Getting your ducks in a row eerste tweede ????? vierde Acquiring - - PowerPoint PPT Presentation

Acqui Acquiring ing or

• rdi

dinal nals and and or

• rdi

dinal nality ty

Caitlin Meyer, Sjef Barbiers & Fred Weerman c.m.meyer@uva.nl

eerste tweede ????? vierde

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Getting your ducks in a row

Is Is num number er uni uniquel quely hum human? an?

(e.g. overviews in Feigenson, Dehaene & Spelke 2004; Spelke & Kinzler 2007)

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Cor Core Knowledg

• wledge of
• f Number

Number

Approximate Number System (ANS) Object Tracking System (OTS) Imprecise Precise Ratio‐sensitive Sensitive to +1 Large quantities Small quantities (<4)

Cor Core kno knowledg ledge + lan language = exa exact num number? ber?

• Language argued (by psychologists) to play a

critical role in development of exact number

– Count list (e.g. Carey) – Quantification & grammatical number (e.g. Spelke)

• So…

– Role of language exactly? – Cross‐linguistic differences? – Effects beyond cardinals?

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Car Cardinal inal acqui acquisi siti tion

• n
• Slow and sequential
• “Knower‐stages”

= tiered acquisition

• Individual variation

– Start & duration

• f each stage

– Exact ages vary between studies

• Mostly English. Also: Japanese, French, Russian,

Slovenian, Saudi Arabic... but not Dutch.

(see e.g. Almoammer et al. 2013)

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Knower‐ levels Begins around Pre 2;0 1 2;0 – 3;0 2 2;6 – 3;9 3 2;8 – 4;0 4 2;8 – 4;5 CP 3;0 – 4;6

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Wh What at about about or

• rdinals?

dinals?

• Natural extension of research on cardinals
• Conceptually (counting principles)
• Linguistically (ordinal = cardinal + –de/–ste)
• Yet have received very little attention

(4 studies in 35 years)

Fischer & Beckey (1990), Miller et al (2000), Colomé & Noël (2012), Koch et al. (in press)

• Data is inconclusive, lacks proper link to cardinals

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Car Cardinals inals & Or Ordi dinal nals in in Dut Dutch

# Car ardinal dinal Ordinal inal # Car ardinal dinal Ordinal inal

1 één eer eer–ste 11 11 elf elf–de 2 twee twee–de 12 12 twaalf twaalf–de 3 drie der der–de 13 13 der–tien der–tien–de 4 vier vier–de 14 14 veer–tien veer–tien–de 5 vijf vijf–de 15 15 vijf–tien vijf–tien–de 6 zes zes–de 16 16 zes–tien zes–tien–de 7 zeven zeven–de 17 17 zeven–tien zeven–tien–de 8 acht acht–ste 18 18 acht–tien acht–tien–de 9 negen negen–de 19 19 negen–tien negen–tien–de 10 10 tien tien–de 20 20 twin–tig twin–tig–ste

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Ques Questions

• ns

How does the acquisition of cardinals in Dutch…

• 1. Relate to the acquisition of cardinals in other

languages?

• 2. Relate to the acquisition of ordinals?

 Pattern and timing

• 3. To what extent does language play a role?

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Hypotheses Hypotheses & Pre Predictions

• Lower ordinals easier than higher ones

– Ordinal acquisition requires knowing its cardinal – The higher the number, the more demanding the task

• Ordinal acquisition is not tiered if language plays a role:

– Irregular morphology might hinder derde ‘third’, and possibly eerste ‘first’ – But superlative morphology might help eerste ‘first’ (cf. Barbiers 2007)

• Children should know to take just one card

(ordinal  singular; cardinals higher than 1  plural)

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Com Comprehensi hension te test st: Gi Give X

• Give‐a‐number, Give me, Give N, Give some pigs

(e.g. Barner et al. 2013; Colomé & Noël 2012; Condry & Spelke, 2008; Huang, Spelke & Snedeker 2010; Le Corre & Carey, 2007; Le Corre, Li, & Jia, 2003; Le Corre, Van de Walle, Brannon, & Carey, 2006; Li, Le Corre, Shui, Jia, & Carey, 2003; Sarnecka & Gelman, 2004; Sarnecka, Kamenskaya, Yamana, Ogura, & Yudovina 2007; Wynn, 1990; Wynn, 1992; et cetera)

• Outcome corresponds with other tasks that aim to

measure cardinal comprehension

(e.g. Le Corre et al. 2006, Le Corre & Carey 2007, Wynn 1992)

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Wh Who ca can help help the the mo monk nkey ey pack pack the the righ right thin things?

