Neural Associations between Inhibitory Control and Counterintuitive Reasoning in Science and Maths in Primary School Children

There is an increasing need to support individuals' science, technology, engineering and mathematics (STEM) skills, not only for personal growth, career opportunities (e.g., Waite & McDonald, 2019; Walker & Zhu, 2013), and economic and technological advancements (e.g., Hanushek & Woessmann, 2008) but also for tackling global challenges, such as climate change and public health crises (e.g., Hotez, 2021). However, learning STEM skills can be challenging, in part due to the prevalence of counterintuitive concepts within the domains of science and mathematics (Mareschal, 2016). Examples of intuitive but incorrect beliefs are that it is warmer in the summer because the Earth is closer to the Sun, that heavier objects fall faster even in a vacuum, and that −3 is less than −8. Therefore, to support the development of STEM skills in the population, a better understanding of maths and science counterintuitive reasoning is crucial.

Recent evidence has suggested that inhibitory control, defined as the suppression of prepotent responses or interfering thoughts (Diamond, 2013; Aron, 2007; Nigg, 2000), supports counterintuitive reasoning. Experimental research exploring scientific and mathematical conceptual change in undergraduates (Shtulman & Valcarcel, 2012) and adolescents (Babai, Eidelman, & Stavy, 2012) have interpreted longer RTs when participants reason about counterintuitive concepts (vs. naive intuitive concepts) as evidence for the involvement of inhibitory control (Mareschal, 2016). The theory is that both the naive intuitive concept and the new counterintuitive concept coexist simultaneously, and inhibitory control suppresses the naive concept, so the counterintuitive concept can come to mind.

Individual differences and intervention studies provide further convergent evidence. Individual differences in inhibitory control have been associated with counterintuitive reasoning in science and maths in adolescents (Brookman-Byrne, Mareschal, Tolmie, & Dumontheil, 2018), young adults (Coulanges et al., 2021), and children (Dumontheil et al., 2023; Wilkinson et al., 2020; Mason, Zaccoletti, Carretti, Scrimin, & Diakidoy, 2019; Vosniadou et al., 2018). Moreover, in a large-scale randomized controlled trial, an intervention increasing children's awareness of the prevalence of counterintuitive concepts and encouraging them to stop and think about their responses in maths and science showed that training children to apply their inhibitory control skills for science and maths reasoning led to improvements in science and maths standardized tests in 9- to 10-year-olds, but not 7- to 8-year-olds (Roy et al., 2019). In addition, in smaller samples, this intervention led to improvements in science and maths counterintuitive reasoning in 7- to 8-year-olds but not 9- to 10-year-olds (Dumontheil et al., 2023; Wilkinson et al., 2020). Although there were age differences, these findings indicate that training children to use their inhibitory control skills can lead to improvements in counterintuitive reasoning, thus supporting the theory that inhibitory control is involved in counterintuitive reasoning.

fMRI research has also provided some evidence consistent with an involvement of inhibitory control in counterintuitive reasoning. It has been found that when adults and adolescents reason about maths or science counterintuitive concepts, greater increases in BOLD signal occur in the dorsolateral pFC (DLPFC), ventrolateral pFC (VLPFC) and ACC (Meier, Wambacher, Vogel, & Grabner, 2022; Allaire-Duquette et al., 2021; Potvin, Malenfant-Robichaud, Cormier, & Masson, 2020; Allaire-Duquette, Bélanger, Grabner, Koschutnig, & Masson, 2019; Brault Foisy, Potvin, Riopel, & Masson, 2015; Masson, Potvin, Riopel, & Foisy, 2014; Stavy, Goel, Critchley, & Dolan, 2006), although the exact loci of increased BOLD signal are inconsistent across studies (see Dumontheil, Brookman-Byrne, Tolmie, & Mareschal, 2022, for a review). These brain regions have been implicated in inhibitory control (e.g., Aron, Robbins, & Poldrack, 2014; Aron, 2007; MacDonald, Cohen, Stenger, & Carter, 2000), along with parietal cortex (for meta-analyses, see Gavazzi et al., 2023; Isherwood, Keuken, Bazin, & Forstmann, 2021; Gavazzi, Giovannelli, Currò, Mascalchi, & Viggiano, 2020; Huang, Su, & Ma, 2020; Guo, Schmitz, Mur, Ferreira, & Anderson, 2018; Hung, Gaillard, Yarmak, & Arsalidou, 2018; Zhang, Geng, & Lee, 2017). In addition, adults with greater scientific and mathematical expertise, compared with novices, have shown increased activation in brain regions associated with inhibitory control when reasoning about counterintuitive problems in their area of expertise. For example, male physics undergraduates, compared with humanities undergraduates, showed greater activation in the right VLPFC and left DLPFC when reasoning about falling objects (Brault Foisy et al., 2015) and in the left VLPFC and left DLPFC when reasoning about electrical circuit counterintuitive problems (Masson et al., 2014). Similar neuroimaging findings were observed in mathematicians compared with nonmathematicians when reasoning about maths-related counterintuitive problems (Meier et al., 2022). Furthermore, chemistry professors have been shown to demonstrate greater activation in the left VLPFC, left DLPFC, pre-SMA, and anterior insula when reasoning about counterintuitive chemistry problems, compared with intuitive ones (Potvin et al., 2020). Taken together, this evidence is consistent with the proposal that, compared with novices, experts' better counterintuitive reasoning skills rely in part on the recruitment of inhibitory control processes.

However, it is unclear the extent to which these patterns of neural activation observed in the pFC specifically reflect the recruitment of inhibitory control processes. Instead, these activations may reflect increased top–down attention and processing of the stimuli (Corbetta & Shulman, 2002) or the recruitment of multidemand processes (Crittenden, Mitchell, & Duncan, 2016; Duncan, 2010). To complicate this further, there is currently no consensus on whether inhibitory control is a unitary or diverse construct; however, it is broadly accepted that inhibitory control can be subdivided into interference control and response inhibition (Diamond, 2013). Interference control refers to the ability to suppress distracting/irrelevant information, memories, or semantic knowledge, whereas response inhibition refers to the ability to suppress a motor response (Diamond, 2013). To better understand whether counterintuitive reasoning in science and maths and inhibitory control tasks recruit similar patterns of neural activation, Dumontheil and colleagues (2022) had adolescents undergo fMRI while answering counterintuitive and noncounterintuitive (control) science and maths questions, alongside three inhibitory control localizer tasks, a simple go/no-go task, a complex go/no-go task (with a 1-back working memory load), and a numerical Stroop task. These tasks measure response inhibition, response inhibition with a working memory load, and interference control, respectively.

There are two complementary ways of analyzing fMRI data to understand whether similar regions of the brain show increased activated across tasks. First, univariate analysis can show mean regional overlap of increased activation. However, to better understand the similarity of patterns of activations across tasks, multivariate similarity analysis can be applied. This approach correlates activation across voxels across tasks within an individual, to quantify the similarity of neural activation across tasks within a brain region. In the study by Dumontheil and colleagues (2022), counterintuitive trials showed increased BOLD signal changes in the DLPFC, VLPFC, and parietal regions compared with control trials, consistent with previous work. Univariate analysis showed that these changes partially overlapped, with increased BOLD signal changes in the complex response inhibition task and interference control task. However, multivariate similarity analysis showed neural similarity between counterintuitive reasoning tasks and both complex go/no-go and numerical Stroop tasks in the right supramarginal gyrus only (Dumontheil et al., 2022). These results suggest that in adolescence, simple response inhibition may be less relevant for counterintuitive reasoning than when it is combined with a working memory load and that the pFC activation observed in previous studies may not necessarily reflect inhibitory control neural processes specifically but instead reflect broader cognitive control neural processes involved in a range of complex tasks (cf. multidemand system; Crittenden et al., 2016; Duncan, 2010). The findings further underscore the importance of using inhibitory control localizers for exploring neural similarities between inhibitory control and counterintuitive reasoning.

