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This article reviews the topics of affect, motivation, working memory, and their relationships to mathematics learning and performance. The underlying factors of interest, motivation, self-efficacy, and maths anxiety, as well as an approach concerning people’s beliefs about fixed versus malleable intelligence, can be grouped into an approach and an avoidance constellation of attitudes and beliefs, with opposite relationships to outcome measures of learning and mastery in maths. This article then considers the research on working memory, showing it to be central to arithmetic and maths processing, and also the principle mental component being disrupted by affective and emotional reactions during problem solving. After discussing the disruptive effects of maths anxiety, choking under pressure, and stereotype threat, the article closes with a brief consideration of how these affective disruptions might be minimized or eliminated.

This article reviews recent research exploring children’s abilities to perform approximate arithmetic with non-symbolic and symbolic quantities, and considers what role this ability might play in mathematics achievement. It has been suggested that children can use their approximate number system (ANS) to solve approximate arithmetic problems before they have been taught exact arithmetic in school. Recent studies provide evidence that preschool children can add, subtract, multiply, and divide non-symbolic quantities represented as dot arrays. Children can also use their ANS to perform simple approximate arithmetic with non-symbolic quantities presented in different modalities (e.g. sequences of tones) or even with symbolic representations of number. This article reviews these studies, and consider whether children’s performance can be explained through the use of alternative non-arithmetical strategies. Finally, it discusses the potential role of this ability in the learning of formal symbolic mathematics.

This review examines brain and cognitive processes involved in arithmetic. I take a distinctly developmental perspective because neither the cognitive nor the brain processes involved in arithmetic can be adequately understood outside the framework of how developmental processes unfold. I review four basic neurocognitive processes involved in arithmetic, highlighting (1) the role of core dorsal parietal and ventral temporal-occipital cortex systems that form basic building blocks from which number form and quantity representations are constructed in the brain; (2) procedural and working memory systems anchored in the basal ganglia and frontoparietal circuits, which create short-term representations that allow manipulation of multiple discrete quantities over several seconds; (3) episodic and semantic memory systems anchored in the medial and lateral temporal cortex that play an important role in long-term memory formation and generalization beyond individual problem attributes; and (4) prefrontal cortex control processes that guide allocation of attention resources and retrieval of facts from memory in the service of goal-directed problem solving. Next I examine arithmetic in the developing brain, first focusing on studies comparing arithmetic in children and adults, and then on studies examining development in children during critical stages of skill acquisition. I highlight neurodevelopmental models that go beyond parietal cortex regions involved in number processing, and demonstrate that brain systems and circuits in the developing child brain are clearly not the same as those seen in more mature adult brains sculpted by years of learning. The implications of these findings for a more comprehensive view of the neural basis of arithmetic in both children and adults are discussed.

This chapter evaluates the contribution of behavioral genetics to the understanding of mathematical development. Quantitative genetic methods are introduced first and are followed by a review of the existing literature on the relative contribution of genes and environments to variation in mathematical ability at different ages and in different populations. The etiology of any observed sex differences in mathematics is also discussed. The chapter reviews literature on multivariate twin research into the etiological links between mathematics and other areas of cognition and achievement; between mathematical ability and disability; and between mathematical achievement and mathematical motivation. In the molecular genetic section, the few molecular genetic studies that have specifically explored mathematical abilities are presented. The chapter concludes by outlining future directions of behavioral genetic research into mathematical learning and potential implications of this research.

What are the brain correlates of numerical disabilities? To date only few studies have examined the neuronal underpinnings of specific numerical learning disabilities like developmental dyscalculia (DD). However, first results provide important insights if and where brains of children diagnosed with DD differ from those of typically achieving peers. Main deficits are apparent in core regions for number processing, which mainly comprise gray, as well as white matter in parietal lobes. Moreover, it already can be demonstrated that brain activation in DD is changing according to learning and intervention. The present chapter will bring together existing puzzle pieces of brain imaging findings in DD, as well as highlight some critical issues that have to be considered when comparing studies including children with DD.

This chapter describes the relation between the imagination and causal cognition, particularly with relevance to recent developments in computational theories of human learning. According to the "probabilistic models" view of human learning, our ability to imagine possible worlds and engage in counterfactual reasoning is closely tied to our ability to think causally. Indeed, the purpose and distinguishing feature of causal knowledge is that it allows one to generate counterfactual inferences. The chapter begins with a brief description of the "probabilistic models" framework of causality and Bayesian learning, and reviews empirical work in that framework, which shows that adults and children use causal knowledge to generate counterfactuals. It also outlines a theoretical argument that suggests that the imagination is central to the process of causal understanding and planning and offers evidence that Bayesian learning also implicates the imaginative process. It concludes with a discussion of how this computational method may be applied to the study of the imagination, more classically construed.

