Teaching to support students' sense-making is challenging. It requires continuous, context-dependent decision-making about which student ideas to pursue, when, how, and why. This paper presents a single case study of an experienced teacher, Nadine, as an illustrative case in order to provide a rich description of this teacher's decisional…

This Family and Practitioner Brief discusses how deaf children who have not had access to a complete language from birth often encounter unique challenges in developing academic language skills, particularly in the realm of inference-making.

Since formal mathematics is discussed in terms of abstract symbols, many students face difficulties to acquire a clear understanding of mathematical concepts and ideas. Transforming abstract or dis-embodied representations of mathematical concepts and ideas into embodied representations is a strategy to make mathematics more tangible and…

This paper introduces two theoretical constructs, open-loop covariation and closed-loop covariation, that combine covariational reasoning and causality to characterize the way that three preservice mathematics teachers conceptualize a feedback loop relationship in a mathematical task related to climate change. The study's results suggest that the…

The modifier effect refers to the fact that the perceived likelihood of a property in a noun category is diminished if the noun is modified. For example, "Pigs live on farms" is rated as more likely than "Dirty pigs live on farms." The modifier effect has been demonstrated in many studies, but the underlying cognitive…

This study aimed to analyze the abstraction process of twelve-grade students' continuity knowledge through the RBC+C abstraction model. With this aim, a semi-constructed interview was conducted with two twelfth-grade students and recorded with a video camera. Two different research problems were addressed in the interview, and the students were…

At the onset of the coronavirus disease (COVID-19) global pandemic, our interdisciplinary team hypothesized that a mathematical misconception--whole number bias (WNB)--contributed to beliefs that COVID-19 was less fatal than the flu. We created a brief online educational intervention for adults, leveraging evidence-based cognitive science…

Understanding how students learn is crucial for helping them succeed. We examined brain function in 107 undergraduate students during a task known to be challenging for many students--physics problem solving--to characterize the underlying neural mechanisms and determine how these support comprehension and proficiency. Further, we applied module…

Although there is no consensus in regard to a unique meaning for abstraction, there is a recognition of the existence of several theories of abstraction, and that the ability to abstract is imperative to learning and doing meaningful mathematics. The theory of "reducing abstraction" maps the abstract nature of mathematics to the nature…

The purpose of this paper is twofold: On the one hand, this work frames a variety of considerations on cognitive processes underlying mathematical concept construction in two research strands, namely an actions-first strand and an objects-first strand, that mainly shapes past and current approaches on abstraction in learning mathematics. This…

Background: We tested the effects of an intervention on the learning of introductory thermodynamics principles. This intervention, OEM-Thermo, is designed to prompt the cognitive operations of meaningful learning: organization, elaboration, and monitoring. We also sought evidence to show that execution of these operations was associated with…

This case study examines the salient features of two individuals' reasoning when confronted with a task concerning the cardinality and associated cardinal number of equinumerous infinite sets. The APOS Theory was used as a framework to interpret their efforts to resolve the "infinite balls paradox" and one of its variants. These cases…

A growing body of research has examined the experiential grounding of scientific thought and the role of experiential intuitive knowledge in science learning. Meanwhile, research in cognitive linguistics has identified many "conceptual metaphors" (CMs), metaphorical mappings between abstract concepts and experiential source domains,…

This paper outlines a theoretical paradigm for distinguishing thinking, knowing and believing. A new taxonomy is presented for categorizing levels of knowing and outlines a structure of justification for each level. The paper discusses and explains the importance of such distinctions in decision making and thinking in general.

This paper considers mathematical abstraction as arising through a natural mechanism of the biological brain in which complicated phenomena are compressed into thinkable concepts. The neurons in the brain continually fire in parallel and the brain copes with the saturation of information by the simple expedient of suppressing irrelevant data and…