The relationship between counterintuitive reasoning and inhibitory control is of particular importance in childhood, as this developmental stage is where many counterintuitive concepts in science and maths first arise, as part of the primary school curriculum. Furthermore, there is an extensive body of literature showing behavioral differences in inhibitory control skills (Constantinidis & Luna, 2019; Lewis, Reeve, Kelly, & Johnson, 2017; Cragg, 2016; Klenberg, Närhi, Korkman, & Hokkanen, 2015; van der Laar, van den Wildenberg, van Boxtel, & van der Molen, 2014; Ordaz, Foran, Velanova, & Luna, 2013; Bedard et al., 2002), as well as differences in the neural correlates of inhibitory control, across development (Ordaz et al., 2013; Durston et al., 2002, 2006; Bunge, Dudukovic, Thomason, Vaidya, & Gabrieli, 2002; Tamm, Menon, & Reiss, 2002; see Kang, Hernández, Rahman, Voigt, & Malvaso, 2022, for a review). Studies have also shown increased positive associations between pFC activation and both interference control (Marsh et al., 2006; Adleman et al., 2002, referred to as self-regulation; Schroeter, Zysset, Wahl, & von Cramon, 2004) and response inhibition performance (Tamm et al., 2002) with age. Finally, there is evidence to suggest that at younger ages, executive function skills and their neural correlates may be less differentiated, but become more differentiated with age (e.g., Hartung, Engelhardt, Thibodeaux, Harden, & Tucker-Drob, 2020; Karr et al., 2018; Lee, Bull, & Ho, 2013, see Fiske & Holmboe, 2019, for a review). Collectively, this evidence suggests that the patterns of neural similarity between inhibitory control and counterintuitive reasoning may differ over the course of development.

Therefore, the present study aimed to investigate neural similarities when primary-school-aged children engaged in counterintuitive science and maths reasoning and two inhibitory control tasks, using univariate and multivariate approaches. It was hypothesized that overlapping neural activation would be observed in DLPFC, VLPFC, and parietal cortex (as per Dumontheil et al., 2022; Potvin et al., 2020) and that neural similarity would be present between counterintuitive reasoning tasks and both interference control and response inhibition tasks.

Fifty-six children aged between 7 and 10 years old (26 female, 30 male, M_age = 9.02 years, SD = 1.01 years) were recruited from Year 3 (n = 25) and Year 5 (n = 31) in 13 schools in England. The children were part of the UnLocke project (www.unlocke.org), which involved the development and assessment of an intervention to encourage children to “Stop & Think” before answering counterintuitive reasoning tasks (see Roy et al., 2019, for details of the randomized controlled trial and Dumontheil et al., 2023, for additional sample information). Twenty-three participants were recruited in October–November 2017 and 33 in March 2018. The original aim, within budgeting constraints, was to recruit a sample of 80 children to assess the impact of the Stop & Think intervention on neural activation. However, recruitment was constrained by the timings of the interventions and our target was not achieved. The final sample is, however, greater than the adolescent sample successfully used in a previous study (Dumontheil et al., 2022; n = 34) and was therefore appropriate to carry out univariate and multivariate fMRI analyses to compare the neural correlates of science and maths counterintuitive reasoning and inhibitory control. A power analysis carried out with G*Power 3.1.9.4 (Faul, Erdfelder, Lang, & Buchner, 2007) suggested that across 50 voxels (our minimum sample size for the definition of ROIs used in the multivariate analyses), a correlation of .334, corresponding to a Fisher's z score of 0.166 (our measure of similarity between tasks), can be detected with 80% power (α = .05). In turn, a sample of 40 participants can give 80% power to find a mean Fisher's z of 0.169 as being significantly greater than zero in a one-sample t test. Our previous study in adolescents reported similarity between maths and science counterintuitive reasoning with Fisher's z scores ranging between 0.22 and 0.28 and similarity between maths and science counterintuitive reasoning and inhibitory control tasks with scores ranging between 0.16 and 0.19. The current sample size is therefore sufficient to detect similar or larger similarity between tasks.

The percentage of children receiving free school meals (an indirect indicator of low household income) ranged between 0.6% and 25.0% across schools (M = 10.1%, SD = 8.2; note 13.6% of primary school pupils received free school meals in England in January 2018; Department for Education, 2018). Participants did not have any known developmental or neurological disorders. Written informed parental consent and verbal assent from each child was collected. Travel expenses were reimbursed, and each child received a small gift plus a digital image of their brain scans for participation. The study was approved by the University College London ethics committee.

Functional neuroimaging data were collected pre- and postintervention, approximately 12 weeks apart. Neural correlates of counterintuitive reasoning and inhibitory control did not prove sensitive enough to detect the effects of intervention with the size of this subsample, even though behavioral intervention effects were observed in much larger cognitive (n = 372; Dumontheil et al., 2023) and randomized controlled trial (n = 5437; Roy et al., 2019) samples. Therefore, for current purposes, data from both time points (T1: pre-intervention, T2: postintervention) were included to increase the power of the study.

Exclusions of participants based on head motion, performance, or unfinished task completion were implemented. Behavioral exclusions were applied if accuracy, RT, or no-response rates were outside 3.29 SDs of the mean. Task runs were excluded for excessive head motion (see the MRI Data Acquisition and Preprocessing section below). Reasons for not completing the tasks included being nervous/uncomfortable in the scanner environment, nausea, and wanting a break. At T2, 17 children did not return for the scanning session and one child attended but was unable to complete any tasks in the scanner due to discomfort when in the scanner. Note that there were no significant differences between those who returned at T2 compared to those who did not in age, sex, nor counterintuitive reasoning and inhibitory control task performance measures (all ps > .071). The final school year group breakdown, sample sizes for each task, and reasons for exclusion can be seen in Table 1.

Participants completed the testing sessions (T1 and T2) at the Birkbeck-UCL Centre for Neuroimaging. Each fMRI session comprised four runs of science and maths counterintuitive reasoning tasks, and one run each of the Animal Size Stroop task and the Pokémon go/no-go task. Total scanning duration was 40–50 min.

The counterintuitive reasoning task consisted of 40 (20 science, 20 maths) age-appropriate, teacher-approved science and maths counterintuitive questions identified during the preparation of the Stop & Think intervention based on the Key Stage 2 National Curriculum for England (Department for Education, 2013a, 2013b) and books highlighting concepts primary school children find counterintuitive (e.g., Ryan & Williams, 2007; Stavy & Tirosh, 1999). The test items largely differed across year groups to reflect age-appropriate syllabus knowledge. However, 25% of questions overlapped between the groups. On each trial, a statement and image appeared on the screen (Figure 1) and participants were asked to answer whether the statement was true or false by pressing a button using the index or middle finger of their right hand.

