Symbolic Representation


Kelly Sheehan, Past Graduate Student in the Uttal Lab

  • This research investigates how children discover the spatial and relational connection between a scale model and the room it represents. How do children come to understand that a model is a symbol for the room? A series of studies investigates the role of overall similarity on children’s understanding of this relation. We are also investigating how a short delay between testing sessions can help children gain insight into this connection when they would initially fail.

Scale Errors Offer Evidence for a Perception-Action Dissociation Early in Life — Full Paper

Judy S. Deloache, David H. UttalKarl S. Rosengren

  • We report a perception-action dissociation in the behavior of normally developing young children. In adults and older children, the perception of an object and the organization of actions on it are seamlessly integrated. However, as documented here, 18- to 30-month-old children sometimes fail to use information about object size and make serious attempts to perform impossible actions on miniature objects. They try, for example, to sit in a dollhouse chair or to get into a small toy car. We interpret scale errors as reflecting problems with inhibitory control and with the integration of visual information for perception and action.

Everyday Scale Errors — full paper

Elizabeth A. WareDavid H. UttalJudy S. DeLoache

  • Young children occasionally make scale errors – they attempt to fit their bodies into extremely small objects or attempt to fit a larger object into another, tiny, object. For example, a child might try to sit in a dollhouse-sized chair or try to stuff a large doll into it. Scale error research was originally motivated by parents’ and researchers’ informal accounts of these behaviors. However, scale errors have only been documented using laboratory procedures designed to promote their occurrence. To formally document the occurrence of scale errors in everyday settings, we posted a survey on the internet. Across two studies, participants reported many examples of everyday scale errors that are similar to those observed in our labs and were committed by children of the same age. These findings establish that scale errors occur in the course of children’s daily lives, lending further support to the account that these behaviors stem from general aspects of visual processing.

Developmental Changes in Children’s Understanding of the Similarity Between Photographs and their Referents — full paper

David H. UttalDedre GentnerLinda L. Hand, and Alison R. Lewis

  • In a series of three experiments, we investigated the development of children’s understanding of the similarities between photographs and their referents. Based on prior work on the development of analogical understanding (e.g. Gentner & Rattermann, 1991), we suggest that the appreciation of this relation involves multiple levels. Photographs are similar to their referents both in terms of the constituent objects and in terms of the relations among these objects. We predicted that children would appreciate object similarity (whether photographs depict the same objects as in the referent scene) before they would appreciate relational similarity (whether photographs depict the objects in the same spatial positions as in the referent scene). To test this hypothesis, we presented 3-, 4-, 5-, 6-, and 7 year-old children and adults with several candidate photographs of an arrangement of objects. Participants were asked to choose which of the photographs was ‘the same’ as the arrangement. We manipulated the types of information the photographs preserved about the referent objects. One set of photographs did not preserve the object properties of the scene. Another set of photographs preserved the object properties of the scene, but not the relational similarity, such that the original objects were depicted but occupied different spatial positions in the arrangement. As predicted, younger children based their choices of the photographs largely on object similarity, whereas older children and adults also took relational similarity into account. Results are discussed in terms of the development of children’s appreciation of different levels of similarity.

Grasping the Nature of Pictures  — full paper

Judy S. Deloache, Sophia L. Pierroutsakos, David H. UttalKarl S. Rosengren, Alma Gottlieb

  • The role of experience in the development of pictoral competence has been the center of substantial debate.  The four studies persented here help resolve the controversy by systematically documenting and examining manual exploration of depicted objects by infants.  We report that 9-month-old infants manually investigate pictures; touching and feeling depicted objects as if they were real objects and even trying to pick them up off the page.  The same behavior was observed in babies from two extremely different societies (the United States and the Ivory Coast).  This investigation of pictures occurs even though infants can discriminate between real objects and their depictions.  By the time infants are 19 months of age, their manual exploration is replaced by pointing at depicted objects.  These results indicate that initial uncertainty about the nature of pictures leads infants to investigate them.  Through experience, infants begin to acquire a concept of a picture.  This concept includes the fact that a picture has a dual nature (it is both an object and a representation of something other than itself), as well as knowledge about the culturally apporpriate use of pictures.

