A first grade student’s exploration of variable and variable notation / Una alumna de primer grado explora las variables y su notación

Abstract

This paper presents a case study of a first grade student to illustrate the diversity of her understandings related to variables and variable notation. While prior research has documented secondary school students’ difficulties with variables and variable notation, we identify many productive understandings in this much younger student, leading us to question the prevailing argument that students might have difficulties with variables due mostly to their own limitations. We draw our data from a teaching experiment that explored functional relationships. Individual interviews were carried out with a subset of the students in the experiment prior to, as well as mid-way through and at the end of the experiment. This paper focuses on a set of three interviews with one of the first grade students. We illustrate the shifts that occurred in the student’s understandings about variables and variable notation across as well as within each of the three interviews.     

Spirituality and child protection in early childhood education: a strengths approach

In recent international and Australian early childhood curriculum guidelines and child-protection policies, the need for teachers of young children to foster spirituality has been highlighted. However, what this might mean in practice has not been widely explored. This article addresses the more controversial issue of spiritual abuse and the right of children to protection in terms of spiritual development. We present a critique of current definitions taken from research and policy documents. Qualitative data provide the research background. Vignettes are presented to give examples of what spiritual harm might look like in practice. Finally, a strengths-based approach is introduced and strategies are suggested in order to explore the potential of the Strengths Approach (a social justice approach originating from social service practice) to aid early years’ teachers to create spiritually protective learning environments. This approach recognises and values children’s holistic development and wellbeing and supports them to appreciate, engage with and question the world around them with a resilient spirit.     

Infants’ sensitivity to uniform connectedness as a cue for perceptual organization

A new grouping principle, uniform connectedness (UC), has been posited to be a basic organizer of visual pattern information, one that takes precedence over other, more classic grouping principles (Palmer & Rock, 1994), but its ontogenetic origins have not previously been investigated. We examined whether 3- to 4-month-olds and 6- to 7-month-olds utilize UC to organize static two-dimensional displays. Infants habituated to uniformly connected patterns exhibited a novelty preference for disconnected element patterns, whereas those without any habituation failed to exhibit a preference. The results indicate that infants are sensitive to UC as a cue for perceptual organization. Prior studies indicate that some Gestalt principles (e.g., common movement) are functional during the first half year of life, but that other principles (e.g., form similarity) are less readily available. The present finding showing that young infants are sensitive to UC points to the foundational nature of this cue and adds to an emerging body of evidence indicating that at least some of the mechanisms believed to produce perceptual organization in adults are already operational in the first months of life. nt]mis|This research was supported by grants from the National Science Foundation (BCS 0224240) and the National Institute of Child Health and Human Development (HD042451).     

How we interact with objects: learning from brain lesions

Motor deficits are the most common outcome of brain damage. Although a large part of such disturbances arises from loss of elementary sensorimotor functions, several syndromes cannot be explained purely on these bases. In this article, we briefly describe higher-order motor impairments, with specific attention to the characteristic ability of the human hand to interact with objects and tools. Disruption of this motor skill at several independent levels is used to outline a comprehensive model, in which various current proposals for a modular organization of hand-object interactions can be integrated. In this model, cortical mechanisms related to object interaction are independent from representations of the semantic features of objects.     

Cultural differences in neural function associated with object processing

Behavioral research suggests that Westerners focus more on objects, whereas East Asians attend more to relationships and contexts. We evaluated the neural basis for these cultural differences in an event-related fMRI study. East Asian and American participants incidentally encoded pictures of (1) a target object alone, (2) a background scene with no discernable target object, and (3) a distinct target object against a meaningful background. Americans, relative to East Asians, activated more regions implicated in object processing, including bilateral middle temporal gyrus, left superior parietal/angular gyrus, and right superior temporal/supramarginal gyrus. In contrast to the cultural differences in object-processing areas, few differences emerged in background-processing regions. These results suggest that cultural experiences subtly direct neural activity, particularly for focal objects, at an early stage of scene encoding.     

Life-span development of visual working memory: when is feature binding difficult?

We asked whether the ability to keep in working memory the binding between a visual object and its spatial location changes with development across the life span more than memory for item information. Paired arrays of colored squares were identical or differed in the color of one square, and in the latter case, the changed color was unique on that trial (item change) or was duplicated elsewhere in the array (color-location binding change). Children (8-10 and 11-12 years old) and older adults (65-85 years old) showed deficits relative to young adults. These were only partly simulated by dividing attention in young adults. The older adults had an additional deficiency, specifically in binding information, which was evident only when item- and binding-change trials were mixed together. In that situation, the older adults often overlooked the more subtle, binding-type changes. Some working memory processes related to binding undergo life-span development in an inverted-U shape, whereas other, bias- and salience-related processes that influence the use of binding information seem to develop monotonically.