The First Step to Learning Place Value: A Role for Physical Models?

Very few questions have cast such an enduring effect in cognitive science as the question of “symbol-grounding”: Do human-invented symbol systems have to be grounded to physical objects to gain meanings? This question has strongly influenced research and practice in education involving the use of physical models and manipulatives. However, the evidence on the effectiveness of physical models is mixed. We suggest that rethinking physical models in terms of analogies, rather than groundings, offers useful insights. Three experiments with 4- to 6-year-old children showed that they can learn about how written multi-digit numbers are named and how they are used to represent relative magnitudes based on exposure to either a few pairs of written multi-digit numbers and their corresponding names, or exposure to multi-digit number names and their corresponding physical models made up by simple shapes (e.g., big-medium-small discs); but they failed to learn with traditional mathematical manipulatives (i.e., base-10 blocks, abacus) that provide a more complete grounding of the base-10 principles. These findings have implications for place value instruction in schools and for the determination of principles to guide the use of physical models.

Transcending the rational symbol system

Symbols support the uniquely human capabilities of language, culture, and thinking. Therefore, cognitive scientists have tried to explain intelligence as founded on Rational Symbol Systems (RSS). RSS use syntactical and logical rules to combine discrete symbols into meaningful expressions and inferences. However, these symbols fail to capture continuous, felt experience. The proposed solution is to ground symbols in situated interactions and subsymbolic networks of associations. Historically, different approaches have attempted to overcome the shortcomings of RSS. These include science, by formalizing and operationalizing symbols; philosophy, by critically analyzing the relation between symbols and reality; art, by evoking subjective experiences; and spirituality, by expanding consciousness. Information technologies, such as artificial intelligence, neural networks, simulations and virtual reality, make it possible to integrate their results. That would allow externalizing and controlling creativity and intuition, thus inaugurating an evolutionary transition to a supra-human level of intelligence, the “Global Brain”.

Verzauberung der Welt? Religiöse Symbolsysteme in Geschichte und Gegenwart

Religion verschwindet im Nebel des Pluralen, verdunstet in der Hitze des Säkularen. So lautet eine gängige These, die an die moderne ‚Meistererzählung‘ von der Entzauberung der Welt und vom Untergang des Religiösen anknüpft. Doch dem postulierten Megatrend vom Verschwinden der Religion steht ihre Rückkehr in vielen Bereichen gesellschaftlichen Lebens entgegen. Die vermeintliche Säkularisierung sieht sich einer Resakralisierung gegenüber. Religion besitzt offenkundig jenseits ihrer vermeintlichen Entzauberung einen produktiven ‚Glutkern‘. Zu denken ist dabei an die Dimension der Transzendenz, die Genese und Durchsetzung von religiös geprägten Werten, die Bedeutung religiöser Symbolsysteme in scheinbar säkularisierten Gesellschaften oder auch Vorstellungen der Heiligkeit von Menschen, Göttern, Lebewesen und Dingen. Die Beiträge von Klaus Bieberstein, Ernst Peter Fischer, Hans Joas, Thomas Laubach, Angelika Neuwirth, Peter B. Steiner und Reinhard Zintl reflektieren diese spannungsvolle Lage und bieten Ansatzpunkte für einen neuen Dialog zwischen Säkularisierung und Sakralisierung. Religion disappears in the fog of plurality, vanishes in the heat of profanity. This is a common thesis that ties in with the modern "master narrative" of the disenchantment of the world and the decline of religion. But the postulated megatrend of the disappearance of religion is countered by its return in many areas of social life. The supposed secularization is confronted with a resacralization. Beyond its supposed disenchantment, religion obviously possesses a productive 'glowing core'. The dimension of transcendence, the genesis and enforcement of religiously shaped values, the significance of religious symbol systems in seemingly secularized societies, or even concepts of the sacredness of people, gods, living beings, and things are all worthy of consideration. The contributions by Klaus Bieberstein, Ernst Peter Fischer, Hans Joas, Thomas Laubach, Angelika Neuwirth, Peter B. Steiner and Reinhard Zintl reflect on this tense situation and offer starting points for a new dialogue between secularization and sacralization.

