Word problems (WPs) belong to the most difficult and complex problem types that pupils encounter during their elementary-level mathematical development. In the classroom setting, they are often viewed as merely arithmetic tasks; however, recent research shows that a number of linguistic verbal components not directly related to arithmetic contribute greatly to their difficulty. In this review, we will distinguish three components of WP difficulty: (i) the linguistic complexity of the problem text itself, (ii) the numerical complexity of the arithmetic problem, and (iii) the relation between the linguistic and numerical complexity of a problem. We will discuss the impact of each of these factors on WP difficulty and motivate the need for a high degree of control in stimuli design for experiments that manipulate WP difficulty for a given age group.

Math anxiety is a common phenomenon which can have a negative impact on numerical and arithmetic performance. However, so far little is known about the underlying neurocognitive mechanisms. This mini review provides an overview of studies investigating the neural correlates of math anxiety which provide several hints regarding its influence on math performance: while behavioral studies mostly observe an influence of math anxiety on difficult math tasks, neurophysiological studies show that processing efficiency is already affected in basic number processing. Overall, the neurocognitive literature suggests that (i) math anxiety elicits emotion- and pain-related activation during and before math activities, (ii) that the negative emotional response to math anxiety impairs processing efficiency, and (iii) that math deficits triggered by math anxiety may be compensated for by modulating the cognitive control or emotional regulation network. However, activation differs strongly between studies, depending on tasks, paradigms, and samples. We conclude that neural correlates can help to understand and explore the processes underlying math anxiety, but the data are not very consistent yet.

Depressive disorders are heterogeneous psychiatric disorders involving deficits in cognitive, psychomotor, and emotional processing. Depressive disorders have a significant genetic component, with severe, recurrent and early-onset forms demonstrating elevated heritability. In this study we genotyped eleven single nucleotide polymorphisms (SNPs) spanning the estrogen receptor alpha gene (ESR1) in a large family-based childhood-onset mood disorder (COMD) sample. None of the individual SNP or global haplotype analyses was significant in the entire COMD sample, but haplotype analysis of three SNPs in strong linkage disequilibrium (rs746432, rs2077647, and rs532010) uncovered an association with COMD, specifically in females. Our data are consistent with previous studies demonstrating a female-specific association between ESR1 and neurobehavioral phenotypes. These results suggest the existence of sex-specific etiological factors in depressive disorders, related to estrogen, with onset in childhood.

Studies in both animals and humans advocate a role for the vasopressin (AVP) system in the aetiology of depressive symptoms. Attention has particularly focused on the role of AVP in the overactivation of the hypothalamic-pituitary-adrenal (HPA)-axis in mood disorders. Elevated AVP plasma levels have been found in mood disorder patients, which are often positively correlated with the severity of symptoms. We recently reported an association between childhood-onset mood disorders (COMD) and polymorphisms in the receptor responsible for the AVP-mediated activation of the HPA-axis (AVPR1B). As genetic variation in the vasopressinergic system could provide a mechanism to explain the endocrine alterations observed in mood disorders, we investigated other genes in this system. The gene encoding AVP is the strongest candidate, particularly as genetic variation in this gene in rodents is associated with anxiety-related behaviours. Six single-nucleotide polymorphisms (SNPs) were genotyped across the AVP gene in a sample comprised of 586 Hungarian nuclear families ascertained through affected probands with a diagnosis of COMD. In addition, AVP coding and putative regulatory regions were screened for mutations using denaturing high-performance liquid chromatography. One SNP, 3' to the AVP, gene reached significance (P = 0.03), as did the overtransmission of a five-marker haplotype with a frequency of 22% (P = 0.0001). The subsequent mutation screen failed to identify any putative functional polymorphisms. The outcome of this study, combined with our previous association between COMD and AVPR1B, implicates genetic variation in vasopressinergic genes in mediating vulnerability to COMD.

Performance on word problems is influenced by linguistic and arithmetic factors, and by their interaction. To study these factors and interactions, we manipulated linguistic and arithmetic factors independently in a within-participant design that included complexity parameters (a) in the domain of arithmetic: carry/borrow (no-carry/borrow vs. carry/borrow), operation (addition vs. subtraction), (b) in the domain of linguistics: nominalization (nominalized vs. verbalized form), and (c) linking the two domains: lexical consistency (linguistic predicate locally consistent vs. inconsistent with mathematical operation). Response times of 25 students solving 320 one-step word problems were measured. All four factors showed a main effect on response times, and interactions between linguistic and arithmetic factors affected response times. These interactions were observed when the linguistic and arithmetic factors were conceptually linked. Our results highlight that not only the linguistic and arithmetic complexities of an item contribute to the difficulty of a word problem, but linguistic and arithmetic factors interact. We discuss the theoretical implications for the numerical and the linguistic domain as well as the possible impact of domain-general characteristics, such as working memory limitations as a potential reason for the observed interactions between numerical and linguistic attributes.