[MATHLINK] Lightning Talks, FRIDAY September 3rd @ 11am EST//4:00pm BST

MCLS Trainee mclstrainee at gmail.com
Wed Sep 1 15:45:13 CST 2021

Dear MCLS Community,

Join us this *Friday, September 3rd @ 11am EST/ 4pm BST. *We'll be hearing
from *eight *MCLS members in quick, 5-minute presentations. Their abstracts
are included at the bottom of this email.

*Jenna Rice (Undergraduate Student, Carleton University):* *Number
Transcoding for French Immersion Students*
*Madeleine Oswald (Doctoral Student, University of Chicago):* *Playing
Games Promotes More Number Talk Than Other Home Activities*
*Maria Glaser (Doctoral Student, Humboldt-Universität zu Berlin):* Are
spatial biases in mental arithmetic domain-specific?
*Elena Leib (Doctoral Student, University of California, Berkeley):* *Testing
the whole number bias hypothesis in children: evidence for the role of
inhibitory control and whole number interference*
*Ilaria Berteletti (Assistant Professor, Gallaudet University):* *The
unexplored role of handshape similarity in processing numbers on the hands.*
*Nachshon Korem (Post Doc, Department of Psychiatry at Yale University
School of Medicine):** Is the working memory math anxiety relation
task-dependent? A network analysis approach study*
*Lauren Anthony (Doctoral Student, University of Wisconsin-Madison):*
the Effects of Equations in Sequence on Problem-Solving Performance and
Relational Reasoning*
*Jeffrey K. Bye (Lecturer, University of Minnesota):** Erroneous estimation
of the factorial function and improvement through calibration experiences*

Join the room at any time from the link https://tinyurl.com/MCLS2021
ID: 225 833 7242, Passcode: MCLS2021).

Thanks so much and we hope to see you this week!
The MCLS Conference Organizing Committee

*Past Events and News:*

   - Did you miss the awesome Academic Job Market panel on August 20th?
   It's posted now on the MCLS Trainee Youtube channel

*Upcoming Events and News:*

   - *Thursday, September 9 @ 9:00am EST // 2:00pm BST* - MCLS 2021
   Symposium "*Symbolic number ordering: Underlying mechanisms and its
   (causal) relation with math performance*", organized by Bert Reynvoet
   (KU Leuven) and Francesco Sella (Loughborough University)
   - *Friday, September 17 @ 11:00am EST // 4:00pm BST* - MCLS 2021
   Symposium "*Accessing to fractional magnitudes: From perception to
   higher cognition*" organized by Yunji Park (Stanford University)

**Check out all past and upcoming events in the MCLS 2021 program by clicking

*September 3rd Lightning Talks - AbstractsJenna Rice (Undergraduate
Student, Carleton University)*
*Number Transcoding for French Immersion Students*
Number transcoding is the process of mapping between the verbal code (e.g.,
four hundred) and the digital code (e.g., 400) of a numeral. Transcoding
can be difficult for young children, especially if the verbal number system
of their language does not reflect the base-ten structure of the Arabic
numeral system. French in particular presents challenges to young
transcoders due to its verbal complexity in the decades 70, 80 and 90. For
example, 72 in French is ‘soixante douze’ (i.e., sixty-twelve). For these
decades, French uses a vigesimal rather than a decade structure. In the
present research, we compared the written transcoding performance of French
immersion students when they transcoded in English versus French. In French
immersion programs, the primary language of instruction is French. Grade 3
students (Mage = 8.8 years) enrolled in French immersion (n = 152)
transcoded the same numbers once in English and once in French, on
different days. Six numerals from each of the hundreds, thousands, ten
thousands, hundred thousands, and millions were selected, with complex
decades located in tens (e.g., 2398, 16070), or ten thousands (e.g., 82067,
574321). As expected, students made more errors on numerals with complex
decades in French than English. Furthermore, individual differences in
number transcoding were related to receptive vocabulary scores in the
language of transcoding. The results provide further evidence for the role
that language plays in number transcoding and, more specifically, for the
effect of the French verbal number system on the development of children’s
transcoding skills.

