scholarly journals “The Play’s the Thing”: Mathematization as Dramatization

Paideusis ◽  
2020 ◽  
Vol 17 (1) ◽  
pp. 35-44
Author(s):  
Dan Mellamphy ◽  
Nandita Biswas Mellamphy

Mobilizing prevalent themes in the fields of mathematics education, literary criticism, and philosophy, this paper contextualizes ‘the mathematical’, ‘mathematical thinking’, and ‘mathematical pedagogy’ with respect to ancient Greek concept of mathesis, modern notions of mathematical agency, the Keatsian concept of negative capability, and the analogy of ‘staging’ a dramatic/mathematical ‘play’. Its central claim is that mathematization is dramatization—that learning mathematics (indeed, learning to learn, which is what the Greek mathesis actually means) is an activity of setting things up and (in this ‘set’ or ‘setting’) allowing things to play out (e-ducere). Beginning with Paul Ernest’s identification of the difference between absolutism and fallibilism in the philosophy of math education, and incorporating concepts from Pythagoras, Hippasus, Heraclitus (the ‘ancients’), Descartes, Kant, Keats (the ‘moderns’), as well as Freud, Heidegger, and Badiou (‘nos prochains’, to quote Klossowski ), we argue that ‘mathematical knowledge’ cannot be understood simply within the framework of logicism, formalism, or even simply as an epistemological articulation. Rather, we endeavour to show that the process of ‘learning mathematically’ allows us to gain insight into the foundations of ‘being’ itself (i.e. ontology). Learning to learn (mathesis) proceeds, as such, by way of staging and playing-out the half-known or unknown (the ill-seen and ill-said) in the hopes of uncovering the mystery (Greek myesis) at the heart of things.

2020 ◽  
Author(s):  
Jennifer McDonald ◽  
Rebecca Merkley ◽  
Jacqueline Mickle ◽  
Lisa Collimore ◽  
Daniel Ansari

Research in cognitive development has highlighted that early numeracy skills are associated with later math achievement, suggesting that these skills should be targeted in early math education. Here we tested whether tools used by researchers to assess mathematical thinking could be useful in the classroom. This paper describes a collaborative project between cognitive scientists and school board researchers/educators implementing numeracy screeners with kindergarten students over the course of three school years. The Give-A-Number task (Wynn, 1990) was used with first-year kindergarten students and the Numeracy Screener [BLINDED] with second-year kindergarten students. Results indicated that educators (N = 59) found the tools feasible to implement and helpful for exploring their students’ thinking and targeting instruction. The Educators’ feedback also helped inform improvements to the implementation of the tools and future directions for both the schools and the researchers. This work emphasizes the importance of transdisciplinary collaboration to address the research-practice gap.


Author(s):  
Martin Camper

Arguing over Texts presents a rhetorical method for analyzing how people disagree over the meaning of texts and how they attempt to reconcile those disagreements through argument. The book recovers and adapts a classification of recurring types of disagreement over textual meaning, invented by ancient Greek and Roman teachers of rhetoric: the interpretive stases. Drawing on the rhetorical works of Aristotle, Cicero, Quintilian, and Hermogenes, the book devotes a chapter to each of the six interpretive stases, which classify issues concerning ambiguous words and phrases, definitions of terms, clashes between the text’s letter and its spirit, internal contradictions, applications of the text to novel cases, and the authority of the interpreter or the text itself. From the dispute over Phillis Wheatley’s allegedly self-racist poetry to the controversy over whether some of Abraham Lincoln’s letters provide evidence he was gay, the book offers examples from religion, politics, history, literary criticism, and law to illustrate that the interpretive stases can be employed to analyze debates over texts in virtually any sphere. In addition to its classical rhetorical foundation, the book draws on research from modern rhetorical theory and language science to elucidate the rhetorical, linguistic, and cognitive grounds for the argumentative construction of textual meaning. The method presented in this book thus advances scholars’ ability to examine the rhetorical dynamics of textual interpretation, to trace the evolution of textual meaning, and to explore how communities ground their beliefs and behaviors in texts.


