Delving Deeper: A New Path to the Quadratic Formula

2008 ◽  
Vol 101 (6) ◽  
pp. 473-478
Author(s):  
Henri Picciotto
Keyword(s):  
Ninth Grade ◽  
Student Understanding ◽  
Symbol Manipulation ◽  
Quadratic Formula ◽  
First Response ◽  
The Subject ◽  
To Come ◽  
State Of Affairs ◽  
Over Time

Many students enter ninth grade already familiar with the quadratic formula. Many others learn it in ninth grade. Some can even sing it! Unfortunately, the formula has little meaning for most students. For many, the traditional derivation of the formula by completing the square (fig. 1), if it is shown to them, is more baffling than illuminating. As a teacher, I value student understanding, and early on in my career as an algebra teacher, I found this state of affairs disturbing. My first response was to have students complete the square repeatedly, using numbers at first and then the parameters, in the hope that this process would lead to understanding. Alas, over time I realized that for many if not most of my students, additional symbol manipulation did not throw additional light on the subject. I needed to come at this lack of understanding some other way.

Science frictions : science, folklore, and "the future"

2019 ◽  
Author(s):  
◽  
London Brickley
Keyword(s):  
Popular Science ◽  
University Of Missouri ◽  
The Future ◽  
Contemporary Status ◽  
The Subject ◽  
To Come ◽  
Scientific Truth ◽  
The University ◽  
Over Time

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Folklore and science, along with the subject of the future which has slowly over time worked its way into the discourses of both, have a long, complicated history together. One that lives on in the present. (And one that might even prevail into the time to come). This work is not entirely that story. But it is a part of it, presented here as it is in the interest of opening new channels of discourse between two areas of research that are often seen by participants on all sides to be rather divergent, if not entirely oppositional to one another. This exploration culminates in a consideration of the contemporary status of popular science trends and how folklore might continue to operate within them--a proposal which identifies an increasingly emergent (although certainly not exclusively novel) form of folk expression that arises out of the friction caused by queries of scientific "truth," "promise," and "possibility" that is still stuck in a liminal wait for "the future." Both a widespread present-day phenomenon and subsequent set of narratives, expressions, beliefs, and actions that this work has chosen to call "science frictions."

Without the Power to Drink or Contract

2020 ◽  
Vol 24 (1) ◽  
pp. 26-48
Author(s):  
Warren Swain
Keyword(s):  
Alcohol Consumption ◽  
Social Activity ◽  
Individual Responsibility ◽  
Roman Law ◽  
Current Position ◽  
Modern Times ◽  
The Will ◽  
The Subject ◽  
The Law ◽  
Over Time

Intoxication as a ground to set aside a contract is not something that has proved to be easy for the law to regulate. This is perhaps not very surprising. Intoxication is a temporary condition of varying degrees of magnitude. Its presence does however raise questions of contractual autonomy and individual responsibility. Alcohol consumption is a common social activity and perceptions of intoxication and especially alcoholism have changed over time. Roman law is surprisingly quiet on the subject. In modern times the rules about intoxicated contracting in Scottish and English law is very similar. Rather more interestingly the law in these two jurisdictions has reached the current position in slightly different ways. This history can be traced through English Equity, the works of the Scottish Institutional writers, the rise of the Will Theory, and all leavened with a dose of judicial pragmatism.

STORYTELLING AND MEANING RECONSTRUCTION: A METAPHORICAL PERSPECTIVE

2016 ◽  
Vol 24 (2) ◽  
pp. 159-169
Author(s):  
M L Mojapelo
Keyword(s):  
Personal Development ◽  
Real Life ◽  
Human Existence ◽  
Meaning Reconstruction ◽  
Changing Patterns ◽  
The Subject ◽  
Changes Over Time ◽  
Over Time

Storytelling consists of an interaction between a narrator and a listener, both of whom assign meaning to the story as a whole and its component parts. The meaning assigned to the narrative changes over time under the influence of the recipient‟s changing precepts and perceptions which seem to be simplistic in infancy and more nuanced with age. It becomes more philosophical in that themes touching on the more profound questions of human existence tend to become more prominently discernible as the subject moves into the more reflective or summative phases of his or her existence. The aim of this article is to demonstrate the metaphorical character of a story, as reflected in changing patterns of meaning assigned to the narrative in the course of the subjective receiver‟s passage through the various stages of life. This was done by analysing meaning, from a particular storytelling session, at different stages of a listener‟s personal development. Meaning starts as literal and evolves through re-interpretation to abstract and deeper levels towards application in real life.