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Desi Design gn

• Cardinals & ordinals: 1 – 2 – 3 – 4 – 8 (– 9)
• Laatste, middelste (‘last’, ‘middel‐est’)
• Degrees of comparison

(e.g. groter ‘bigger’, grootste ‘biggest’)

• Each condition: x 3
• Total: 77 ‘packing events’, 2 trials
• 2 sessions
• Can you count to 20?

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Pa Participants

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3‐year‐olds 4‐year‐olds 5 & 6 yrs N 31 (F: 42.0% ) 26 (F: 46.1%) 20 (F: 59.9%) Age range 2;11 – 3;11 4;0 – 4;11 5;0 – 6;4 Mean 3;6 4;6 5;6 SD 3.5 months 3.1 months 5.13 months

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CARDI CARDINALS ALS

Knower‐levels & counting

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Kn Knower‐le levels ls

• To be an n‐knower, a child had to

– give n correctly 2 out of 3 times, AND – give n in response to a different cardinal at most

• nce.

(e.g. Le Corre & Carey 2007)

• Compared to model in Negen et al. (2012)

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Car Cardinals: inals: kno knower er‐le levels ls

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3‐year‐olds 4‐year‐olds

Le Level n CP‐knowers 36 4‐knowers 16 3‐knowers 1 2‐knowers 12 1‐knowers 9 Pre‐knowers 3

WH WHAT ABOUT ABOUT ORDI ORDINALS? NALS?

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Or Ordi dinal nal kno knower ers

To be an nth‐knower, a child had to ‐ give the nth correctly 2 out of 3 times, AND ‐ give the nth in response to a different ordinal at most once.

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0% 20% 40% 60% 80% 100% 1st 2nd 3rd 4th 8th & 9th

% Corr Correct ect re responses to to or

• rdinals

dinals by by kno knower er‐le level

Pre‐to‐3‐ knowers 4‐knowers CP‐knowers

Degr Degrees ees of

• f co

comp mparison: % co correct

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97,20% 87,64% 100,00% 95,12% 97,67% 96,67%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Comparatives Superlatives Comparatives Superlatives Comparatives Superlatives 3‐year‐olds 4‐year‐olds 5‐&‐6‐year‐olds

Pre Pre‐to to‐3: 3: first bi bias as

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0% 10% 20% 30% 40% 50% 60% 70% 80% correct first

• ther (incorrect)

last

% of

• f re

responses on

• n 2nd

nd – 9

– 9th

th

1st 'passers' (47.6%) 1st 'failers' (52.4%)

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Pre Pre‐to to‐3: 3: not not a mes mess

• Children were engaged:

– Comparatives & superlatives were no problem – At least some cardinals went well

• Exhibit some knowledge:

– Children know to take just one card! ( SG/PL distinction) – Some children show a clear bias…

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0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

"1st‐knowers" "2nd‐knowers" "3rd‐knowers" "4th‐knowers" "8th & 9th‐ knowers"

% who pass on other stimuli Children who pass on given ordinals

If If yo you kno know the the n‐th, what what other

• ther or
• rdi

dinal nals do do yo you kno know?

1st 2nd 3rd 4th 8th & 9th

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• Knowing a given ordinal doesn’t guarantee knowledge of the previous ordinal.
• Low before high
• Derde ‘third’ is harder than tweede ‘second’ and vierde ‘fourth’
• Eerste ‘first’ not harder

Or Ordi dinal nal‐kno knower er pa patterns erns

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0,00% 10,00% 20,00% 30,00% 40,00% 50,00% 1st only 1st, 2nd, 4th only 1st‐4th All but 3rd Other All Pre‐to‐3‐kowers 4‐knowers CP‐knowers

Ques Question

• n

If irregular morphology is to blame for derde ‘third’, why isn’t eerste ‘first’ hard, too?  Eerste is more frequent? But then what about tweede?  Barbiers (2007): eerste is a superlative.

• PL noun modification (de eerste boeken, de meeste boeken)
• –ste reduction (dit stuk is het leukst(e)/het eerst(e)/*het achtst)
• Aller intensification (allermooiste, allereerste, *allertweede)
• Regular degrees of comparison (eer, eerder, eerst)

Well, then superlatives should be easy… And they are.

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So… So…

• Pre‐to‐three:

– Just one card (sg/pl distinction) – First bias

• High ordinals are hard for extra‐linguistic reasons
• Derde ‘third’ is hard because it’s irregular
• Eerste ‘first’ is an irregular ordinal, but a fine

superlative

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New New ques questions ns

• If morphological transparency is key, then

– Are analytic ordinals acquired before synthetic

• nes? (E.g. would auto drie ‘car three’ be easier

than derde auto ‘third car’?)