*Madeleine Oswald (Doctoral Student, University of Chicago)*
*Playing Games Promotes More Number Talk Than Other Home Activities*
Parental math talk as well as engaging in math related activities at home
are related to children’s numerical abilities (e.g. Gunderson & Levine
2011; Purpura et al., 2020). Previous research shows parent math talk
varies across different activities (Anderson, 1997; Ramani et al., 2015),
however these studies used a limited number of experimenter provided
activities. It is unknown which spontaneous everyday activities generate
the most math talk. Using 90-minute video recordings of 38-month-old
children’s naturalistic home interactions, we categorized children’s
activities into 13 broad categories (Arts, Building, Basic-care, Chores,
Discipline, Electronicmedia, Food, Games, Performing-knowledge,
Physical-play, Pretend-play, Print-media, Unstructured). Parent’s
child-directed speech was transcribed and searched for instances of number
words. Children hear the highest amount of number words as well as the
greatest density of number words during Games. This complements previous
research showing that experience playing games is positively correlated
with numeric ability (Ramani & Siegler, 2009). Future analyses will explore
other types of math talk including relational vocabulary (e.g. bigger,
smaller, more, less) and spatial words (e.g. square, diagonal, above).

*Maria Glaser (Doctoral Student, Humboldt-Universität zu Berlin)*
*Are spatial biases in mental arithmetic domain-specific?*
The field of numerical cognition has seen a recent rise of studies
demonstrating shifts of spatial attention to the right (left) during
addition (subtraction) processing. For example, Glaser & Knops (2020)
observed shifts to the right in two-digit addition but no shifts in
subtraction processing. These findings have been taken as evidence for the
spatial organisation of the numerical representation that is operated upon.
Nevertheless, another branch of research in cognitive psychology has shown
that cognitive load or reduced alertness can lead to rightward shifts of
attention. Because the combination of a measurement of spatial attention
and an arithmetic operation creates a dual-task paradigm with increased
task load, the question of the contributions of domain-general (task load)
and domain-specific (arithmetic processing) factors to the observed spatial
biases arises. To investigate the impact of task load on spatial attention
in a non-arithmetic dual-task setup we measured spatial attention via a
temporal order judgment task in the context of an analogy task (dual-task,
high load) and alone (baseline: single-task, low load). Results showed no
significant difference in spatial attention between the baseline and the
analogy task. This indicates that the attentional shifts observed in the
context of arithmetic processing are due to domain-specific task components
(arithmetic processing and the spatial layout of its underlying numerical
representation), rather than domain-general factors like the cognitive load
that such a dual-task situation entails.

*Elena Leib (Doctoral Student, University of California, Berkeley)*
*Testing the whole number bias hypothesis in children: evidence for the
role of inhibitory control and whole number interference*
The whole number bias hypothesis suggests that a primary source of rational
number difficulties is interference from whole number knowledge (Ni & Zhou,
2005). Here, we tested two implications of this hypothesis involving
inhibitory control (IC) and whole number knowledge, in the realm of
fractions. First, if resolving interference is crucial for rational number
understanding, we would expect IC to be predictive of fraction comparison
performance, even after accounting for working memory (WM), the most robust
predictor of math outcomes. Second, if whole number knowledge interferes
with fraction processing, we would expect it to paradoxically predict worse
fraction outcomes, despite its typical positive association with math
outcomes (Schneider et al., 2017). To investigate these hypotheses, we
analyzed data from a fraction comparison task, a whole number comparison
task, a WM composite score, and an IC composite score from 780 3rd, 5th,
and 7th graders from the San Francisco Bay Area. Using linear models, we
found that IC reliably predicts fraction performance over and above
contributions of WM. For whole number knowledge, results were mixed. Whole
number knowledge positively predicted fraction comparison outcomes for the
7th graders, for easy comparisons. However, it also predicted slower
response times on easy and hard comparisons, for these students, suggesting
interference in performance from whole number knowledge. These findings
highlight the role of inhibitory control in rational number performance and
expand our knowledge of the contexts where whole number knowledge helps or
hinders rational number understanding.

*Ilaria Berteletti (Assistant Professor, Gallaudet University)*
*The unexplored role of handshape similarity in processing numbers on the
With two simple experiments we investigate the overlooked influence of
handshape similarity for processing numerical information conveyed on the
hands. In most finger-counting sequences there is a tight relationship
between the number of fingers raised and the numerical value represented.
This creates a possible confound where numbers closer to each other are
also represented by handshapes that are more similar. By using the ASL
number signs we are able to dissociate between the two variables
orthogonally. First, we test the effect of handshape similarity in a
same/different judgment task in a group of hearing non-signers and then
test the interference of handshape in a number judgment task in a group of
native ASL signers. Our results show an effect of handshape similarity and
its interaction with numerical value even in the group of native signers
for whom these handshapes are linguistic symbols and not a learning tool
for acquiring numerical concepts. Because prior studies have never
considered handshape similarity, these results open new directions for
understanding the relationship between fingerbased counting, internal hand
representations and numerical proficiency.

