scholarly journals STRATEGIES OF REDUCTION OF ABSTRACTION IN ABSTRACT ALGEBRA

2020 ◽  
Vol 8 (11) ◽  
pp. 245-250
Author(s):  
Ruma Manandhar ◽  
Lekhnath Sharma
Keyword(s):  
Reflective Thinking ◽  
Mental Image ◽  
Mathematical Structure ◽  
Abstract Algebra ◽  
First Person ◽  
Mathematical Entity ◽  
Mathematical Concepts ◽  
Lead Teachers ◽  
Making Sense ◽  
Students As Teachers

This article is based on the study, which tries to unpack strategies of reduction of abstraction in learning abstract algebra from learners’ perspective. Ethnography was used to collect the required information. The study found the strategies of reduction of abstraction in abstract algebra are: making sense and meaning through previous experiences and existing knowledge an analogical creation of mental image, using first person language in course of doing mathematics by students as teachers do in the classroom for logical arguments, focusing on “symbol” or some mathematical entity to manage abstraction for their idiosyncratic understandings of abstract mathematical structure rather than the reflective thinking, using students own idiosyncratic figures to reduce the degrees of complexity of mathematical concepts. This study can lead teachers of abstract algebra to a new awareness of their teaching strategies and their practices.

Graph Embedding Using Dissimilarities with Applications in Classification

2013 ◽  
pp. 363-380
Author(s):  
Horst Bunke ◽  
Kaspar Riesen
Keyword(s):  
Pattern Recognition ◽  
Nearest Neighbor ◽  
Graph Matching ◽  
Graph Embedding ◽  
Mathematical Structure ◽  
Object Representations ◽  
Mathematical Concepts ◽  
Novel Approach ◽  
Representational Power ◽  
Mathematical Operations

The domain of graphs contains only little mathematical structure. That is, most of the basic mathematical operations, actually required by many standard computer vision and pattern recognition algorithms, are not available for graphs. One of the few mathematical concepts that has been successfully transferred from the vector space to the graph domain is distance computation between graphs, commonly referred to as graph matching. Yet, distance-based pattern recognition is basically limited to nearest-neighbor classification. The present chapter reviews a novel approach for graph embedding in vector spaces built upon the concept of graph matching. The key-idea of the proposed embedding method is to use the distances of an input graph to a number of training graphs, termed prototypes, as vectorial description of the graph. That is, all graph matching procedures proposed in the literature during the last decades can be employed in this embedding framework. The rationale for such a graph embedding is to bridge the gap between the high representational power and flexibility of graphs and the large amount of algorithms available for object representations in terms of feature vectors. Hence, the proposed framework can be considered a contribution towards unifying the domains of structural and statistical pattern recognition.

scholarly journals Categorical structures as expressing tool for differential calculus

2014 ◽  
Vol 4 (3) ◽  
Author(s):  
William Steingartner ◽  
Davorka Radaković
Keyword(s):  
Mathematical Modeling ◽  
Computer Science ◽  
Differential Calculus ◽  
Mathematical Structure ◽  
Mathematical Concepts ◽  
Special Category

AbstractCategory is a mathematical structure consisting of objects and morphisms between objects with some specific properties. Categories examine in abstract way the properties of particular mathematical concepts by formalizing them as collections of objects and morphisms. Categorical structures are widely used in computer science for exact mathematical modeling. This paper highlights the most typical use of categories for constructing the model of part of differential calculus by using special category named arrow category; and codomain and domain functors.

scholarly journals Narrative reflective writing: "It got easier as I went along"

2008 ◽  
Vol 8 (2) ◽  
pp. 383-400
Author(s):  
Gary Barkhuizen ◽  
Phil Benson
Keyword(s):  
Reflective Thinking ◽  
Reflective Writing ◽  
Narrative Writing ◽  
Teachers Perceptions ◽  
Supportive Environment ◽  
Making Sense ◽  
Before And After ◽  
Natural Way

It has been argued that narrative is a natural way of making sense of experience and that it has a particular value in fostering teachers' reflective thinking. This paper looks at these arguments critically through a study of teachers' responses to narrative writing tasks in coursework. The study focuses on the teachers' perceptions of their enjoyment, anxieties, confidence and understanding in relation to narrative writing before and after the coursework. Findings tentatively indicate that narrative writing did come naturally to most of the teachers but that their responses became more positive as they developed experience in narrative writing within a supportive environment.

scholarly journals I Might be Fundamentally Mistaken

2017 ◽  
Vol 9 (3) ◽  
pp. 1-22 ◽  
Author(s):  
Michael Ridge
Keyword(s):  
Moral Belief ◽  
Moral Judgments ◽  
First Person ◽  
Ordinary People ◽  
Realist Theory ◽  
Making Sense ◽  
Moral Content ◽  
Simon Blackburn ◽  
Moral Error ◽  
Influential Paper