• And if children have a rule, then

– Are ungrammatical but ‘regularized’ forms comprehensible for children who don’t know the exceptions? I.e. what about *driede (‘threeth’)?

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SNE SNEAK PREVIEW PREVIEW

Preliminary results follow‐up study

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CP CP‐kno knower ers: s: sy synthetic vs vs analy analytic ic

• r
• rdinals

dinals

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0% 20% 40% 60% 80% 100% 1 2 3 4 6 8 9 % CP‐knowers who pass Tested ordinals Synthetic (N‐de) Analytic (Car N)

Derde, auto drie, *driede

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0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Fail Pass Fail Pass Fail Pass derde ('third') auto drie ('car three') driede ('threeth') derde ('third' ) auto drie ('car three') driede ('threeth') (A (Also lso) pass… pass…

Conclusion Conclusion

• 1. The tiered pattern of cardinal acquisition is universal,

the timing is not.

• 2. Ordinal acquisition is not tiered like cardinals.
• 3. The pattern and timing of ordinal acquisition is

influenced by different language‐specific factors, such as: ‐ (ir)regular ordinal morphology, ‐ superlative morphology, ‐ and the singular‐plural distinction.

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Sel Select cted ed ref refere rences

Alm Almoam ammer, A., A., J.

• J. Sulliv

Sullivan an, C.

• C. Donlan,

Donlan, F.

• F. Ma

Maruši rušič, R.

• R. Žauc

Žaucer, T.

• T. O'

O'Donnel Donnell & D.

• D. Barner
• Barner. (2013

(2013). Grammatical morphology as a source of early number word meanings. Proceedings of the National Academy of Sciences, 110, 18448‐18453. Barbier Barbiers, S.

• S. (2007).

007). Indefinite numerals ONE and MANY and the cause of ordinal suppletion. Lingua 117, 859–880. Car Carey, S.

• S. (2009).

2009). The origin of concepts. New York: Oxford University Press. Colo Colomé, À. À. & M. M.‐P.

• P. Noël

Noël (2012). 012). One first? Acquisition of the cardinal and ordinal use of numbers in preschoolers. Journal of Experimental Child Psychology, 133, 233‐247. Feig igenson, enson, L., L., S.

• S. Dehaene

Dehaene & E.

• E. Spelk

Spelke (2004 (2004). Core systems of number. TRENDS in Cognitive Sciences, 8(7), 301‐314. Iz Izar ard, V. V., P.

• P. Pic

Pica, E.

• E. S.
• S. Spelk

Spelke & S.

• S. Dehaene

Dehaene (2008). 2008). Exact equality and successor function: two key concepts on the path towards understanding exact numbers. Philosophical Psychology, 21(4), 491‐505. Ko Koch, C. C., A.

• A. Thie

Thiel, l, E.

• E. Sanf

Sanfelic elici & P.

• P. Sc

Schu hulz lz (2015). 015). On the acquisition of ordinal numbers in German. In E. Ruigendijk &

• C. Hamann (eds.), Proceedings of GALA 2013. Cambridge. MA: Cambridge Scholar Publishing.

Le Le Corr Corre, e, M.

• M. & S.
• S. Car

Carey (2007). 007). One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles. Cognition 105, 395–438. Sarne Sarnecka, B.

• B. W.

W., V.

• V. G.
• G. Ka

Kamenskaya ya, Y.

• Y. Ya

Yamana, T.

• T. Ogur

Ogura & Y.

• Y. Yudo

dovina vina (2007). 007). From Grammatical Number to Exact Numbers: Early Meanings of One, Two, and Three in English, Russian and Japanese. Cognitive Psychology 55(2), 136– 168. Spelk Spelke, E.

• E. S.
• S. & K.
• K. D.
• D. Ki

Kinzle nzler (2007). 2007). Core knowledge. Developmental Science 10(1), 89–96. Wynn, nn, K.

• K. (1992).

992). Children’s acquisition of the number words and the counting system. Cognitive Psychology, 24, 220– 251.

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Acknowledg Acknowledgem emen ents ts

• All the children who participated, and their parents,

(pre‐)schools and daycare centers;

• Sabi

Sabine ne va van Re Reijen, Iris Craane, Heleen de Vries, Renske van der Mooren & Marthe Dekker for their experimental assistance.

• The NWO Horizon Knowledge & Culture group for

their feedback and suggestions.

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Thank Thank yo you!

Caitlin Meyer, Sjef Barbiers & Fred Weerman c.m.meyer@uva.nl

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