Two runs of maths and two of science were completed in an alternating pattern counterbalanced across participants, with 10 counterintuitive reasoning trials per run. A response could be made after 1.5 sec of the stimulus presentation. After 14 sec, the response cues were outlined in a red border to prompt a response. A baseline task of black animal silhouettes facing either to the left or right (Figure 1B) was presented between counterintuitive trials for up to 20 sec or until the participants made a response. Participants were asked to press a button corresponding to the direction the animal was facing; the silhouette remained on the screen until participants made a response, up to a maximum of 1 sec, and the interstimuli interval was randomized between 0 and 200 msec, with a mean of 100 msec. This baseline task encouraged participants to disengage from the previous counterintuitive question and prevented boredom (see Dumontheil et al., 2022, for a similar approach). Although we used matched noncounterintuitive trials in a previous study in adolescents (Dumontheil et al., 2022), here, a baseline task was used for pragmatic reasons relating to the length of time that 7- to 10-year-old children can deliver high-quality data within the scanner and to limit the complexity of the design to test for intervention effects. There were four fixation blocks, presented after the second, fifth, seventh, and last trials, which lasted 10, 15, 10, and 5 sec, respectively.

The Animal Size Stroop task is a modified age-appropriate version of the Stroop task (Morris, Farran, & Dumontheil, 2019; Merkley, Thompson, & Scerif, 2016). In this task, two well-known animals of different sizes were shown on each trial and participants were asked to press the button corresponding to the side of the “larger animal in real life.” On congruent trials, the biologically larger animal was shown as a larger image than the biologically smaller animal (Figure 2A). On incongruent trials, the biologically larger animal was shown as a smaller picture than the biologically smaller animal (Figure 2A). The Animal Size Stroop followed a block design, with alternating congruent and mixed (50% congruent, 50% incongruent) blocks of 12 trials. Congruent and incongruent trials in the mixed blocks were presented in a pseudorandom order, with no more than three congruent or incongruent trials in a row. The mixed blocks were expected to engage greater interference control than the congruent-only blocks. There were five blocks of each type, resulting in 60 congruent trials in congruent blocks, and 30 congruent and 30 incongruent trials in mixed blocks. Task blocks lasted 22.8 sec and were separated by instruction screens presented for 2 sec that stated, “Big animals are always big” (congruent block) or “Big animals are sometimes small” (mixed block). On each trial the stimuli remained on the screen for 1.7 sec or until the participant responded, a fixation cross was then shown until 1.9 sec after the start of the trial. There were four fixation blocks, occurring after the second, fifth, seventh, and last blocks and lasting 10, 15, 10, and 5 sec, respectively. Accuracy and RT were used as behavioral performance measures.

The Animal Size Stroop task is a variation of the numerical Stroop task used by Dumontheil and colleagues (2022) and was used to maximize the age appropriateness of the materials. Both variants have the key design characteristic that the stimulus has two properties potentially driving incompatible responses (the size of the stimulus vs. the size of the animal in real life in the Animal Size Stroop / the digits presented vs. the quantity of digits presented in the numerical Stroop), and inhibitory control is required to generate responses according to the less-salient dimension.

A modified age-appropriate version of the go/no-go task was used to measured response inhibition. If a blue or green Pokémon was presented on screen, the participants were asked to press the button corresponding to the side the Pokémon was presented on. If an orange Pokémon was presented, participants were asked to withhold a response (Figure 2B). This task comprised six go and six mixed (50% go, 50% no-go) alternating blocks. Each block consisted of 16 trials, resulting in 96 go trials in go blocks, and 48 go trials and 48 no-go trials in mixed blocks, presented in a pseudorandom order, with no more than three go or no-go trials in a row. The mixed blocks were expected to engage greater response inhibition than the go-only block. Blocks were separated by 2-sec instruction screens showing a blue and a green square with ticks or a green square with a tick and an orange square with a cross. Stimuli were presented for 400 msec, and participants had a maximum of 1 sec to respond. Trials were separated by a variable interstimulus interval of 0–400 msec, leading to average intertrial interval of 1.2 sec. There were four fixation blocks, occurring after the second, seventh, eleventh, and final task blocks lasting 10, 15, 10, and 5 sec, respectively. In addition to accuracy and RT, the difference between the z scores of the hit rate and false alarms was calculated in mixed blocks to obtain a d′ score combining performance on go and no-go trials (Stanislaw & Todorov, 1999; Hautus, 1995).

A 1.5 Tesla Siemens Avanto MRI scanner with a 30-channel head coil was used to collect structural and functional images. BOLD signal data were acquired using the Centre for Magnetic Resonance Research multiband EPI sequence (Xu et al., 2013) 4× acceleration, leak block on (Cauley, Polimeni, Bhat, Wald, & Setsompop, 2014) with the following parameters: repetition time = 1000 msec, echo time = 45 msec, resolution = 3 × 3 × 3 mm³, 44 slices covering most of the cerebrum. Structural anatomical scans were collected using a T1-weigthed magnetization prepared rapid gradient echo sequence with 2× generalized auto calibrating partial parallel acquisition acceleration. The parameters were as follows: 176 slices, repetition time = 2730 msec, echo time = 3.57 msec, resolution = 1 × 1 × 1 mm³, duration of scan = 5.5 min. The structural scan was carried out between the counterintuitive reasoning task and the inhibitory control task runs.

MRI scans were preprocessed and analyzed using SPM12 (www.fil.ion.ucl/uk/spm/software/spm12/) in MATLAB R2022b/R2023a. Excessive head motion outliers were calculated. Using the six realignment parameter estimates (translations and rotations), framewise displacement was calculated as a scalar measure of head motion for each volume. Volumes with a framewise displacement greater than 0.9 mm were excluded from the general linear model estimation and modeled with a regressor of no interest. Runs with more than 15% of volumes excluded and/or those with a root-mean-square movement greater than 1.5 mm were excluded from the fMRI analysis (Siegel et al., 2014).

The first eight volumes were removed to allow for equilibrium effects. Functional images were realigned to the mean image using a second degree B-spline interpolation. The structural image was then bias-field corrected and co-registered to the mean-realigned functional image of the first counterintuitive task run. For the inhibitory control tasks, the functional images were co-registered to the co-registered structural scans and the same normalization parameters were applied. The co-registered structural image was then segmented based on Montreal Neurological Institute (MNI) registered International Consortium for Brain Mapping tissue probability maps. The realigned functional images were normalized using the spatial normalization parameters and smoothed using an 8-mm FWHM Gaussian kernel.

Behavioral data were analyzed using RStudio 2023.03.0, running R 4.3.0, using the lme4 package to run mixed linear model analyses and restricted maximum likelihood methods of estimation. Linear mixed models (LMMs) were chosen to better account for missing data points and increase power. Assumptions of LMMs were checked to ensure that the residuals were approximately normally distributed. To account for the within-subject nature of the models, participant was included as a random effect (random intercepts only) in the models. p Values and approximations for degrees of freedom were calculated for F-tests and follow-up pairwise t tests using Satterthwaite's method for computing denominator degrees of freedom. Satterthwaite's method has been shown to produce acceptable Type 1 errors rates with smaller samples (<144 observations; Luke, 2017). Estimated marginal means were obtained from pairwise comparisons calculated using the emmeans() function. p Values for these comparisons were adjusted with a Tukey test, to control for Type I errors and to better account for unequal group sizes.