Pointing Out the Role of Maps and Gestures in Spatial Development

Megan SauterEllen ReynoldsDavid H. UttalSusan Goldin-Meadow, and

Susan Levine

  • Using maps influences how we think about space (Uttal & Wellman, 1989; Liben, 1999; Uttal, 2000) by allowing us to see, and to think about, spatial relations that would be difficult to acquire from direct experience. Maps can also influence the way we communicate spatial information. Here we investigated the influence of using a map on the development of spatial thinking and spatial communication. We asked children to communicate locations that they had learned from a map or from navigation alone. Interestingly, the influence of maps first appears in the gestures of children when communicating space and not in their speech. We suggest that this finding may reflect that maps and gesture share similarities in terms of communicating spatial relations in a visual, integrated manner.

Symbolic and Concrete Knowledge in Learning Two-Digit Subtraction

David H. Uttal, Meredith Amaya, Maria Del Rosario MaitaLinda L. HandKate O’Doherty, and Judy S. DeLoache

  • In this research we investigated possible causes explaining the difficulty that students have in transferring what they learn from using manipulatives to more formal written representations. The primary goal of this research was investigate children’s learning and transfer from both manipulatives and the traditional written method. We focused on a classic mathematics problem: double-digit subtraction. Results indicate that the fundamental challenge in integrating manipulatives into mathematics instruction is the mismatch between the format in which children learn and how they are tested. Our results suggest that the two instruction methods lead children to approach the problems differently and that these approaches may not be immediately compatible with solving problems in the other format. Children instructed in either format were able to demonstrate extremely high levels of competence within a short period of instruction as long as they continued to be tested in the same format in which there were initially instructed. It was only when children were required to solve the problems in the opposite format that performance broke down. Thus, our research suggest that using exclusively either written instruction or manipulatives-based methods of instruction may not be adequate as long as the goal is for children to be able to solve problems in the same format as instructed.

Countering Diagrammatic Narratives: The effect of animation on the interpretation of evolution

Camillia MatukDavid H. Uttal and Caroline Crouch

  • Many students’ prior intuitive understanding of evolution is of a journey of one species through various states of transformation through increasingly sophisticated and complex forms. In accord with this folk theory, students tend to incorrectly interpret the cladogram – a diagram of species phylogenetic relationships – as a chronology of events. In individual clinical interviews with 73 undergraduate students, we explore the relationship between symbolic meaning and diagrammatic structure in the interpretative process. In Study 1, we illustrate how elements of students’ narrative understandings, including a clear beginning, and determinate end; a sequence of events; and a plot with characters acting toward a goal, are easily mapped onto the structure of the diagram. In Study 2, we use animation to impose a presentation sequence  upon the cladogram that counters this typical folk narrative interpretation. Our findings suggest that intuitive spatial metaphors can be reversed, and visual structure and spatial location flexibly interpreted. Notably, we found that the effect of Good Continuation and the appeal of the folk theory of evolution remain powerful organizers of perception. This research illustrates a case of interpretation as an interaction between conceptual knowledge and diagrammatic structure. It investigates the boundaries of symbolic interpretation, and suggests visual designs for pedagogical forms – bridging representations to scaffold the understanding of a notation so crucial to evolutionary biology.

Inventing an Intuitive Representation of Relatedness

Camillia MatukDavid H. Uttal and Caroline Crouch

  • Students have difficulty reading cladograms – diagrams of evolutionary relationships among species. Their systematic errors suggest a problematic interaction between diagrammatic structure and existing misconceptions of evolution. In this study, we ask: Is there a more intuitive representation of the concept relatedness? In individual clinical interviews across two studies, we gave 33 undergraduate students hypothetical data sets, and asked them to invent representations to show relative relationships among items. Students later viewed a standard cladogram solution to the same task, and were asked to reason about the relationships shown. Study 1 suggests that actively constructing a personally meaningful representational system primes students to later perceive functional aspects of the conventional diagram, and detracts them from their otherwise intuitive narrative interpretations. Study 2 shows an effect of content assumptions on the kinds of diagrams invented, and on students’ strategies for subsequently reasoning with the standard diagram. Where most research into learning from scientific representations tends to focus on the various ways in which students misunderstand them, this project highlights the important role of students’ prior conceptual knowledge, and of the representational resources they bring to the task – each of which shapes interpretations of unfamiliar diagrams, and is necessary to acknowledge when designing effective instructional supports and interventions.

