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.

Arithmetic, philosophical issues in

2018 ◽  
Author(s):  
Michael Potter
Keyword(s):  
Natural Number ◽  
Decision Procedure ◽  
Mathematical Induction ◽  
Universal Quantifier ◽  
Number Concept ◽  
Special Character ◽  
The Status ◽  
Proof By Induction ◽  
Philosophy Of Arithmetic ◽  
Principle Of Mathematical Induction

The philosophy of arithmetic gains its special character from issues arising out of the status of the principle of mathematical induction. Indeed, it is just at the point where proof by induction enters that arithmetic stops being trivial. The propositions of elementary arithmetic – quantifier-free sentences such as ‘7+5=12’ – can be decided mechanically: once we know the rules for calculating, it is hard to see what mathematical interest can remain. As soon as we allow sentences with one universal quantifier, however – sentences of the form ‘(∀x)f(x)=0’ – we have no decision procedure either in principle or in practice, and can state some of the most profound and difficult problems in mathematics. (Goldbach’s conjecture that every even number greater than 2 is the sum of two primes, formulated in 1742 and still unsolved, is of this type.) It seems natural to regard as part of what we mean by natural numbers that they should obey the principle of induction. But this exhibits a form of circularity known as ‘impredicativity’: the statement of the principle involves quantification over properties of numbers, but to understand this quantification we must assume a prior grasp of the number concept, which it was our intention to define. It is nowadays a commonplace to draw a distinction between impredicative definitions, which are illegitimate, and impredicative specifications, which are not. The conclusion we should draw in this case is that the principle of induction on its own does not provide a non-circular route to an understanding of the natural number concept. We therefore need an independent argument. Four broad strategies have been attempted, which we shall consider in turn.

Higher is Faster

2015 ◽  
Vol 33 (2) ◽  
pp. 179-198 ◽  
Author(s):  
Hila Tamir-Ostrover ◽  
Zohar Eitan
Keyword(s):  
Experimental Design ◽  
Empirical Studies ◽  
Music Training ◽  
Factors Affecting ◽  
Pitch Change ◽  
Musical Pitch ◽  
Pitch Direction ◽  
Pitch Structure ◽  
Musical Tempo

While determining an appropriate tempo is crucial to music performers, composers and listeners, few empirical studies have investigated the musical factors affecting tempo choices. In two experiments we examined how aspects of musical pitch affect tempo choice, by asking participants (musically trained and untrained) to adjust the tempi of melodic sequences varying in pitch register and pitch direction, as well as sequences typically associated with specific registers in common period music. In Experiment 1, faster tempi were assigned to higher registers. Specific melodic direction (rise vs. fall) did not affect tempo preferences; nevertheless, pitch change in both directions elicited faster tempi than a repeating, unchanging pitch. The effect of register on tempo preference was stronger for participants with music training, and also (unexpectedly) for female participants. In Experiment 2, melodic figures typically related to lower and higher parts in common-period music were associated with slower and faster tempi, respectively. Results support a “holistic” notion of musical tempo, viewing the choice of proper tempo as determined by interactions among diverse musical dimensions, including aspects of pitch structure, rather than by rhythmic considerations alone. The experimental design presented here can be further applied to explore the effects of other musical parameters on tempo preferences.

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 Cross-domain effect of pitch processing in lexical and melodic contexts reflected by non-musicians: An MEG study

2020 ◽  
pp. 85-90
Author(s):  
Zhaowei Liu ◽  
◽  
Yun Nan ◽  
Lingxi Lu ◽  
Wei Cui ◽  
...  
Keyword(s):  
Brain Activity ◽  
Activity Patterns ◽  
Music Training ◽  
Pitch Processing ◽  
Cross Domain ◽  
Musical Pitch ◽  
Language And Music ◽  
Perceptual Abilities ◽  
Cortical Regions ◽  
Brain Behavior

The pitch processing of language and music is generally considered engaging overlapped neural correlates. Previous studies on musicians showed that the ability of pitch processing in music could be transferred to language. It is known that music training can facilitate neural processing of speech, however, the underlying neural mechanisms of pitch processing of language and music are not fully understood, especially in non-musicians. Using magnetoencephalography, we presented a pitch anomaly paradigm which consists of language/music phrases ending in either congruous or incongruous tones/pitches to non-musicians. We found the distinctive brain activity patterns in two groups with high and low musical pitch perceptual abilities. The brain-behavior results showed a positive correlation between the performance of musical pitch tasks and the activation of the left frontotemporal cortical regions elicited by lexical tones. Our results suggested that the cross-domain effect of language and music could be generalized to people without formal music training.

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.

scholarly journals Parent-Child Talk about Early Numeracy

2019 ◽  
Vol 1 ◽  
pp. 48-68
Author(s):  
Ashli-Ann Douglas ◽  
Erica L Zippert ◽  
Bethany Rittle-Johnson
Keyword(s):  
School Readiness ◽  
Early Numeracy ◽  
Number Concepts ◽  
Number Concept ◽  
Parents And Children ◽  
Early Number ◽  
Role Of Parents ◽  
Specific Number ◽  
Parent Child

The goal of the study was to examine how the type of informal number activity in which parents and their preschoolers engage and parents’ math-related beliefs relate to parent-child exploration of an advanced early number concept. Parents and their preschoolers (n = 46) engaged in a videotaped play session and parents were surveyed about their math-related beliefs. The findings indicate that the type of informal number activity that parents chose to play with their children predicted how frequently they explored an advanced early number concept with them. Additionally, some but not all parents’ math-related beliefs were related to parent-child number talk. These results suggest that identifying games that facilitate specific number concepts may be a good way for researchers to help parents and children explore more advanced early number concepts frequently. The results also highlight the need for additional research on the role of parents’ math-related beliefs in their support of their children’s early learning and school readiness.

scholarly journals Measuring toddlers non-symbolic number processing

2021 ◽  
Author(s):  
Marcus Lindskog ◽  
Victoria Simms
Keyword(s):  
Young Children ◽  
Poor Performance ◽  
Number Processing ◽  
Mathematical Ability ◽  
Comparison Task ◽  
Number Concepts ◽  
Processing Task ◽  
Number Concept ◽  
Verbal Instructions ◽  
Symbolic Number

Much research has investigated children’s non-symbolic number processing and its relation to mathematical ability. However, surprisingly few studies have investigated performance in 18-36 month-olds, where symbolic number concepts begin to emerge, and the extent results indicate poor performance. We tested 74 2 - 3.5 year-olds recruited from two sites (Ulster and Uppsala). They completed a novel dot-comparison task where children were shown, but not verbally instructed, how pushing a more numerous array resulted in reward and a Give-N task. Overall, participants performed above chance on the dot comparison task, indicating that non-symbolic number processing skills can be measured in toddlers without verbal instructions. We found no relation between performance on the non-symbolic number processing task and knower-level. Our results warrant two conclusions. First, verbal instructions involving the concept of more are not necessary to measure non-symbolic number processing skills in young children. Second, the development of a symbolic number concept seems independent of the development of non-symbolic comparison skills but may become artificially related when researchers use quantifiers such as “more” to measure the former.

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
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