Children engage with art, music, dance, and theater as early as they can move, make noise, and play. Yet theories of aesthetic responses are missing a developmental perspective. Large questions remain about the development of aesthetic response and reasoning, including whether there is a qualitative difference between children’s aesthetic reasoning and appreciation and adults’ reasoning and appreciation, how childhood artistic activities are linked to adult artistic activities, and how aesthetic responses are tied to other developmental processes in social, emotional, and cognitive development. Significant work in other areas such as intention processing, understanding of representation, emotion understanding, and attention points to developmental trajectories in aesthetics, but this work has only rarely been applied within or across art forms. Open questions across art forms, types of responses, and ages of development mean fertile ground for researchers interested in appreciation, understanding, and reactions to art, dance, music, and theater.

Children in the bottom quartile of mathematics achievement are at high risk for underemployment in adulthood. These children include the roughly 7% of students with a mathematical learning disability (MLD) and another 10% of students with persistent low achievement (LA) that is not attributable to intelligence. The poor mathematics achievement of children who compose groups of MLD and LA students appears to be related to one or several deficits; specifically, (1) a delay in the development and poor fidelity of the system for representing approximate magnitudes; (2) difficulty mapping Arabic numerals, number words, and rational numbers onto associated quantities; (3) poor conceptual understanding of some arithmetic concepts; (4) developmental delay in the learning of mathematical procedures; and (5) difficulty committing basic arithmetic facts to or retrieving them from long-term memory. Children with MLD also have concurrent working memory deficits that exacerbate their mathematics-specific deficits and delays.

Although studies indicate that aging impacts a number of cognitive abilities, this research has largely been confined to Western samples. This chapter reviews the budding literature on cross-cultural differences in cognitive aging. Although cultures largely converge in the effects of aging on basic processes including speed, working memory, and cortical thinning, some aspects of memory appear to differ with age across cultures. For example, the content of autobiographical memory and the influence of categorization on long-term memory differ across cultures for older adults. Cultural differences are particularly robust in the domain of social cognition, including stereotypes and expectations about memory with age, wisdom, and emotional processing and memory. The chapter concludes with a consideration of some of the methodological challenges and suggestions for promising future directions, with the authors advocating for additional cognitive aging research with a cross-cultural perspective.

Children learn to think through the appropriation, use, and adaptation of social practices and the material and symbolic tools of their culture. Social processes are the means through which these practices and tools become part of the child’s cognitive repertoire. To describe cognition in childhood from a cultural perspective, this chapter discusses the sociocultural approach to cognitive development along with ideas from evolutionary developmental psychology that support this view. It focuses on four social learning processes through which children come to understand and engage in culture: behavioral observation, sharing of knowledge in reciprocal interaction, explicit efforts to instruct or transmit knowledge, and participation in cultural activities. Empirical support for each of these processes is also discussed.

This chapter discusses the ways in which research findings about the genetic, developmental, neuroanatomical, and behavioral characteristics of persons with Williams syndrome (WS) are incorporated into theoretical models of gene—environment interactions, and it critically evaluates the rationale and assumptions of each approach. It demonstrates that, despite the wealth of findings from research into WS, developmental questions concerning the link of genes to behavioral outcomes are yet to be resolved. The chapter discusses three approaches to the neurocognitive study of WS, including neuropsychological approaches; bridging gene, brain, and cognition; and developmental approaches. Differences in objectives, assumptions, hypotheses, and consequently, the in methodology of these approaches are addressed. The analysis will focus on how these approaches apply to WS as an illustration of their broader applicability to special populations in general.

Cued Speech (CS), a manual communication system that functions entirely in the absence of speech or hearing, makes use of visual information from lipreading combined with handshapes positioned in different places around the face in order to deliver completely unambiguous information about syllables and phonemes of spoken language. On the basis of behavioral and neuroimaging data, we argue here that manual, not lipread, information plays the primary role in the processing of CS. We also argue that CS combined with a cochlear implant (CI) is a powerful tool. We review the available literature showing that CS enhances speech perception in CI children, and it also favors the appropriate development of the three R’s (reading, rhyming, and remembering). The chapter concludes with considerations regarding the future of CS systems and the necessity to explicitly train deaf children with CIs to use not only auditory information but also visual speech information.

Mathematical competence rests on developing knowledge of concepts and of procedures (i.e. conceptual and procedural knowledge). Although there is some variability in how these constructs are defined and measured, there is general consensus that the relations between conceptual and procedural knowledge are often bi-directional and iterative. The chapter reviews recent studies on the relations between conceptual and procedural knowledge in mathematics and highlights examples of instructional methods for supporting both types of knowledge. It concludes with important issues to address in future research, including gathering evidence for the validity of measures of conceptual and procedural knowledge and specifying more comprehensive models for how conceptual and procedural knowledge develop over time.

