In this paper, we trace the development of our theorizing about students' mathematical understanding, showing how the adoption of an enactivist perspective has transformed our gaze in terms of the objects of our studies and occasioned for us new methods of data analysis. Drawing on elements of Pirie-Kieren (P-K) Theory for the Dynamical Growth of…

Immediate and lasting effects of music or second-language training were examined in early childhood using event-related potentials. Event-related potentials were recorded for French vowels and musical notes in a passive oddball paradigm in thirty-six 4- to 6-year-old children who received either French or music training. Following training, both…

Prior studies suggest that struggling to make sense of mathematics is a necessary component of learning mathematics with understanding. Little research exists, however, on what the struggles look like for middle school students and how they can be productive. This exploratory case study, which used episodes as units of analysis, examined 186…

The ability to mentally rotate objects in space has been singled out by cognitive scientists as a central metric of spatial reasoning (see Jansen, Schmelter, Quaiser-Pohl, Neuburger, & Heil, 2013; Shepard & Metzler, 1971 for example). However, this is a particularly undeveloped area of current mathematics curricula, especially in North…

Implementing online technologies alone cannot ensure learning. A verified approach is needed to optimize the pedagogical effect of online learning. Previous studies have suggested that the application of the modality principle in multimedia design improves the efficiency of learning by reducing cognitive load. Nevertheless, this design approach…

This randomized controlled trial evaluated the efficacy of a computer software (i.e., "Mind Reading") and in vivo rehearsal treatment on the emotion decoding and encoding skills, autism symptoms, and social skills of 43 children, ages 7-12 years with high-functioning autism spectrum disorder (HFASD). Children in treatment (n = 22)…

The current research evaluated the extent to which the grain size of recall practice for lengthy text material affects recall during practice and subsequent memory. The "grain size hypothesis" states that a smaller vs. larger grain size will increase retrieval success during practice that in turn will enhance subsequent memory for…

Impaired face perception in autism spectrum disorders is thought to reflect a perceptual style characterized by componential rather than configural processing of faces. This study investigated face processing in adolescents with autism spectrum disorders using the Thatcher illusion, a perceptual phenomenon exhibiting "inversion effects"…

We demonstrate that a particular blended learning space is especially productive in developing understanding of energy transfers and transformations. In this blended space, naturally occurring learner interactions like body movement, gesture, and metaphorical speech are blended with a conceptual metaphor of energy as a substance in a class of…

The use of mathematics performance tasks can provide a window into how a student is applying mathematics to various situations, how they are reasoning mathematically and how they are applying conceptual knowledge through problem solving and critical thinking. The purpose of this study was to investigate, according to the elementary mathematics…

We report results from the following three analyses of PARCC [Partnership for Assessment of Readiness for College and Careers] cognitive complexity measures, based on 2014 field test item and task development and field test data. We conducted classification and regression tree analyses using 2014 PARCC field test data to do the following: (1)…

This article illustrates the importance of one's initial thoughts in problem solving through an entertaining example.

Recent research indicates that epigenetic mechanisms and, in particular, the post-translational modification (PTM) of histones may contribute to memory encoding and storage. Among the dozens of possible histone PTMs, the methylation/demethylation of lysines in the N-terminal tail of histone H3 exhibits particularly strong links with cognitive…

The decision making process is central to the practice of a clinician and has traditionally been described in terms of the hypothetico-deductive model. More recently, models adapted from cognitive psychology, such as the dual process and script theories have proved useful in explaining patterns of practice not consistent with purely cognitive…

It is widely suggested that ASD is characterized by atypical local/global processing, but the published findings are contradictory. In an effort to resolve this question, we tested a large group of children on both a free-choice task and an instructed task using hierarchical local-global stimuli. We find that although children with autism showed a…