive flexibility mechanism. Set-shifting indices (switching and mixing costs) did not correlate with flexibility measures in language, math, or perception, arguing against equating cognitive flexibility with shifting. Instead, the pattern of weak, selective correlations and the factor structure indicate domain-specific organization: shifting measures cluster together; math accuracies cluster together; perceptual switching RT is isolated; and a cross-domain speed factor links math and language RTs. Links between RAT and math control accuracy likely reflect general cognitive resources (e.g., diligence or intelligence) and processing speed rather than a shared flexibility mechanism. The association between ambiguous figure switching RT and both RAT accuracy and math flexibility accuracy is consistent with shared conflict monitoring or time-dependent processes for reinterpreting stimuli. Taken together, the data align with accounts positing flexibility as an emergent, context-sensitive property of subsystem interactions, rather than a single ability, and suggest that flexible behavior across domains relies on distinct configurations of mechanisms.

This study contributes evidence that cognitive flexibility is not reducible to set shifting and does not appear as a unitary mechanism spanning language, mathematics, perception, and executive control tasks. Instead, flexibility exhibits task- and domain-specific components, with a modest shared factor reflecting processing speed across math and language. Future work should replicate these findings across broader populations and settings, incorporate multiple measures of executive functions (e.g., inhibition, working memory, conflict monitoring), examine links with personality traits (e.g., openness) and general anxiety, and clarify terminology across cognitive vs psychological flexibility. Establishing domain-specific labels (e.g., language flexibility, mathematical flexibility) may better capture the phenomenon if flexibility proves domain-bound.

• Online administration reduced experimental control (e.g., environment, distractions, device variability) and may affect reliability/validity despite generally coherent within-task patterns.
• Only one specific set-shifting paradigm was used; other shifting tasks with different demands might yield different associations.
• Sample limitations: predominantly first-year undergraduates (many psychology majors) and relatively few male participants may limit generalizability.
• Small effect sizes in MANOVA and correlations; potential subtle differences between country subsamples warrant further investigation.
• Ambiguous figures’ validity metrics are not established; math task reliability was moderate (α≈.61). Replication with diversified measures and controlled lab settings is recommended.