Can Prosody Disambiguate
Mathematical Structure?
It Depends Who's Listening.
Michael Phelan
@phelanguist
SVALP
April 1, 2016
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Three times five minus two times two is eleven, but
three times five minus two times two is eighteen.
-L. Bloomfield (1939)
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Three times five minus two times two is eleven, but
three times five minus two times two is eighteen.
-L. Bloomfield (1939)
(3 · 5) – (2 · 2) = 11
3 · ((5 – 2) · 2) = 18
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Do talkers disambiguate mathematical
expressions? Do listeners understand?
Are there limits to disambiguation?
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Do talkers disambiguate mathematical
expressions? Do listeners understand?
Are there limits to disambiguation?
Do the answers to these questions
depend on math ability?
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Prosody often signals sentence structure
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Prosody often signals sentence structure
- Complex NP (Lehiste, 1973)
- PP attachment (Cooper & Paccia-Cooper, 1980)
- Prep/verb particle (Price et al, 1991)
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Prosody often signals sentence structure
- Complex NP (Lehiste, 1973)
- PP attachment (Cooper & Paccia-Cooper, 1980)
- Prep/verb particle (Price et al, 1991)
Listeners make use of these distinctions
- With explicit attention to meanings
(Lehiste, Olive, & Streeter, 1976)
- Without explicit attention
(Speer, Schafer, & Warren, 2011)
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A few studies have used mathematical
stimuli:
A + (E ∙ O)
(A + E) ∙ O
(Streeter, 1978)
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A few studies have used mathematical
stimuli:
A + (E ∙ O)
(A + E) ∙ O
(Streeter, 1978)
A, + E, ∙ O
(Wagner & Crivellaro, 2010)
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A few studies have used mathematical
stimuli:
A + (E ∙ O)
(A + E) ∙ O
(Streeter, 1978)
A, + E, ∙ O
(Wagner & Crivellaro, 2010)
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Two studies with more complex stimuli
O'Malley, Kloker, and
Dara-Abrams (1973)
Holm, Bailey, & Laborde (1999)
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Role of mathematical ability very unclear
- Aware/unaware of ambiguity
- “Used to listening to equations”
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Why not a math test?
(Phelan, 2012)
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Many speakers
used felicitous
prosody to
disambiguate
Prosodic grouping
mostly matched
syntactic grouping
(Phelan, 2012)
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Felicitous prosody
positively
correlated with
accuracy (p < 0.05)
Infelicitous prosody
negatively
correlated with
item score (p < 0.01)
and overall test
score (p < 0.05)
(Phelan, 2012)
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Speakers are producing disambiguating
prosody.
Can listeners use it?
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Speakers are producing disambiguating
prosody.
Can listeners use it?
(Phelan, 2014)
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Stimuli:
- Clips from previous production exp.
- 44 with two answer choices (Easy)
- 22 with three (Medium) or five (Hard)
(Phelan, 2014)
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Stimuli:
- Clips from previous production exp.
- 44 with two answer choices (Easy)
- 22 with three (Medium) or five (Hard)
- 8 non-math English items
- PP, RC, NP ambiguities
- Pick appropriate paraphrase
(Phelan, 2014)
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Subjects:
15 Children, ages 7 – 17
14 Adults, ages 30 – 59
Recruited at science museum
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Results:
Trial Type
Accuracy (Chance)
Easy
60.7% ***
(50%)
Medium
39.4% **
(33%)
Hard
19.9%
(20%)
English
77.1% ***
(50%)
(Phelan, 2014)
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English performance correlated with
math performance for both groups, but
more strongly for adults.
Kids
Eng ~ Math
Correlation
r = .588
Adults
r = .712
(Phelan, 2014)
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Results by age:
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Results by age:
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Results by age:
?
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Follow up:
More subjects, demographic info:
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Follow up:
More subjects, demographic info:
- 117 subjects, ages 9 – 73
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Follow up:
More subjects, demographic info:
- 117 subjects, ages 9 – 73
- Questionnaire asking about
- Math use in job/major
(y/n)
- Self rating of math skill (1-7)
- Nervous/uncomfortable (1-7)
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Only “Easy” math trials
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Only “Easy” math trials
Mixed with picture matching for English
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Results
Math Accuracy by Age Group
100
90
% Chose Intended Expression
80
70
60
67.6
68.4
67.8
YA – No
YA – Yes
OA – No
65.2
55.5
50
40
30
20
10
0
Kids
OA – Yes
Age Group
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35
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Across age group, neither self-rating
nor nervous rating do correlates with
math accuracy
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Within age group, self-rating and
nervous rating do correlates with math
accuracy
Group
Self Rating
Nervous
Kids
r = 0.182
-.187
YA – No Math
0.396
0.290
YA – Math
X
0.383
OA – No Math
0.226
X
OA - Math
0.228
-0.239
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Accounting for differences?
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Accounting for differences?
Blocked vs. Unblocked design
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Accounting for differences?
Blocked vs. Unblocked design
Pictures too distracting?
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Accounting for differences?
Blocked vs. Unblocked design
Pictures too distracting?
Individual differences in prosodic
processing swamp group effects
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Conclusions There are interesting variations in how
people use prosody to disambiguate speech.
Some people are terrible at this in math, and
in non-math. What accounts for this
variability?
Everyone has important limits on prosodic
disambiguation.
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Acknowledgments
Many thanks to Shari Speer, Cynthia Clopper,
Mary Beckman, Laura Wagner, and the
Speerlab and Phonies groups at OSU
Important feedback from Speech Prosody
2012 and 2014 attendees
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