[MATHLINK] (no subject)
MCLS Trainee
mclstrainee at gmail.com
Wed Oct 20 16:33:05 CST 2021
Dear MCLS Community,
Please be sure to join us for our next session this *Thursday, October 21st
at 6pm PST // 9pm EST // 2 am Friday BST // 9am Friday Hong Kong *for the
next round of lightning talks!
You'll have the opportunity to hear from Winnie Chan (Assistant Professor,
University of Hong Kong), Elisabeth Marchand (Doctoral Student, University
of California San Diego), Nicholas Vest (Doctoral Student, University of
Wisconsin-Madison), Terry Wong (Assistant Professor, The University of Hong
Kong), Alison Vrabec (Graduate Student, University of Dayton), Jake Kaufman
(Doctoral Student, Vanderbilt University), Josh Medrano (Doctoral Student,
University of Maryland - College Park), and Rui Meng (Graduate Student,
University of Wisconsin Madison)!
The full abstract for each presentation are available at the bottom of this
email.
*Click to join the meeting at anytime*: https://tinyurl.com/MCLS2021
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(Meeting ID: 225 833 7242, Password: MCLS2021)
Hope to see you there!
The MCLS Conference Organizing Committee
------------------------------
*Past Events and News: *
- Last week, Mary DePascale and colleagues presented a symposium on Math
Anxiety. This video will soon be available to watch on the MCLS
Trainee Youtube channel!
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*Upcoming Events and News:*
- Join us next week on *Friday, October 29th @ 11am EST* for our *last
round of Lightning talks in 2021*!
- We'll hear from Marta Fedele, Roberto A. Abreu-Mendoza, Caroline
Byrd Hornburg, Lília Marcelino, Ludovica Veggiotti, Juan
Antonio Álvarez
Montesinos, Ilaria Berteletti, and Serena Dolfi.
- Access rest of the MCLS 2021 program by clicking here.
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------------------------------
*Abstracts*
*Winnie Chan (Assistant Professor, University of Hong Kong)*
*Knowledge of Mathematical Vocabularies Predicting Early Mathematical
Performance*
Learning mathematics requires knowledge of math-related vocabularies. For
instance, we use “total” to refer to the sum of quantities and “difference”
to refer to the amount by which one quantity is larger or smaller than the
other quantity. Previous studies have shown that knowledge of mathematical
vocabularies is predictive of children’s mathematical performance. However,
it is unclear how important such knowledge is when compared to other
domain-specific skills (e.g., approximate number system,
symbolic-nonsymbolic mapping, and knowledge of number system), which also
play a crucial role in mathematical development. To fill the gap,
eighty-two Chinese-speaking children (mean age=4.36 years) were asked to
complete a series of mathematical tasks, including a problem solving task,
a mathematical vocabulary task, a numerosity comparison task for tapping
into approximate number, a number line estimation task and a numerical
mapping task for tapping into symbolic-nonsymbolic mapping, and a number
comparison task and a next number task for tapping into the knowledge of
number system. Results showed that, after taking into account the control
measures (i.e., age, nonverbal intelligence, listening comprehension
skills, verbal and visuospatial working memory), knowledge of mathematical
vocabularies explained an additional 4% variance of problem solving
performance above and beyond the series of domain-specific tasks. This
indicates that knowledge of mathematical vocabularies has a unique role to
play on top of the domain-specific skills in children’s mathematical
performance.
*Elisabeth Marchand (Doctoral Student, University of California San Diego)*
*Do bilingual children subitize differently across languages?*
Previous studies of bilingual children have shown that children classified
as subset-knowers don’t tend to be at the same subset-knower level (e.g.,
2-knower) in their first (L1) and second language (L2), whereas children
who are classified as CP-knowers in their L1 tend to be CP- knowers as well
in their L2. This raises the possibility that bilingual children, once they
become CP-knowers in their L1, might automatically become CP-knowers in
their L2 despite not having passed through all the same subset stages -
i.e., by virtue of a transfer of procedural counting knowledge across their
two languages. To explore this possibility, we investigated the subitizing
abilities of bilingual children. We tested 51 children (target N=64; M age
= 4 years 11 months, SD = 0.74) in both their languages using the
Give-a-Number (GN) task to identify children who were CP-knowers in both
languages, as well as a subitizing task. Preliminary results showed that
bilingual CP-knowers are overall accurate at subitizing quantities 1 to 3,
but that for sets ranging from 2 - 4 there is a consistent difference in
subitizing accuracy across L1 and L2. So far, these results suggest that
bilingual children’s representations of small number words are not
comparably robust across languages. This also suggests that bilingual
children, at least in their L2, can conceptualize the CP-rule as a counting
procedure that operates in parallel with acquiring robust representations
of small sets. Data collection is still in progress and we plan to conduct
additional analyses on the relationship between bilinguals’ counting and
subitizing skills to further understand how counting develops in this
population.
