Transcript Cultural and Linguistic Resources to Promote Problem

Communicating Mathematical
Thinking: Latino/a Kindergarteners’
Use of Language to Solve Word
Problems
Sylvia Celedón-Pattichis, UNM
Mary Marshall, UNM
Erin Turner, UA
CEMELA is a Center for Learning and
Teaching supported by the National
Science Foundation, grant number
ESI-0424983.
Young Children’s Communication &
Problem Solving

Problem solving and communication as integral
to learning mathematics (NCTM, 2000)
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Often underestimated problem solving capacity
of young children
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(CGI Studies, Carpenter, Fennema, et al.)
Lack of research in how Latino children
communicate their mathematical thinking in their
native language, Spanish (Blum-Martínez)
Young Latino/as & Problem Solving

Latino students represent fastest growing
group in public schools

Nearly half (45%) are English Language
Learners (Kohler & Lazarín, 2007)
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Persistent achievement gap between
Latino students and white and Asian
counterparts
Focus of our Research

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Research from a larger kindergarten study
Study focuses on problem solving and
communication
Investigation of Latino students’
mathematical communication related to their
problem-solving strategies
Theoretical Perspectives

Socio-cultural Perspective on Learning (JohnSteiner & Mahn, 1996; Nelson, 1991; Vygotsky,
1986)

Discourse and Learning Mathematics (Cobb,
1997; Saxe, 2002; Moschkovich, 2002)

Socioconstructivist Theory (Cobb 1997; Cobb &
Yackel, 1996)

Cognitively Guided Instruction (Carpenter et al.,
1993; Carpenter et al., 1994)
Setting
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One kindergarten classrooms, low SES school with
predominantly Latino student population (87%)
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Focused on 8 students in the pre-post assessments
Teacher
Ms. Arenas
Students/Class
Mexican Immigrant, ELLs
Bilingual Classroom
Lang. of
Instruction
Spanish
Methods
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Larger Study
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Weekly Classroom Observations
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Video-taped, transcribed, coded
Teacher Interviews
Pre and Post Clinical Interview Assessments
(Ginsburg, 1983)
 Administered in student’s dominant language, all but
one case in Spanish
 Language coded for connections to story, strategy,
metacognition, and students’ ability to discuss their
thinking.
Sample Assessment Items
Pre-Assessment Version
(n=8 students)
Post-Assessment Version
(n=16 students)
Maya has 6 candies. Her brother gives
her 3 more. How many candies does
she have now? (JOIN)
Julio has 6 candies. His sister gives him
6 more candies. How many candies
does Julio have now? (JOIN)
Javier has 3 pockets. He puts 2 pennies Sara has 3 bags of marbles. There are 6
in each pocket. How many pennies does marbles in each bag. How many
Javier have now? (MULTIPLICATION)
marbles does Sara have altogether?
(MULTIPLICATION)
There are 8 marbles. 2 friends want to
share the marbles so that they each get
the same amount. How many marbles
can each friend have? (DIVISION)
Estevan had 15 marbles. He shared with
3 friends so each friend got the same
number of marbles. How many marbles
did each friend get? (DIVISION)
Pre-Assessment ProblemSolving Results


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Most students could count small set of
objects (under 10)
Half of students solved basic addition (6+3)
and basic subtraction problem (10-4)
Multiplication, division and compare
problems were much more challenging
(17%, 25%, 0%)
Pre-Assessment Language
Results
• Explanations were short and sometimes
vague.
• Students could remember elements of the
story, but saw it as a starting point for
creative adaptation.
• When students solved with direct modeling,
they could say how they counted and repeat
the process aloud.
Portrait of Instruction
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Problem solving lessons
conducted twice a week,
for about 30 minutes
Average of 5 problems
per lesson
Both whole group and
small group formats used
Students had access to a
range of tools
Two Preliminary Language
Themes for Post-Assessment

Students use language as a way to think
about their thinking (metacognition).

Students used language to connect the story
to their model.
Metacognition
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Students had the psychological tools
available to begin to talk about how
they were making sense of the
problem (John-Steiner & Mahn, 1996;
Vygotsky, 1986).

They also began to recognize that
problem solving involved a mental
process.
Gerardo’s Post Assessment
(1)

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“Mi mente estaba
pensando que era doce.
Y yo también. Y
luego…y luego lo
conté.”
“My mind was thinking it
was twelve. And me too.
And then…and then I
counted.”
Gerardo’s Post Assessment
(2)

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I: How did you count? Show me.
G: “Con mi voz adentro.” “With my voice
inside.”
Connecting the Story to the
Model
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Language
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mediates students’ mathematical
understanding.
gives them an entry point to understand
the mathematical situation.
provides them a way to explain their
thinking.
helps them connect the mathematical
model to the story.
Video Case: Connecting the
Story to the Model (2)

Dalia solves a Join Change
Unknown problem in October
(4,7) and then in May (7,11).
Post Assessment Results (n=16)
Problem Type
% Correct % Correct
(Carpenter)
Join Result Unk (6+6)
88
NA
Separate Result Unk (13-5)
94
73
Join Change Unk (7+__=11)
75
74
Multiplication (6x3)
81
71
Partitive Division (15÷3)
75
70
Measurement Division (10÷2)
69
71
Multi-Step (2x4) - 3
63
64
Conclusions (1)

Students solved much broader range of
problems than national assessment of 22,000
kindergarteners would predict


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18% solved addition and subtraction
2% solved basic multiplication and division
(NCES, 2005)
Students used language that was
sophisticated and focused on the problem.
Conclusions (2)

Students showed an emergent ability to think
about their thinking as they solved problems
(Aunola et al., 2004).

Native language learning gave students
access to the psychological and linguistic
tools that helped them make sense of the
mathematics (Baker, 2006).
Questions?

Paper available at:

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CEMELA website
 Select Research, then Presentations
http://math.arizona.edu/~cemela/english/research/2007_pr
esentations.php
Sylvia Celedón-Pattichis [email protected]
Mary Marshall [email protected]
Erin Turner [email protected]