Towards a symbol literacy approach in the education of children

Abstract

Children enter a world that is full of symbols, most of which have become inaccessible. This is true not only because of a positivistic attitude that views analogical truth as nonsensical, but also because of the fragmentation that we experience. This situation is impoverishing children’s awareness, connectedness as well as their ability to access and express existential concerns and the answers different generations have tried to provide. It is for this reason that children need to learn a variety of symbols and the ‘grammar’ of how they form meaning. A symbolic literacy approach not only helps them to read symbols but also enables them to formulate meaning and to connect with the deeper reality and facilitates their ability to transcend physical reality. The paper will also refer to the development of an interdisciplinary pedagogy and its implementation through a project that is being done in collaboration with Maltese primary schools.     

Matching of numerical symbols with number of responses by pigeons

Pigeons were trained to peck a certain number of times on a key that displayed one of several possible numerical symbols. The particular symbol displayed indicated the number of times that the key had to be pecked. The pigeons signalled the completion of the requirement by operating a separate key. They received a food reward for correct response sequences and time-out penalties for incorrect response sequences. In the first experiment nine pigeons learned to allocate 1, 2, 3 or 4 pecks to the corresponding numerosity symbols s ₁, s ₂, s ₃ and s ₄ with levels of accuracy well above chance. The second experiment explored the maximum set of numerosities that the pigeons were capable of handling concurrently. Six of the pigeons coped with an s ₁–s ₅ task and four pigeons even managed an s ₁–s ₆ task with performances that were significantly above chance. Analysis of response times suggested that the pigeons were mainly relying on a number-based rather than on a time-based strategy. Received: 11 October 1999 / Accepted after revision: 27 January 2000     

Continuous visual properties of number influence the formation of novel symbolic representations

Numerical symbols are thought to be mapped onto preexisting nonsymbolic representations of number. A growing body of evidence suggests that nonsymbolic numerical processing is significantly influenced by the associated visual properties of continuous quantity (e.g., surface area, density), but their role in the acquisition of novel symbols is unknown. Forty undergraduate students were trained to associate novel abstract symbols with numerical magnitudes. Half of the symbols were associated with nonsymbolic arrays in which total surface area and numerosity were correlated (“congruent”), and the other symbols were associated with arrays in which total surface area was equated across numerosities (“incongruent”). As numbers are represented in multiple formats (words, digits, nonsymbolic arrays), we also tested whether providing auditory nonword labels facilitated symbol learning. Following training, participants engaged in speeded comparisons of the newly learnt symbols. Comparisons were affected by the ratio between the numerosities associated with each symbol, a characteristic marker of numerical processing. Furthermore, comparisons were hardest for large-ratio comparisons of symbols associated with incongruent area and numerosity pairing during learning. In turn, these findings call for the further investigation of visual parameters on the development of numerical cognition.     

Brief non-symbolic,approximate number practice enhances subsequent exact symbolic arithmetic in children

Recent research reveals a link between individual differences in mathematics achievement and performance on tasks that activate the approximate number system (ANS): a primitive cognitive system shared by diverse animal species and by humans of all ages. Here we used a brief experimental paradigm to test one causal hypothesis suggested by this relationship: activation of the ANS may enhance children’s performance of symbolic arithmetic. Over 2 experiments, children who briefly practiced tasks that engaged primitive approximate numerical quantities performed better on subsequent exact, symbolic arithmetic problems than did children given other tasks involving comparison and manipulation of non-numerical magnitudes (brightness and length). The practice effect appeared specific to mathematics, as no differences between groups were observed on a comparable sentence completion task. These results move beyond correlational research and provide evidence that the exercise of non-symbolic numerical processes can enhance children’s performance of symbolic mathematics.     

Waiting by mistake: Symbolic representation of rewards modulates intertemporal choice in capuchin monkeys,preschool children and adult humans