The meaning of the Ceprotan tradition in bersih desa for the people of Sekar village

The purifying tradition carried out by the Sekar Village community is always accompanied by a traditional ceremony called Ceprotan. This Ceprotan traditional ceremony only exists in Sekar Village. Its implementation load with folklore values that the local people believe. This study aimed to know the meaning of the Ceprotan tradition for the people of Sekar village. This research used a qualitative method with a phenomenological approach. The intake of informants was done through the purposive sampling technique. Data obtained using both secondary and polymer data. Data collection techniques used were interviews, observation, and documentation. To ensure the validity of the data, the researcher used source triangulation techniques on the data obtained. The data were then analyzed with cultural interpretation techniques or the "thick description" approach by Clifford Geertz to interpret the symbol systems of cultural meaning in a deep painting. This study's findings were that the village's purifying tradition accompanied by the Ceprotan traditional ceremony carried out by the Sekar Village community, especially Krajan Lor and Krajan Kidul Hamlets, was done as an expression of gratitude, hope, and prayer to God Almighty for good things. Based on cultural practitioners' symbolic activities that appeared and were interpreted, this tradition was also carried out as a form of appreciation and reminder to the ancestors of Sekar Village, which until now is believed by the community as Danyang who consider influencing the survival of the local people. This belief contains in the folklore of the origin of Sekar Village. It continues to maintain as a form of refinement of the customs and culture of Sekar Village.

Computer code comprehension shares neural resources with formal logical inference in the fronto-parietal network

Despite the importance of programming to modern society, the cognitive and neural bases of code comprehension are largely unknown. Programming languages might ‘recycle’ neurocognitive mechanisms originally developed for natural languages. Alternatively, comprehension of code could depend on fronto-parietal networks shared with other culturally-invented symbol systems, such as formal logic and symbolic math such as algebra. Expert programmers (average 11 years of programming experience) performed code comprehension and memory control tasks while undergoing fMRI. The same participants also performed formal logic, symbolic math, executive control, and language localizer tasks. A left-lateralized fronto-parietal network was recruited for code comprehension. Patterns of activity within this network distinguish between ‘for’ loops and ‘if’ conditional code functions. In terms of the underlying neural basis, code comprehension overlapped extensively with formal logic and to a lesser degree math. Overlap with executive processes and language was low, but laterality of language and code covaried across individuals. Cultural symbol systems, including code, depend on a distinctive fronto-parietal cortical network.

Purposeful problem solving practices in Te Kākano

Mathematical learning is an integral part of early childhood education (ECE). In Aotearoa New Zealand there is a range of valuable curriculum resources including Te Kākano, a “living, evolving” framework of purposeful activities, to assist teachers to notice and respond to mathematics learning. This article aims to contribute towards this evolution by suggesting mathematical problem solving become more explicitly embedded within Te Kākano. This would be one way of keeping mathematical practices at the forefront of early childhood mathematics education supporting children to be creative mathematical problem solvers as they develop early understandings of mathematics symbol systems and technologies.

Symbol Systems and Social Structures

Symbol systems and social structures are prominent concepts with long historical legacies in the social sciences. This chapter traces how symbol systems and social structures have been theorized independently of each other in the social sciences during the 20th century, before elaborating the ways in which sociologists have theorized the relationship between the two. Marx, Weber, and Simmel offered important ideas about this relationship, but Durkheim’s account of the social origins of mental structures provides the most direct and elaborated theory about the relationship between mental and social structures within the classical sociological period. Subsequently, we trace Durkheim’s legacy through three contemporary perspectives: field theory, neo-institutionalism, and culture and cognition. While maintaining analytical continuity with the Durkheimian tradition, these perspectives also represent new theoretical, analytical, and methodological advances in locating and specifying correspondences between symbol systems and social structures. Nevertheless, we find that pressing questions remain pertaining to how symbol systems and social structures interrelate, and how exactly this relationship shapes both cognition and action.