In the science and maths counterintuitive reasoning task, LMMs were conducted on mean accuracy and RT (combining correct and incorrect trials) data with discipline, year, and timepoint as fixed effects and participant as a random effect. LMMs were also conducted on mean accuracy and RT for correct trials in the inhibitory control tasks, with trial type, year, and timepoint as fixed effects and participant as random effects. For all LMMs, effect sizes for the fixed effects are reported as standardized regression coefficients. These were calculated using the standardize_parameters() function, as part of the effectsize package. The function was implemented using the refit method and robust = FALSE argument.

To test whether there were significant associations between counterintuitive reasoning and inhibitory control performance, LMMs were carried out with science or maths accuracy as the dependent variable, timepoint and year and their interaction as fixed effects, subject as a random effect, and (i) Pokémon go/no-go d′, (ii) Animal Stroop incongruent RT (controlling for congruent in congruent block RT), or iii) Animal Stroop incongruent accuracy (controlling for congruent in congruent block accuracy) as covariates.

Volumes acquired during each run were treated as separate time series. For each series, the variance in the BOLD signal was decomposed using general linear models. In the science and maths counterintuitive reasoning tasks, trials were modeled with a box-car regressor with individual RTs providing the duration of each trial. The implicit baseline included the fixation and animal silhouette task. Contrast images for the counterintuitive trials were calculated separately for science and maths. Inhibitory control tasks were modeled using a block design, including a box-car regression with duration of 2 sec representing the instruction screen at the start of each block. Block designs were used to increase the signal-to-noise ratio. For the Animal Size Stroop task, box-car regressors modeled the congruent, mixed, and fixation blocks, and first-level contrast images between mixed and congruent blocks were calculated. For the Pokémon go/no-go task, box-car regressors modeled go, mixed, and fixation blocks, and first-level contrast images between go-mixed and go blocks were calculated. All regressors were convolved with the standard canonical hemodynamic response function and, together with the separate regressors representing each censored volume and the session mean, comprised the full model for each run. A high-pass filter (cutoff = 128 sec) and an auto-regressive model of order one correction for serial autocorrelation were applied.

Four two-sample t tests between year groups were conducted on the following contrasts: (i) maths counterintuitive reasoning, (ii) science counterintuitive reasoning, (iii) Animal Size Stroop mixed blocks > congruent blocks, and (iv) Pokémon go/no-go mixed blocks > go blocks. Where participants had data at both timepoints, contrast images were averaged using ImCalc. For the counterintuitive reasoning task, a participant × discipline × year flexible factorial design analysis was conducted, modeling the interaction between discipline and year, with participant as a main effect (to take into account the repeated-measures nature of the data).

For the second-level analyses, SPM maps were thresholded at p < .001 uncorrected at voxel-level and FWE-corrected p < .05 at the cluster level. In addition, voxels significant at whole-brain FWE-corrected p < .05 are reported. All coordinates given are in MNI space, and region labeling was performed using the Automatic Anatomical Labelling toolbox (Rolls, Huang, Lin, Feng, & Joliot, 2020).

ROIs were identified from the univariate analysis of the two inhibitory control tasks, using a threshold of p < .001 uncorrected and a minimum cluster size of 50 voxels. For large clusters, WFU_Pickatlas (Maldjian, Laurienti, & Burdette, 2004; Maldjian, Laurienti, Kraft, & Burdette, 2003) and Automatic Anatomical Labelling atlas (Tzourio-Mazoyer et al., 2002) were used to separate large regions into smaller ROIs based on anatomical labels. ROI MNI coordinates, cluster size, and center of mass were identified using MarsBaR (Brett, Anton, Valabregue, & Poline, 2002).

Multivariate correlation analysis was applied to determine whether, beyond spatial overlap, there was neural similarity between the inhibitory control and science and maths counterintuitive reasoning tasks. For each voxel in each cluster, the parameter estimates of each contrast of interest were extracted using MarsBaR. Kendall's tau correlations were calculated across the voxels of each cluster within participants for four task comparisons of interest: (1) Stroop versus science, (2) Stroop versus maths, (3) Pokémon versus science, and (4) Pokémon versus maths (n = 42, 41, 44, and 42, respectively), plus one reference comparison: maths versus science (n = 50). Note that only participants with neuroimaging data (either T1, T2, or an average across both timepoints) for both tasks could be included in each comparison. Kendall's tau correlations were calculated as the data did not meet assumptions for a normal distribution. Kendall's τ values were transformed into Pearson's r (r = sin(0.5 × π × τ)), which were then transformed into Fisher's z scores (z = 0.5 × ln ((1 + r)/(1 − r)); Walker, 2003) to allow further statistical analysis. The term similarity scores will be used to refer to these Fisher's z scores.

Intercepts from one-way ANOVAs on the similarity scores, with year group as a factor, were used to assess whether the similarity scores were significantly greater than zero using SPSS 29. Similarity was assessed between (i) science and maths counterintuitive reasoning and the Animal Size Stroop task separately in the 12 Animal Size Stroop ROIs, (ii) science and maths counterintuitive reasoning and the Pokémon task separately in the two Pokémon ROIs, and (iii) science and maths counterintuitive reasoning on all 14 ROIs. Multiple comparisons were adjusted for across all these analyses using the Benjamini-Hochberg method to adjust false discovery rate (FDR). This adjustment ranks the p values observed in a set of comparisons and identifies an upper bound for p values that fixes the expected proportion of false positives among all rejections of the null hypotheses to a criterion, 5% in this case (Benjamini & Hochberg, 1995).

We conducted 2 × 2 (Year × Discipline) mixed repeated-measures ANOVAs for the 12 ROIs derived from the Animal Size Stroop task and the two ROIs derived from the Pokémon go/no-go task, to assess whether the multivariate similarities of each inhibitory control task differed between science and maths and between year groups. Finally, to assess whether individual variability in neural similarity predicted counterintuitive reasoning behavioral performance, the science and maths similarity scores were averaged across Animal Size Stroop ROIs and correlated with science and maths accuracy on the counterintuitive reasoning task, respectively. As only one Pokémon go/no-go ROI showed significant similarity between math counterintuitive reasoning with the go/no-go task, the similarity score for this ROI was correlated with maths accuracy.

Descriptive statistics for the science and maths counterintuitive reasoning tasks are reported in Table 2, estimated marginal means are reported in the following text, and effect sizes for the LMMs are presented in Table 3. LMMs showed overall higher accuracy in maths (M = 57.8%, SE = 2.0%) compared with science (M = 50.7%, SE = 1.7%), F(1, 111.5) = 15.22, p < .001, and significantly greater accuracy at T2 (M = 56.5%, SE = 2.0%) than T1 (M = 52.1%, SE = 1.6%), F(1, 135.7) = 5.12, p = .025, but no significant differences in accuracy between year groups, nor an interaction, were observed, Fs < 1.62, ps > .21. As mean accuracy was ∼50%, accuracy scores for each question were calculated to determine whether participants were consistently answering at chance or whether mean accuracy differed on a trial-by-trial basis (see Table A1 in the Appendix). The results show a range of mean accuracy scores, demonstrating that the children were engaged, and the questions varied in difficulty. Children responded faster at T2 (M = 6656 msec, SE = 181) than T1 (M = 7045 msec, SE = 158), F(1, 119.9) = 7.78, p = .006, but there was no significant difference between disciplines, F = 3.49, p = .064, or year groups, F = 0.81, p = .37, and no significant interactions, Fs < 1.41 and ps > .24.