2021 ◽  
Vol 11 (6) ◽  
pp. 289
Author(s):  
Jaime Huincahue ◽  
Rita Borromeo-Ferri ◽  
Pamela Reyes-Santander ◽  
Viviana Garrido-Véliz

School is a space where learning mathematics should be accompanied by the student’s preferences; however, its valuation in the classroom is not necessarily the same. From a quantitative approach, we ask from the mathematical thinking styles (MTS) theory about the correlations between preferences of certain MTS and mathematical performance. For this, a valid test instrument and a sample of 275 16-year-old Chilean students were used to gain insight into their preferences, beliefs and emotions when solving mathematical tasks and when learning mathematics. The results show, among other things, a clear positive correlation between mathematical performance and analytical thinking style, and also evidence the correlation between self-efficacy, analytical thinking and grades. It is concluded that students who prefer the analytical style are more advantageous in school, since the evaluation processes have a higher valuation of analytic mathematical thinking.


Adam alemi ◽  
2021 ◽  
Vol 90 (4) ◽  
pp. 53-65
Author(s):  
V. Dunaev ◽  
◽  
V. Kurganskaya ◽  

The article deals with a number of cultural and historical forms of implementation of the principle of coevolution of technologies and the semantic organization of society. Using Plato's cosmogony as an example, the use of numerical symbolism as a matrix of the divine creation of the world and the human soul is analyzed. The article analyzes the difference between technologies introduced by ancient Greek philosophers and the philosophy of Taoism in China, based on: 1) on the cultivation of natural processes, and 2) on giving the material substrate any arbitrary shapes. The role of this difference in the endowment of ethical characteristics and power functions of key mythological characters is shown. Using the example of the mythological symbolization of metallurgy and blacksmithing, the features of the archaic perception of complex technological processes are analyzed. On the example of the architectural design of the "Panopticon" by I. Bentham, one of the first social technologies and its role in the transformation of the concept of power and the ways of its implementation is considered. Various forms of realization of the idea of the panopticon with the help of digital information and communication technologies are analyzed.


Kavkaz-forum ◽  
2021 ◽  
Author(s):  
Р.Н. АБИСАЛОВА

В статье рассмотрен один из мотивов осетинского Даредзановского эпоса – мотив прикованного героя, еще в древности вошедший в мифологию, фольклор, литературу многих народов и получивший название «мотив Прометея». Образ Прометея относится к «вечным образам» мировой художественной культуры. История прикования и освобождения Прометея и в древнегреческой мифологии, и в трагедии Эсхила позиционируется как топонимически привязанная к Кавказу. Именно здесь сюжет о наказанном Богом и прикованном богатыре получил распространение в национальных мифах и эпических преданиях – грузинских, осетинских, кабардинских, абхазских, вайнахских, армянских и др. Эти лаконичные предания об Амиране-Амране, по мнению Вс.Ф. Миллера, – кульминационные во всех источниках, рассказывающих об этом герое. Рассмотрены как древнегреческий Прометей, так и кавказские, в первую очередь осетинские, прикованные герои, представленные в работах Вс.Ф. Миллера, Г.Н. Потанина, Дз. Гатуева, Д.А. Калоевой, З.Г. Тменовой, Ю.А. Дзиццоты, Х.Ф. Цгоева и др. Образ Амирана сравнивается с соответствующими ему героями кавказских эпосов. При всей схожести мотивов богоборчества и наказания героя прикованием к скале или столбу нельзя не отметить отличия осетинского Амирана от остальных. В Даредзановских сказаниях он героическая личность, истинный богатырь, совершающий множество подвигов, побеждающий великанов, помогающий всем нуждающимся. Сын племянницы Бога, герой близок к народу, он побеждает врагов не только ради демонстрации силы, ловкости, хитрости, но и для спасения родных и друзей. В отличие от большинства кавказских прикованных героев, освобождение Амирана не предвещает гибель мира, напротив, осетинский Амиран, в случае освобождения, даст людям свободу и счастье. Многие мотивы в преданиях об Амране соотносятся с мотивами Нартовского эпоса. Амиран-Амран приравнивается к любимым героям осетинской Нартиады – Сослану, Батразу, Урузмагу, Шатане. В работе его образ рассмотрен для подтверждения объективной закономерности подобной репрезентации осетинского героя. The article deals with one of the motives of the Ossetian Daredzanian epic − the motive of the chained hero, which in ancient times entered the mythology, folklore, literature of many peoples and was called the "Prometheus motive". The image of Prometheus belongs to the "eternal images" of world art culture. The history of the chaining and liberation of Prometheus, both in ancient Greek mythology and in the tragedy of Aeschylus, is positioned as toponymically tied to the Caucasus. It was here that the plot about the God-punished and chained hero became widespread in national myths and epic legends − Georgian, Ossetian, Kabardian, Abkhaz, Vainakh, Armenian, etc. These laconic legends about Amiran-Amran, according to Vs.F. Miller, are culminating in all the sources telling about this hero. Both the ancient Greek Prometheus and the Caucasian, primarily Ossetian, chained heroes presented in the works of Vs.F. Miller, G.N. Potanin, Dz. Gatuev, D.A. Kaloeva, Z.G. Tmenova, Yu.A. Dzizzoity, Kh.F. Tsgoev and others. The image of Amiran is compared with the corresponding heroes of the Caucasian epics. With all the similarity of the motives of fighting against God and the punishment of the hero by being chained to a rock or a pillar, one cannot fail to note the difference between the Ossetian Amiran and the others. In Daredzan's legends, he is a heroic person, a true hero who performs many feats, conquers giants, and helps all those in need. The son of the niece of God, the hero is close to the people, he defeats enemies not only for the sake of demonstrating strength, dexterity, cunning, but also to save family and friends. Unlike most of the Caucasian chained heroes, the release of Amiran does not portend the death of the world, on the contrary, the Ossetian Amiran, if liberated, will give people freedom and happiness. Many motives in the legends about Amran correlate with the motives of the Nartov epic. Amiran-Amran is equated with the favorite heroes of the Ossetian Nartiada - Soslan, Batraz, Uruzmag, Shatana. In the work, his image is considered to confirm the objective regularity of such a representation of the Ossetian hero.