*Nachshon Korem (Post Doc, Department of Psychiatry at Yale University
School of Medicine)*
*Is the working memory math anxiety relation task-dependent?*
A network analysis approach study Working memory (WM) and affect toward
mathematics were found to be linked to math performance. Early theories
suggested that the relation between Math anxiety (MA) and math performance
can be explained by MA related thoughts occupying WM resources. In
contrast, newer theories, based on structural equation models (SEM),
suggest that MA has a direct (non WM related) effect on math performance.
SEM uses a latent approach that enables one to look at tasks at the “macro”
level. Here, in an attempt to better understand the WM-MA link inside the
WM-MA-Math performance network, we took another approach, looking at the
“micro” level. Using a network approach, we investigated the partial
correlation matrix between (1) MA, (2) WM tasks with and without math load,
and (3) math performance. The network analysis suggested that while both WM
and MA were strongly related to math performance, only WM tasks that
included manipulations of numbers were found to be correlated to MA. To
check the robustness of the model, we replicated the results using an
online dataset made available by Skagerlund et al (2019). This robust model
further confirms that the MA-Math performance link is not WM dependent, and
more interestingly, that the WM-MA link is task-dependent.

*Lauren Anthony (Doctoral Student, University of Wisconsin-Madison)*
*Examining the Effects of Equations in Sequence on Problem-Solving
Performance and Relational Reasoning* Mathematics, by its very nature, is
rife with patterns. However, students frequently treat mathematics as a
series of isolated and unlinked exercises. Prior research has demonstrated
that certain math tasks afford individuals opportunities to notice and
reason about mathematical structure; and these experiences have been shown
to positively impact subsequent math performance. The current study
examined whether experience with extending mathematical patterns affected
adults’ ability to solve equations that involved patterns and/or to reason
about mathematical relationships in new contexts. It was hypothesized that
experience with patterning tasks would facilitate attention to consistent
relationships within and across equations, thereby improving performance on
related math tasks. Conversely, the ability to reason algebraically about
the structure of the underlying pattern may be better supported by explicit
instruction that clearly describes the relational structure of practiced
equations. Consistent with our first hypothesis, participants who were
given 13 trials of pattern extension experience then went on to demonstrate
both more efficient (i.e., faster response times) and more accurate
problem-solving at posttest relative to individuals who were not given
experience solving problems that contained a salient pattern (rather these
participants viewed a worked example alongside explicit instruction before
solving equations). However, there was no difference between the groups in
the ability to abstract the structure of the underlying mathematical
relationships. These findings suggest that patterning tasks like those used
in this study may be useful in supporting math performance.

*Jeffrey K. Bye (Lecturer, University of Minnesota)*
* Erroneous estimation of the factorial function and improvement through
calibration experiences*
Factorials are important for counting collections in discrete probability
and combinatorics. However, people have difficulty reasoning about them.
Tversky and Kahneman (1973) found that under time pressure, people
massively underestimate the expansion of 8! (correct value 40,320), and
that the degree of their underestimation is less when the product is
presented in descending order (8x7x6x5x4x3x2x1; Median=2,250) vs. ascending
order (1x2x3x4x5x6x7x8; Median=512). We attempted to replicate both
findings in a sample of N = 140 participants and to assess whether
calibration reduces underestimation errors. Participants first estimated
both orders (counterbalanced). We replicated the massive underestimation on
the first attempt but failed to replicate the effect of order
between-subjects. However, participants significantly improved their
estimates when answering the descending order after the ascending order, a
within-subjects effect not previously demonstrated. Participants were then
calibrated to the correct value for either 6! or 10! and estimated both
orders of 8! a second time. Participants who received the larger
calibration value (10!) made much more accurate estimates for 8!
(Median=38,000), which in fact did not differ statistically from the
correct value. Participants who received the smaller calibration (6!) still
grossly underestimated 8! (Median=2,678.5), despite 8! being closer to 6!
than 10! in linear and log units. Our findings suggest that people’s
underestimation may be (1) lessened by the presentation of descending after
ascending order, and (2) greatly reduced by providing an upper-bound
reference (10!). This may have implications for mathematics and computer
science instruction.

More information about the MATHLINK mailing list