Accuracy significantly differed across Trial Type, F(2, 154.5) = 17.49, p < .001. Higher accuracy was observed in congruent trials in congruent blocks (M = 96.1%, SE = 0.88) than in congruent trials in mixed blocks (M = 92.4%, SE = 0.88, p = .002) and incongruent trials in mixed blocks (M = 90.4%, SE = 0.88, p < .001). However, congruent and incongruent trials in the mixed block did not significantly differ, p = .10. No significant differences in accuracy were observed between Timepoints or Year groups, and there were no significant interactions, all Fs < 0.76, ps > .39. As expected, Animal Size Stroop RT also differed across trial type, F(2, 152.8) = 124.39, p < .001; mean RT was lower in congruent trials of congruent blocks (M = 749 msec, SE = 15, p < .001) than on congruent trials of mixed blocks (M = 896 msec, SE = 14, p < .001) and highest in incongruent trials of mixed blocks (M = 940 msec, SE = 14, p < .002). Children were quicker at T2 (M = 847 msec, SE = 15) than T1 (M = 876 msec, SE = 13), F(1, 167.6) = 6.16, p = 0.014, and Year 5 children responded more quickly (M = 826 msec, SE = 16) than Year 3 children (M = 897 msec, SE = 20), F(1, 43.2) = 7.46, p = .009, but there were no significant interactions, Fs < 0.88 and ps > .42.

In the Pokémon go/no-go task, accuracy differed between Trial Types, F(2, 155.1) = 19.22, p < .001; accuracy was greater on go trials in mixed blocks (M = 86.8%, SE = 1.5) than in go trials in the go blocks (M = 82.1%, SE = 1.5%) and lowest in no-go trials in mixed block (M = 76.7%, SE = 1.5%, all pairwise comparisons ps < .012). There were no significant differences between Year groups, or Timepoints, and no interactions, Fs < 3.07 and ps > .081. Participants responded more quickly on go trials in go blocks (M = 510 msec, SE = 8) than mixed blocks (M = 574 msec, SE = 8), F(1, 90.7) = 156.02, p < .001, and more quickly at T2 (M = 534 msec, SE = 9) than T1 (M = 551 msec, SE = 8), F(1, 103.9) = 7.22, p = .008. No significant difference was observed between year groups, F(1, 44.7) = 3.94, p = .053. There were significant Trial Type × Year, F(1, 90.7) = 4.36, p = .039, and a Trial Type × Timepoint × Year interactions, F(1, 90.7) = 4.65, p = .034. Follow-up analyses showed that there was a greater difference in go trials RT between go and mixed blocks in Year 3 children (M_diff = 74.6 msec, p < .001) than Year 5 children (M_diff = 53.2 msec, p < .001), and that Year 3 children showed a decrease in RT between T1 and T2 in go trials in go blocks (p = .001), but not go trials in mixed blocks (p = .789), whereas Year 5 children did not show significant differences in RT over time, in either trial type (ps > .22; Figure 3). Analysis of d′ in mixed blocks showed no significant differences between year groups nor timepoints, with no significant interaction (Fs < 1.75, ps > .19).

Inhibitory control measures did not significantly predict counterintuitive reasoning accuracy in maths nor science. For the science LMMs, all Fs < 1.90, ps > .173. For the maths LMMs, all Fs < 0.45, ps > .504.

Science and maths counterintuitive reasoning trials were associated with increases in activation in a broad network of frontal, parietal, temporal, and occipital regions (Figure 4A and B; see Tables A2 and A3 in the Appendix for details). Activation in the science and maths counterintuitive reasoning contrasts broadly overlapped; however, maths counterintuitive reasoning was associated with greater activation in right superior pFC and extended further in left superior pFC (Figure 5A), and there were additional differences between disciplines in the intensity of the BOLD signal. Compared with science, maths counterintuitive reasoning was associated with greater activation intensity in bilateral parietal cortices, including bilateral superior and inferior gyri (Brodmann area [BA] 40), as well as bilateral precuneus (BA 7), bilateral inferior temporal gyri (BA 37/20), a cluster across bilateral superior and middle frontal gyri (BA 6/8/45/46), extending into bilateral SMA on the medial wall, the right frontal operculum and the ACC (BA 32) and clusters in the precentral gyri (BA 6), extending to the inferior frontal gyrus (BA 44), and in the cerebellum (Table A4). The opposite contrast showed greater activation intensity in science counterintuitive reasoning than maths in the inferior and middle occipital gyri (BA 18/19) extending to posterior middle temporal gyri (BA 20), along the length of the fusiform gyri (BA 37) and into anterior hippocampi, as well as in anterior middle temporal gyri (BA 38) extending into temporal poles (BA 48/22) and the left orbital frontal gyrus (BA 47; Table A4).

A flexible factorial analysis showed a significant Discipline × Year interaction in two clusters: the right inferior frontal gyrus (BA 45 [39, 38, 8]) and ACC (BA 24 [3, 26, 17]). In both these clusters, greater activation was observed in Year 5 than Year 3 in maths, and greater activation in Year 3 than Year 5 in science.

The Animal Size Stroop task was used as an interference control task. Comparing mixed incongruent/congruent blocks to congruent blocks showed large clusters of increased activation in broad bilateral occipital and parietal regions (Figure 4C, Table A5). More specifically, in the superior parietal lobule, inferior parietal lobule and precuneus, as well as the fusiform gyrus, superior and inferior occipital gyri, and some of the calcarine gyrus. Additional clusters were observed in bilateral superior and inferior frontal gyri and left precentral gyrus. The Pokémon go/no-go task was used as a measure of response inhibition. Comparing mixed go/no-go blocks to go blocks showed increased activation in the right superior parietal gyrus extending to the precuneus and a cluster in the right superior frontal gyrus (Figure 4D, Table A5). No significant differences in activation were observed between Year groups in either inhibitory control task.

Clusters from the Pokémon and Animal Size Stroop univariate analysis were used as ROIs in the subsequent multivariate pattern analysis, using a threshold of p < .001 uncorrected at the voxel level and a minimum cluster size of 50 voxels. Two clusters from the Pokémon and eight clusters from the Animal Size Stroop univariate analysis were identified (Table 3). One large Animal Size Stroop cluster was split into six clusters using left and right occipital, parietal, and temporal lobes regions from WFUPickAtlas as masks and MarsBaR. This resulted in separate left superior and inferior temporal clusters but a single right temporal cluster. The large cluster also extended to the top of the superior cerebellum; however, this region was not included as it was likely an artifact from smoothing. Note that two clusters in the right thalamus and right reticular formation extending into the caudate nucleus were excluded from a subsequent analysis, as this article's hypotheses focused on cortical regions. The resulting 12 Animal Stroop clusters are listed in Table 3. Note that there is overlap between the Pokémon precuneus/superior parietal cluster and the Animal Size Stroop parietal cluster and overlap between the two task ROIs in the superior frontal gyrus (see Figure 5B; Table 4).