Introduction

2018 ◽  
Author(s):  
Chakravarthi Ram-Prasad
Keyword(s):  
Philosophical Tradition ◽  
Phenomenological Tradition ◽  
The Third ◽  
Western Philosophical Tradition ◽  
The Subject ◽  
To Come

The Introduction outlines the various chapters. It then situates the question of ‘body’ in the modern Western philosophical tradition following Descartes, and argues that this leaves subsequent responses to come under one of three options: metaphysical dualism of body and subject; any anti-dualist reductionism; or the overcoming of the divide. Describing the Phenomenology of Merleau-Ponty as a potent example of the third strategy, the Introduction then suggests his philosophy will function as foil to the ecological phenomenology developed and presented in the book. Moreover, one approach within the Western Phenomenological tradition, of treating phenomenology as a methodology for the clarification of experience (rather than the means to the determination of an ontology of the subject) is compared to the approach in this book. Since classical India, while understanding dualism, did not confront the challenge of Descartes (for better or for worse), its treatment of body follows a different trajectory.

Imagining Sonic Stories

2019 ◽  
pp. 441-457
Author(s):  
Vincent Meelberg
Keyword(s):  
Temporal Development ◽  
Sound Collage ◽  
The Subject ◽  
Over Time

Sonic narratives are the subject of Vincent Meelberg’s chapter, in which he discusses the capacity of sound not only to trigger narratives but also to tell stories that unfold over time. Meelberg uses his own sound collage work as an example of how narratives can be created through a sequence of sounds. He argues that sonic narratives emerge when the sequence of sounds represents a temporal development. Examples are provided that show how this temporal development emerges from either the referential qualities (hearing a succession of concrete events) or the acoustic qualities (e.g., the succession of tension and release) of the sound.

Wolfgang and Petra Lubitz, eds., Trotsky Bibliography: An International Classified List of Publications about Leon Trotsky and Trotskyism 1905–1998. Third completely revised and enlarged edition. Vols. 1–2. Munich: K. G. Saur, 1999. 840 pp. DM 368 cloth.

2001 ◽  
Vol 60 ◽  
pp. 232-233
Author(s):  
Gerd Callesen
Keyword(s):  
The Subject ◽  
Leon Trotsky ◽  
State Of Affairs ◽  
Definition Of ◽  
Political Value ◽  
Broad Approach

This bibliography is quite an impressive effort. It is extensive, thorough, structurally sound, and contains excellent indexes. In short, it is a truly useful tool for anyone who, for scholarly or political reasons, takes an interest in Trotsky and Trotskyism. Of course, the definition of Trotskyism is somewhat blurred; too many people have used the concept subjectively, either with positive or negative connotations, for it to signify anything unambiguous. The Lubitzes have done their utmost to remedy this state of affairs by disregarding sectarian restraints and by choosing a broad approach to the subject; they have even gone to the extreme of including some anti-Trotskyist effusions of no real scholarly or current political value.

scholarly journals Joint Action without Mutual Beliefs

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Giacomo Figà Talamanca
Keyword(s):  
Social Cognition ◽  
Joint Action ◽  
Common Ground ◽  
Mental States ◽  
Human Beings ◽  
Cooperative Hunting ◽  
Mutual Awareness ◽  
Shared Practice ◽  
State Of Affairs ◽  
Over Time

Abstract Joint action among human beings is characterized by using elaborate cognitive feats, such as representing the mental states of others about a certain state of affairs. It is still debated how these capacities evolved in the hominid lineage. I suggest that the consolidation of a shared practice over time can foster the predictability of other’s behavior. This might facilitate the evolutionary passage from inferring what others might know by simply seeing them and what they are viewing towards a mutual awareness of each other’s beliefs. I will examine the case for cooperative hunting in one chimpanzee community and argue that it is evidence that they have the potential to achieve common ground, suggesting that the consolidation of a practice might have supported the evolution of higher social cognition in the hominid lineage.

scholarly journals Using Cartographies to Map Time and Space in Teacher Learning in and Outside School

2021 ◽  
Vol 20 ◽  
pp. 160940692199290
Author(s):  
Paulo Padilla-Petry ◽  
Fernando Hernández-Hernández ◽  
Joan-Anton Sánchez-Valero
Keyword(s):  
Secondary School ◽  
Teacher Learning ◽  
Secondary School Teachers ◽  
Leisure Activities ◽  
Visual Methods ◽  
School Teachers ◽  
Video Recordings ◽  
The Subject ◽  
Pedagogical Relations ◽  
Over Time