*Nicholas Vest (Doctoral Student, University of Wisconsin-Madison)*
*How do children’s concepts of zero relate to their understanding of
integers?*
A foundational mathematical concept that is challenging for learners is
that of integers. Integers extend natural numbers {1, 2, ...} with zero and
negatives and are sometimes referred to as the foundation of numerical
thinking. However, concepts of zero are typically introduced before
negative integers and are difficult for young children to understand. It
may be children acquire a vague numerical concept of zero early (e.g., zero
is nothing), and that this concept shifts in formal education (e.g., via
activities with number lines). According to Varma and Schwartz (2011),
because zero and negative integers do not have readily available perceptual
mappings, children initially understand them by using symbolic rules (e.g.,
-x is always less than +x or +y). It is possible that as children begin to
use number lines with integers, they acquire a new concept of zero as the
symmetry point between positives and negatives. In the current study, we
sought to address the following questions: (1) What are children’s concepts
of zero? (2) Do children’s concepts of zero relate to their understanding
of integers? We addressed these questions in a sample of children in grades
4 through 7 (N = 75, M age = 11.37). We found that (1) most children had a
concept of zero as nothing and some had a concept of zero as the symmetry
point, (2) older children were more likely to have a concept of zero as the
symmetry point, and (3) children’s concepts of zero were associated with
their performance on a number line placement task. These findings raise new
questions about links between understanding of zero and negative integers,
and about activities that may foster progressions in understanding of
integers more broadly.
*Terry Wong (Assistant Professor, The University of Hong Kong)*
*The ability to identity word problem types longitudinally predicts
children’s mathematical problem-solving*
Many children face difficulties in solving word problems, but we have yet
learned enough about the sources of such difficulties. The current study
examined whether the ability to classify word problems into different word
problem types played a significant role in children’s mathematical
problem-solving. Over 200 fifth graders were given a word problem reasoning
task in which they had to match word problems with schematic diagrams that
depict different word problem types. They were also tested on their
mathematical problem-solving multiple times. The ability to match word
problems to the corresponding schematic diagrams was shown to be
longitudinally predictive of children’s mathematical problem-solving
performance even after controlling for the autoregressor effect. Such a
relation was mediated by children’s ability to convert word problems into
the correct number sentences/equations. The findings not only highlight the
importance of recognizing the underlying word problem type in mathematical
problem-solving, but also provide a practical tool to assess such an
ability.
*Alison Vrabec (Graduate Student, University of Dayton)*
*Exploring the Effects of an Adaptive Number eBook on Parental Attitudes
toward Mathematics*
Mathematical knowledge is vitally important to young children’s
development, as research demonstrates that it is a strong predictor of
their later academic achievement. Developing these skills early in life is
crucial, as it allows children the opportunity to develop the necessary
foundational skills for early schooling instruction. Parental attitudes
toward a particular subject have been demonstrated to affect the amount of
time they dedicate to teaching their children said subject. This study
examined the effects of a novel adaptive number eBook on parental
attitudes towards mathematics (n=65), and also explored if parents’
perceptions of their child’s global math skills and numerical comparison
skills increased after reading the number eBook. Overall, significant
differences between eBook types (adaptive/non-adaptive/control) were found
for parental perceptions of children’s numerical comparison skills, but
results indicated no significant differences for parental attitudes toward
mathematics or parental perceptions of children’s global math skills.
Effect sizes indicated that the use of the adaptive eBook may have
positively impacted parental attitudes in a small way (F(ηp2)= 0.79(0.04),
marginal M=3.59), and may have positively impacted parent perception of
children’s specific math skills (F(ηp2)=4.64(0.21), marginal M=3.69). These
findings, their implications, and suggestions for future research are
discussed.