Significant multivariate similarity (mean similarity scores greater than zero) was observed between the Animal Size Stroop and maths counterintuitive reasoning tasks in all 12 clusters (η_p² = .205–.624), and with the science counterintuitive reasoning task in 11/12 clusters (η_p² = .163–.767; Figure 6A). No significant multivariate similarity was observed between the Pokémon go/no-go ROIs and science counterintuitive reasoning tasks, but significant multivariate similarity was observed with maths counterintuitive reasoning in the right precuneus/superior parietal gyrus ROI only (η_p² = .197; Figure 6B). For comparison, multivariate similarly was explored between the science and maths counterintuitive reasoning tasks. This showed significant similarity in all ROIs, with a higher magnitude than those observed between counterintuitive reasoning and inhibitory control tasks (η_p² = .740–.950; Figure 6A and B).

Mixed Discipline × Year group ANOVAs conducted on the similarity scores showed significant differences between disciplines in three Animal Size Stroop ROIs (Figure 6). The left superior frontal gyrus cluster showed greater similarity scores between the Animal Size Stroop task and maths (M = 0.272) than science counterintuitive reasoning (M = 0.069), F(1, 39) = 8.06, p_FDR = .033, η_p² = .171. Reversely, the right inferior/middle temporal gyri ROI and the left inferior temporal gyrus ROI showed greater similarity with science than maths (right hemisphere: F(1, 39) = 11.68, p_FDR = .010, η_p² = .230, science: M = 0.475, maths: M = 0.360; left hemisphere: F(1, 39) = 11.89, p_FDR = .010, η_p² = .234, science: M = 0.547, maths: M = 0.424). Note that the right superior frontal gyrus and left parietal lobe clusters also showed significant differences between disciplines, but these did not survive FDR adjustments (Figure 6). No other significant differences between disciplines in any other ROIs were detected (p_FDRs > .126), and no significant year group differences nor Discipline × Year interactions were identified (p_FDRs > .646).

Finally, Animal Size Stroop and math counterintuitive reasoning similarity scores (averaged across ROIs) were found to positively correlate with maths counterintuitive reasoning accuracy, r(39) = .40, p = .009. No similar association was found for science, r(39) = .24, p = .881, nor between Pokémon go/no-go and math counterintuitive reasoning similarity score in the superior parietal lobe/precuneus ROI and maths counterintuitive reasoning accuracy, r(40) = .15, p = .330.

Multivariate similarity analysis of fMRI data was used to investigate the role of inhibitory control in science and maths counterintuitive reasoning in primary-school-aged children. We found significant neural similarity between an interference control task and both maths and science counterintuitive reasoning in almost all brain regions that showed increased activation during the interference control task. This included DLPFC, VLPFC, and parietal cortex, as per our hypothesis, plus temporal and occipital regions. In brain areas showing increased activation during response inhibition, significant neural similarity was observed between the response inhibition task and maths counterintuitive reasoning in the right precuneus/superior parietal gyrus only. These findings suggest that in children, science and maths counterintuitive reasoning and inhibitory control, specifically interference control, exhibit similar neural activation. This is consistent with the hypothesis that inhibitory control plays a role in counterintuitive reasoning derived from previous research in adolescents and adults.

Behavioral analysis of counterintuitive reasoning task accuracy suggested the difficulty of the tasks were well matched across year groups, as no significant differences in performance across year groups were observed. There was an improvement in performance from T1 to T2, likely reflecting school-based science and maths learning over the 12-week period between scans, as well as possible practice effects. This matches results from a larger cohort (which partially includes this neuroimaging cohort), showing improved performance in a different science and maths counterintuitive reasoning task over a 12-week period (Dumontheil et al., 2023). In the current study, children were significantly slower but more accurate in maths compared with science trials, suggesting that slowing down benefits maths counterintuitive reasoning accuracy (or that children who are better at counterintuitive reasoning take longer to answer). This idea supports the theory that during counterintuitive reasoning, additional cognitive processes are required to suppress the naive intuitive concepts, and concurs with behavioral studies that found slower responses resulted in better performance in counterintuitive reasoning tasks (e.g., Babai et al., 2012).

We observed increased BOLD signal in the science and maths counterintuitive reasoning tasks in large clusters in bilateral occipital, temporal, and parietal areas, extending to the pFC. This concurs with previous research exploring the neural correlates of science and maths counterintuitive reasoning in adults (Meier et al., 2022; Allaire-Duquette et al., 2021; Brault Foisy et al., 2015; Masson et al., 2014; Stavy et al., 2006) and adolescents (Dumontheil et al., 2022; Allaire-Duquette et al., 2019). However, in the current study, much broader regions of increased activation were detected. It is possible that children recruit broader brain regions than adolescents or adults when reasoning about counterintuitive concepts. Alternatively, the broader activation more plausibly reflects the fact that in the present study counterintuitive trials were not compared with control noncounterintuitive trials; thus, this activation also likely reflects the cognitive processing of text, images, and broader reasoning recruited in the task. This control condition was not included in the current study for pragmatic reasons. Future work may wish to investigate the neural correlates of maths and science counterintuitive reasoning using matched noncounterintuitive control trials (as done by, e.g., Meier et al., 2022; Dumontheil et al., 2022; Allaire-Duquette et al., 2019, 2021) to better isolate the specific neural signature of counterintuitive reasoning in children.

Differences in BOLD signal between disciplines were also observed. Although a previous study in adolescents did not find differences between science and maths counterintuitive reasoning activation when compared with noncounterintuitive trials (Dumontheil et al., 2022), in the current study, counterintuitive reasoning in maths compared with science led to activation extending further into the superior parietal cortex and superior frontal cortex, in particular in the right hemisphere, as well as greater increases in BOLD signal in bilateral parietal cortex and both lateral and medial aspects of the pFC. In contrast, counterintuitive science reasoning in science trials, compared with maths trials, was associated with greater increases in BOLD signal in occipital and temporal regions. The stimuli varied in many ways across science subjects and maths topics, with the use of drawings, text, and symbols. Differences between maths and science stimuli may have driven some of the different brain activity patterns observed.

Studies of the neural correlates of maths in children tend to focus on arithmetic and suggest a shift from pFC to posterior parietal cortex and then angular gyrus activation, when children move from calculation to retrieval strategies (Peters & De Smedt, 2018). However, few studies have investigated neural correlates of mathematics across a broader range of subjects, as was used here, that is, arithmetic, as well as geometry and graphs. Amalric and Dehaene (2016) found that when adult professional mathematicians listened to maths statements across a range of topics (analysis, algebra, topology, and geometry) and judged their accuracy, compared with nonmaths statements, they recruited a consistent network of bilateral intraparietal, inferior temporal, and dorsal pFC regions. Frontal and parietal cortical regions have therefore been implicated in mathematical reasoning across ages. In science, in contrast, distinct neural correlates have been found for different aspects of physics (Mason & Just, 2016), suggesting that science may draw on more domain-specific skills. Scientific reasoning has been associated with activation in lateral prefrontal areas supporting diverse executive functions, but also with activation of the medial temporal lobes, which Nenciovici, Allaire-Duquette, and Masson (2019) argue could reflect the recruitment of declarative memory processes, and influence of prior knowledge, on scientific reasoning. However, there is a lack of neuroimaging research on the development of the neural correlates of science reasoning in mid-childhood that the present results could be compared with.