The global shift toward inclusive education for deaf and hard-of-hearing (DHH) learners in recent years aims to address their needs to access a full curriculum and learn with their hearing age peers in a regular school environment. However positive these objectives are, individual DHH students educated in such an environment continue to face difficulty in various degrees. In this chapter, we discuss an alternative approach that combines the concepts of sign bilingualism and co-enrollment in educating both DHH and hearing students in a regular school environment, as well as outcomes of a recent inclusive deaf education program implemented in Hong Kong that bears such characteristics. We focus on the DHH students’ bimodal bilingual development in HKSL, oral Cantonese and written Chinese that is based on Mandarin grammar, in terms of group data and case studies. Patterns of language use in such a co-enrollment setting are also reported. Taken together, the results suggest that “dual-immersion” bilingual education in co-enrollment settings creates ample opportunities for social interactions between the DHH and hearing members of the school community, thereby creating a linguistically rich environment to support DHH students’ language development and education.

This chapter discusses heterogeneous aspects of developmental dyscalculia (DD) in terms of behaviour, cognitive operations, and neural structures. It has been suggested that DD is an isolated learning deficiency, involves a domain-specific deficit (in the capacity to enumerate), and a specific neural deficiency (in the intraparietal sulcus). We present findings that (1) DD involves both domain-specific and domain-general abilities; (2) in many cases behaviours, as well as cognition in those with DD are characterized by deficits in other areas, such as attention or memory and not only as a number sense deficiency; and (3) studies of the neural structures involved in DD reveal areas and mechanisms that hint toward heterogeneous damage. We suggest that similar to other learning disabilities, heterogeneity is the rule, rather than an exception. Accordingly, in order to reach a comprehensive understanding of DD, studies should aim at unravelling the basis for this heterogeneity.

Do adults from different age groups vary in the intensity or the variability of their everyday affective experiences? Are there age-related differences in the likelihood of encountering, and in the intensity of affectively reacting to, affect-eliciting events in daily life? Do individuals from different age groups differ in the complexity of their everyday affective lives? We review evidence on these questions currently available from ambulatory assessment studies. Ambulatory assessment refers to a group of research techniques—such as diary or experience sampling methods—that repeatedly capture everyday experiences as they naturally occur in people’s daily lives. We summarize the strengths and challenges of ambulatory assessment methods, discuss the available evidence from ambulatory assessment studies on age differences in everyday affective experiences and stability, and summarize research on possible factors that may contribute to these effects. Here, we address findings on age differences in the likelihood of encountering distressing experiences, on age differences in people’s affective reactions to such events, and on age differences in people’s affect regulation orientations. We also review ambulatory assessment evidence on age differences in the complexity of everyday affective experiences.

In this chapter, we discuss Fredda Blanchard-Fields’ important contribution to the understanding of emotional regulation in later life by relating it to a recent cognitive-developmental theory (Dynamic Integration Theory [DIT]) that posits joint development and aging of the cognitive-executive and emotional systems. This conception, inspired by the work of Jean Piaget, describes cognitive-emotional development during the first part of the lifespan as a process in which the capacity for sustaining emotional tension becomes raised as higher order cognitive representations become part of a common regulatory network. This process raises the functional tension threshold range over which emotional equilibrium is maintained. In contrast to earlier development, aging is characterized by a lowering of tension thresholds that brings greater vulnerability to high levels of activation in conditions that are novel and involve a great deal of effort. In contrast, well-automated knowledge and crystallized knowledge can provide a degree of buffering against these negative changes and is, at times, even related to increases in the depth and integration of experience.

Until recently, the dearth of normative literacy data for deaf children and adults has made it difficult to know what was typical for this group, and therefore it has been challenging to determine whether a deaf individual’s profile of skills was uneven or discrepant. In this chapter, we present an in-depth case study of a deaf child referred with suspected dyslexia. An approach to assessment is outlined and test findings are presented, comparing the child’s test scores with the profile of dyslexia reported for hearing children. The deaf child’s pattern of performance is then placed in the context of findings from a large sample of deaf children who were part of a recently completed UK research study investigating reading and dyslexia in deaf children.

Early number competencies predict later mathematical learning. Weaknesses in number, number relations, and number operations can be reliably identified before school entry in first grade. Income status, associated early home and preschool opportunities, and general cognitive capacity all influence children’s level of numerical knowledge. Interventions based on a developmental progression and targeted to specific areas of number, such as the ability to count and sequence numbers, compare numerical quantities, and add and subtract small quantities, have shown positive, meaningful, and lasting effects on children’s achievement. Guided practice is effective when configured to support efficient counting strategies, frequent correct responding, and meta-cognitive behaviour and when contextualized with a strong focus on number knowledge tutoring.

Many of the benefits conveyed to memory by socioemotional processing are preserved even as adults age. Like young adults, older adults are more likely to remember emotional information than neutral information and to benefit from self-referential processing of information. There is, however, one age-related change in emotional memory that has garnered widespread discussion in the psychological literature: the “positivity effect,” or the tendency for older adults to remember proportionally more positive information than do young adults. This essay discusses how an affective neuroscience perspective is revealing what aspects of socioemotional processing change with aging, shedding light on why aging preserves the memory benefits conveyed by socioemotional processing while at the same time influencing the valence of information that is most likely to be remembered.