*Jake Kaufman (Doctoral Student, Vanderbilt University)*
*Exploring the Mechanisms Underlying the Relationship Between Early Number
and Language Skills*
The goal of this pilot study was to identify how phonological skill and
semantic knowledge differentially relate to Arabic number understanding.
Past research has used either phonological skill or semantic knowledge as a
proxy for language skill in general without considering the contributions
of each component of language (e.g. Purpura & Reid, 2016); and we do not
have clear knowledge of the mechanisms underlying these relationships
(Purpura et al., 2017). Participants were 17 children (56.3% female)
between 50 and 60 months of age (M = 56 months, SD = 3 months) with data
collection ended early due to COVID. Participants completed a phonological
rhyme judgment task, semantic meaning judgment task, Arabic number
comparison task, and verbal counting task. Our primary measure was reaction
time. Mediation analyses with bootstrap resampling indicated no support for
our indirect phonological skill hypothesis, where we hypothesized counting
skill to mediate the relationship between phonological skill and Arabic
number understanding. We did find support for our direct semantic knowledge
hypothesis. Individuals who were faster at deciding if items were related
on our semantic meaning judgment task were also faster at deciding which
numeral was larger on small distance trials (e.g. 5|3). This suggests
semantic knowledge and Arabic number understanding may share an underlying
symbol mapping mechanism, with those who are more efficient at this mapping
being able to more quickly access the meaning associated with a picture or
numeral. Future work examining our indirect phonological skill hypothesis
should explore counting tasks that involve skills needed to perform number
comparisons as potential mediators.
*Josh Medrano (Doctoral Student, University of Maryland - College Park)*
*Influences of numerical and non-numerical inhibitory control tasks on
children and adults' arithmetic skills: A path analytical approach*
Existing research shows that individuals' performance on numerical and
nonnumerical inhibitory control tasks contributes to their mathematical
skills differently. In the current study, we sought to partially replicate
Gilmore et al.'s (2015) paper on inhibition and arithmetic skills.
Eighty-four children and 170 adults completed a nonsymbolic comparison task
(measuring numerical inhibitory control); an animal comparison task
(nonnumerical inhibitory control); and four arithmetic assessments
measuring arithmetic fluency, procedural calculation, conceptual knowledge,
and order of operations performance. We analyzed their data through two
separate measured variable path analyses instead of a hierarchical
regression framework to control for covariance among the variables. We
found that children’s numerical but not nonnumerical inhibitory control had
a causal influence on their procedural knowledge, factual knowledge, and
order of operations performance. Their inhibitory control did not influence
their conceptual knowledge. On the other hand, adults’ numerical inhibitory
control had a causal influence only on their conceptual knowledge, while
their nonnumerical inhibitory control only influenced their factual and
procedural knowledge. Their inhibitory control did not influence their
order of operations performance. Both models had a good fit. The current
findings contribute to the debate on whether nonsymbolic comparisons are
inherently inhibitory control tasks. We assumed that they do, and our
analysis suggests the idea that there might be a developmental difference
in how the inhibitory control task used here contributes to mathematical
skills, as others have suggested (Reynvoet et al., 2021).
*Rui Meng (Graduate Student, University of Wisconsin Madison)*
*Linking representations of equality in first-grade mathematics lessons in
China*
This research investigated how teachers link (connect and contrast)
representations of equality in elementary mathematics classrooms in China.
We analyzed three first-grade lessons on equality that included instruction
about the equal sign, the greater-than sign, and the less-than sign. In
each lesson, we identified linking episodes, defined as segments of
discourse in which the teacher connected representations. For each linking
episode, we identified the specific representations that were linked, the
types of representations linked, and the modalities teachers used to link
representations. There were three main findings. First, teachers
highlighted links between representations in many, varied ways. They
frequently linked representations multimodally, using gestures as well as
speech to refer to representations as they connected them. Links that were
crucial to the lesson were often stated repeatedly and in multiple ways
(e.g., stating the relation and then denying the opposite, or stating the
relation in both forward and reverse directions). Second, teachers
frequently engaged students in linking representations. Thus, the content
of linking episodes was often distributed between the teacher and students.
Third, within segments of the lessons, the sequence of representations
often aligned with principles of concreteness fading (i.e., the
concrete-representational-abstract sequence). This work highlights the
range and variability of ways in which teachers link representations of
mathematical ideas within classroom instruction. Further, it suggests new
directions for the analysis of instructional discourse and how such
discourse supports student learning.
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