Differences in BOLD signal across disciplines were also observed as an interaction with year group. Although there was no difference in BOLD signal changes during counterintuitive reasoning as a whole between year groups, significant Discipline × Year interactions were found in the right inferior frontal gyrus and ACC, with greater activation in Year 5 than Year 3 in maths and greater activation in Year 3 than Year 5 in science. This is of interest considering the right inferior frontal gyrus (IFG) is thought to be involved in inhibitory control (Aron et al., 2014; Aron, 2007) and the ACC in error detection (e.g., Carter et al., 1998). It is possible that these differences reflect the fact that different problems were presented to Year 3 and Year 5 children. Despite these trials being designed based on the Key Stage 2 maths and science U.K. national curriculum, we could not control for the children's individual school syllabus and whether the concepts had been learned recently or potentially many months previously. For example, Year 5 children could have recently learned about certain mathematical counterintuitive concepts present in the current study and were thus better able to identify the trials as counterintuitive and recruit inhibitory control to answer correctly. Future similar work may wish to collect data on the school syllabus to account for this possibility.

As expected, incongruent trials were associated with lower accuracy and longer RTs in the Animal Size Stroop task. There was also a mixing cost on congruent trials, with lower accuracy and longer RT in congruent trials in mixed blocks compared with congruent-only blocks. There was no significant difference in accuracy between year groups. Year 5 children responded overall faster than Year 3 children; however, this was not specific to incongruent trials, implying we did not find evidence of greater efficiency in inhibitory control skills in the older children. This age group difference may instead reflect maturation of processing speed or motor responses.

In the interference control task, the contrast mixed > congruent showed increased activation in large occipital and parietal areas and small clusters in frontal regions. These findings in children broadly fit with results of individual studies and meta-analyses investigating the neural correlates of interference control in adults and adolescents using variations of the Stroop task, which report increased activation in parietal and occipital cortex, as well as VLPFC and DLPFC (Dumontheil et al., 2022; Isherwood et al., 2021; Huang et al., 2020; Hung et al., 2018; Zhang et al., 2017; Xu, Xu, & Yang, 2016; Cieslik, Mueller, Eickhoff, Langner, & Eickhoff, 2015; Laird et al., 2005). Although studies exploring the neural correlates of interference control in typically developing children are limited (see Kang et al., 2022, for a review), broad occipital and parietal activation has been observed in another fMRI study exploring the (color) Stroop effect in children of this age, suggesting this broad pattern of increased activation could reflect inhibitory control in children (Adleman et al., 2002).

RTs for the response inhibition were slower, but accuracy higher in go trials of the mixed blocks than the pure go blocks, suggesting that because of the possibility of no-go trials in mixed blocks, participants slowed down, leading to higher accuracy in the left/right response in go trials. Whether because of development or practice effects, Year 3 children responded faster on go trials in go blocks at T2 than T1. As expected, accuracy was lowest in the no-go trials in the mixed block.

The contrast go/no-go > go blocks showed greater activation in the right superior parietal/precuneus and right superior frontal gyrus only. DLPFC and parietal cortex, among other regions, have been observed in meta-analyses exploring action withholding tasks (e.g., go/no-go tasks) in adults (Gavazzi et al., 2020; Guo et al., 2018; Cieslik et al., 2015; Criaud & Boulinguez, 2013). However, our findings do not concur with the prominent theory that the right IFG is central to response inhibition (Aron et al., 2014; Aron, 2007, 2011). One interpretation is that the right IFG is associated with response inhibition in adults, but less consistently in children (Suskauer et al., 2008; Bunge et al., 2002; Durston et al., 2002; see Kang et al., 2022). Interestingly, Bunge and colleagues (2002) found that 8- to 12-year-old children with better no-go performance showed greater bilateral inferior parietal activation, whereas children with worse no-go performance showed greater bilateral DLPFC and left VLPFC activation. Neither group showed increased activation in the right VLPFC, which was observed in adults. Therefore, posterior activation may be more involved in inhibitory control in children (Bunge et al., 2002).

Lack of significant effects can also be due to a lack of power. The current study used a block design, which is thought to be more sensitive to changes in the BOLD signal than an event-related design (Bunge et al., 2002). However, event-related designs may be more sensitive to transient activation associated with response inhibition on no-go trials specifically. This was also a limitation of the study by Dumontheil and colleagues (2022), which did not find increases in activation in simple mixed go/no-go blocks versus pure go blocks in adolescents.

In the current study, univariate activation in the Animal Size Stroop and Pokémon go/no-go task partly overlapped in right superior parietal cortex and right superior frontal gyrus. A previous study similarly found limited overlap of activation between interference control and response inhibition in 8- to 12-year-old children, compared with much more widespread overlap in adults, strongest in the right VLPFC (Bunge et al., 2002). However, further research, for example, contrasting block and event-related designs, is needed to assess the extent to which these two tasks have similar neural signatures in children or whether these differences reflect methodological differences.

Contrary to a previous study in a larger sample (Wilkinson et al., 2020), here, we did not find behavioral evidence for a role of inhibitory control in counterintuitive reasoning. This is likely due to the limited sample size in the current study. In contrast, univariate and multivariate analysis of the neuroimaging data suggest a role of inhibitory control in counterintuitive reasoning in science and maths in this age group.

Most of the regions identified in the interference control task showed univariate overlap with the activation observed during science and maths counterintuitive reasoning, although the occipital and parietal interference clusters were slightly broader than those observed during counterintuitive reasoning. In line with the broader frontal and parietal activation observed during maths than science counterintuitive reasoning, maths also showed greater univariate activation overlap with interference control in these regions. This univariate overlap includes regions that also showed overlap between science and maths counterintuitive reasoning and an interference control task (numerical Stroop) in adolescents, specifically in the right middle frontal and right parietal lobe (Dumontheil et al., 2022); however, the overlap in children appears much broader. In contrast, limited univariate overlap in activation was observed between the frontal and parietal clusters identified in the response inhibition task and science and maths counterintuitive reasoning. The adolescent study (Dumontheil et al., 2022) did not observe increased activation in the simple go/no-go task, potentially due to a lack of sensitivity in the task, making comparisons to the current study challenging.

Although overlap of activation was observed in the univariate analyses, these could still reflect recruitment of different neural populations. Multivariate similarity analyses were therefore carried out to complement the univariate analyses. Significant multivariate similarity was observed between interference control and counterintuitive reasoning tasks in (i) all 12 clusters showing increased BOLD signal in the interference control task for maths and (ii) all clusters, except the left superior frontal gyrus, for science. Multivariate similarity was significantly higher for maths than science in the left superior frontal gyrus and significantly stronger for science than maths in temporal clusters bilaterally. These results broadly fit with the fact that there was more superior frontal gyrus activation for maths than science and more temporal activation for science than maths counterintuitive reasoning in the univariate analyses. As per our hypothesis, neural similarity was observed in parietal cortex, DLPFC, and VLPFC, including the right IFG, although the cluster in BA 44 was more superior than VLPFC activation observed in previous studies in BA 47 when comparing counterintuitive and intuitive trials (Stavy & Babai, 2010) or in BA 45 or 47 when comparing counterintuitive reasoning in experts versus novices (Allaire-Duquette et al., 2019; Brault Foisy et al., 2015; Masson et al., 2014). In addition, significant neural similarity was observed in occipital and temporal regions, likely reflecting visual and memory retrieval processes required in both counterintuitive reasoning and the Animal Size Stroop incongruent > congruent contrasts. These findings suggest that counterintuitive reasoning and interference control recruit partially overlapping neural populations.

