Getting your ducks in a ro et al.pdf · Comparatives Superlatives Comparatives Superlatives...

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Acquiring ordinals and ordinality Caitlin Meyer, Sjef Barbiers & Fred Weerman [email protected] eerste tweede ????? vierde 1 Getting your ducks in a row

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Acquiring ordinals and ordinality

Caitlin Meyer, Sjef Barbiers & Fred [email protected]

eerste tweede ????? vierde

1

Getting your ducks in a row

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Is number uniquely human?

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

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Core Knowledge of NumberApproximate Number System 

(ANS)Object Tracking System 

(OTS)Imprecise Precise

Ratio‐sensitive Sensitive to +1Large quantities Small quantities (<4)

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Core knowledge + language = exact number?

• 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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Cardinal acquisition

• Slow and sequential • “Knower‐stages”= tiered acquisition

• Individual variation– Start & duration 

of 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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What about ordinals?

• 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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Cardinals & Ordinals in Dutch

# Cardinal Ordinal # Cardinal Ordinal1 één eer–ste 11 elf elf–de2 twee twee–de 12 twaalf twaalf–de3 drie der–de 13 der–tien der–tien–de4 vier vier–de 14 veer–tien veer–tien–de5 vijf vijf–de 15 vijf–tien vijf–tien–de6 zes zes–de 16 zes–tien zes–tien–de7 zeven zeven–de 17 zeven–tien zeven–tien–de8 acht acht–ste 18 acht–tien acht–tien–de9 negen negen–de 19 negen–tien negen–tien–de10 tien tien–de 20 twin–tig twin–tig–ste

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Questions

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 & 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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Comprehension test: 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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Who can help the monkey pack the right things? 

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Design

• 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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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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CARDINALSKnower‐levels & counting

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Knower‐levels

• 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 once.(e.g. Le Corre & Carey 2007)

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

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Cardinals: knower‐levels

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3‐year‐olds 4‐year‐olds

Level n

CP‐knowers 36

4‐knowers 16

3‐knowers 1

2‐knowers 12

1‐knowers 9

Pre‐knowers 3

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WHAT ABOUT ORDINALS?

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Ordinal knowers

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

% Correct responses to ordinals by knower‐level

Pre‐to‐3‐knowers

4‐knowers

CP‐knowers

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Degrees of comparison: % 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

Supe

rlatives

Comparatives

Supe

rlatives

Comparatives

Supe

rlatives

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

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Pre‐to‐3: first bias

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

correct first other (incorrect) last

% of responses on 2nd – 9th

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

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Pre‐to‐3: not a 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 o

n other stim

uli

Children who pass on given ordinals

If you know the n‐th, what other ordinals do you 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

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Ordinal‐knower patterns

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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

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Question

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…

• 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 questions

• If morphological transparency is key, then– Are analytic ordinals acquired before synthetic ones? (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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SNEAK PREVIEWPreliminary  results follow‐up study

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CP‐knowers: synthetic vs analytic ordinals

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0%

20%

40%

60%

80%

100%

1 2 3 4 6 8 9

% CP‐know

ers who

 pass

Tested ordinals

Synthetic (N‐de)Analytic (Car N)

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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')

(Also) pass…

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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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Selected referencesAlmoammer, A., J. Sullivan, C. Donlan, F. Marušič, R. Žaucer, T. O'Donnell & D. Barner. (2013). Grammatical morphology as a source of early number word meanings. Proceedings of the National Academy of Sciences, 110, 18448‐18453.Barbiers, S. (2007). Indefinite numerals ONE and MANY and the cause of ordinal suppletion. Lingua 117, 859–880.Carey, S. (2009). The origin of concepts. New York: Oxford University Press.Colomé, À. & M.‐P. Noël (2012). One first? Acquisition of the cardinal and ordinal use of numbers in preschoolers. Journal of Experimental Child Psychology, 133, 233‐247.Feigenson, L., S. Dehaene & E. Spelke (2004). Core systems of number. TRENDS in Cognitive Sciences, 8(7), 301‐314.Izard, V., P. Pica, E. S. Spelke & S. Dehaene (2008). Exact equality and successor function: two key concepts on the path towards understanding exact numbers. Philosophical Psychology, 21(4), 491‐505.Koch, C., A. Thiel, E. Sanfelici & P. Schulz (2015). On the acquisition of ordinal numbers in German. In E. Ruigendijk & C. Hamann (eds.), Proceedings of GALA 2013. Cambridge. MA: Cambridge Scholar Publishing.Le Corre, M. & S. Carey (2007). One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles. Cognition 105, 395–438.Sarnecka, B. W., V. G. Kamenskaya, Y. Yamana, T. Ogura & Y. Yudovina (2007). From Grammatical Number to Exact Numbers: Early Meanings of One, Two, and Three in English, Russian and Japanese. Cognitive Psychology 55(2), 136–168.Spelke, E. S. & K. D. Kinzler (2007). Core knowledge. Developmental Science 10(1), 89–96.Wynn, K. (1992). Children’s acquisition of the number words and the counting system. Cognitive Psychology, 24, 220–251.

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Acknowledgements

• All the children who participated, and their parents, (pre‐)schools and daycare centers; 

• Sabine van 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 you!Caitlin Meyer, Sjef Barbiers & Fred Weerman

[email protected]

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