In the Delay choice task subjects choose between a smaller immediate option and a larger delayed option. This paradigm, also known as intertemporal choice task, is frequently used to assess delay tolerance, interpreting a preference for the larger delayed option as willingness to wait. However, in the Delay choice task subjects face a dilemma between two preferred responses: “go for more” (i.e., selecting the larger, but delayed, option) vs. “go for sooner” (i.e., selecting the immediate, but smaller, option). When the options consist of visible food amounts, at least some of the choices of the larger delayed option might be due to a failure to inhibit a prepotent response towards the larger option rather than to a sustained delay tolerance. To disentangle this issue, we tested 10 capuchin monkeys, 101 preschool children, and 88 adult humans in a Delay choice task with food, low-symbolic tokens (objects that can be exchanged with food and have a one-to-one correspondence with food items), and high-symbolic tokens (objects that can be exchanged with food and have a one-to-many correspondence with food items). This allows evaluating how different methods of representing rewards modulate the relative contribution of the “go for more” and “go for sooner” responses. Consistently with the idea that choices for the delayed option are sometimes due to a failure at inhibiting the prepotent response for the larger quantity, we expected high-symbolic tokens to decrease the salience of the larger option, thus reducing “go for more” responses. In fact, previous findings have shown that inhibiting prepotent responses for quantity is easier when the problem is framed in a symbolic context. Overall, opting for the larger delayed option in the visible-food version of the Delay choice task seems to partially result from an impulsive preference for quantity, rather than from a sustained delay tolerance. In capuchins and children high-symbolic stimuli decreased the individual’s preference for the larger reward by distancing from its appetitive features. Conversely, the sophisticated symbolic skills of adult humans prevented the distancing effect of high-symbolic stimuli in this population, although this result may be due to methodological differences between adult humans and the other two populations under study. Our data extend the knowledge concerning the influence of symbols on both human and non-human primate behavior and add a new element to the interpretation of the Delay choice task. Since high-symbolic stimuli decrease the individual’s preference for the larger reward by eliminating those choices due to prepotent responses towards the larger quantity, they allow to better discriminate responses based on genuine delay aversion. Thus, these findings invite greater caution in interpreting the results obtained with the visible-food version of the Delay choice task, which may overestimate delay tolerance.     

The approximate number system is not predictive for symbolic number processing in kindergarteners

The relation between the approximate number system (ANS) and symbolic number processing skills remains unclear. Some theories assume that children acquire the numerical meaning of symbols by mapping them onto the preexisting ANS. Others suggest that in addition to the ANS, children also develop a separate, exact representational system for symbolic number processing. In the current study, we contribute to this debate by investigating whether the nonsymbolic number processing of kindergarteners is predictive for symbolic number processing. Results revealed no association between the accuracy of the kindergarteners on a nonsymbolic number comparison task and their performance on the symbolic comparison task six months later, suggesting that there are two distinct representational systems for the ANS and numerical symbols.     

Is it life or is it Memorex? Video as a representation of reality

This paper offers an overview of research on infants’ early behavior toward televised images, followed by an account of the development of representational competence with video. Several aspects of representation are involved in young children’s understanding and use of video. From a very young age, children form mental representations of the contents of video, making sense of realistic images of familiar things. Children also notice and represent information regarding video itself (e.g., its 2-dimensionality). An important development occurs when children represent the relation between video and reality: at first, toddlers appear to categorize video as separate from reality, but eventually children recognize realistic video images as physical representations (symbols) of events they have not directly perceived. A mature representation of video takes into account genre (e.g., news, drama) and reality status based on recognition that video can (but does not always) represent real events.     

Symbols of Diaspora Jewish identity: An international survey and multi-dimensional analysis

Symbols are important in representing religious and ethnic identity, particularly in the postmodern age. Using a case study of Jewish adolescents, this article explores the use of symbols in expressing identity. A structural typology of symbols is developed, based on responses to a list of 20 symbols of Jewish identity by over 40,000 Jewish youth from around the world, who were surveyed during educational tours to Israel. The multi-dimensional smallest space analysis (SSA) technique is used to develop the typology by graphically representing the correlations between the symbols. Symbols representing the struggle of the weak against the strong are at the core of the typology. This core is surrounded by sets of symbols related to religion, family, Israel, the Holocaust, justice, and contribution to world culture. A parallel centre–periphery structure indicates that people are more central symbols than places or objects. Sub-populations of self-defined “religious” and “non-religious” Jewish youth are compared in relation to this typology of symbols by introducing them into the SSA as “external variables”. Applications of the typology of symbols to other ethnic and religious groups are explored.     

Foundations of Representation: Where Might Graphical Symbol Systems Come From?

It has been suggested that iconic graphical signs evolve into symbolic graphical signs through repeated usage. This article reports a series of interactive graphical communication experiments using a 'pictionary' task to establish the conditions under which the evolution might occur. Experiment 1 rules out a simple repetition based account in favor of an account that requires feedback and interaction between communicators. Experiment 2 shows how the degree of interaction affects the evolution of signs according to a process of grounding. Experiment 3 confirms the prediction that those not involved directly in the interaction have trouble interpreting the graphical signs produced in Experiment 1. On the basis of these results, this article argues that icons evolve into symbols as a consequence of the systematic shift in the locus of information from the sign to the users' memory of the sign's usage supported by an interactive grounding process.