Lockwood has argued that taking a set-oriented perspective is critical for successful combinatorial enumeration. To date, however, the research literature has not yet captured the cognitive processes involved in taking such a perspective. In this theoretical paper, we elaborate the constructs of spatial structuring and spatial-numerical linked…

This review describes a computational approach for modeling the development of speech motor control in infants. We address the development of two levels of control: articulation of individual speech sounds (defined here as phonemes, syllables, or words for which there is an optimized motor program) and production of sound sequences such as phrases…

Predictive processing (PP) has been repeatedly presented as a unificatory account of perception, action, and cognition. In this paper, we argue that this is premature: As a unifying theory, PP fails to deliver general, simple, homogeneous, and systematic explanations. By examining its current trajectory of development, we conclude that PP remains…

One characteristic of high-quality mathematics teaching is supporting students in engaging in tasks of high cognitive demand. In this paper, we explore relationships between two elementary teachers' efforts to integrate computational thinking (CT) practices--abstraction, debugging, and decomposition--into their mathematics instruction and their…

While patterning was commonly seen as evidence of mathematical thinking, interdisciplinary interest has recently increased due to pattern-recognition applications in artificial intelligence. Within two empirical studies, we analyze the analogical-transfer capability of primary school students when completing three types of bi-dimensional patterns,…

This lecture reports on aspects of a larger research programme focused on studying mental mathematics in elementary and secondary mathematics classrooms. It specifically addresses an unplanned aspect that became salient through the work conducted in these classrooms. In this research programme, mental mathematics sessions are designed on a variety…

The natural numbers may be our simplest, most useful, and best-studied abstract concepts, but their origins are debated. I consider this debate in the context of the proposal, by Gallistel and Gelman, that natural number system is a product of cognitive evolution and the proposal, by Carey, that it is a product of human cultural history. I offer a…

If educators presuppose that brain and mind are synonymous, perhaps it is out of necessity. Such an equivalency might be required in order for mind to be accessible, knowable and a "thing" like the brain is. Such a presupposition, that mind is a thing which we can understand nonetheless rests on an insecure foundation. As suggested by…

Consciousness remains a mystery--"a phenomenon that people do not know how to think about--yet" (Dennett, D. C., 1991, p. 21). Here, I consider how the connectionist perspective on information processing may help us progress toward the goal of understanding the computational principles through which conscious and unconscious processing…

The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…

The focus of the current proposal is to examine the effect of two dynamic simulations on the participants' conceptions of rate of change. Conceptions of rate of change were measured according to Carlson et al.'s (2002) Mental Actions framework and how the participants related the physical simulations to the graphical representations (Heid, et al.,…

Judea Pearl has argued that counterfactuals and causality are central to intelligence, whether natural or artificial, and has helped create a rich mathematical and computational framework for formally analyzing causality. Here, we draw out connections between these notions and various current issues in cognitive science, including the nature of…

In a seminal 1977 article, Rumelhart argued that perception required the simultaneous use of multiple sources of information, allowing perceivers to optimally interpret sensory information at many levels of representation in real time as information arrives. Building on Rumelhart's arguments, we present the Interactive Activation…

In this essay, I explore how cognitive science could illuminate the concept of beauty. Two results from the extensive literature on aesthetics guide my discussion. As the term "beauty" is overextended in general usage, I choose as my starting point the notion of "perfect form." Aesthetic theorists are in reasonable agreement about the criteria for…

Acquisition of relational knowledge is a core process in cognitive development. Relational knowledge is dynamic and flexible, entails structure-consistent mappings between representations, has properties of compositionality and systematicity, and depends on binding in working memory. We review three types of computational models relevant to…