Natural number concepts: No derivation without formalization

2008 ◽  
Vol 31 (6) ◽  
pp. 666-667
Author(s):  
Paul Pietroski ◽  
Jeffrey Lidz
Keyword(s):  
Natural Number ◽  
Building Blocks ◽  
Logical Space ◽  
Number Concepts ◽  
New Concepts

AbstractThe conceptual building blocks suggested by developmental psychologists may yet play a role in how the human learner arrives at an understanding of natural number. The proposal of Rips et al. faces a challenge, yet to be met, faced by all developmental proposals: to describe the logical space in which learners ever acquire new concepts.

Do mental magnitudes form part of the foundation for natural number concepts? Don't count them out yet

2008 ◽  
Vol 31 (6) ◽  
pp. 644-645 ◽  
Author(s):  
Hilary Barth
Keyword(s):  
Natural Number ◽  
Number Concepts ◽  
Form Part

AbstractThe current consensus among most researchers is that natural number is not built solely upon a foundation of mental magnitudes. On their way to the conclusion that magnitudes do not form any part of that foundation, Rips et al. pass rather quickly by theories suggesting that mental magnitudes might play some role. These theories deserve a closer look.

scholarly journals The emergence of children’s natural number concepts: Current theoretical challenges

2021 ◽  
Author(s):  
Francesco Sella ◽  
Emily Slusser ◽  
Darko Odic ◽  
Attila Krajcsi
Keyword(s):  
Natural Number ◽  
Number Concepts

The origins of number: Getting developmental

2008 ◽  
Vol 31 (6) ◽  
pp. 662-662
Author(s):  
Kelly S. Mix
Keyword(s):  
Natural Number ◽  
Real Time ◽  
Explanatory Power ◽  
Future Research ◽  
Number Concepts ◽  
Developmental Issues

AbstractRips et al. raise important questions about the relation between infant quantification and achievement of natural number concepts. However, they may be oversimplifying the interactions that characterize actual development in real time. Though they propose a worthwhile agenda for future research, its explanatory power will be limited if it does not address developmental issues with greater sensitivity.

Set representations required for the acquisition of the “natural number” concept

2008 ◽  
Vol 31 (6) ◽  
pp. 655-656 ◽  
Author(s):  
Justin Halberda ◽  
Lisa Feigenson
Keyword(s):  
Natural Number ◽  
Building Blocks ◽  
Number Concept ◽  
Set Representations ◽  
Individual Objects

AbstractRips et al. consider whether representations of individual objects or analog magnitudes are building blocks for the concept natural number. We argue for a third core capacity – the ability to bind representations of individuals into sets. However, even with this addition to the list of starting materials, we agree that a significant acquisition story is needed to capture natural number.

SDN and NFV in the mobile core: Approaches and challenges

2015 ◽  
Vol 57 (5) ◽  
Author(s):  
Michael Jarschel ◽  
Arsany Basta ◽  
Wolfgang Kellerer ◽  
Marco Hoffmann
Keyword(s):  
Mobile Networks ◽  
Research Question ◽  
Software Defined Networking ◽  
Building Blocks ◽  
Core Network ◽  
Open Research ◽  
New Concepts ◽  
Network Functions ◽  
Development Paths ◽  
Mobile Core Network

AbstractThe introduction of Software Defined Networking (SDN) and Network Functions Virtualization (NFV) has transformed the way networks will be built in the future. This development also applies to mobile networks and their evolution. How the SDN and NFV concepts will be integrated exactly is still an open research question with multiple approaches and techniques in discussion. This article provides an overview of the current discussion points with regard to development paths, building blocks, deployment scenarios, and the opportunities and challenges of the new concepts in the mobile core network context.

The generative basis of natural number concepts

2008 ◽  
Vol 12 (6) ◽  
pp. 213-218 ◽  
Author(s):  
Alan M. Leslie ◽  
Rochel Gelman ◽  
C.R. Gallistel
Keyword(s):  
Natural Number ◽  
Number Concepts

On Offer Shai’s Contribution to Mechanical Engineering and Design

2017 ◽  
Author(s):  
Yoram Reich ◽  
Elad Hahn ◽  
Michael Slavutin
Keyword(s):  
Research Program ◽  
Mechanical Engineering ◽  
Discrete Systems ◽  
Building Blocks ◽  
New Methods ◽  
New Concepts ◽  
Combinatorial Representations

This paper presents the contribution of Offer Shai to mechanical engineering and design. Over a period of three decades Shai has created an impressive research program that is founded on solid mathematical grounds — combinatorial representations of systems. On this foundation he made contributions that ranged from inventing new concepts in mechanics (e.g., face force), new ways to characterize systems (e.g., singularity positions), new ways to create building blocks to model discrete systems (e.g., Assur graphs and their synthesis), and new methods in design (e.g., infused design). This paper summarizes some of these contributions in an attempt to describe the breadth and depth and attract researchers to continue develop his ideas.

Music training, engagement with sequence, and the development of the natural number concept in young learners

2008 ◽  
Vol 31 (6) ◽  
pp. 652-653 ◽  
Author(s):  
Martin F. Gardiner
Keyword(s):  
Natural Number ◽  
Learning Support ◽  
Number Concepts ◽  
Music Training ◽  
Number Concept ◽  
Young Learners ◽  
Musical Pitch ◽  
Innate Ability

AbstractStudies by Gardiner and colleagues connecting musical pitch and arithmetic learning support Rips et al.'s proposal that natural number concepts are constructed on a base of innate abilities. Our evidence suggests that innate ability concerning sequence (“Basic Sequencing Capability” or BSC) is fundamental. Mathematical engagement relating number to BSC does not develop automatically, but, rather, should be encouraged through teaching.

Mathematical Roots: Get Primed to the Basic Building Blocks of Numbers

2007 ◽  
Vol 13 (2) ◽  
pp. 122-127
Author(s):  
Christiana Robbins ◽  
Thomasenia Lott Adams
Keyword(s):  
Natural Number ◽  
Building Blocks ◽  
Number System ◽  
Prime Numbers ◽  
Natural Numbers

In his book Elements, Euclid established that certain numbers are the building blocks of our natural number system. He revealed that these natural numbers could be “decomposed” into their smallest units as products of specific numbers. Numbers that can only be factored by themselves and 1 are called “prime numbers” and comprise part of the basic building blocks of numbers.

scholarly journals Cluster Preface: Metathesis Reactions beyond Olefins

Synlett ◽  
2019 ◽  
Vol 30 (17) ◽  
pp. 1952-1953
Author(s):  
Bill Morandi
Keyword(s):  
Organic Chemistry ◽  
Research Program ◽  
Research Group ◽  
Chemical Biology ◽  
Materials Science ◽  
Building Blocks ◽  
Associate Professor ◽  
Independent Research ◽  
Max Planck ◽  
New Concepts

studied at the ETH Zurich from 2003–2012, earning a B.Sc. in biology, an M.Sc. in chemical biology and a Ph.D. in organic chemistry working with Prof. Erick M. Carreira. After a postdoc with Prof. Robert H. Grubbs at CalTech, he led an independent Max Planck Research Group from 2014–2018 at the Max-Planck-Institut für Kohlenforschung, Germany. Since July 2018, he is a tenured Associate Professor at the ETH Zurich where he holds a chair in synthetic organic chemistry. His independent research program targets the development of new concepts in catalysis, with a particular emphasis on employing inexpensive and sustainable catalysts to transform broadly available feedstocks, such as polyols and hydrocarbons, into valuable building blocks for applications in medicine and materials science.

Sign in / Sign up

Export Citation Format

Share Document