This article explores the relations between teachers’ visual cartographies and oral narratives to better understand the spatial and temporal relations on teacher learning. It builds on a research project whose main questions were: 1) How and where do secondary school teachers learn to teach? 2) What are the consequences of this learning in their pedagogical relations and their students’ learning processes and results? Since narrative research has been a common way of approaching the subject and have led to an emphasis on learning as a journey across contexts and over time, some of its contributions to explore teachers’ learning paths are theoretically discussed, and visual methods, particularly cartographies, are also examined. Furthermore, the article presents the analysis of cartographies and video recordings of 29 secondary school teachers focusing on the interactions in different spaces and moments in time described by them. Findings suggest that learning to be a teacher may happen in interactions with objects, people and spaces beyond the boundaries of school, university and formal places of training and learning. They also show that the rhizomatic character of the cartographies may not prevent teleological thinking or the idea that any kind of learning is purposeful. Finally, this paper concludes that teachers’ learning does not fit the representational frame that distinguishes between formal contents and leisure activities, classrooms and private spaces, lessons and bodies, emotions and knowledge.

scholarly journals Influence of Hydrogeochemistry on Tunnel Drainage in Evaporitic Formations: El Regajal Tunnel Case Study (Aranjuez, Spain)

2021 ◽  
Vol 13 (3) ◽  
pp. 1505
Author(s):  
Ignacio Menéndez Pidal ◽  
Jose Antonio Mancebo Piqueras ◽  
Eugenio Sanz Pérez ◽  
Clemente Sáenz Sanz
Keyword(s):  
High Speed ◽  
Civil Engineering ◽  
Saturation Index ◽  
The Subject ◽  
Under Construction ◽  
Underground Flow ◽  
Very High ◽  
Over Time

Many of the large number of underground works constructed or under construction in recent years are in unfavorable terrains facing unusual situations and construction conditions. This is the case of the subject under study in this paper: a tunnel excavated in evaporitic rocks that experienced significant karstification problems very quickly over time. As a result of this situation, the causes that may underlie this rapid karstification are investigated and a novel methodology is presented in civil engineering where the use of saturation indices for the different mineral specimens present has been crucial. The drainage of the rock massif of El Regajal (Madrid-Toledo, Spain, in the Madrid-Valencia high-speed train line) was studied and permitted the in-situ study of the hydrogeochemical evolution of water flow in the Miocene evaporitic materials of the Tajo Basin as a full-scale testing laboratory, that are conforms as a whole, a single aquifer. The work provides a novel methodology based on the calculation of activities through the hydrogeochemical study of water samples in different piezometers, estimating the saturation index of different saline materials and the dissolution capacity of the brine, which is surprisingly very high despite the high electrical conductivity. The circulating brine appears unsaturated with respect to thenardite, mirabilite, epsomite, glauberite, and halite. The alteration of the underground flow and the consequent renewal of the water of the aquifer by the infiltration water of rain and irrigation is the cause of the hydrogeochemical imbalance and the modification of the characteristics of the massif. These modifications include very important loss of material by dissolution, altering the resistance of the terrain and the increase of the porosity. Simultaneously, different expansive and recrystallization processes that decrease the porosity of the massif were identified in the present work. The hydrogeochemical study allows the evolution of these phenomena to be followed over time, and this, in turn, may facilitate the implementation of preventive works in civil engineering.

scholarly journals A LOOK INTO CIRCULAR ECONOMY RESEARCH: EXPLORING THE BIO AND TECHNO CYCLES AND THE NEED FOR DUAL CIRCULARITY

2021 ◽  
Vol 1 ◽  
pp. 121-130
Author(s):  
Julija Metic ◽  
Tim C. McAloone ◽  
Daniela C. A. Pigosso
Keyword(s):  
Circular Economy ◽  
Biological Cycle ◽  
Systematic Analysis ◽  
Technological Cycle ◽  
Business Perspective ◽  
Subject Areas ◽  
The Subject ◽  
To Come

AbstractThis study undertakes a systematic analysis of literature within Circular Economy (CE) in an industrial perspective, with a focus on understanding the consideration of the biological and technological cycles, as well as dual circularity. The paper articulates the key research differences, gaps and trends on the basis of publication evolution, key subject areas, influential journals and keywords co-occurrence mapping. The analysis shows the increasing publication trend with dominance of technological cycle and a wide variety of subject areas incorporated in CE biological, technological and dual cycles. Due to the multidisciplinary and transversal nature of CE, as well as its diverse interpretation and applications, an expansion and consolidation of the subject areas and journals are expected in the years to come. Analysis of co-occurrence on the authors' keywords underlined a limited focus of a business perspective research within the biological cycle, heterogeneous and proactive technological cycle but fragmented research on dual circularity. Further analysis of synergies and limitations is necessary to enhance business effectiveness towards enhanced sustainability.

Sign in / Sign up

Export Citation Format

Share Document