A total of 136 eighth-grade math students from 2 Singapore schools learned from either productive failure (PF) or vicarious failure (VF). PF students "generated" solutions to a complex problem targeting the concept of variance that they had not learned yet before receiving instruction on the targeted concept. VF students…

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, implicit in…

Gestures are often taken as evidence that the body is involved in thinking and speaking about the ideas expressed in those gestures. In this article, we present evidence drawn from teachers' and learners' gestures to make the case that mathematical knowledge is embodied. We argue that mathematical cognition is embodied in 2 key senses: It is based…

"The Journal of the Learning Sciences" has devoted this special issue to the study of embodied cognition (as it applies to mathematics), a topic that for several decades has gained attention in the cognitive sciences and in mathematics education, in particular. In this commentary, the author aims to address crucial questions in embodied…

For a long time, the body has had a bad rap among some big names in the Western philosophical tradition. Plato and Descartes come quickly to mind as particularly bad rappers. But it appears that the body is making a comeback in the cognitive and learning sciences. Long banished from the main stage by an idealized, inside-the-head…

In this article we contribute a perspective on mathematical embodied cognition consistent with a phenomenological understanding of perception and body motion. It is based on the analysis of 4 selected episodes in 1 session of an undergraduate mathematics class. The theme of this particular class session was the geometric interpretation of the…

Many types of learning require the mapping of information across situations. The proposed organizational framework extends the cognitive study of mappings across problems to include mappings across representations, solutions, and sociocultural contexts. I apply one-to-one, one-to-many, and partial mappings to analyze representative cases that…

As transfer researchers have begun to investigate a broader range of phenomena, they have correspondingly put forward new processes to provide explanatory accounts for the occurrence of transfer. This move coincides with a call to acknowledge the contribution of social interactions, language, cultural artifacts, and normed practices to the…

Some intensive quantities, such as slope, velocity, or likelihood, are perceptually privileged in the sense that they are experienced as holistic, irreducible sensations. However, the formal expression of these quantities uses "a/b" analytic metrics; for example, the slope of a line is the quotient of its rise and run. Thus, whereas students'…

Feedback is generally considered a beneficial learning tool, and providing feedback is a recommended instructional practice. However, there are a variety of feedback types with little guidance on how to choose the most effective one. We examined individual differences in working memory capacity as a potential moderator of feedback type. Second-…

In problem-based learning students are responsible for their own learning process, which becomes evident when they must act independently, for example, when selecting literature resources for individual study. It is a matter of debate whether it is better to have students select their own literature resources or to present them with a list of…

Subjective cognitive load (CL) rating scales are widely used in educational research. However, there are still some open questions regarding the point of time at which such scales should be applied. Whereas some studies apply rating scales directly after each step or task and use an average of these ratings, others assess CL only once after the…

Though the testing-effect can be boosted by including a restudy phase after answering test questions, we do not know precisely why it does so. One possible explanation is being tested here. The present study measured attention allocation during initial reading and rereading with a remote eye tracker to gain information on the cognitive processes…

Investigations of people's understanding of the evolution of species have focused mainly on secondary school and university students. Very few investigations have taken into consideration younger students, and none have related children's ideas about the origin of species to formal instruction on this topic. To help fill this gap, the present…

Many approaches to the transfer problem argue that transfer depends on the recognition of the same or similar abstract "structure" in 2 different situations. However, mainstream cognitive perspectives and contrasting Piagetian constructivist accounts differ in their conceptualizations of structure. These differences, not clearly articulated in the…