Heroes, Villains and Viruses: How graphic narratives teach science

Camillia MatukJudy Diamond and David H. Uttal

  • Virology has come to figure prominently in our day-to-day lives such that a basic understanding of viruses and infection is necessary to make informed personal and family health decisions. Comic books have unique narrative and motivational properties that hold tremendous potential for such a public education effort. However, we know little of the process of interpreting graphic narratives, let alone of graphic narratives that illustrate complex processes such as viral infection and the immune response. Here, we present findings from interviews with four 13-year old readers of a graphic story created to educate and incite interest in concepts of virology. Through a rich microgenetic analysis, we illustrate how readers make sense of complicated biological processes through an interaction between their prior knowledge, and of various visual narrative elements in the comics genre. This research investigates when and how particular graphic storytelling devices may help or hinder understanding, and begins to describe components of literacy in reading science comics. Ultimately, this work informs the design and use of comics as entry‐points into obscure and complicated scientific topics, and importantly, as objects to stimulate youths’ interest for future learning.

Manipulatives as Symbols: A new perspective on the use of concrete objects to teach mathematics — full paper

David H. Uttal, Kathyrn V. Scudder and Judy S. DeLoache

  • This article offers a new perspective on the use of concrete objects to teach mathematics. It is commonly assumed that concrete manipulatives are effective because they allow children to perform mathematics without understanding arbitrary, written mathematical symbols. We argue that the sharp distinction between concrete and abstract forms of mathematical expression may not be justified. We believe instead that manipulatives are also symbols; teachers intend for them to stand for or represent a concept or written symbol. Consequently, research on how young children comprehend symbolic relations is relevant to studying their comprehension of manipulatives. We review evidence that many of the problems that children encounter when using manipulatives are very similar to problems that they have using other symbol systems such as scale models. Successful use of manipulatives depends on treating them as symbols rather than as substitutes for symbols.

The Development of Early Symbolization: Educational implications — full paper

Judy S. DeloacheDavid H. Uttal and Sophia L. Pierroutsakos

  • Research on the symbolic functioning of very young children has important implications for educational materials. We argue that there are no transparent symbols; one can never assume that what seems to be an obvious symbolic relation is obvious to young children. We have discovered that young children have particular difficulty understanding and using symbols that are themselves interesting objects. A symbol, such as a scale model of a room that is salient and appealing as an object, requires a dual representation: To use a model, one must simulaneously represent both the model itself and its referent. Resarch on young children’s undersanding and use of models indicates that they have particular difficulty achieving dual representation. This work has clear implications for the use of symbolic objects for educational purposes. We discuss several examples of commonly used symbolic objects, suggesting that the may be less helpful to young learners that is generally assumed.

Early Cognitive Development: The Comprehension and Use of Symbolic Objects

Maria del Rosario Maita, and Olga Peralta

  • In this research we studied the impact of instruction in the early comprehension of a symbolic object.  Specifically, we studied if and when adult teaching affects the comprehension and use of a simple map by very young children (30, 36, 42 and 46 month-olds).  The studies employed a task in which children have to use a map in order to find a toy in a room.  First we explored at which age children understand the representational function of a map without any instruction at all.  Results show that 36 month old children do not comprehend the relation on their own, at 42 months of age half of them do understand this relation and half do not.  Only starting at 46 months do most children spontaneously comprehend the map-room relation.  Then, we investigated if it is possible to teach the symbolic function of maps.  We found that 36 month olds succeed in using a map symbolically after being explicityly instructed.  However, children only 6 months younger (30 month olds) did not.  This research shows tha tearly comprehension of a symbolic object is not solely dependent on age; adult teaching is also crucial at some points in development.

How We Read Graphs

Stacey Parrott, Steve Franconeri, David H. Uttal

  • The use of graphs to display quantitative information is ubiquitous, making them an excellent case study of object processing in visual cognition.  For example, bar graphs better convey discrete relations (X is bigger than Y) whereas line graphs are better suited to convey continuous relations (X grows with Y), and this difference may be due to different visual processing routines for each graph type (Zacks and Tversky, 1999).  The present study provides preliminary evidence to suggest that bar graphs are processed not holistically, but sequentially, and in left to right order.