Significant neural similarity was observed between counterintuitive reasoning and the response inhibition task in the left precuneus/superior parietal gyrus cluster only, and only for maths. These regions have been associated with functions such as visuomotor processing, manipulation of information in working memory, and attention (Alahmadi, 2021; Cavanna & Trimble, 2006), processes likely involved in both the response inhibition and maths counterintuitive reasoning trials. However, no significant similarity was observed in the right superior frontal gyrus cluster, a region thought to be involved in impulse control and motor urgency (Hu, Ide, Zhang, & Li, 2016), suggesting that the overlap between response inhibition and maths counterintuitive reasoning may reflect working memory more than inhibitory control processes. As only limited increased activation was observed in the response inhibition task, further work is needed to confirm these results.

To date, one other study has used multivariate similarity analysis to determine neural similarity between inhibitory control and counterintuitive reasoning tasks, a study conducted in adolescents (Dumontheil et al., 2022). Interestingly, Dumontheil and colleagues (2022) showed neural similarity between maths and science counterintuitive reasoning (combined) with interference control (numerical Stroop) and response inhibition (complex go/no-go) in the supramarginal gyrus/intraparietal sulcus only. The researchers concluded that these results suggested that working memory, attention, or mental imagery may be more relevant to counterintuitive reasoning than inhibitory control. These differences in findings between adolescents and children may be methodological, for example, the slightly different methods for creating ROIs, or the age-appropriate variations in inhibitory control tasks used; however, these tasks were designed to isolate inhibitory control processes using tight contrasts, regardless of variations in content. Alternatively, the differences may be developmental. Children may use broader regions to elicit inhibitory control and reasoning processes than adolescents. One might speculate that repetition of facts for formal qualifications during adolescence may lead to a stronger dependency on memory retrieval for counterintuitive reasoning in this age group, as opposed to inhibitory control; whereas children are likely to have been introduced to counterintuitive concepts more recently, without intense repetition, leading to a greater reliance on inhibitory control and broader recruitment of frontal and parietal regions. Another possible reason for the greater neural similarity is that interference control may be recruited in childhood for science and maths reasoning more broadly, beyond reasoning about counterintuitive problems specifically. Indeed, Cragg, Keeble, Richardson, Roome, and Gilmore (2017) found that a numerical interference control task was associated with overall arithmetic factual knowledge and procedural skills, across age groups.

Although the Stop & Think intervention was designed on the premise that training children to use their inhibitory control skills would be most effective when implemented in a specific context (science and maths), here, we used domain-general tests of inhibitory control. It is possible that greater univariate overlap and multivariate similarity would have been observed if the inhibitory control tasks used numerical and science stimuli. However, in our previous study in adolescents, the interference control task used numerical stimuli and only showed limited similarity with the science and maths counterintuitive reasoning task. Future work could use domain-general and domain-specific inhibitory control tasks, or tasks with more varied stimuli.

The multivariate similarity analyses revealed some differences between disciplines. Neural similarity between the interference control task and counterintuitive reasoning was observed in the superior frontal gyrus for maths trials, but not science trials, which could reflect greater working memory and spatial processing required in maths (El-Baba & Schury, 2024; du Boisgueheneuc et al., 2006) as compared with science. Conversely, significantly greater neural similarity was observed between interference control and science trials, as compared with maths trials in bilateral (predominantly inferior) temporal gyri. We speculate that this reflects an increased semantic memory processing and visual perception load (Patel, Biso, & Fowler, 2024) in science trials compared with maths. Again, these differences may in part relate to differences in the visual representation of the maths and science problems. Complementing the univariate analyses, these results indicated that science and maths counterintuitive reasoning show many similarities, but also some differences in the neural engagement.

Interestingly, when assessing whether individual differences in neural similarity between science and maths reasoning tasks and inhibitory control tasks associated with counterintuitive reasoning accuracy, we observed a significant positive correlation between maths counterintuitive reasoning and interference control tasks similarity scores, averaged across ROIs, and maths counterintuitive reasoning accuracy. This finding provides further evidence for a role of interference control in maths counterintuitive reasoning. No similar association was observed for science or with the response inhibition task similarity score. This may imply a lesser role of interference control in science counterintuitive reasoning. Alternatively, the fact that maths accuracy was overall higher and more variable across participants than science accuracy may reflect greater individual differences in successful counterintuitive reasoning and use of interference control by children in maths than science, which may have resulted in the observed correlation.

Taken together, the univariate and multivariate findings from this study suggest that inhibitory control plays a role in science and maths counterintuitive reasoning in childhood, and the current evidence suggests that interference control may play a greater role than response inhibition. The findings point to a putative neural mechanism behind inhibitory control interventions, which promote science and maths academic outcomes. For example, the Stop & Think intervention (Dumontheil et al., 2023; Gauthier, Porayska-Pomsta, Dumontheil, Mayer, & Mareschal, 2022; Gauthier, Porayska-Pomsta, Mayer, et al., 2022; Wilkinson et al., 2020) could allow children to resolve the interference between intuitive and correct conceptual understandings and lead to more accurate responses. Future work may wish to investigate whether interference control interventions within maths and science domains can improve maths and science educational outcomes in this age group and whether domain-specific response inhibition interventions can produce similar results.

Neural similarity between counterintuitive reasoning and inhibitory control tasks was investigated in primary-school-aged children. Multivariate neural similarity was observed in a broad network of brain regions between maths and science counterintuitive reasoning tasks and interference control tasks, and to a much lesser extent with response inhibition tasks. These findings provide evidence for the theory that inhibitory control plays a role in counterintuitive reasoning in children and may have implications for understanding the mechanisms behind inhibitory control interventions designed to improve maths and science academic outcomes.

Corresponding author: Lucy R. J. Palmer, Department of Psychological Sciences, Birkbeck, University of London, Malet Street, London, WC1E 7HX, UK, e-mail: [email protected].

Data are available through the Birkbeck Research Data Repository.

Lucy R. J. Palmer: Formal analysis; Writing—Original draft; Writing—Review & editing. Dilini K. Sumanapala: Data curation; Formal analysis. Denis Mareschal: Conceptualization; Funding acquisition; Project administration; Supervision; Writing—Review & editing. Iroise Dumontheil: Conceptualization; Data curation; Formal analysis; Funding acquisition; Supervision; Writing—Original draft; Writing—Review & editing. The UnLocke Team: Conceptualization; Data curation; Funding acquisition; Project administration.

Funding was provided by Birkbeck College and a joint award from the Education Endowment Foundation (grant number: N - 1343) and The Wellcome Trust.

Retrospective analysis of the citations in every article published in this journal from 2010 to 2021 reveals a persistent pattern of gender imbalance: Although the proportions of authorship teams (categorized by estimated gender identification of first author/last author) publishing in the Journal of Cognitive Neuroscience (JoCN) during this period were M(an)/M = .407, W(oman)/M = .32, M/W = .115, and W/W = .159, the comparable proportions for the articles that these authorship teams cited were M/M = .549, W/M = .257, M/W = .109, and W/W = .085 (Postle and Fulvio, JoCN, 34:1, pp. 1–3). Consequently, JoCN encourages all authors to consider gender balance explicitly when selecting which articles to cite and gives them the opportunity to report their article's gender citation balance. The authors of this paper report its proportions of citations by gender category to be: M/M = .365; W/M = .349; M/W = .111; W/W = .175.