This developmental account of executive function (EF) argues that domain-general analogical processes build a functional hierarchy of skills, which vary on a continuum of abstraction, and become increasingly differentiated over time. The paper begins by showing how a functional hierarchy can capture important aspects of EF development, including…

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…

In this paper, we offer a novel framework for analyzing the Opportunities for Reasoning-and-Proving (ORP) in mathematical tasks. By drawing upon some tenets of the commognitive framework, we conceptualize learning and teaching mathematics via reasoning and proving both as enacting reasoning processes (e.g., conjecturing, justifying) in the…

To help students acquire mathematics and science knowledge and competencies, educators typically use multiple external representations (MERs). There has been considerable interest in examining ways to present, sequence, and combine MERs. One prominent approach is the concreteness fading sequence, which posits that instruction should start with…

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,…

We propose that research on text-graphic processing could be strengthened by the inclusion of relational reasoning perspectives. We briefly outline four aspects of relational reasoning: "analogies," "anomalies," "antinomies", and "antitheses". Next, we illustrate how text-graphic researchers have been…

Relational aspects of professional practice demand increasing attention in research on work and learning. However, little is known about how knowledge is enacted in practices where different people work together. Working in partnership with clients surfaces a number of epistemic demands, responses to which are poorly understood. This paper…

Taking as a point of departure that consciousness of time is pivotal to historical consciousness, this paper explores intuitive temporal experiences as opposed to the less intuitive temporal experience connected with historical consciousness. The intuitive daily/cyclic, social and mythical temporal awareness is being opposed to historical…

The body of research examining students' graphing understandings across STEM fields indicates students are not developing productive meanings for graphs. We conjecture such failings may, in part, be explainable by features of students' use of coordinate systems and graphing activity that are under examined. In this theoretical report, we present a…

Science education communities around the world have increasingly emphasized engaging students in the disciplinary practices of science as they engage in high levels of reasoning about scientific ideas. Consistently, this is a critical moment in time in the USA as it goes through a new wave of science education reform within the context of Next…

Applying knowledge from one context to another is a notoriously difficult problem, both for children and adults, but lies at the heart of educational endeavors. Analogical reasoning is a cognitive underpinning of the ability to notice and draw similarities across contexts. Reasoning by analogy is especially challenging for students, who must…

Mathematical discussions in which students compare alternative solutions to a problem can be powerful modes for students to engage and refine their misconceptions into conceptual understanding, as well as to develop understanding of the mathematics underlying common algorithms. At the same time, these discussions are challenging to lead…

The observation that the human mind operates in two distinct thinking modes--intuitive and analytical- have occupied psychological and educational researchers for several decades now. Much of this research has focused on the explanatory power of intuitive thinking as source of errors and misconceptions, but in this article, in contrast, we view…

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic…

Plausibility judgments rarely have been addressed empirically in conceptual change research. Recent research, however, suggests that these judgments may be pivotal to conceptual change about certain topics where a gap exists between what scientists and laypersons find plausible. Based on a philosophical and empirical foundation, this article…