Communicating Mathematical Thinking: Latino/a Kindergarteners’

Use of Language to Solve Word Problems

Sylvia Celedón-Pattichis, UNMMary 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)

Often underestimated problem solving capacity of young children (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)

Persistent achievement gap between Latino students and white and Asian counterparts

Focus of our Research

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 (John-

Steiner & 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 One kindergarten classrooms, low SES school with

predominantly Latino student population (87%)

Focused on 8 students in the pre-post assessments

Teacher Students/Class Lang. of Instruction

Ms. Arenas Mexican Immigrant, ELLsBilingual Classroom

Spanish

Methods Larger Study

Weekly Classroom Observations 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 ItemsPre-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 in each pocket. How many pennies does Javier have now? (MULTIPLICATION)

Sara has 3 bags of marbles. There are 6 marbles in each bag. How many 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 Problem-Solving Results

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 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 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) “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) I: How did you count? Show me. G: “Con mi voz adentro.” “With my voice

inside.”

Connecting the Story to the Model Language

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 NASeparate Result Unk (13-5) 94 73Join Change Unk (7+__=11) 75 74Multiplication (6x3) 81 71Partitive Division (15÷3) 75 70Measurement Division (10÷2) 69 71Multi-Step (2x4) - 3 63 64

Conclusions (1)

Students solved much broader range of problems than national assessment of 22,000 kindergarteners would predict 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:

CEMELA website Select Research, then Presentations

http://math.arizona.edu/~cemela/english/research/2007_presentations.php

Sylvia Celedón-Pattichis sceledon@unm.edu Mary Marshall mmarshal@unm.edu Erin Turner eturner@email.arizona.edu