Quasi-realism aspires to preserve the intelligibility of the realist-sounding moral judgments of ordinary people. These judgments include ones of the form, “I believe that p, but I might be mistaken,” where “p” is some moral content. The orthodox quasi-realist strategy (famously developed by Simon Blackburn) is to understand these in terms of the agent’s worrying that some improving change would lead one to aban-don the relevant moral belief. However, it is unclear whether this strate-gy generalizes to cases in which the agent takes their error to be funda-mental in a sense articulated by Andy Egan. In an influential paper, Egan argues that it does not. Egan suggests that Blackburn’s approach is the only game in town for the quasi-realist when it comes to making sense of judgment of fallibility, and therefore concludes that Blackburn’s ina-bility to handle worries about fundamental moral error refutes quasi-realism tout court. Egan’s challenge has generated considerable discus-sion. However, in my view, we have not yet gotten to the heart of the matter. I argue that what is still needed is a fully general, quasi-realist-friendly theory of the nature of first-person judgments of fallibility, such that these judgments are demonstrably consistent with judging that the belief is stable in Egan’s sense. In this article, I develop and defend a fully general quasi-realist theory of such judgments, which meets this demand. With this theory in hand, I argue that Egan’s challenge can be met. Moreover, my discussion of how the challenge is best met provides an elegant diagnosis of where Egan’s argument against goes wrong. On my account, Egan’s argument equivocates at a key point between a “could” and a “would.”

What Youth Want

2017 ◽  
Author(s):  
Avi Max Spiegel
Keyword(s):  
Young People ◽  
Collective Action ◽  
Life Histories ◽  
Participant Observation ◽  
Sense Of Self ◽  
First Person ◽  
New Politics ◽  
Making Sense ◽  
Personal Empowerment ◽  
Islamist Movements

This chapter continues the discussion of the lives of young Islamists, focusing on their articulations of their hopes and goals. Analyzing the trove of data that the author uncovered from first-person narratives and life histories, transcripts, and extended participant observation, the author found that young people were looking for nothing less than a new sense of self. Their decisions are multiple, multilayered, and constantly renegotiated, but they can only be understood by making sense of the new identities that are sustained by their collective action. The author argues that Islamism is not simply ideological; it is instrumental—an avenue to a new identity, to new ways of seeing and thinking about themselves. The author dubs this the new politics of personal empowerment, where Islamist movements are reimagined as individual improvement factories: places to go not simply to become better Muslims, but to better their lot in life or the perception of that lot.

The Problem of Moral Obligation

2019 ◽  
pp. 24-65
Author(s):  
R. Jay Wallace
Keyword(s):  
First Person ◽  
Reasons For Action ◽  
Practical Deliberation ◽  
Making Sense ◽  
Person Perspective ◽  
Course Of Action ◽  
Philosophical Account ◽  
Normative Significance ◽  
First Person Perspective ◽  
The Right

This chapter looks at the issue of the normative significance of moral requirements in the first-person perspective of deliberation. Moral conclusions are customarily treated as considerations that matter within an agent's practical decision-making. That a course of action would be impermissible, for instance, or morally the right thing to do, are conclusions that appear to have direct relevance for practical deliberation, which agents who are reasoning correctly will take appropriately into account in planning their future activities. The philosophical problem in this area is often understood to be the problem of making sense of the reason-giving force of morality. That is, an account of moral rightness or permissibility should shed light on the standing of these considerations as reasons for action, which count for and against actions in the first-person perspective of agency. However, this conventional understanding seriously underdescribes the challenge that faces a philosophical account of morality.

Graph Embedding Using Dissimilarities with Applications in Classification

2012 ◽  
pp. 156-173
Author(s):  
Horst Bunke ◽  
Kaspar Riesen
Keyword(s):  
Pattern Recognition ◽  
Nearest Neighbor ◽  
Graph Matching ◽  
Graph Embedding ◽  
Mathematical Structure ◽  
Object Representations ◽  
Mathematical Concepts ◽  
Novel Approach ◽  
Representational Power ◽  
Mathematical Operations

The domain of graphs contains only little mathematical structure. That is, most of the basic mathematical operations, actually required by many standard computer vision and pattern recognition algorithms, are not available for graphs. One of the few mathematical concepts that has been successfully transferred from the vector space to the graph domain is distance computation between graphs, commonly referred to as graph matching. Yet, distance-based pattern recognition is basically limited to nearest-neighbor classification. The present chapter reviews a novel approach for graph embedding in vector spaces built upon the concept of graph matching. The key-idea of the proposed embedding method is to use the distances of an input graph to a number of training graphs, termed prototypes, as vectorial description of the graph. That is, all graph matching procedures proposed in the literature during the last decades can be employed in this embedding framework. The rationale for such a graph embedding is to bridge the gap between the high representational power and flexibility of graphs and the large amount of algorithms available for object representations in terms of feature vectors. Hence, the proposed framework can be considered a contribution towards unifying the domains of structural and statistical pattern recognition.

Making Sense out of Cents

2004 ◽  
Vol 11 (4) ◽  
pp. 188-192
Author(s):  
Claire Wiener ◽  
Carolyn Smith
Keyword(s):  
Mathematical Knowledge ◽  
Elementary Student ◽  
Mathematical Concepts ◽  
Daily Lives ◽  
Making Sense ◽  
Natural Way

Literature is a great vehicle to teach mathematical concepts to the elementary student. Through literature, children can demonstrate their mathematical knowledge by using these concepts in context (Anderson and Anderson 1995). Recognizing the relevance of mathematics in their daily lives is essential for students. As Leitze (1997) explains, “This mathematicsliterature connection is a natural way for teachers to allow students to see mathematics in everyday society, to give meaning to mathematics, and to make it come alive” (p. 398).

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