scholarly journals Making mathematical meaning: From preconcepts to pseudoconcepts to concepts

Pythagoras ◽  
2006 ◽  
Vol 0 (63) ◽  
Author(s):  
Margot Berger
Keyword(s):  
Mathematical Knowledge ◽  
Concept Formation ◽  
Mathematical Object ◽  
Mathematical Concept ◽  
The Body ◽  
Mathematical Meaning ◽  
University Level ◽  
Mathematical Signs

I argue that Vygotsky’s theory of concept formation (1934/1986) is a powerful framework within which to explore how an individual at university level constructs a new mathematical concept. In particular I argue that this theory can be used to explain how idiosyncratic usages of  mathematical signs by students (particularly when just introduced to a new mathematical object) get transformed into mathematically acceptable and personally meaningful usages. Related to this, I argue that this theory is able to bridge the divide between an individual’s mathematical knowledge and the body of socially sanctioned mathematical knowledge. I also demonstrate an application of the theory to an analysis of a student’s activities with a ‘new’ mathematical object.

Note on Suppes' "Mathematical concept formation."

1967 ◽  
Vol 22 (5) ◽  
pp. 400-401 ◽  
Author(s):  
Lawrence T. Frase
Keyword(s):  
Concept Formation ◽  
Mathematical Concept

Medically Modified Eyes

2018 ◽  
Vol 2 (4) ◽  
pp. 491-511
Author(s):  
Emily R. Cain
Keyword(s):  
Cataract Surgery ◽  
Concept Formation ◽  
Sensory Perception ◽  
The Body ◽  
Safe Procedure ◽  
Elite Group ◽  
Visual Component ◽  
Medical Component ◽  
Repeated Contact

In Paedagogus 1.6.28, Clement describes baptism through the metaphor of a cataract surgery that enables the percipient to see God. In antiquity, cataract surgery was neither a common nor a safe procedure, which raises the question: why does Clement use such an unlikely metaphor for baptism? In this article, I demonstrate that this medical metaphor of cataract surgery enabled Clement to blur the line between the physical and the spiritual. The visual component of the metaphor allowed Clement to draw from Epicurean sensory perception and epistemology, which understood objects to emit tiny films that entered the eye of the body, with repeated contact leading to concept formation, in order to describe how the eye of the soul could see God once it has been transformed through baptism. For Clement, it is only through baptism that the cataract can be removed, thereby providing the baptized Christian with deified eyes to see God. In addition to having her cataract removed, according to Clement, the nature of the baptized Christian's vision changes from intromission to extramission, from receiving films to emitting a visual ray back to the divine. I further argue that the medical component of the metaphor allows Clement to describe the baptized Christian as fundamentally different from the rest of humanity and as part of an elite group that has undergone this uncommon and dangerous cataract surgery. Through these two aspects of his metaphor, Clement describes and defines Christians in terms of their medically modified eyes that enable them to see and to know God.

scholarly journals Questionable Use of the Mathematical Concept of Equivalence by Psychologists

2014 ◽  
Vol 7 (2) ◽  
pp. 124-126
Author(s):  
Makoto Yamaguchi
Keyword(s):  
Empirical Research ◽  
Equivalence Relation ◽  
Concept Formation ◽  
Mathematical Concept

Psychologists have applied the mathematical concept of an equivalence relation to such topics as concept formation and foundations of language. This line of research is not without controversies, and most researchers have only intuitive understanding of this mathematical concept. In this article, accessible explanations are provided on fundamental issues that have implications for empirical research.

scholarly journals Iconicity in mathematical notation: Commutativity and symmetry

2020 ◽  
Vol 6 (3) ◽  
pp. 378-392
Author(s):  
Theresa Elise Wege ◽  
Sophie Batchelor ◽  
Matthew Inglis ◽  
Honali Mistry ◽  
Dirk Schlimm
Keyword(s):  
Empirical Test ◽  
Mathematical Concept ◽  
Mathematical Notation ◽  
Controlled Experiments ◽  
Visual Appearance ◽  
Vast Array ◽  
Mathematical Performance ◽  
Early Formulation ◽  
Mathematical Signs

Mathematical notation includes a vast array of signs. Most mathematical signs appear to be symbolic, in the sense that their meaning is arbitrarily related to their visual appearance. We explored the hypothesis that mathematical signs with iconic aspects – those which visually resemble in some way the concepts they represent – offer a cognitive advantage over those which are purely symbolic. An early formulation of this hypothesis was made by Christine Ladd in 1883 who suggested that symmetrical signs should be used to convey commutative relations, because they visually resemble the mathematical concept they represent. Two controlled experiments provide the first empirical test of, and evidence for, Ladd’s hypothesis. In Experiment 1 we find that participants are more likely to attribute commutativity to operations denoted by symmetric signs. In Experiment 2 we further show that using symmetric signs as notation for commutative operations can increase mathematical performance.

scholarly journals From Odd Encounters to a Prospective Confluence: Dance-Philosophy

2015 ◽  
Vol 1 (1) ◽  
pp. 7 ◽  
Author(s):  
Bojana Cvejić
Keyword(s):  
Concept Formation ◽  
Body Movement ◽  
The Body ◽  
Western Philosophy ◽  
Ontological Status ◽  
Meaning Production ◽  
The Status ◽  
General Ontology ◽  
The Relationship ◽  
Point Of Departure

This text inquires into the relationship between Western philosophy and Western theatre dance from their odd encounters in modernity to the current affiliations between contemporary choreographic poetics, critical theory and contemporary philosophical thought. The point of departure for the inquiry is a discussion of the three problems that have structured the historically vexed relationship between dance and philosophy: dance’s belated acquisition of the status of an art discipline, the special ontological status of the work of dance, and the limits of dance’s meaning-production set by the theme of bodily movement’s “ephemerality” and “disappearance.” After critically examining the approaches of Alain Badiou and Jacques Rancière in whose philosophies dance is relegated to a metaphor or, even worse, to an ahistorical conduit for a general ontology, the author makes a case for another movement of thought that arises in dance practice and is at the same time philosophical, rooted in Spinoza’s (and Deleuze’s) principle of expression. Demonstrating how choreographers, like Xavier Le Roy and Jonathan Burrows, create by “posing problems,” Cvejić presents a theory of “expressive concepts,” whereby choreography contributes to a philosophical rethinking of the relationship between the body, movement and time. This points to the new prospects of a kind of “dance-philosophy,” in which the epistemic hierarchy is reversed: the stake is no longer in what philosophy could do for dance, but how an experimental, radically pragmatic orientation in dance offers a practical framework for theorizing perception, concept-formation and other philosophical issues.

scholarly journals Exponential functions through a real-world context

2020 ◽  
Vol 3 (10) ◽  
Author(s):  
Natalija Budinski
Keyword(s):  
Exponential Function ◽  
Real World ◽  
Mathematical Knowledge ◽  
Mathematical Concept ◽  
Exponential Functions

The exponential function as a mathematical concept plays an important role in the corpus of mathematical knowledge, but unfortunately students have problems grasping it. Paper exposes examples of exponential function application in a real-world context.

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