How Do Executive Functions Influence Children's Reasoning About Counterintuitive Concepts in Mathematics and Science?

Many scientific and mathematical concepts are counterintuitive because they conflict with misleading perceptual cues or incorrect naive theories that we build from our everyday experiences of the world. Executive functions (EFs) influence mathematics and science achievement, and inhibitory control (IC), in particular, might facilitate counterintuitive reasoning. Stop & Think (S&T) is a computerised learning activity that trains IC skills. It has been found effective in improving primary children's mathematics and science academic performance in a large scale RCT trial (Palak et al., 2019; Wilkinson et al., Journal of Cognitive Enhancement, 4, 296-314, 2020). The current study aimed to investigate the role of EFs and the moderating effects of S&T training on counterintuitive mathematics and science reasoning. A sample of 372 children in school Years 3 (7- to 8-year-olds) and 5 (9- to 10-year-olds) were allocated to S&T, active control or teaching as usual conditions, and completed tasks assessing verbal and visuospatial working memory (WM), IC, IQ, and counterintuitive reasoning, before and after training. Cross-sectional associations between counterintuitive reasoning and EF were found in Year 5 children, with evidence of a specific role of verbal WM. The intervention benefited counterintuitive reasoning in Year 3 children only and EF measures were not found to predict which children would most benefit from the intervention. Combined with previous research, these results suggest that individual differences in EF play a lesser role in counterintuitive reasoning in younger children, while older children show a greater association between EFs and counterintuitive reasoning and are able to apply the strategies developed during the S&T training to mathematics and science subjects. This work contributes to understanding why specifically the S&T intervention is effective. This work was preregistered with the ISRCTN registry (TRN: 54726482) on 10/10/2017. Supplementary Information: The online version contains supplementary material available at 10.1007/s41465-023-00271-0.

Domain-Specific Inhibitory Control Training to Improve Children's Learning of Counterintuitive Concepts in Mathematics and Science.

Evidence from cognitive neuroscience suggests that learning counterintuitive concepts in mathematics and science requires inhibitory control (IC). This prevents interference from misleading perceptual cues and naïve theories children have built from their experiences of the world. Here, we (1) investigate associations between IC, counterintuitive reasoning, and academic achievement and (2) evaluate a classroom-based computerised intervention, called Stop & Think, designed to embed IC training within the learning domain (i.e. mathematics and science content from the school curricula). Cross-sectional analyses of data from 627 children in Years 3 and 5 (7- to 10-year-olds) demonstrated that IC, measured on a Stroop-like task, was associated with counterintuitive reasoning and mathematics and science achievement. A subsample (n = 456) participated either in Stop & Think as a whole-class activity (teacher-led, STT) or using individual computers (pupil-led, STP), or had teaching as usual (TAU). For Year 3 children (but not Year 5), Stop & Think led to better counterintuitive reasoning (i.e. near transfer) in STT (p < .001, ηp 2 = .067) and STP (p < .01, ηp 2 = .041) compared to TAU. Achievement data was not available for Year 3 STP or Year 5 STT. For Year 3, STT led to better science achievement (i.e. far transfer) compared to TAU (p < .05, ηp 2 = .077). There was no transfer to the Stroop-like measure of IC. Overall, these findings support the idea that IC may contribute to counterintuitive reasoning and mathematics and science achievement. Further, we provide preliminary evidence of a domain-specific IC intervention with transferable benefits to academic achievement for Year 3 children.

Intermediates control domain swapping during folding of p13suc1.

The 13-kDa protein p13(suc1) has two folded states, a monomer and a structurally similar domain-swapped dimer formed by exchange of a beta-strand. The refolding reaction of p13(suc1) is multiphasic, and in this paper we analyze the kinetics as a function of denaturant and protein concentration and compare the behavior of wild type and a set of mutants previously designed with dimerization propensities that span 9 orders of magnitude. We show that the folding reactions of wild type and all mutants produce the monomer predominantly despite their very different equilibrium behavior. However, the addition of low concentrations of denaturant in the refolding buffer leads to thermodynamic control of the folding reaction with products that correspond to the wild type and mutant equilibrium dimerization propensities. We present evidence that the kinetic control in the absence of urea arises because of the population of the folding intermediates. Intermediates are usually considered to be detrimental to folding because they slow down the reaction; however, our work shows that intermediates buffer the monomeric folding pathway against the effect of mutations that favor the nonfunctional, dimeric state at equilibrium.

The structure of the transition state for folding of domain-swapped dimeric p13suc1.

suc1 has two native states, a monomer and a domain-swapped dimer, in which one molecule exchanges a beta strand with an identical partner. Thus, monomer and dimer have the same structures but are topologically distinct. Importantly, residues that exchange are part of the folding nucleus of the monomer and therefore forming these interactions in the dimer would be expected to incur a large entropic cost. Here we present the transition state for folding/unfolding of domain-swapped dimeric suc1 and compare it with its monomeric counterpart. The same overall structure is observed in the two transition states but the phi values are consistently higher for the domain-swapped dimer. Thus, a greater entropic penalty for bringing together the key interactions in the dimer is overcome by mobilizing more contacts in the transition state, thereby achieving a greater enthalpic gain.

Folding and association of the human cell cycle regulatory proteins ckshs1 and ckshs2.

The two human proteins ckshs1 and ckshs2 are each 79 amino acids in length and consist of a four-stranded beta-sheet capped at one end by two alpha-helices. They are members of the cks family of essential cell cycle regulatory proteins that can adopt two native states, a monomer and a domain-swapped dimer formed by exchange of a C-terminal beta-strand. ckshs1 and ckshs2 both have marginal thermodynamic stability (the free energies of unfolding at 25 degrees C are 3.0 and 2.5 kcal/mol, respectively) and low kinetic stability (the rates of unfolding in water are approximately 1 s(-1)). Refolding of their denatured states to the monomeric forms of the proteins is slowed by transient oligomerization that is likely to occur via domain swapping. The folding behavior of ckshs1 and ckshs2 is markedly different from that of suc1, the cks protein from Schizosaccharomyces pombe, but the domain swapping propensities are similar. The greater thermodynamic and kinetic stability of suc1 and the population of a folding intermediate are most likely a consequence of its larger size (113 residues). The similarity in the domain swapping propensities, despite the contrast in other biophysical properties, may be attributable to the common double-proline motif in the hinge loop that connects the swapped domain to the rest of the protein. The motif was shown previously for suc1 to control the equilibrium between the monomer and the domain-swapped dimer. Finally, according to our model, the kinetic barrier separating the monomer and the domain-swapped dimer arises because the protein must unfold for beta-strand exchange to occur. Consistent with this, interconversion between the two states is much faster in the human proteins than it is for suc1, reflecting the faster unfolding rates of the former.