What Is Mathematical Intuition?

2006 ◽  
pp. 37-45
Keyword(s):  
Mathematical Intuition

Peran Mathematical Intuition dalam Pembelajaran Matematika

2019 ◽  
Vol 5 (2) ◽  
pp. 12-24
Author(s):  
Mohamad Gilar Jatisunda ◽  
Dede Salim Nahdi
Keyword(s):  
Mathematical Intuition

Setiap manusia terlahir dengan memiliki kemampuan yang berbeda tergantung pemberian perlakuan atau stimulus. Hal inilah yang menyebabkan manusia harus mengenal apa yang dimaksud sebagai intuisi. Dengan intuisi memberikan peran pengetahuan dalam memutuskan dan bertindak lebih efektif.. Manusia dapat memperoleh pengetahuan melalui intuisi. Intuisi bukanlah suatu metode namun intuisi merupakan sebuah jenis kognisi. Terdapat tiga macam kognisi yaitu formal, algoritmik dan intuitif. Pemahaman konsep matematika dapat berlangsung sebagai interaksi antara kognisi formal, kognisi algoritmik, dan kognisi intuitif. Intuisi diakui oleh matematikawan banyak terlibat dalam kegiatan bermatematika. Walaupun pada kenyataan masih saja kontroversial, Situasi yang paling menguntungkan dalam pembelajaran matematika adalah dimana intuisi siswa dengan konsep matematika secara formal sejalan, tetapi akan menjadi masalah jika sering kali terjadi dalam pengajaran matematika adalah penerimaan siswa secara intuitif bertentangan dengan konsep matematika secara formal dan mengakibatkan terjadinya konflik kognitif bahkan bias kognitif yang dapat merintangi siswa untuk mempelajari matematika

scholarly journals Global Workspace, Self, and Mathematical Intuition

2018 ◽  
Vol 2 (4) ◽  
pp. 01-05
Author(s):  
Robert Skopec
Keyword(s):  
Neural Network ◽  
Molecular Mechanisms ◽  
Temporal Information ◽  
The Self ◽  
Human Consciousness ◽  
Mathematical Intuition ◽  
The World ◽  
Global Workspace

In human consciousness a world of separated objects is perceived by an inner observer as an feeling of One-self. A topological correlation of the Self to the world, by either emerging all separated objects into one or splitting the Self in as many disconnected Sub-selves as there are objects perceived. The Self is generated in a neural network by algorithmic compression of spatial and temporal information into a toponeuronal structure (TNS). A correlation of an inner observer to parts of a structure inevitably entails a correlation to the whole, serving of the Self. Molecular mechanisms for the generation of a TNS in a neural network will be discussed.

Gödel's Conceptual Realism

2005 ◽  
Vol 11 (2) ◽  
pp. 207-224 ◽  
Author(s):  
Donald A. Martin
Keyword(s):  
Set Theory ◽  
Bertrand Russell ◽  
Sense Perception ◽  
Sense Experience ◽  
Mathematical Intuition ◽  
Conceptual Realism ◽  
Kurt Gödel ◽  
Real Objects ◽  
The Continuum

Kurt Gödel is almost as famous—one might say “notorious”—for his extreme platonist views as he is famous for his mathematical theorems. Moreover his platonism is not a myth; it is well-documented in his writings. Here are two platonist declarations about set theory, the first from his paper about Bertrand Russell and the second from the revised version of his paper on the Continuum Hypotheses.Classes and concepts may, however, also be conceived as real objects, namely classes as “pluralities of things” or as structures consisting of a plurality of things and concepts as the properties and relations of things existing independently of our definitions and constructions.It seems to me that the assumption of such objects is quite as legitimate as the assumption of physical bodies and there is quite as much reason to believe in their existence.But, despite their remoteness from sense experience, we do have something like a perception also of the objects of set theory, as is seen from the fact that the axioms force themselves upon us as being true. I don't see any reason why we should have less confidence in this kind of perception, i.e., in mathematical intuition, than in sense perception.The first statement is a platonist declaration of a fairly standard sort concerning set theory. What is unusual in it is the inclusion of concepts among the objects of mathematics. This I will explain below. The second statement expresses what looks like a rather wild thesis.

Mathematical Intuition

1985 ◽  
pp. 49-64
Author(s):  
Philip Kitcher
Keyword(s):  
Mathematical Intuition

Platonism and mathematical intuition in Kurt Gödel's thought

Kurt Gödel ◽  
2010 ◽  
pp. 326-355
Author(s):  
Charles Parsons
Keyword(s):  
Mathematical Intuition

Parsons on Mathematical Intuition and Obviousness

2000 ◽  
pp. 219-231 ◽  
Author(s):  
Michael D. Resnik
Keyword(s):  
Mathematical Intuition

Intuition in Mathematics: a Perceptive Experience

2017 ◽  
Vol 48 (1) ◽  
pp. 1-38 ◽  
Author(s):  
Alexandra Van-Quynh
Keyword(s):  
Data Collection ◽  
Phenomenological Method ◽  
Generic Structure ◽  
Interview Method ◽  
Mathematical Intuition ◽  
Data Collection And Analysis

This study applied a method of assisted introspection to investigate the phenomenology of mathematical intuition arousal. The aim was to propose an essential structure for the intuitive experience of mathematics. To achieve an intersubjective comparison of different experiences, several contemporary mathematicians were interviewed in accordance with the elicitation interview method in order to collect pinpoint experiential descriptions. Data collection and analysis was then performed using steps similar to those outlined in the descriptive phenomenological method that led to a generic structure that accounts for the intuition surge in the experience of mathematics which was found to have four irreducible structural moments. The interdependence of these moments shows that a perceptualist view of intuition in mathematics, as defended by Chudnoff (Chudnoff, 2014), is relevant to the characterization of mathematical intuition. The philosophical consequences of this generic structure and its essential features are discussed in accordance with Husserl’s philosophy of ideal objects and theory of intuition.

A Computer Graphics System for Polynomials

1974 ◽  
Vol 67 (2) ◽  
pp. 111-113
Author(s):  
Ben Shneiderman
Keyword(s):  
Computer Graphics ◽  
Subject Matter ◽  
Complex Interaction ◽  
Mathematical Intuition ◽  
Fundamental Goal ◽  
The Subject ◽  
Computer Graphics System

The development of mathematical intuition is a fundamental goal of a well-designed course in mathematics. The superior instructor teaches more than operations or rules of transformation; he seeks to convey a deeper understanding of the subject matter, which enables a student to have insight and to derive new results. Often, the complexity of a problem prevents the instructor from making such a presentation, and the student fails to grasp the complex interaction of the components of the problem.

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