Author(s):  
Linda Zagzebski

The concept of perfect goodness had a central place in ancient Greek and medieval philosophy, and is still frequently discussed in contemporary natural theology. Medieval philosophers adopted the idea from the philosophies of Plato and Aristotle, with the difference that they identified perfect goodness with a personal God. In ancient and medieval philosophy the concept is primarily a metaphysical one, since goodness was thought to be extensionally equivalent to being, but it is secondarily a moral concept referring to the distinctive sort of goodness appropriate to those beings that have wills. Thus it is fundamental to a long tradition on the metaphysical basis of value which lasted from Plato until at least the sixteenth century. In Plato, perfect goodness is the Form of the Good, upon which everything that has being is ontologically and causally dependent. In Aristotle, the good is identified with the end or purpose of a natural being. The good is that towards which all things move for the fulfilment of their natures. By the time of Aquinas, medieval philosophers had identified the good in both the Platonic and Aristotelian senses with the Christian God and had argued that God is both the perfectly good creative source and the perfectly good end of all beings other than himself. The concept of a perfectly good being in Christian philosophical theology faces two major kinds of difficulty. One is the problem that perfect goodness appears to be incompatible with the divine attributes of omnipotence and freedom of the divine will. And if a perfectly good being does not have a will that is free in a morally significant sense, that being seems to lack goodness in the moral sense of goodness. The second kind of problem is that the existence of a being who is both omnipotent and perfectly good seems to be incompatible with the existence of evil. In spite of these problems, there is a strong attraction to the idea of a perfectly good God in contemporary philosophical theology. The category of perfect goodness is therefore one of the most persistent of the concepts in the Platonic legacy.


2007 ◽  
Vol 101 (4) ◽  
pp. 250-256 ◽  
Author(s):  
Kathleen S. Himmelberger ◽  
Daniel L. Schwartz

The Standards developed by the National Council of Teachers of Mathematics (2000) state that instructional programs should enable all students to communicate mathematical ideas. The Standards indicate that good communication includes the ability to express organized and precise ideas as well as the ability to analyze and evaluate the mathematical thinking of others. Learning mathematics goes beyond procedural fluency; it also includes learning to discuss mathematical ideas. For this purpose, small groups have become a frequent configuration in the mathematics classroom. When combined with a suitable exercise, small-group discussions can have positive effects on mathematical understanding.


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