Communicating Mathematical Thinking: Latino/a Kindergarteners’ Use of Language to Solve Word Problems

1. 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 Learningand Teaching supported by the National Science Foundation, grant number ESI-0424983.

2. 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)

3. 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

4. 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

5. 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)

6. Setting • One kindergarten classrooms, low SES school with predominantly Latino student population (87%) • Focused on 8 students in the pre-post assessments

7. 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.

8. Sample Assessment Items

9. 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%)

10. 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.

11. 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

12. 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.

13. 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.

14. “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 (1)

15. Gerardo’s Post Assessment (2) • I: How did you count? Show me. • G: “Con mi voz adentro.” “With my voice inside.”

16. 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.

17. 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).

18. Post Assessment Results (n=16)

19. 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.

20. 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).

21. 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