scholarly journals Analysis of students difficulties in mathematical abstraction thinking in the mathematics statistic course

2021 ◽  
Vol 1918 (4) ◽  
pp. 042112
Author(s):  
A Nurrahmah ◽  
Zaenuri ◽  
Wardono
Keyword(s):  
Mathematical Abstraction

scholarly journals Mathematical Abstraction of Year 9 Students Using Realistic Mathematics Education Based on the Van Hiele Levels of Geometry

2019 ◽  
Vol 6 (1) ◽  
pp. 1-12
Author(s):  
Heris Hendriana ◽  
Nelly Fitriani
Keyword(s):  
High School Students ◽  
Mathematics Education ◽  
Traditional Learning ◽  
Realistic Mathematics Education ◽  
Reflective Abstraction ◽  
Van Hiele ◽  
Level Of Abstraction ◽  
Realistic Mathematics ◽  
Van Hiele Levels ◽  
Mathematical Abstraction

Previous research regarding abstraction has not discussed abstraction qualitatively based on van Hiele levels. Thus, it is necessary to study abstraction analysis based on van Hiele levels through Realistic Mathematics Education (RME) approach. The purpose of this research was to analyze mathematical abstraction based on van Hiele levels of geometry (VHLG) through RME and traditional learning approach reviewed from the levels of prior knowledge. This research employed a descriptive qualitative method involving Year 9 junior high school students as the subjects. The instruments were a mathematical abstraction test, van Hiele geometry test, and interview guidelines. The results of the high- and medium-ability students in the classroom using RME approach showed that VHLG was at the Deduction level and the abstraction ability was dominated by Empirical and Reflective Abstraction, whereas the low-ability students are at the level of Abstraction, they had imperfect Empirical and Reflective Abstraction. As for the high-ability students in the traditional learning classroom, the VHLG was at the level of Abstraction; their Reflective Abstraction was at the Representation level. While concerning the low- and medium-ability students, the VHLG was at the Analysis level; they mastered the Reflective Abstraction at the level of Recognition. This study indicates that the RME approach can trigger the development of mathematical abstraction, and accelerate the van Hiele levels of geometry progress.

Knotting Mechanisms and a Knotting Theory

1998 ◽  
Author(s):  
Shahram Payandeh ◽  
Alan J. Lomax
Keyword(s):  
Degrees Of Freedom ◽  
Knot Theory ◽  
Design Concept ◽  
Haptic Interface ◽  
Design Features ◽  
Operation System ◽  
Remote Manipulation ◽  
Challenging Tasks ◽  
Mathematical Abstraction ◽  
Practical Design

Abstract In the filed of remote manipulation, it is generally required to manipulate objects through elongated tools or through a tele-operation system. In the field of EndoSurgery, one of the challenging tasks for the surgeons is the notion of knotting a suture. This is done by using long graspers and needle drivers which have constrained degrees of freedom caused by the ports of entry to the surgical area. In general, this task is the most time consuming one and requires degree of dexterity which is not available. The objective of this paper is to present an overview of the patented design features of various knotting assisting mechanisms which have been invented for automating aspect of knotting and discussion on a novel and practical design concept. Then this paper presents how the notion of the Knot Theory which is mathematical abstraction can be extended to develop a Graphical Surgeon Interface (GSI) in order to guide the operator during the remote manipulation of the suture during the knotting task and also during the training phases using a haptic interface device.

scholarly journals “Statistics 103” for Multitarget Tracking

Sensors ◽  
2019 ◽  
Vol 19 (1) ◽  
pp. 202 ◽  
Author(s):  
Ronald Mahler
Keyword(s):  
Point Process ◽  
Information Fusion ◽  
Theoretical Foundation ◽  
Measure Theory ◽  
Multitarget Tracking ◽  
Mathematical Abstraction ◽  
Finite Set ◽  
Theoretic Point

The finite-set statistics (FISST) foundational approach to multitarget tracking and information fusion was introduced in the mid-1990s and extended in 2001. FISST was devised to be as “engineering-friendly” as possible by avoiding avoidable mathematical abstraction and complexity—and, especially, by avoiding measure theory and measure-theoretic point process (p.p.) theory. Recently, however, an allegedly more general theoretical foundation for multitarget tracking has been proposed. In it, the constituent components of FISST have been systematically replaced by mathematically more complicated concepts—and, especially, by the very measure theory and measure-theoretic p.p.’s that FISST eschews. It is shown that this proposed alternative is actually a mathematical paraphrase of part of FISST that does not correctly address the technical idiosyncrasies of the multitarget tracking application.

Computation, Interpretation, and Mediation

2017 ◽  
Author(s):  
Paul Kockelman
Keyword(s):  
Computer Science ◽  
Universal Grammar ◽  
Linguistic Anthropology ◽  
Linguistic Relativity ◽  
Fundamental Importance ◽  
Language Recognition ◽  
Face To Face ◽  
Context Sensitive ◽  
Universal Turing Machine ◽  
Mathematical Abstraction

The chapter shows the fundamental importance of ideas from computer science to the concerns of linguistic anthropology (and to the concerns of culture-rich and context-sensitive approaches to communication more generally). It reviews some of the key concepts and claims of computer science (language, recognition, automaton, Universal Turing Machine, and so forth). It argues that the sieve, as both a physical device and an analytic concept, is of fundamental importance not just to anthropology, but also to linguistics, biology, philosophy, and critical theory. And it argues that computers, as both engineered and imagined, are essentially text-generated and text-generating sieves. In relating computer science to linguistic anthropology, this chapter also attempts to build bridges between long-standing rivals: face to face interaction and mathematical abstraction, linguistic relativity and universal grammar, mediators and intermediaries.

By Way of Introduction

1988 ◽  
Vol 35 (6) ◽  
pp. 2-3
Author(s):  
Francis (Skip) Fennell
Keyword(s):  
Second Graders ◽  
Mathematical Abstraction

What's the rush? Why are we pushing kids to mathematical abstraction so quickly? Do we really need to accelerate the mathematic curriculum so that some topic are introduced far too early while others are barely mentioned? Is it any wonder that many first and second graders impulsively complete mathematics activitie as rapidly as possible, for the mere satisfaction of being “done first”?

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